{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 1.2 kg and a = 8.65 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 10.38, \"unit\": \"N\"}", "dedupe_signature": "09c20bea4bab126a6948c4bb6f125d7bfaab1b3bd6b6e6806d6108e8535143b6", "difficulty": "easy", "final_answer": {"answer": 10.38, "unit": "N"}, "id": "force_000000_1.2_8.65", "license": "Apache-2.0", "prompt": "A cart has mass 1.2 kg and measured acceleration 8.65 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 1.2 kg and a = 8.65 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 8.65, "mass": 1.2}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 23.35^2 and multiply by 0.5 * 18.75.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 5111.4609, \"unit\": \"J\"}", "dedupe_signature": "83706137a30aa1590c56a01413f955d1e5b809c741e69197790e83b1c7c188a8", "difficulty": "easy", "final_answer": {"answer": 5111.4609, "unit": "J"}, "id": "ke_000001_18.75_23.35", "license": "Apache-2.0", "prompt": "A body of mass 18.75 kg moves at 23.35 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 23.35^2 and multiply by 0.5 * 18.75.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 18.75, "velocity": 23.35}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=45 degrees through the sine of 2 theta.\n3. Substitute v=10.8 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 11.8899, \"unit\": \"m\"}", "dedupe_signature": "04201160189895fd03a25b5efba393fd75a3df315577c20e01a0d6beb6d3673e", "difficulty": "medium", "final_answer": {"answer": 11.8899, "unit": "m"}, "id": "projectile_range_000002_10.8_45", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 10.8 m/s and angle 45 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=45 degrees through the sine of 2 theta.\nSubstitute v=10.8 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 45, "gravity": 9.81, "speed": 10.8}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1210 * 2.365 * 10.\nFinal: {\"answer\": 28616.5, \"unit\": \"J\"}", "dedupe_signature": "5a7f93e3c157237db74bb7b1dc7e5d7d21d8efd318b98339ea65e981290ec0b4", "difficulty": "easy", "final_answer": {"answer": 28616.5, "unit": "J"}, "id": "heat_q_000004_1210_2.365_10", "license": "Apache-2.0", "prompt": "A 1210 g sample has specific heat 2.365 J/(g*K). How much heat is needed to raise its temperature by 10 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1210 * 2.365 * 10.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 10, "heat_capacity": 2.365, "mass_g": 1210}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=35 V and R=195.1 ohm.\nFinal: {\"answer\": 6.2788, \"unit\": \"W\"}", "dedupe_signature": "8064f52e5c6334c49458c8a4fdb66697a0f6bcd33959332678f12297a741648b", "difficulty": "easy", "final_answer": {"answer": 6.2788, "unit": "W"}, "id": "ohm_power_000005_35_195.1", "license": "Apache-2.0", "prompt": "A resistor has resistance 195.1 ohm and voltage 35 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=35 V and R=195.1 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 195.1, "voltage": 35.0}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 2.36 mol * 100.087 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 236.2053, \"unit\": \"g\"}", "dedupe_signature": "6ea9c865703a8b85cfa75b2907ca5e4161fbdb8ec2df6fef81443b35262ee2f8", "difficulty": "medium", "final_answer": {"answer": 236.2053, "unit": "g"}, "id": "stoich_mass_000007_calcium_carbonate_2.36", "license": "Apache-2.0", "prompt": "A sample contains 2.36 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 2.36 mol * 100.087 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "calcium carbonate", "molar_mass": 100.087, "moles": 2.36}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.78 y, so each step multiplies y by 1 - h*0.78.\n3. Apply that update for 3 steps and round the final state.\nFinal: {\"answer\": 15.6617, \"unit\": \"state_units\"}", "dedupe_signature": "0373e8d6fdf1dfc6322fd1fecc0d7fb58da64971babdc1e3489fcdde8fd1a983", "difficulty": "medium", "final_answer": {"answer": 15.6617, "unit": "state_units"}, "id": "euler_decay_000009_69_0.78_0.5_3", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.78 y with y(0)=69, step size h=0.5, for 3 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.78 y, so each step multiplies y by 1 - h*0.78.\nApply that update for 3 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 69.0, "rate": 0.78, "step": 0.5, "steps": 3}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.28 and add it to the current value.\nFinal: {\"answer\": [1.566, 1.956, 2.13], \"unit\": \"temperature_units\"}", "dedupe_signature": "529b08cc3dcbea632c37d5fbea4e92c251256ec70cd191394c6910dda4ee50cb", "difficulty": "hard", "final_answer": {"answer": [1.566, 1.956, 2.13], "unit": "temperature_units"}, "id": "heat_step_000011_0.28_1.45_1.65_1.55_2.9_1.5", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.45, right=1.5; current interior values are [1.65, 1.55, 2.9]. Use r=0.28. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.28 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [1.65, 1.55, 2.9], "left": 1.45, "r": 0.28, "right": 1.5}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kelvin equals Celsius plus 273.15.\n2. Apply the conversion factor directly to the given value.\n3. Compute -20.5 + 273.15.\nFinal: {\"answer\": 252.65, \"unit\": \"K\"}", "dedupe_signature": "081e4f571b3127f8ad607a78e7a385e62956f2c6ff5029e25f6a021d39582e1b", "difficulty": "easy", "final_answer": {"answer": 252.65, "unit": "K"}, "id": "unit_convert_000012_c_to_k_-20.5", "license": "Apache-2.0", "prompt": "Convert -20.5 degC to K. Return the converted value with unit.", "reasoning_trace": "Kelvin equals Celsius plus 273.15.\nApply the conversion factor directly to the given value.\nCompute -20.5 + 273.15.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": -20.5}, "verifier": {"formula": "value + 273.15", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. grams cancel with J/(g*K), and kelvin cancels, leaving joules\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "00993ceed0409c2a599fd8dfbb972d370dbb9747d8b5137b7fea981a40db8aa4", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_000015_consistent_4153435f_131890", "license": "Apache-2.0", "prompt": "In model card equation case 131890, check dimensional consistency for Q = m * c * DeltaT. The left side has dimensions J and the right side has dimensions J. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\ngrams cancel with J/(g*K), and kelvin cancels, leaving joules\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "Q = m * c * DeltaT"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef weighted_sum_000016(values, weights):\n    if len(values) != len(weights):\n        raise ValueError('length mismatch')\n    return sum(value * weight for value, weight in zip(values, weights))\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"weighted_sum_000016\"}", "dedupe_signature": "3c520a77aff0c6c0f6d3a4a0326b0bbab6f0c31d35d9d1c4a859fab9965128b5", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "weighted_sum_000016"}, "id": "code_000016_weighted_sum_000016", "license": "Apache-2.0", "prompt": "Write a Python function weighted_sum_000016(values, weights) that returns sum(value*weight). Raise ValueError when the two inputs have different lengths. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "weighted_sum_000016"}, "verifier": {"function": "weighted_sum_000016", "tests": ["assert weighted_sum_000016([2, 3], [4, 5]) == 23", "assert weighted_sum_000016([], []) == 0", "try:\n    weighted_sum_000016([1], [1, 2])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=34 degrees through the sine of 2 theta.\n3. Substitute v=60.7 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 348.2365, \"unit\": \"m\"}", "dedupe_signature": "d8d40fe1c3a47d30dc93b5318b0db91c4d7ff9266893afdaebc4be4df32e62fd", "difficulty": "medium", "final_answer": {"answer": 348.2365, "unit": "m"}, "id": "projectile_range_000020_60.7_34", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 60.7 m/s and angle 34 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=34 degrees through the sine of 2 theta.\nSubstitute v=60.7 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 34, "gravity": 9.81, "speed": 60.7}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=200.3 V and R=93.4 ohm.\nFinal: {\"answer\": 429.5513, \"unit\": \"W\"}", "dedupe_signature": "129aee5c8ea19cdd67c9b8371e3d561a69caa5b7bee60ec5130f9d0e7ea36043", "difficulty": "easy", "final_answer": {"answer": 429.5513, "unit": "W"}, "id": "ohm_power_000023_200.3_93.4", "license": "Apache-2.0", "prompt": "A resistor has resistance 93.4 ohm and voltage 200.3 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=200.3 V and R=93.4 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 93.4, "voltage": 200.3}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=789.5 mg, t=296.5 h, and T_half=47.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 10.4302, \"unit\": \"mg\"}", "dedupe_signature": "3ba2cd84feaf26933e1df14deb7d210e741397aaa3871c9f897d5e5505e6053f", "difficulty": "medium", "final_answer": {"answer": 10.4302, "unit": "mg"}, "id": "half_life_000024_789.5_47.5_296.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 789.5 mg. Its half-life is 47.5 hours. How many mg remain after 296.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=789.5 mg, t=296.5 h, and T_half=47.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 296.5, "half_life": 47.5, "initial_amount": 789.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 1.47 mol * 58.44 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 85.9068, \"unit\": \"g\"}", "dedupe_signature": "e7751515430579a1ac31ec36eb4c3d52d2706e83cbe0fa796cc28f4437e45ba0", "difficulty": "medium", "final_answer": {"answer": 85.9068, "unit": "g"}, "id": "stoich_mass_000025_sodium_chloride_1.47", "license": "Apache-2.0", "prompt": "A sample contains 1.47 mol of sodium chloride. Using molar mass 58.44 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 1.47 mol * 58.44 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "sodium chloride", "molar_mass": 58.44, "moles": 1.47}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 1100 mL to 1.1 L.\n3. Compute M = 1.005 / 1.1.\nFinal: {\"answer\": 0.9136, \"unit\": \"mol/L\"}", "dedupe_signature": "6fb33aad72a7943e617a33172b11769ce5aa9f42a0110e990ad4648770e00db7", "difficulty": "medium", "final_answer": {"answer": 0.9136, "unit": "mol/L"}, "id": "molarity_000026_1.005_1100", "license": "Apache-2.0", "prompt": "A solution contains 1.005 mol of solute in 1100 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 1100 mL to 1.1 L.\nCompute M = 1.005 / 1.1.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 1.005, "volume_ml": 1100}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.08 y, so each step multiplies y by 1 - h*0.08.\n3. Apply that update for 4 steps and round the final state.\nFinal: {\"answer\": 7.0267, \"unit\": \"state_units\"}", "dedupe_signature": "1f84531eacd6fcf9befbe9fa91b915ee78072550b366e7b962b1c3a802528193", "difficulty": "medium", "final_answer": {"answer": 7.0267, "unit": "state_units"}, "id": "euler_decay_000027_9_0.08_0.75_4", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.08 y with y(0)=9, step size h=0.75, for 4 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.08 y, so each step multiplies y by 1 - h*0.08.\nApply that update for 4 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 9.0, "rate": 0.08, "step": 0.75, "steps": 4}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-7.3)=-33.84 and f(-6.3)=-30.04.\n3. The interval width is 1.\nFinal: {\"answer\": -31.94, \"unit\": \"area_units\"}", "dedupe_signature": "fc7106612533edb6fe4fd304c9c55795c35a60328a79e27251ba387bff18f70e", "difficulty": "medium", "final_answer": {"answer": -31.94, "unit": "area_units"}, "id": "trapz_linear_000028_3.8_-6.1_-7.3_-6.3", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=3.8x+-6.1 from x=-7.3 to x=-6.3. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-7.3)=-33.84 and f(-6.3)=-30.04.\nThe interval width is 1.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -6.1, "slope": 3.8, "x0": -7.3, "x1": -6.3}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kelvin equals Celsius plus 273.15.\n2. Apply the conversion factor directly to the given value.\n3. Compute 176.5 + 273.15.\nFinal: {\"answer\": 449.65, \"unit\": \"K\"}", "dedupe_signature": "277ce7941d09914595050b9493e30b7b7875b81af811d76f9b1ff0dced92d809", "difficulty": "easy", "final_answer": {"answer": 449.65, "unit": "K"}, "id": "unit_convert_000030_c_to_k_176.5", "license": "Apache-2.0", "prompt": "Convert 176.5 degC to K. Return the converted value with unit.", "reasoning_trace": "Kelvin equals Celsius plus 273.15.\nApply the conversion factor directly to the given value.\nCompute 176.5 + 273.15.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 176.5}, "verifier": {"formula": "value + 273.15", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-6.1, -1.75], \"unit\": \"dimensionless\"}", "dedupe_signature": "1f37ffb46d5b9d28cee258944676c8bf1559150fab09b8b830dd2baebb415b86", "difficulty": "medium", "final_answer": {"answer": [-6.1, -1.75], "unit": "dimensionless"}, "id": "line_two_point_000032_-10.5_1.75_-6.1_-1.75", "license": "Apache-2.0", "prompt": "A line passes through points (-10.5, 62.3) and (1.75, -12.425). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -10.5, "x2": 1.75, "y1": 62.3, "y2": -12.424999999999999}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. velocity divided by time is acceleration\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "99779b846f47c792e3848539c4db17e845e5afdb42c7efb7fe9ce8f9d64e8211", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_000033_inconsistent_c1271127_463582", "license": "Apache-2.0", "prompt": "In simulation spec case 463582, check dimensional consistency for x = v / t. The left side has dimensions m and the right side has dimensions m/s^2. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nvelocity divided by time is acceleration\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "x = v / t"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef safe_mean_000034(values):\n    if not values:\n        raise ValueError('safe_mean requires at least one value')\n    return sum(values) / len(values)\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"safe_mean_000034\"}", "dedupe_signature": "ef369f9dc91b9ac4354fc88811e27c7e3ed1ea081bf9f7a2aa74155b36bbebb0", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "safe_mean_000034"}, "id": "code_000034_safe_mean_000034", "license": "Apache-2.0", "prompt": "Write a Python function safe_mean_000034(values) that returns the arithmetic mean. It must raise ValueError for an empty input and must not mutate the input list. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "safe_mean_000034"}, "verifier": {"function": "safe_mean_000034", "tests": ["assert safe_mean_000034([2, 4, 6]) == 4", "xs = [1, 2, 3]; assert safe_mean_000034(xs) == 2 and xs == [1, 2, 3]", "try:\n    safe_mean_000034([])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: rate_constant, number_of_steps.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"rate_constant\", \"number_of_steps\"]}", "dedupe_signature": "dd4c58d32e64fcca1413160d597eeb1f0683e8a0771cb6707858628c925972d2", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["rate_constant", "number_of_steps"]}, "id": "abstain_000035_rate_constant_number_of_steps", "license": "Apache-2.0", "prompt": "Use explicit Euler for dy/dt = -k y. The prompt gives y(0)=44 and h=1.45, but omits both k and the number of steps. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: rate_constant, number_of_steps.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["rate_constant", "number_of_steps"]}, "verifier": {"missing": ["rate_constant", "number_of_steps"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 14.4 kg and a = 12.95 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 186.48, \"unit\": \"N\"}", "dedupe_signature": "1544364f2a4aed612561d024e305cf84610983a2b8869aace2fceae1bbdde396", "difficulty": "easy", "final_answer": {"answer": 186.48, "unit": "N"}, "id": "force_000036_14.4_12.95", "license": "Apache-2.0", "prompt": "A cart has mass 14.4 kg and measured acceleration 12.95 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 14.4 kg and a = 12.95 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 12.95, "mass": 14.4}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 6.3^2 and multiply by 0.5 * 4.5.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 89.3025, \"unit\": \"J\"}", "dedupe_signature": "92c6dd34a2598cc41361f49ae6641a7108108a23e8359ac45119c434a1448f6d", "difficulty": "easy", "final_answer": {"answer": 89.3025, "unit": "J"}, "id": "ke_000037_4.5_6.3", "license": "Apache-2.0", "prompt": "A body of mass 4.5 kg moves at 6.3 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 6.3^2 and multiply by 0.5 * 4.5.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 4.5, "velocity": 6.3}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=71 degrees through the sine of 2 theta.\n3. Substitute v=7.6 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 3.6249, \"unit\": \"m\"}", "dedupe_signature": "280268c9dc5de6869e5d40676561d314f9a30c7029f13ed7ec949668b3b980f5", "difficulty": "medium", "final_answer": {"answer": 3.6249, "unit": "m"}, "id": "projectile_range_000038_7.6_71", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 7.6 m/s and angle 71 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=71 degrees through the sine of 2 theta.\nSubstitute v=7.6 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 71, "gravity": 9.81, "speed": 7.6}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 5.46 * 8.314 * 482 / 94.0.\nFinal: {\"answer\": 232.7672, \"unit\": \"kPa\"}", "dedupe_signature": "c9d9f9e4bc661ac291d058e7876cd5471aea3391fc5650c30a9154cebc158f3a", "difficulty": "medium", "final_answer": {"answer": 232.7672, "unit": "kPa"}, "id": "ideal_gas_000039_5.46_482_94.0", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=5.46 mol, T=482 K, and V=94.0 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 5.46 * 8.314 * 482 / 94.0.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 5.46, "temp_k": 482, "volume_l": 94.0}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 55 * 4.66 * 75.\nFinal: {\"answer\": 19222.5, \"unit\": \"J\"}", "dedupe_signature": "0ae96c4b209e502afbdfb47037a355a4112e665f1eab49621f7897d0b4ebb822", "difficulty": "easy", "final_answer": {"answer": 19222.5, "unit": "J"}, "id": "heat_q_000040_55_4.66_75", "license": "Apache-2.0", "prompt": "A 55 g sample has specific heat 4.66 J/(g*K). How much heat is needed to raise its temperature by 75 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 55 * 4.66 * 75.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 75, "heat_capacity": 4.66, "mass_g": 55}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=562 mg, t=287 h, and T_half=68.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 30.7954, \"unit\": \"mg\"}", "dedupe_signature": "8188a5284f52f5c045a816c198d322748e595f621209cc60c5ecbaec51d232f1", "difficulty": "medium", "final_answer": {"answer": 30.7954, "unit": "mg"}, "id": "half_life_000042_562_68.5_287", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 562 mg. Its half-life is 68.5 hours. How many mg remain after 287 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=562 mg, t=287 h, and T_half=68.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 287.0, "half_life": 68.5, "initial_amount": 562.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 7.31 mol * 44.01 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 321.7131, \"unit\": \"g\"}", "dedupe_signature": "d6c8d258205a14c558be125e98c58431e474bf86f0ade61ced100fc2ceac3735", "difficulty": "medium", "final_answer": {"answer": 321.7131, "unit": "g"}, "id": "stoich_mass_000043_carbon_dioxide_7.31", "license": "Apache-2.0", "prompt": "A sample contains 7.31 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 7.31 mol * 44.01 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "carbon dioxide", "molar_mass": 44.01, "moles": 7.31}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 3185 mL to 3.185 L.\n3. Compute M = 4.765 / 3.185.\nFinal: {\"answer\": 1.4961, \"unit\": \"mol/L\"}", "dedupe_signature": "70023d191a16ef61a48b7e7223f91337bd1d997b25170631c07f09b7cf729c63", "difficulty": "medium", "final_answer": {"answer": 1.4961, "unit": "mol/L"}, "id": "molarity_000044_4.765_3185", "license": "Apache-2.0", "prompt": "A solution contains 4.765 mol of solute in 3185 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 3185 mL to 3.185 L.\nCompute M = 4.765 / 3.185.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 4.765, "volume_ml": 3185}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-9.1)=19.8 and f(-6.3)=14.2.\n3. The interval width is 2.8.\nFinal: {\"answer\": 47.6, \"unit\": \"area_units\"}", "dedupe_signature": "71d13d67e0b8d9352387a9a6eb8323ec3f836e69977b8f3e8974cf5fef979887", "difficulty": "medium", "final_answer": {"answer": 47.6, "unit": "area_units"}, "id": "trapz_linear_000046_-2_1.6_-9.1_-6.3", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-2x+1.6 from x=-9.1 to x=-6.3. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-9.1)=19.8 and f(-6.3)=14.2.\nThe interval width is 2.8.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 1.6, "slope": -2.0, "x0": -9.1, "x1": -6.3}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.3 and add it to the current value.\nFinal: {\"answer\": [1.35, 1.81, 1.4], \"unit\": \"temperature_units\"}", "dedupe_signature": "724430d322fda90f3849feb39e1cfd99976494885942830bc0b7308832aa80c2", "difficulty": "hard", "final_answer": {"answer": [1.35, 1.81, 1.4], "unit": "temperature_units"}, "id": "heat_step_000047_0.3_-1.2_2.85_1.9_0.65_1.9", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-1.2, right=1.9; current interior values are [2.85, 1.9, 0.65]. Use r=0.3. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.3 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [2.85, 1.9, 0.65], "left": -1.2, "r": 0.3, "right": 1.9}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 19254.0 / 1000.\nFinal: {\"answer\": 19.254, \"unit\": \"kg\"}", "dedupe_signature": "170105de5c912d8d792bf8d68808938056b1724f778fe56877a6c0a5f6cffb54", "difficulty": "easy", "final_answer": {"answer": 19.254, "unit": "kg"}, "id": "unit_convert_000048_g_to_kg_19254", "license": "Apache-2.0", "prompt": "Convert 19254 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 19254.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 19254.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=90 degrees and keep the unit as newtons.\nFinal: {\"answer\": [0.0, 289.5], \"unit\": \"N\"}", "dedupe_signature": "d5d56e948ac80e593d6444bae4cd5ba52fb533d6e939c3e7e54f0cbbdd37e1ea", "difficulty": "medium", "final_answer": {"answer": [0.0, 289.5], "unit": "N"}, "id": "vector_components_000049_289.5_90", "license": "Apache-2.0", "prompt": "A vector has magnitude 289.5 N at 90 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=90 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 90, "magnitude": 289.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [0.0, -20.75], \"unit\": \"dimensionless\"}", "dedupe_signature": "256bd3b3a25f745ee2f5022faa0da8bf25e4ffb6435104858ca035ce124a110e", "difficulty": "medium", "final_answer": {"answer": [0.0, -20.75], "unit": "dimensionless"}, "id": "line_two_point_000050_3.25_16_0_-20.75", "license": "Apache-2.0", "prompt": "A line passes through points (3.25, -20.75) and (16, -20.75). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 3.25, "x2": 16.0, "y1": -20.75, "y2": -20.75}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. mass times acceleration has newton dimensions\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "d2381fcc3464df2ffd114e2893ea2563c4fef9214e859131ec9667576d592c0e", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_000051_consistent_03f5e041_476206", "license": "Apache-2.0", "prompt": "In lab notebook case 476206, check dimensional consistency for F = m * a. The left side has dimensions kg*m/s^2 and the right side has dimensions kg*m/s^2. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nmass times acceleration has newton dimensions\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "F = m * a"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef pairwise_ratios_000052(numerators, denominators):\n    if len(numerators) != len(denominators):\n        raise ValueError('length mismatch')\n    out = []\n    for numerator, denominator in zip(numerators, denominators):\n        if denominator == 0:\n            raise ValueError('zero denominator')\n        out.append(numerator / denominator)\n    return out\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"pairwise_ratios_000052\"}", "dedupe_signature": "40f9a1a45b19d843eb4ee8aa7e814c7fbb4ce06a48133c0df1174e1b12b6b35c", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "pairwise_ratios_000052"}, "id": "code_000052_pairwise_ratios_000052", "license": "Apache-2.0", "prompt": "Write a Python function pairwise_ratios_000052(numerators, denominators) that returns a list of n/d values. Raise ValueError if lengths differ or any denominator is zero. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "pairwise_ratios_000052"}, "verifier": {"function": "pairwise_ratios_000052", "tests": ["assert pairwise_ratios_000052([2, 9], [4, 3]) == [0.5, 3.0]", "try:\n    pairwise_ratios_000052([1], [0])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass", "try:\n    pairwise_ratios_000052([1, 2], [1])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: required_fields, allowed_transformations.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"required_fields\", \"allowed_transformations\"]}", "dedupe_signature": "c9d7b46750dea45dc14e73df96fec20f3ab7692c3777172b526fae025051c0d6", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["required_fields", "allowed_transformations"]}, "id": "abstain_000053_required_fields_allowed_transformations", "license": "Apache-2.0", "prompt": "Write a sanitizer for valid registry survey records in release 430157, but the prompt does not state which fields are required or which transformations are allowed. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: required_fields, allowed_transformations.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["required_fields", "allowed_transformations"]}, "verifier": {"missing": ["required_fields", "allowed_transformations"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 16.5 kg and a = 2.95 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 48.675, \"unit\": \"N\"}", "dedupe_signature": "70f3e90c329c21c45b39fe64fc1ceb65dfbce58b0535bf991d25d15130ea1a51", "difficulty": "easy", "final_answer": {"answer": 48.675, "unit": "N"}, "id": "force_000054_16.5_2.95", "license": "Apache-2.0", "prompt": "A cart has mass 16.5 kg and measured acceleration 2.95 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 16.5 kg and a = 2.95 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 2.95, "mass": 16.5}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 13.8^2 and multiply by 0.5 * 24.45.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 2328.129, \"unit\": \"J\"}", "dedupe_signature": "a57bef5ece3186fb7825fe19cda03e8a299298d1303c8de17e8270f06f414f40", "difficulty": "easy", "final_answer": {"answer": 2328.129, "unit": "J"}, "id": "ke_000055_24.45_13.8", "license": "Apache-2.0", "prompt": "A body of mass 24.45 kg moves at 13.8 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 13.8^2 and multiply by 0.5 * 24.45.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 24.45, "velocity": 13.8}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1570 * 1.775 * 1.\nFinal: {\"answer\": 2786.75, \"unit\": \"J\"}", "dedupe_signature": "726154edb5109f38e2bd61541006bf9b9bf783c230bb44ea9391ce117b0cefe5", "difficulty": "easy", "final_answer": {"answer": 2786.75, "unit": "J"}, "id": "heat_q_000058_1570_1.775_1", "license": "Apache-2.0", "prompt": "A 1570 g sample has specific heat 1.775 J/(g*K). How much heat is needed to raise its temperature by 1 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1570 * 1.775 * 1.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 1, "heat_capacity": 1.775, "mass_g": 1570}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=173.3 V and R=22.3 ohm.\nFinal: {\"answer\": 1346.7664, \"unit\": \"W\"}", "dedupe_signature": "c0b2ae3e9834a6e85edbcc7dc93f1b5a6f816413e6948d57564b25ea4019bfbb", "difficulty": "easy", "final_answer": {"answer": 1346.7664, "unit": "W"}, "id": "ohm_power_000059_173.3_22.3", "license": "Apache-2.0", "prompt": "A resistor has resistance 22.3 ohm and voltage 173.3 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=173.3 V and R=22.3 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 22.3, "voltage": 173.3}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=393 mg, t=221 h, and T_half=109.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 97.014, \"unit\": \"mg\"}", "dedupe_signature": "704123ff0a9a4206e2d2fa993c304acad98703013a48613256dbfc6318ed0ce7", "difficulty": "medium", "final_answer": {"answer": 97.014, "unit": "mg"}, "id": "half_life_000060_393_109.5_221", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 393 mg. Its half-life is 109.5 hours. How many mg remain after 221 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=393 mg, t=221 h, and T_half=109.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 221.0, "half_life": 109.5, "initial_amount": 393.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 4.27 mol * 180.156 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 769.2661, \"unit\": \"g\"}", "dedupe_signature": "c141cf1e7798c7a01ddda5cb2e42685167a0249a16384c7a4a68f41f885c583e", "difficulty": "medium", "final_answer": {"answer": 769.2661, "unit": "g"}, "id": "stoich_mass_000061_glucose_4.27", "license": "Apache-2.0", "prompt": "A sample contains 4.27 mol of glucose. Using molar mass 180.156 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 4.27 mol * 180.156 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "glucose", "molar_mass": 180.156, "moles": 4.27}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.86 y, so each step multiplies y by 1 - h*0.86.\n3. Apply that update for 4 steps and round the final state.\nFinal: {\"answer\": 1.4324, \"unit\": \"state_units\"}", "dedupe_signature": "7ddd1de854ad8599beba76bced92081e967deb76da06e4ddef17aa527324dbfc", "difficulty": "medium", "final_answer": {"answer": 1.4324, "unit": "state_units"}, "id": "euler_decay_000063_6_0.86_0.35_4", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.86 y with y(0)=6, step size h=0.35, for 4 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.86 y, so each step multiplies y by 1 - h*0.86.\nApply that update for 4 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 6.0, "rate": 0.86, "step": 0.35, "steps": 4}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-8.3)=-11.13 and f(0.3)=6.93.\n3. The interval width is 8.6.\nFinal: {\"answer\": -18.06, \"unit\": \"area_units\"}", "dedupe_signature": "b9bef2923c3bde8ddf6b9b60d75f687cab5b09dfb23cce55f2420048720f1f75", "difficulty": "medium", "final_answer": {"answer": -18.06, "unit": "area_units"}, "id": "trapz_linear_000064_2.1_6.3_-8.3_0.3", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=2.1x+6.3 from x=-8.3 to x=0.3. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-8.3)=-11.13 and f(0.3)=6.93.\nThe interval width is 8.6.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 6.3, "slope": 2.1, "x0": -8.3, "x1": 0.29999999999999893}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.34 and add it to the current value.\nFinal: {\"answer\": [0.809, 1.448, 0.869], \"unit\": \"temperature_units\"}", "dedupe_signature": "0fdd44cf26a669b947baa35355762a810eeaf1f7b6f384f70642473f808244ae", "difficulty": "hard", "final_answer": {"answer": [0.809, 1.448, 0.869], "unit": "temperature_units"}, "id": "heat_step_000065_0.34_-1.9_2.9_1.55_-0.1_1.1", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-1.9, right=1.1; current interior values are [2.9, 1.55, -0.1]. Use r=0.34. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.34 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [2.9, 1.55, -0.1], "left": -1.9, "r": 0.34, "right": 1.1}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 100 centimeters in one meter.\n2. Apply the conversion factor directly to the given value.\n3. Compute 4181.5 / 100.\nFinal: {\"answer\": 41.815, \"unit\": \"m\"}", "dedupe_signature": "f8e44263bda0d2d6274cb30dac0c3b3967fe96294a5c11a24fd9e97ff0e07922", "difficulty": "easy", "final_answer": {"answer": 41.815, "unit": "m"}, "id": "unit_convert_000066_cm_to_m_4181.5", "license": "Apache-2.0", "prompt": "Convert 4181.5 cm to m. Return the converted value with unit.", "reasoning_trace": "There are 100 centimeters in one meter.\nApply the conversion factor directly to the given value.\nCompute 4181.5 / 100.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 4181.5}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=233 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-133.0011, -176.4984], \"unit\": \"N\"}", "dedupe_signature": "0669679251b1bde5a2e77f5590cd5f93ed2c4e99d472537cae6e876956250f9b", "difficulty": "medium", "final_answer": {"answer": [-133.0011, -176.4984], "unit": "N"}, "id": "vector_components_000067_221_233", "license": "Apache-2.0", "prompt": "A vector has magnitude 221 N at 233 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=233 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 233, "magnitude": 221.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-4.0, -0.75], \"unit\": \"dimensionless\"}", "dedupe_signature": "b7fab05e3dc3f7b1155f8446470aa3704821b9374f43f55bfc26e763e660ab0a", "difficulty": "medium", "final_answer": {"answer": [-4.0, -0.75], "unit": "dimensionless"}, "id": "line_two_point_000068_18.25_24.75_-4_-0.75", "license": "Apache-2.0", "prompt": "A line passes through points (18.25, -73.75) and (24.75, -99.75). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 18.25, "x2": 24.75, "y1": -73.75, "y2": -99.75}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. coulomb per second is ampere\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "326f42a9ba8f001742dd32011e17d053777b1d7a73d7c2252a469de7cf5e9104", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_000069_consistent_8b38953d_89868", "license": "Apache-2.0", "prompt": "In quality-control check case 89868, check dimensional consistency for I = Q / t. The left side has dimensions A and the right side has dimensions A. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\ncoulomb per second is ampere\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "I = Q / t"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef normalize_000070(values):\n    total = sum(values)\n    if total == 0:\n        raise ValueError('cannot normalize zero-sum values')\n    return [v / total for v in values]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"normalize_000070\"}", "dedupe_signature": "0b18f591732d0f125e8745c6b8cd1a3bc3479e7c22bae92fa0238a0f7a36d04c", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "normalize_000070"}, "id": "code_000070_normalize_000070", "license": "Apache-2.0", "prompt": "Write a Python function normalize_000070(values) that returns a new list whose values sum to 1. Raise ValueError if the sum is zero. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "normalize_000070"}, "verifier": {"function": "normalize_000070", "tests": ["out = normalize_000070([2, 3, 5]); assert len(out) == 3", "assert abs(sum(normalize_000070([2, 3, 5])) - 1.0) < 1e-12", "assert normalize_000070([1, 1]) == [0.5, 0.5]", "try:\n    normalize_000070([1, -1])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: left_boundary, right_boundary.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"left_boundary\", \"right_boundary\"]}", "dedupe_signature": "8935b841d51b9ca5b1bfdc37472d52050ee7b8ee038e515c207009ec6f4bf49d", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["left_boundary", "right_boundary"]}, "id": "abstain_000071_left_boundary_right_boundary", "license": "Apache-2.0", "prompt": "Solve the 1D heat equation after one finite-difference step. The prompt gives r=0.12 and interior values [-1.45, -0.9, -1.3], but gives no boundary values. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: left_boundary, right_boundary.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["left_boundary", "right_boundary"]}, "verifier": {"missing": ["left_boundary", "right_boundary"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 20.6 kg and a = 12.1 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 249.26, \"unit\": \"N\"}", "dedupe_signature": "5ee2b128bce58976a226084be9566cdb438ab1a7a759dca6640bf236ed593432", "difficulty": "easy", "final_answer": {"answer": 249.26, "unit": "N"}, "id": "force_000072_20.6_12.1", "license": "Apache-2.0", "prompt": "A cart has mass 20.6 kg and measured acceleration 12.1 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 20.6 kg and a = 12.1 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 12.1, "mass": 20.6}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 25.6^2 and multiply by 0.5 * 19.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 6225.92, \"unit\": \"J\"}", "dedupe_signature": "60a843b140436eb7f1a17af5f5e1e0ae84558fb2c35d56e88c7de95e8edad1cf", "difficulty": "easy", "final_answer": {"answer": 6225.92, "unit": "J"}, "id": "ke_000073_19_25.6", "license": "Apache-2.0", "prompt": "A body of mass 19 kg moves at 25.6 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 25.6^2 and multiply by 0.5 * 19.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 19.0, "velocity": 25.6}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=59 degrees through the sine of 2 theta.\n3. Substitute v=11.3 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 11.4927, \"unit\": \"m\"}", "dedupe_signature": "4a917d2a4f1895eec6ecb470a03703bfebe18c2f5f4f1b19b855727e91608fd9", "difficulty": "medium", "final_answer": {"answer": 11.4927, "unit": "m"}, "id": "projectile_range_000074_11.3_59", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 11.3 m/s and angle 59 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=59 degrees through the sine of 2 theta.\nSubstitute v=11.3 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 59, "gravity": 9.81, "speed": 11.3}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=987 mg, t=86.5 h, and T_half=80.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 468.6516, \"unit\": \"mg\"}", "dedupe_signature": "a19b8926dd65515b4308251342b06416e09e947d7122a91d5ef56bab5b7aa81e", "difficulty": "medium", "final_answer": {"answer": 468.6516, "unit": "mg"}, "id": "half_life_000078_987_80.5_86.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 987 mg. Its half-life is 80.5 hours. How many mg remain after 86.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=987 mg, t=86.5 h, and T_half=80.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 86.5, "half_life": 80.5, "initial_amount": 987.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 6.29 mol * 100.087 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 629.5472, \"unit\": \"g\"}", "dedupe_signature": "f2c3844781bd647c73458ea8e348d02db0c86137bfaef61e234aa23440586051", "difficulty": "medium", "final_answer": {"answer": 629.5472, "unit": "g"}, "id": "stoich_mass_000079_calcium_carbonate_6.29", "license": "Apache-2.0", "prompt": "A sample contains 6.29 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 6.29 mol * 100.087 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "calcium carbonate", "molar_mass": 100.087, "moles": 6.29}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 1180 mL to 1.18 L.\n3. Compute M = 2.735 / 1.18.\nFinal: {\"answer\": 2.3178, \"unit\": \"mol/L\"}", "dedupe_signature": "fff4e1d53447784ec2170b74491d5bc7f778e38313436a0488beb84a8d703a72", "difficulty": "medium", "final_answer": {"answer": 2.3178, "unit": "mol/L"}, "id": "molarity_000080_2.735_1180", "license": "Apache-2.0", "prompt": "A solution contains 2.735 mol of solute in 1180 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 1180 mL to 1.18 L.\nCompute M = 2.735 / 1.18.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 2.735, "volume_ml": 1180}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.17 y, so each step multiplies y by 1 - h*0.17.\n3. Apply that update for 8 steps and round the final state.\nFinal: {\"answer\": 17.6153, \"unit\": \"state_units\"}", "dedupe_signature": "3792e143db6fa4a0157fa84b7f06a85ee45feefa6bff48a887fbb0eadc1a927d", "difficulty": "medium", "final_answer": {"answer": 17.6153, "unit": "state_units"}, "id": "euler_decay_000081_66.5_0.17_0.9_8", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.17 y with y(0)=66.5, step size h=0.9, for 8 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.17 y, so each step multiplies y by 1 - h*0.17.\nApply that update for 8 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 66.5, "rate": 0.17, "step": 0.9, "steps": 8}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-9.9)=33.73 and f(-2.5)=13.75.\n3. The interval width is 7.4.\nFinal: {\"answer\": 175.676, \"unit\": \"area_units\"}", "dedupe_signature": "5a63f5ddeb5de57e75f28ed780e5450a87fe2a789a3fee117b0bfdb8eed6c46e", "difficulty": "medium", "final_answer": {"answer": 175.676, "unit": "area_units"}, "id": "trapz_linear_000082_-2.7_7_-9.9_-2.5", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-2.7x+7 from x=-9.9 to x=-2.5. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-9.9)=33.73 and f(-2.5)=13.75.\nThe interval width is 7.4.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 7.0, "slope": -2.7, "x0": -9.9, "x1": -2.5}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 44644.0 / 1000.\nFinal: {\"answer\": 44.644, \"unit\": \"kg\"}", "dedupe_signature": "4b1e61afcbd787a29e76e5c521da25b9cdfb587debd09b170c52d8316ded5963", "difficulty": "easy", "final_answer": {"answer": 44.644, "unit": "kg"}, "id": "unit_convert_000084_g_to_kg_44644", "license": "Apache-2.0", "prompt": "Convert 44644 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 44644.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 44644.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-8.7, 20.25], \"unit\": \"dimensionless\"}", "dedupe_signature": "0162806822173dfe74b7136ad8e212471b361d423510c38d6a49b6aa84bf656a", "difficulty": "medium", "final_answer": {"answer": [-8.7, 20.25], "unit": "dimensionless"}, "id": "line_two_point_000086_1.75_7.5_-8.7_20.25", "license": "Apache-2.0", "prompt": "A line passes through points (1.75, 5.025) and (7.5, -45). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 1.75, "x2": 7.5, "y1": 5.025000000000002, "y2": -45.0}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: volume.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"volume\"]}", "dedupe_signature": "7f8597d3bef67546acffe2d0e407856cadacf660bf5f77928f7a74aacfa8453a", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["volume"]}, "id": "abstain_000089_volume", "license": "Apache-2.0", "prompt": "Compute pressure from the ideal gas law. The prompt gives n=1.71 mol and T=579 K, but does not give volume. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: volume.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["volume"]}, "verifier": {"missing": ["volume"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 5.8 kg and a = 13.4 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 77.72, \"unit\": \"N\"}", "dedupe_signature": "1f151c17e5b30f7b46b5024efa1f691d815a21dd2d9324e2dc3f8292f2b59b6b", "difficulty": "easy", "final_answer": {"answer": 77.72, "unit": "N"}, "id": "force_000090_5.8_13.4", "license": "Apache-2.0", "prompt": "A cart has mass 5.8 kg and measured acceleration 13.4 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 5.8 kg and a = 13.4 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 13.4, "mass": 5.8}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 9.25^2 and multiply by 0.5 * 20.85.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 891.9891, \"unit\": \"J\"}", "dedupe_signature": "828815539985e09e9785b9b6024ada4045833e16e589c25f418f91dc2aaea728", "difficulty": "easy", "final_answer": {"answer": 891.9891, "unit": "J"}, "id": "ke_000091_20.85_9.25", "license": "Apache-2.0", "prompt": "A body of mass 20.85 kg moves at 9.25 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 9.25^2 and multiply by 0.5 * 20.85.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 20.85, "velocity": 9.25}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=75 degrees through the sine of 2 theta.\n3. Substitute v=74.5 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 282.8874, \"unit\": \"m\"}", "dedupe_signature": "6370c18accdcb306d0d05262b5c172721a8408b6f1f2971eb638c42e90cbeb4a", "difficulty": "medium", "final_answer": {"answer": 282.8874, "unit": "m"}, "id": "projectile_range_000092_74.5_75", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 74.5 m/s and angle 75 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=75 degrees through the sine of 2 theta.\nSubstitute v=74.5 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 75, "gravity": 9.81, "speed": 74.5}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 5.42 * 8.314 * 570 / 72.9.\nFinal: {\"answer\": 352.3357, \"unit\": \"kPa\"}", "dedupe_signature": "c882e0ac568b345b8a2f5f40d8a0c2eb4c7241199cdfb8227ec95ce555f10bab", "difficulty": "medium", "final_answer": {"answer": 352.3357, "unit": "kPa"}, "id": "ideal_gas_000093_5.42_570_72.9", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=5.42 mol, T=570 K, and V=72.9 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 5.42 * 8.314 * 570 / 72.9.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 5.42, "temp_k": 570, "volume_l": 72.9}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=91.1 V and R=111.4 ohm.\nFinal: {\"answer\": 74.4992, \"unit\": \"W\"}", "dedupe_signature": "714654d9c62ba8302a75b85510f0afb3aaa1408cce5d4baca4db28e79d0b9b3b", "difficulty": "easy", "final_answer": {"answer": 74.4992, "unit": "W"}, "id": "ohm_power_000095_91.1_111.4", "license": "Apache-2.0", "prompt": "A resistor has resistance 111.4 ohm and voltage 91.1 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=91.1 V and R=111.4 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 111.4, "voltage": 91.1}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=754.5 mg, t=143 h, and T_half=84.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 233.4661, \"unit\": \"mg\"}", "dedupe_signature": "83a5f64c8c64dc32d12d6aabc0b7c45bd7136f9bff78a706e5ec16a9a5c05f67", "difficulty": "medium", "final_answer": {"answer": 233.4661, "unit": "mg"}, "id": "half_life_000096_754.5_84.5_143", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 754.5 mg. Its half-life is 84.5 hours. How many mg remain after 143 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=754.5 mg, t=143 h, and T_half=84.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 143.0, "half_life": 84.5, "initial_amount": 754.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 355 mL to 0.355 L.\n3. Compute M = 4.355 / 0.355.\nFinal: {\"answer\": 12.2676, \"unit\": \"mol/L\"}", "dedupe_signature": "55b015009458c84a98e644c4d8392b0f24d7c6c12bdd9135661b399170860f81", "difficulty": "medium", "final_answer": {"answer": 12.2676, "unit": "mol/L"}, "id": "molarity_000098_4.355_355", "license": "Apache-2.0", "prompt": "A solution contains 4.355 mol of solute in 355 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 355 mL to 0.355 L.\nCompute M = 4.355 / 0.355.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 4.355, "volume_ml": 355}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.87 y, so each step multiplies y by 1 - h*0.87.\n3. Apply that update for 3 steps and round the final state.\nFinal: {\"answer\": 3.8554, \"unit\": \"state_units\"}", "dedupe_signature": "5d26fa70e9e9d0b4145467044c135fae5af959e12e249b2ececf7c4cb3fc435b", "difficulty": "medium", "final_answer": {"answer": 3.8554, "unit": "state_units"}, "id": "euler_decay_000099_47_0.87_0.65_3", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.87 y with y(0)=47, step size h=0.65, for 3 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.87 y, so each step multiplies y by 1 - h*0.87.\nApply that update for 3 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 47.0, "rate": 0.87, "step": 0.65, "steps": 3}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(0.9)=-13.84 and f(6.1)=-6.56.\n3. The interval width is 5.2.\nFinal: {\"answer\": -53.04, \"unit\": \"area_units\"}", "dedupe_signature": "24c2f6ac28dd852520f92bc75bd1ebee43cfd56e81c407c43f0e8bbe3228df1a", "difficulty": "medium", "final_answer": {"answer": -53.04, "unit": "area_units"}, "id": "trapz_linear_000100_1.4_-15.1_0.9_6.1", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=1.4x+-15.1 from x=0.9 to x=6.1. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(0.9)=-13.84 and f(6.1)=-6.56.\nThe interval width is 5.2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -15.1, "slope": 1.4, "x0": 0.9, "x1": 6.1000000000000005}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.36 and add it to the current value.\nFinal: {\"answer\": [0.802, -0.128, -0.86], \"unit\": \"temperature_units\"}", "dedupe_signature": "252c6091088ab7e37ebe695d5844284193115cf7312dac08090611254c5ab77d", "difficulty": "hard", "final_answer": {"answer": [0.802, -0.128, -0.86], "unit": "temperature_units"}, "id": "heat_step_000101_0.36_1.85_1.9_-1.1_-1.4_-0.2", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.85, right=-0.2; current interior values are [1.9, -1.1, -1.4]. Use r=0.36. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.36 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [1.9, -1.1, -1.4], "left": 1.85, "r": 0.36, "right": -0.2}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kelvin equals Celsius plus 273.15.\n2. Apply the conversion factor directly to the given value.\n3. Compute 114.5 + 273.15.\nFinal: {\"answer\": 387.65, \"unit\": \"K\"}", "dedupe_signature": "9be5b14dfbe353d39d246a820ed4b9f5f1aaeaa7323a45df3cead1c9f7cea522", "difficulty": "easy", "final_answer": {"answer": 387.65, "unit": "K"}, "id": "unit_convert_000102_c_to_k_114.5", "license": "Apache-2.0", "prompt": "Convert 114.5 degC to K. Return the converted value with unit.", "reasoning_trace": "Kelvin equals Celsius plus 273.15.\nApply the conversion factor directly to the given value.\nCompute 114.5 + 273.15.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 114.5}, "verifier": {"formula": "value + 273.15", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=78 degrees and keep the unit as newtons.\nFinal: {\"answer\": [42.6219, 200.5203], \"unit\": \"N\"}", "dedupe_signature": "e246de3bb772749e3cfcb628270b47d5b77872796704d12f55ffa4d05f9caa88", "difficulty": "medium", "final_answer": {"answer": [42.6219, 200.5203], "unit": "N"}, "id": "vector_components_000103_205_78", "license": "Apache-2.0", "prompt": "A vector has magnitude 205 N at 78 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=78 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 78, "magnitude": 205.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-8.85, -16.0], \"unit\": \"dimensionless\"}", "dedupe_signature": "bbe4502e7d6c9a801c2ffec55aa442bc8515714c3ddfe01d3cc8654a5131ca04", "difficulty": "medium", "final_answer": {"answer": [-8.85, -16.0], "unit": "dimensionless"}, "id": "line_two_point_000104_-13.5_-6.75_-8.85_-16", "license": "Apache-2.0", "prompt": "A line passes through points (-13.5, 103.475) and (-6.75, 43.7375). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -13.5, "x2": -6.75, "y1": 103.475, "y2": 43.7375}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. speed squared over acceleration has units of meters\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "655b2ebecaa4a028bc064d0b2da86e7a630df898ec113f9c48f2f741a5da7d09", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_000105_consistent_741d4e34_426072", "license": "Apache-2.0", "prompt": "In student derivation case 426072, check dimensional consistency for R = v^2 * sin(theta) / g. The left side has dimensions m and the right side has dimensions m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nspeed squared over acceleration has units of meters\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "R = v^2 * sin(theta) / g"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef clamp_000106(x, lo, hi):\n    if lo > hi:\n        raise ValueError('lo must be <= hi')\n    return min(max(x, lo), hi)\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"clamp_000106\"}", "dedupe_signature": "d5d30a2ee2b483e584831a97d472d16ee5ee45d682c7ccb5a42da537a834f1d9", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "clamp_000106"}, "id": "code_000106_clamp_000106", "license": "Apache-2.0", "prompt": "Write a Python function clamp_000106(x, lo, hi) that clips x into the inclusive interval [lo, hi]. It must raise ValueError if lo > hi. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "clamp_000106"}, "verifier": {"function": "clamp_000106", "tests": ["assert clamp_000106(5, 0, 10) == 5", "assert clamp_000106(-2, 0, 10) == 0", "assert clamp_000106(12, 0, 10) == 10", "try:\n    clamp_000106(1, 3, 2)\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: target_schema, valid_examples.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"target_schema\", \"valid_examples\"]}", "dedupe_signature": "b8ae608a74582856820195192976708339955b64c354341a26f84c9c494eed0b", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["target_schema", "valid_examples"]}, "id": "abstain_000107_target_schema_valid_examples", "license": "Apache-2.0", "prompt": "Write a parser that converts each warehouse crop record from batch 305743 into the correct schema, but the prompt does not include the target schema or examples. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: target_schema, valid_examples.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["target_schema", "valid_examples"]}, "verifier": {"missing": ["target_schema", "valid_examples"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 14.45 kg and a = 5.15 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 74.4175, \"unit\": \"N\"}", "dedupe_signature": "1040212e97e0686568aa32ce6c032e2cd33863aebe81e810c8b71f88a645dcfd", "difficulty": "easy", "final_answer": {"answer": 74.4175, "unit": "N"}, "id": "force_000108_14.45_5.15", "license": "Apache-2.0", "prompt": "A cart has mass 14.45 kg and measured acceleration 5.15 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 14.45 kg and a = 5.15 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 5.15, "mass": 14.45}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 6.7^2 and multiply by 0.5 * 15.45.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 346.7752, \"unit\": \"J\"}", "dedupe_signature": "f70ca2b7906cf3901c763688ccdea5ebf1b2b6442ceb4142bd4efad10e1bb0a3", "difficulty": "easy", "final_answer": {"answer": 346.7752, "unit": "J"}, "id": "ke_000109_15.45_6.7", "license": "Apache-2.0", "prompt": "A body of mass 15.45 kg moves at 6.7 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 6.7^2 and multiply by 0.5 * 15.45.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 15.45, "velocity": 6.7}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 4.42 * 8.314 * 388 / 25.5.\nFinal: {\"answer\": 559.1442, \"unit\": \"kPa\"}", "dedupe_signature": "017866bef0afd586f14f704e7924d291dbfe0b7b5a15c756a663074922dbb3ae", "difficulty": "medium", "final_answer": {"answer": 559.1442, "unit": "kPa"}, "id": "ideal_gas_000111_4.42_388_25.5", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=4.42 mol, T=388 K, and V=25.5 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 4.42 * 8.314 * 388 / 25.5.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 4.42, "temp_k": 388, "volume_l": 25.5}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=29.7 V and R=165.7 ohm.\nFinal: {\"answer\": 5.3234, \"unit\": \"W\"}", "dedupe_signature": "2dbe4ae6179c91f6f75017c081cc76cef42d34d4218169aef2163f31883d365b", "difficulty": "easy", "final_answer": {"answer": 5.3234, "unit": "W"}, "id": "ohm_power_000113_29.7_165.7", "license": "Apache-2.0", "prompt": "A resistor has resistance 165.7 ohm and voltage 29.7 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=29.7 V and R=165.7 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 165.7, "voltage": 29.7}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=613.5 mg, t=233 h, and T_half=80.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 82.5107, \"unit\": \"mg\"}", "dedupe_signature": "a7a904bc47f80c8341a11fda30e9d01614ab4435f122b2d143009b3bb5d14807", "difficulty": "medium", "final_answer": {"answer": 82.5107, "unit": "mg"}, "id": "half_life_000114_613.5_80.5_233", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 613.5 mg. Its half-life is 80.5 hours. How many mg remain after 233 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=613.5 mg, t=233 h, and T_half=80.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 233.0, "half_life": 80.5, "initial_amount": 613.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 2.56 mol * 58.44 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 149.6064, \"unit\": \"g\"}", "dedupe_signature": "3603ca23738155d7a92ab257b820b9a7c393494158cdd39b22789971498053ea", "difficulty": "medium", "final_answer": {"answer": 149.6064, "unit": "g"}, "id": "stoich_mass_000115_sodium_chloride_2.56", "license": "Apache-2.0", "prompt": "A sample contains 2.56 mol of sodium chloride. Using molar mass 58.44 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 2.56 mol * 58.44 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "sodium chloride", "molar_mass": 58.44, "moles": 2.56}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.88 y, so each step multiplies y by 1 - h*0.88.\n3. Apply that update for 12 steps and round the final state.\nFinal: {\"answer\": 0.0, \"unit\": \"state_units\"}", "dedupe_signature": "e928d0c32aed6aa214237192d53106d147e76aed8fc69e3a5717ba81bcad76bc", "difficulty": "medium", "final_answer": {"answer": 0.0, "unit": "state_units"}, "id": "euler_decay_000117_11.5_0.88_1.4_12", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.88 y with y(0)=11.5, step size h=1.4, for 12 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.88 y, so each step multiplies y by 1 - h*0.88.\nApply that update for 12 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 11.5, "rate": 0.88, "step": 1.4, "steps": 12}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(3.3)=21.48 and f(12.8)=55.68.\n3. The interval width is 9.5.\nFinal: {\"answer\": 366.51, \"unit\": \"area_units\"}", "dedupe_signature": "9db8a75821cd73f00b73dbb5fac9e330ae3f3f04922037b51b46553c161ef56e", "difficulty": "medium", "final_answer": {"answer": 366.51, "unit": "area_units"}, "id": "trapz_linear_000118_3.6_9.6_3.3_12.8", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=3.6x+9.6 from x=3.3 to x=12.8. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(3.3)=21.48 and f(12.8)=55.68.\nThe interval width is 9.5.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 9.6, "slope": 3.6, "x0": 3.3, "x1": 12.8}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.4 and add it to the current value.\nFinal: {\"answer\": [0.18, -0.7, -0.37], \"unit\": \"temperature_units\"}", "dedupe_signature": "099e13a3ba3a89ef291a63b31981c6a7961f6012c74cf67ab243c4308846604b", "difficulty": "hard", "final_answer": {"answer": [0.18, -0.7, -0.37], "unit": "temperature_units"}, "id": "heat_step_000119_0.4_-0.15_-1.6_1.4_-0.85_-1.9", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-0.15, right=-1.9; current interior values are [-1.6, 1.4, -0.85]. Use r=0.4. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.4 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-1.6, 1.4, -0.85], "left": -0.15, "r": 0.4, "right": -1.9}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 100 centimeters in one meter.\n2. Apply the conversion factor directly to the given value.\n3. Compute 4606.5 / 100.\nFinal: {\"answer\": 46.065, \"unit\": \"m\"}", "dedupe_signature": "ecc482a0dd3f47133fd5320f3092b07f3ffb1a67497ed7a2f7ec2cafa4928c46", "difficulty": "easy", "final_answer": {"answer": 46.065, "unit": "m"}, "id": "unit_convert_000120_cm_to_m_4606.5", "license": "Apache-2.0", "prompt": "Convert 4606.5 cm to m. Return the converted value with unit.", "reasoning_trace": "There are 100 centimeters in one meter.\nApply the conversion factor directly to the given value.\nCompute 4606.5 / 100.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 4606.5}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=201 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-397.7053, -152.6647], \"unit\": \"N\"}", "dedupe_signature": "07bfada1befddd03d67df0a4d5d4eace281fa7f3b8776aa6d760c2051ab63ed5", "difficulty": "medium", "final_answer": {"answer": [-397.7053, -152.6647], "unit": "N"}, "id": "vector_components_000121_426_201", "license": "Apache-2.0", "prompt": "A vector has magnitude 426 N at 201 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=201 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 201, "magnitude": 426.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. m*v is momentum, not energy\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "d89d9f08fc265701d424a312903f907d285d0765ac870ca1002893251b19f610", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_000123_inconsistent_1e14b074_384919", "license": "Apache-2.0", "prompt": "In instrument manual case 384919, check dimensional consistency for E = m * v. The left side has dimensions kg*m^2/s^2 and the right side has dimensions kg*m/s. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nm*v is momentum, not energy\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "E = m * v"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: volume.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"volume\"]}", "dedupe_signature": "164bad3e381acc6ed9ce173086881cb9a30f5e16c69e4323f2e6dce0700bf56e", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["volume"]}, "id": "abstain_000125_volume", "license": "Apache-2.0", "prompt": "Compute pressure from the ideal gas law. The prompt gives n=5.89 mol and T=458 K, but does not give volume. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: volume.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["volume"]}, "verifier": {"missing": ["volume"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 23.65 kg and a = 12.6 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 297.99, \"unit\": \"N\"}", "dedupe_signature": "889d9168e7fd8289ad0b5acca7e3c76b66144ba15b57393f95b9652419c5064a", "difficulty": "easy", "final_answer": {"answer": 297.99, "unit": "N"}, "id": "force_000126_23.65_12.6", "license": "Apache-2.0", "prompt": "A cart has mass 23.65 kg and measured acceleration 12.6 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 23.65 kg and a = 12.6 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 12.6, "mass": 23.65}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 3.15^2 and multiply by 0.5 * 8.85.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 43.9071, \"unit\": \"J\"}", "dedupe_signature": "db6416f992c2b1c78b576ebc8a9f19442e45960f08dc17aca3a0682d6fb5a34a", "difficulty": "easy", "final_answer": {"answer": 43.9071, "unit": "J"}, "id": "ke_000127_8.85_3.15", "license": "Apache-2.0", "prompt": "A body of mass 8.85 kg moves at 3.15 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 3.15^2 and multiply by 0.5 * 8.85.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 8.85, "velocity": 3.15}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=29 degrees through the sine of 2 theta.\n3. Substitute v=78.1 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 527.2949, \"unit\": \"m\"}", "dedupe_signature": "abc8cea16da173fe7217e07637bfb363d4907772acef52b8316d30d4dc56605a", "difficulty": "medium", "final_answer": {"answer": 527.2949, "unit": "m"}, "id": "projectile_range_000128_78.1_29", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 78.1 m/s and angle 29 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=29 degrees through the sine of 2 theta.\nSubstitute v=78.1 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 29, "gravity": 9.81, "speed": 78.1}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 1.8 * 8.314 * 371 / 28.6.\nFinal: {\"answer\": 194.129, \"unit\": \"kPa\"}", "dedupe_signature": "52cc9508a4d60184a9150989b29b6570186f04f5daa36b290573b3bbada1afec", "difficulty": "medium", "final_answer": {"answer": 194.129, "unit": "kPa"}, "id": "ideal_gas_000129_1.8_371_28.6", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=1.8 mol, T=371 K, and V=28.6 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 1.8 * 8.314 * 371 / 28.6.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 1.8, "temp_k": 371, "volume_l": 28.6}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 525 * 3.36 * 108.\nFinal: {\"answer\": 190512.0, \"unit\": \"J\"}", "dedupe_signature": "bf451c979c85fee90d29082719ac44f0c185503b12b6e44e22c0c655dcea04db", "difficulty": "easy", "final_answer": {"answer": 190512.0, "unit": "J"}, "id": "heat_q_000130_525_3.36_108", "license": "Apache-2.0", "prompt": "A 525 g sample has specific heat 3.36 J/(g*K). How much heat is needed to raise its temperature by 108 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 525 * 3.36 * 108.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 108, "heat_capacity": 3.36, "mass_g": 525}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 0.81 mol * 100.087 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 81.0705, \"unit\": \"g\"}", "dedupe_signature": "1564d0e22cfc4f600b322f37adfd10ccae0f760a4083a5f4f3a88bc3ffba1667", "difficulty": "medium", "final_answer": {"answer": 81.0705, "unit": "g"}, "id": "stoich_mass_000133_calcium_carbonate_0.81", "license": "Apache-2.0", "prompt": "A sample contains 0.81 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 0.81 mol * 100.087 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "calcium carbonate", "molar_mass": 100.087, "moles": 0.81}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 4545 mL to 4.545 L.\n3. Compute M = 4.165 / 4.545.\nFinal: {\"answer\": 0.9164, \"unit\": \"mol/L\"}", "dedupe_signature": "1146af47427e1172eaa537e5337545e25d607a7f0ee6c9ce642a2aa412e1cd9e", "difficulty": "medium", "final_answer": {"answer": 0.9164, "unit": "mol/L"}, "id": "molarity_000134_4.165_4545", "license": "Apache-2.0", "prompt": "A solution contains 4.165 mol of solute in 4545 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 4545 mL to 4.545 L.\nCompute M = 4.165 / 4.545.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 4.165, "volume_ml": 4545}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(2.5)=18.8 and f(11.6)=82.5.\n3. The interval width is 9.1.\nFinal: {\"answer\": 460.915, \"unit\": \"area_units\"}", "dedupe_signature": "500928e09f8c3c47967f0f136bf79ee7a6be34ae687f3ecbff6f14f6634e12e8", "difficulty": "medium", "final_answer": {"answer": 460.915, "unit": "area_units"}, "id": "trapz_linear_000136_7_1.3_2.5_11.6", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=7x+1.3 from x=2.5 to x=11.6. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(2.5)=18.8 and f(11.6)=82.5.\nThe interval width is 9.1.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 1.3, "slope": 7.0, "x0": 2.5, "x1": 11.6}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.22 and add it to the current value.\nFinal: {\"answer\": [-0.049, 0.97, 1.102], \"unit\": \"temperature_units\"}", "dedupe_signature": "1188d9efff18923b71f65df159a8864d95ebf05e243878ce6203c2ac25f0a6d7", "difficulty": "hard", "final_answer": {"answer": [-0.049, 0.97, 1.102], "unit": "temperature_units"}, "id": "heat_step_000137_0.22_2.0_-1.6_1.85_1.3_-0.15", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=2, right=-0.15; current interior values are [-1.6, 1.85, 1.3]. Use r=0.22. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.22 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-1.6, 1.85, 1.3], "left": 2.0, "r": 0.22, "right": -0.15}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 39476.0 / 1000.\nFinal: {\"answer\": 39.476, \"unit\": \"kg\"}", "dedupe_signature": "03fa34003b34124a0b64be4e0dc7560b93fbb35dc370a33b757661033503dd5d", "difficulty": "easy", "final_answer": {"answer": 39.476, "unit": "kg"}, "id": "unit_convert_000138_g_to_kg_39476", "license": "Apache-2.0", "prompt": "Convert 39476 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 39476.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 39476.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [9.3, 8.0], \"unit\": \"dimensionless\"}", "dedupe_signature": "24d64c7afc776bd192a5b08fc1137f2aa8bf087b4240f669c8e75d33052c335a", "difficulty": "medium", "final_answer": {"answer": [9.3, 8.0], "unit": "dimensionless"}, "id": "line_two_point_000140_-1.75_8.75_9.3_8", "license": "Apache-2.0", "prompt": "A line passes through points (-1.75, -8.275) and (8.75, 89.375). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -1.75, "x2": 8.75, "y1": -8.275000000000002, "y2": 89.375}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. lever arm times force has torque dimensions\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "dcd4c7ba6ac9c41e1945b54ed1abe093455d505db91118b79fe6f87f8bdfa87a", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_000141_consistent_5ca82cb9_746972", "license": "Apache-2.0", "prompt": "In instrument manual case 746972, check dimensional consistency for tau = r * F. The left side has dimensions N*m and the right side has dimensions N*m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nlever arm times force has torque dimensions\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "tau = r * F"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\nimport math\n\ndef unit_vector_000142(x, y):\n    norm = math.hypot(x, y)\n    if norm == 0:\n        raise ValueError('zero vector has no direction')\n    return (x / norm, y / norm)\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"unit_vector_000142\"}", "dedupe_signature": "810f649f2624a398f1266d20abad5e1aa054f5a48137469524c8e65ba66250cc", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "unit_vector_000142"}, "id": "code_000142_unit_vector_000142", "license": "Apache-2.0", "prompt": "Write a Python function unit_vector_000142(x, y) that returns the 2D unit vector as a tuple. Raise ValueError for the zero vector. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "unit_vector_000142"}, "verifier": {"function": "unit_vector_000142", "tests": ["ux, uy = unit_vector_000142(3, 4); assert abs(ux - 0.6) < 1e-12 and abs(uy - 0.8) < 1e-12", "assert unit_vector_000142(0, 5) == (0, 1)", "try:\n    unit_vector_000142(0, 0)\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: left_boundary, right_boundary.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"left_boundary\", \"right_boundary\"]}", "dedupe_signature": "c23b9c8282134ab4c394cd23c49cebeb095407414ef97f8cfd715bd16a8fa27a", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["left_boundary", "right_boundary"]}, "id": "abstain_000143_left_boundary_right_boundary", "license": "Apache-2.0", "prompt": "Solve the 1D heat equation after one finite-difference step. The prompt gives r=0.12 and interior values [1.55, -0.5, 1.15], but gives no boundary values. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: left_boundary, right_boundary.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["left_boundary", "right_boundary"]}, "verifier": {"missing": ["left_boundary", "right_boundary"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 6.2 kg and a = 5.65 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 35.03, \"unit\": \"N\"}", "dedupe_signature": "58f15b69a56ac0b4a1c6a50c815f8ce019adb04b956f796ba4e99b15192dd118", "difficulty": "easy", "final_answer": {"answer": 35.03, "unit": "N"}, "id": "force_000144_6.2_5.65", "license": "Apache-2.0", "prompt": "A cart has mass 6.2 kg and measured acceleration 5.65 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 6.2 kg and a = 5.65 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 5.65, "mass": 6.2}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 19.35^2 and multiply by 0.5 * 16.4.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 3070.2645, \"unit\": \"J\"}", "dedupe_signature": "869b11afcbd6e28dca024b0c68e1f29ad1cc63fb06c3215d681b2b655df848cc", "difficulty": "easy", "final_answer": {"answer": 3070.2645, "unit": "J"}, "id": "ke_000145_16.4_19.35", "license": "Apache-2.0", "prompt": "A body of mass 16.4 kg moves at 19.35 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 19.35^2 and multiply by 0.5 * 16.4.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 16.4, "velocity": 19.35}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 4.73 * 8.314 * 395 / 41.6.\nFinal: {\"answer\": 373.4005, \"unit\": \"kPa\"}", "dedupe_signature": "a4e3c68b134411dba0311239483678566cda13c43f87a932ce57cdc86bc8fe46", "difficulty": "medium", "final_answer": {"answer": 373.4005, "unit": "kPa"}, "id": "ideal_gas_000147_4.73_395_41.6", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=4.73 mol, T=395 K, and V=41.6 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 4.73 * 8.314 * 395 / 41.6.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 4.73, "temp_k": 395, "volume_l": 41.6}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1135 * 4.61 * 49.\nFinal: {\"answer\": 256385.15, \"unit\": \"J\"}", "dedupe_signature": "c6d45f115074b2603823a5df3ca663da5c2e2876d50ffb18544c7960f11cf095", "difficulty": "easy", "final_answer": {"answer": 256385.15, "unit": "J"}, "id": "heat_q_000148_1135_4.61_49", "license": "Apache-2.0", "prompt": "A 1135 g sample has specific heat 4.61 J/(g*K). How much heat is needed to raise its temperature by 49 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1135 * 4.61 * 49.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 49, "heat_capacity": 4.61, "mass_g": 1135}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=183 V and R=170.8 ohm.\nFinal: {\"answer\": 196.0714, \"unit\": \"W\"}", "dedupe_signature": "2925e52cd9dd9960ba98639c1d32f9c90557fb5bb42e81e75e6ce8895d45fa0f", "difficulty": "easy", "final_answer": {"answer": 196.0714, "unit": "W"}, "id": "ohm_power_000149_183_170.8", "license": "Apache-2.0", "prompt": "A resistor has resistance 170.8 ohm and voltage 183 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=183 V and R=170.8 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 170.8, "voltage": 183.0}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=151.5 mg, t=317 h, and T_half=111 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 20.9274, \"unit\": \"mg\"}", "dedupe_signature": "745e1350abc53f738c97a2409ba461a1b41aa161f07938afd7f44b4af9d14945", "difficulty": "medium", "final_answer": {"answer": 20.9274, "unit": "mg"}, "id": "half_life_000150_151.5_111_317", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 151.5 mg. Its half-life is 111 hours. How many mg remain after 317 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=151.5 mg, t=317 h, and T_half=111 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 317.0, "half_life": 111.0, "initial_amount": 151.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 7.88 mol * 18.015 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 141.9582, \"unit\": \"g\"}", "dedupe_signature": "99d42f82a3e5f30f108ea876992687675869f2959718c816281920d0a0ec8b54", "difficulty": "medium", "final_answer": {"answer": 141.9582, "unit": "g"}, "id": "stoich_mass_000151_water_7.88", "license": "Apache-2.0", "prompt": "A sample contains 7.88 mol of water. Using molar mass 18.015 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 7.88 mol * 18.015 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "water", "molar_mass": 18.015, "moles": 7.88}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-3.1)=22.27 and f(1.2)=-10.84.\n3. The interval width is 4.3.\nFinal: {\"answer\": 24.5745, \"unit\": \"area_units\"}", "dedupe_signature": "08bb0fa8f90067b52d35dd837b95c6e7ff034937214a7567a00bab4e1c276695", "difficulty": "medium", "final_answer": {"answer": 24.5745, "unit": "area_units"}, "id": "trapz_linear_000154_-7.7_-1.6_-3.1_1.2", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-7.7x+-1.6 from x=-3.1 to x=1.2. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-3.1)=22.27 and f(1.2)=-10.84.\nThe interval width is 4.3.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -1.6, "slope": -7.7, "x0": -3.1, "x1": 1.1999999999999997}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.42 and add it to the current value.\nFinal: {\"answer\": [1.07, 0.039, 0.379], \"unit\": \"temperature_units\"}", "dedupe_signature": "ea9cb53d34bbe07ad3a1223642a6484f1f61ed2ab4b906957f1994de5fb95a1b", "difficulty": "hard", "final_answer": {"answer": [1.07, 0.039, 0.379], "unit": "temperature_units"}, "id": "heat_step_000155_0.42_-0.3_-0.4_3.0_-0.65_-1.85", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-0.3, right=-1.85; current interior values are [-0.4, 3.0, -0.65]. Use r=0.42. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.42 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-0.4, 3.0, -0.65], "left": -0.3, "r": 0.42, "right": -1.85}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=309 degrees and keep the unit as newtons.\nFinal: {\"answer\": [229.3873, -283.2697], \"unit\": \"N\"}", "dedupe_signature": "34271ddc88b7d94b67c2685a71cb6809d8bc773d68489b0ece76e4aeae478145", "difficulty": "medium", "final_answer": {"answer": [229.3873, -283.2697], "unit": "N"}, "id": "vector_components_000157_364.5_309", "license": "Apache-2.0", "prompt": "A vector has magnitude 364.5 N at 309 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=309 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 309, "magnitude": 364.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. m*v is momentum, not energy\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "54b01469bea9adb3630256f80eb4bbc82e73a80275d89f96124f4bc8d7c61a91", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_000159_inconsistent_1e14b074_254165", "license": "Apache-2.0", "prompt": "In quality-control check case 254165, check dimensional consistency for E = m * v. The left side has dimensions kg*m^2/s^2 and the right side has dimensions kg*m/s. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nm*v is momentum, not energy\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "E = m * v"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef safe_mean_000160(values):\n    if not values:\n        raise ValueError('safe_mean requires at least one value')\n    return sum(values) / len(values)\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"safe_mean_000160\"}", "dedupe_signature": "8bf6633931fc3e523f67c2ba8c04a395d4d7d55f7c4d170ce3c554aeb3f2f7da", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "safe_mean_000160"}, "id": "code_000160_safe_mean_000160", "license": "Apache-2.0", "prompt": "Write a Python function safe_mean_000160(values) that returns the arithmetic mean. It must raise ValueError for an empty input and must not mutate the input list. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "safe_mean_000160"}, "verifier": {"function": "safe_mean_000160", "tests": ["assert safe_mean_000160([2, 4, 6]) == 4", "xs = [1, 2, 3]; assert safe_mean_000160(xs) == 2 and xs == [1, 2, 3]", "try:\n    safe_mean_000160([])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: volume.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"volume\"]}", "dedupe_signature": "f7f98deaebb599d07bc576520d471887534b25834133cc808b1139ecebd3996f", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["volume"]}, "id": "abstain_000161_volume", "license": "Apache-2.0", "prompt": "Compute pressure from the ideal gas law. The prompt gives n=3.48 mol and T=407 K, but does not give volume. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: volume.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["volume"]}, "verifier": {"missing": ["volume"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=76 degrees through the sine of 2 theta.\n3. Substitute v=25 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 29.9103, \"unit\": \"m\"}", "dedupe_signature": "82add1b14ecebebdad0b90aed5c130719aadb50b319b85f71805102852335b8f", "difficulty": "medium", "final_answer": {"answer": 29.9103, "unit": "m"}, "id": "projectile_range_000164_25_76", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 25 m/s and angle 76 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=76 degrees through the sine of 2 theta.\nSubstitute v=25 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 76, "gravity": 9.81, "speed": 25.0}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 5.32 * 8.314 * 287 / 44.2.\nFinal: {\"answer\": 287.1979, \"unit\": \"kPa\"}", "dedupe_signature": "eb3d728e00cad1213fae9ca85150521117ac09520ea958bd32451e3564b7572c", "difficulty": "medium", "final_answer": {"answer": 287.1979, "unit": "kPa"}, "id": "ideal_gas_000165_5.32_287_44.2", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=5.32 mol, T=287 K, and V=44.2 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 5.32 * 8.314 * 287 / 44.2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 5.32, "temp_k": 287, "volume_l": 44.2}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=32.5 mg, t=86 h, and T_half=11 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 0.144, \"unit\": \"mg\"}", "dedupe_signature": "934b01cae38c906709586fe0280b467f02974cc01ba9d0a79e0cc1d0e43ee429", "difficulty": "medium", "final_answer": {"answer": 0.144, "unit": "mg"}, "id": "half_life_000168_32.5_11_86", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 32.5 mg. Its half-life is 11 hours. How many mg remain after 86 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=32.5 mg, t=86 h, and T_half=11 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 86.0, "half_life": 11.0, "initial_amount": 32.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 3.7 mol * 100.087 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 370.3219, \"unit\": \"g\"}", "dedupe_signature": "17f823528e2890dd9f1617c0fc7e3f07f723fc7f6db6a08e311e3cb86563a1a7", "difficulty": "medium", "final_answer": {"answer": 370.3219, "unit": "g"}, "id": "stoich_mass_000169_calcium_carbonate_3.7", "license": "Apache-2.0", "prompt": "A sample contains 3.7 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 3.7 mol * 100.087 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "calcium carbonate", "molar_mass": 100.087, "moles": 3.7}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 3600 mL to 3.6 L.\n3. Compute M = 3.9 / 3.6.\nFinal: {\"answer\": 1.0833, \"unit\": \"mol/L\"}", "dedupe_signature": "0b471266a6c77bf23052b5ba170163053a10521b97d0078fcec3389c5ae9ba15", "difficulty": "medium", "final_answer": {"answer": 1.0833, "unit": "mol/L"}, "id": "molarity_000170_3.9_3600", "license": "Apache-2.0", "prompt": "A solution contains 3.9 mol of solute in 3600 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 3600 mL to 3.6 L.\nCompute M = 3.9 / 3.6.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 3.9, "volume_ml": 3600}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.23 y, so each step multiplies y by 1 - h*0.23.\n3. Apply that update for 2 steps and round the final state.\nFinal: {\"answer\": 23.7239, \"unit\": \"state_units\"}", "dedupe_signature": "f917aa0ba5232532ffe6fbb908e61bc7dcfd46b0522e01b9aeead7c271f95815", "difficulty": "medium", "final_answer": {"answer": 23.7239, "unit": "state_units"}, "id": "euler_decay_000171_78_0.23_1.95_2", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.23 y with y(0)=78, step size h=1.95, for 2 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.23 y, so each step multiplies y by 1 - h*0.23.\nApply that update for 2 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 78.0, "rate": 0.23, "step": 1.95, "steps": 2}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(6.1)=31 and f(16)=110.2.\n3. The interval width is 9.9.\nFinal: {\"answer\": 698.94, \"unit\": \"area_units\"}", "dedupe_signature": "5bf9b0144f60b68d7ef664db162326517e29c8fcab785e7c9bb2f9060ee46a33", "difficulty": "medium", "final_answer": {"answer": 698.94, "unit": "area_units"}, "id": "trapz_linear_000172_8_-17.8_6.1_16", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=8x+-17.8 from x=6.1 to x=16. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(6.1)=31 and f(16)=110.2.\nThe interval width is 9.9.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -17.8, "slope": 8.0, "x0": 6.1, "x1": 16.0}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.14 and add it to the current value.\nFinal: {\"answer\": [1.129, 1.716, 0.974], \"unit\": \"temperature_units\"}", "dedupe_signature": "8eecb4eb0866accd535071b4cf8c4bd0f4c9c32e4a7587af8b2c2579320659f1", "difficulty": "hard", "final_answer": {"answer": [1.129, 1.716, 0.974], "unit": "temperature_units"}, "id": "heat_step_000173_0.14_1.8_0.8_2.15_0.4_2.75", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.8, right=2.75; current interior values are [0.8, 2.15, 0.4]. Use r=0.14. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.14 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [0.8, 2.15, 0.4], "left": 1.8, "r": 0.14, "right": 2.75}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=1 degrees and keep the unit as newtons.\nFinal: {\"answer\": [74.4887, 1.3002], \"unit\": \"N\"}", "dedupe_signature": "c08d39d970371bedc45d33044bd6b9bb6b4219e980978c96d325730df7a9bf93", "difficulty": "medium", "final_answer": {"answer": [74.4887, 1.3002], "unit": "N"}, "id": "vector_components_000175_74.5_1", "license": "Apache-2.0", "prompt": "A vector has magnitude 74.5 N at 1 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=1 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 1, "magnitude": 74.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-1.75, -8.5], \"unit\": \"dimensionless\"}", "dedupe_signature": "d6c209dc6e2a81964979a51087936044d9b2fb37043b8c9e1aff84c34ca79f25", "difficulty": "medium", "final_answer": {"answer": [-1.75, -8.5], "unit": "dimensionless"}, "id": "line_two_point_000176_11.75_16.5_-1.75_-8.5", "license": "Apache-2.0", "prompt": "A line passes through points (11.75, -29.0625) and (16.5, -37.375). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 11.75, "x2": 16.5, "y1": -29.0625, "y2": -37.375}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. m*v is momentum, not energy\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "cf1f0641bf17087e8693c62eb65da58979920a1e27ee9742b1b485d7257c77d8", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_000177_inconsistent_1e14b074_227898", "license": "Apache-2.0", "prompt": "In model card equation case 227898, check dimensional consistency for E = m * v. The left side has dimensions kg*m^2/s^2 and the right side has dimensions kg*m/s. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nm*v is momentum, not energy\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "E = m * v"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef threshold_flags_000178(values, threshold):\n    return [value >= threshold for value in values]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"threshold_flags_000178\"}", "dedupe_signature": "4d87311d01df79579422048b75a582f992d7a77aefeb966df56ae8bfbe210a42", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "threshold_flags_000178"}, "id": "code_000178_threshold_flags_000178", "license": "Apache-2.0", "prompt": "Write a Python function threshold_flags_000178(values, threshold) that returns a list of booleans showing whether each value is greater than or equal to threshold. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "threshold_flags_000178"}, "verifier": {"function": "threshold_flags_000178", "tests": ["assert threshold_flags_000178([1, 2, 3], 2) == [False, True, True]", "assert threshold_flags_000178([], 5) == []", "assert threshold_flags_000178([-1, 0], 0) == [False, True]"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: volume.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"volume\"]}", "dedupe_signature": "0212e735c673abc2acc1b485fdabdf3f75f88e3d51491e1f9f95e8d720a2615f", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["volume"]}, "id": "abstain_000179_volume", "license": "Apache-2.0", "prompt": "Compute pressure from the ideal gas law. The prompt gives n=5.17 mol and T=415 K, but does not give volume. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: volume.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["volume"]}, "verifier": {"missing": ["volume"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 2.6 kg and a = 5.3 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 13.78, \"unit\": \"N\"}", "dedupe_signature": "c0e60a2f0988297466872477f4199c76f8c90da78994a50dcfb3d7a4a17f056e", "difficulty": "easy", "final_answer": {"answer": 13.78, "unit": "N"}, "id": "force_000180_2.6_5.3", "license": "Apache-2.0", "prompt": "A cart has mass 2.6 kg and measured acceleration 5.3 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 2.6 kg and a = 5.3 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 5.3, "mass": 2.6}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 4^2 and multiply by 0.5 * 21.7.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 173.6, \"unit\": \"J\"}", "dedupe_signature": "c4d91b14371bd23dbe295cbe19b65394ec300e0aee9a3dbdbdc5a65c1bf06cd2", "difficulty": "easy", "final_answer": {"answer": 173.6, "unit": "J"}, "id": "ke_000181_21.7_4", "license": "Apache-2.0", "prompt": "A body of mass 21.7 kg moves at 4 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 4^2 and multiply by 0.5 * 21.7.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 21.7, "velocity": 4.0}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=26 degrees through the sine of 2 theta.\n3. Substitute v=47.9 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 184.3037, \"unit\": \"m\"}", "dedupe_signature": "c56d3ee913e3cbdd8321330e27a9837bd32852665e89e06d336397d3b8d8372a", "difficulty": "medium", "final_answer": {"answer": 184.3037, "unit": "m"}, "id": "projectile_range_000182_47.9_26", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 47.9 m/s and angle 26 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=26 degrees through the sine of 2 theta.\nSubstitute v=47.9 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 26, "gravity": 9.81, "speed": 47.9}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 0.44 * 8.314 * 346 / 116.6.\nFinal: {\"answer\": 10.8553, \"unit\": \"kPa\"}", "dedupe_signature": "2bb44c7f9a4ac8946282757c0fcf6264532f1e46a2365c1428a1b6bdc228e2b6", "difficulty": "medium", "final_answer": {"answer": 10.8553, "unit": "kPa"}, "id": "ideal_gas_000183_0.44_346_116.6", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=0.44 mol, T=346 K, and V=116.6 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 0.44 * 8.314 * 346 / 116.6.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 0.44, "temp_k": 346, "volume_l": 116.6}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=59.5 V and R=99.2 ohm.\nFinal: {\"answer\": 35.688, \"unit\": \"W\"}", "dedupe_signature": "824d2cccfa16b7e8da45fd0a9ad57a542d7511d50d82bcfe1644f796ab510ef5", "difficulty": "easy", "final_answer": {"answer": 35.688, "unit": "W"}, "id": "ohm_power_000185_59.5_99.2", "license": "Apache-2.0", "prompt": "A resistor has resistance 99.2 ohm and voltage 59.5 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=59.5 V and R=99.2 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 99.2, "voltage": 59.5}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=206 mg, t=170.5 h, and T_half=88 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 53.7801, \"unit\": \"mg\"}", "dedupe_signature": "fee0a95dc889ef52a554dcc9bb4ab1734a161c40b0865eaf4538dd386a26dbb4", "difficulty": "medium", "final_answer": {"answer": 53.7801, "unit": "mg"}, "id": "half_life_000186_206_88_170.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 206 mg. Its half-life is 88 hours. How many mg remain after 170.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=206 mg, t=170.5 h, and T_half=88 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 170.5, "half_life": 88.0, "initial_amount": 206.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 1.58 mol * 58.44 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 92.3352, \"unit\": \"g\"}", "dedupe_signature": "55298baef8fe7a1dbec81f8fb2520a743ea71375625ae923bf3c1a393e43d833", "difficulty": "medium", "final_answer": {"answer": 92.3352, "unit": "g"}, "id": "stoich_mass_000187_sodium_chloride_1.58", "license": "Apache-2.0", "prompt": "A sample contains 1.58 mol of sodium chloride. Using molar mass 58.44 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 1.58 mol * 58.44 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "sodium chloride", "molar_mass": 58.44, "moles": 1.58}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 4710 mL to 4.71 L.\n3. Compute M = 1.145 / 4.71.\nFinal: {\"answer\": 0.2431, \"unit\": \"mol/L\"}", "dedupe_signature": "543c4f8d59f129a906f512be9c9d7cc6b4f761a6e175a7f020b448d67fd23c50", "difficulty": "medium", "final_answer": {"answer": 0.2431, "unit": "mol/L"}, "id": "molarity_000188_1.145_4710", "license": "Apache-2.0", "prompt": "A solution contains 1.145 mol of solute in 4710 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 4710 mL to 4.71 L.\nCompute M = 1.145 / 4.71.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 1.145, "volume_ml": 4710}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.59 y, so each step multiplies y by 1 - h*0.59.\n3. Apply that update for 7 steps and round the final state.\nFinal: {\"answer\": 0.0, \"unit\": \"state_units\"}", "dedupe_signature": "59c425145a92e6aac06008d0c3a260183c2edfb6cc758294840a696fe432de4e", "difficulty": "medium", "final_answer": {"answer": 0.0, "unit": "state_units"}, "id": "euler_decay_000189_17_0.59_1.75_7", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.59 y with y(0)=17, step size h=1.75, for 7 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.59 y, so each step multiplies y by 1 - h*0.59.\nApply that update for 7 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 17.0, "rate": 0.59, "step": 1.75, "steps": 7}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-6.4)=-10.9 and f(1.9)=-2.6.\n3. The interval width is 8.3.\nFinal: {\"answer\": -56.025, \"unit\": \"area_units\"}", "dedupe_signature": "599e9149caa98292b1e8c298754f283c872f86a615a8eb21d74b72696dc45cdd", "difficulty": "medium", "final_answer": {"answer": -56.025, "unit": "area_units"}, "id": "trapz_linear_000190_1_-4.5_-6.4_1.9", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=1x+-4.5 from x=-6.4 to x=1.9. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-6.4)=-10.9 and f(1.9)=-2.6.\nThe interval width is 8.3.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -4.5, "slope": 1.0, "x0": -6.4, "x1": 1.9000000000000004}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.06 and add it to the current value.\nFinal: {\"answer\": [0.296, -0.88, 1.4], \"unit\": \"temperature_units\"}", "dedupe_signature": "aca815dceb09c71d9bf3c8318b084728b86cf5a0b339a7f9d753d5eaac6cb825", "difficulty": "hard", "final_answer": {"answer": [0.296, -0.88, 1.4], "unit": "temperature_units"}, "id": "heat_step_000191_0.06_-1.25_0.5_-1.15_1.7_-0.45", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-1.25, right=-0.45; current interior values are [0.5, -1.15, 1.7]. Use r=0.06. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.06 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [0.5, -1.15, 1.7], "left": -1.25, "r": 0.06, "right": -0.45}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-0.4, -15.5], \"unit\": \"dimensionless\"}", "dedupe_signature": "d9531def3e8b3c23bb046889d4fd31dc70a56273051874885a399139da0b26fd", "difficulty": "medium", "final_answer": {"answer": [-0.4, -15.5], "unit": "dimensionless"}, "id": "line_two_point_000194_12_19_-0.4_-15.5", "license": "Apache-2.0", "prompt": "A line passes through points (12, -20.3) and (19, -23.1). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 12.0, "x2": 19.0, "y1": -20.3, "y2": -23.1}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: launch_angle_or_vertical_velocity.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"launch_angle_or_vertical_velocity\"]}", "dedupe_signature": "3fed6d69730e191c4d6652ae1f038e421421c20844211e07757a8a9cabcc731b", "difficulty": "easy", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["launch_angle_or_vertical_velocity"]}, "id": "abstain_000197_launch_angle_or_vertical_velocity", "license": "Apache-2.0", "prompt": "Compute projectile range on level ground. The prompt gives initial speed 82.7 m/s but does not give launch angle or vertical velocity. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: launch_angle_or_vertical_velocity.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["launch_angle_or_vertical_velocity"]}, "verifier": {"missing": ["launch_angle_or_vertical_velocity"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 10.9 kg and a = 7.45 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 81.205, \"unit\": \"N\"}", "dedupe_signature": "9be6851f860e91f97456513c23b82b464783b9b45742f47e2c1b2a693d206cda", "difficulty": "easy", "final_answer": {"answer": 81.205, "unit": "N"}, "id": "force_000198_10.9_7.45", "license": "Apache-2.0", "prompt": "A cart has mass 10.9 kg and measured acceleration 7.45 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 10.9 kg and a = 7.45 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 7.45, "mass": 10.9}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 11^2 and multiply by 0.5 * 21.55.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 1303.775, \"unit\": \"J\"}", "dedupe_signature": "6a07ec5af1c9868c29dbf9c13978f99bbdf91ee13bf324ceb38c72f529bd1fcd", "difficulty": "easy", "final_answer": {"answer": 1303.775, "unit": "J"}, "id": "ke_000199_21.55_11", "license": "Apache-2.0", "prompt": "A body of mass 21.55 kg moves at 11 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 11^2 and multiply by 0.5 * 21.55.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 21.55, "velocity": 11.0}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=43 degrees through the sine of 2 theta.\n3. Substitute v=61.7 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 387.1169, \"unit\": \"m\"}", "dedupe_signature": "7eed77edb22b5b321ab2da8727f9a92b10e11129c6d978f2dbbdfe2c328505d6", "difficulty": "medium", "final_answer": {"answer": 387.1169, "unit": "m"}, "id": "projectile_range_000200_61.7_43", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 61.7 m/s and angle 43 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=43 degrees through the sine of 2 theta.\nSubstitute v=61.7 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 43, "gravity": 9.81, "speed": 61.7}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 0.85 * 8.314 * 410 / 59.6.\nFinal: {\"answer\": 48.6146, \"unit\": \"kPa\"}", "dedupe_signature": "ffac766260c9c5dd352ca7a96c1afc6a7b5debcb1f782b16e3a28afe7e8cc8a6", "difficulty": "medium", "final_answer": {"answer": 48.6146, "unit": "kPa"}, "id": "ideal_gas_000201_0.85_410_59.6", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=0.85 mol, T=410 K, and V=59.6 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 0.85 * 8.314 * 410 / 59.6.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 0.85, "temp_k": 410, "volume_l": 59.6}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 95 * 3.795 * 73.\nFinal: {\"answer\": 26318.325, \"unit\": \"J\"}", "dedupe_signature": "afe82e8c1139ff95f1eddf795dc55985a3bb39a659754d717e9e432168873c7f", "difficulty": "easy", "final_answer": {"answer": 26318.325, "unit": "J"}, "id": "heat_q_000202_95_3.795_73", "license": "Apache-2.0", "prompt": "A 95 g sample has specific heat 3.795 J/(g*K). How much heat is needed to raise its temperature by 73 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 95 * 3.795 * 73.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 73, "heat_capacity": 3.795, "mass_g": 95}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=150.6 V and R=127.4 ohm.\nFinal: {\"answer\": 178.0248, \"unit\": \"W\"}", "dedupe_signature": "c9889a77122954a4bc83165e0b38e75829dac9463981532912e258d103fa9aed", "difficulty": "easy", "final_answer": {"answer": 178.0248, "unit": "W"}, "id": "ohm_power_000203_150.6_127.4", "license": "Apache-2.0", "prompt": "A resistor has resistance 127.4 ohm and voltage 150.6 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=150.6 V and R=127.4 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 127.4, "voltage": 150.6}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=695.5 mg, t=301.5 h, and T_half=9.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 0.0, \"unit\": \"mg\"}", "dedupe_signature": "8070ba97fea905b605db2a1eec5512fea85ffad671daa91281733dd9b8c39830", "difficulty": "medium", "final_answer": {"answer": 0.0, "unit": "mg"}, "id": "half_life_000204_695.5_9.5_301.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 695.5 mg. Its half-life is 9.5 hours. How many mg remain after 301.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=695.5 mg, t=301.5 h, and T_half=9.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 301.5, "half_life": 9.5, "initial_amount": 695.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 1.87 mol * 18.015 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 33.6881, \"unit\": \"g\"}", "dedupe_signature": "5bc6e320d4efdb6e8fe3f4ee14fdab7379e74de7f790b7a4d864d961b4149f24", "difficulty": "medium", "final_answer": {"answer": 33.6881, "unit": "g"}, "id": "stoich_mass_000205_water_1.87", "license": "Apache-2.0", "prompt": "A sample contains 1.87 mol of water. Using molar mass 18.015 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 1.87 mol * 18.015 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "water", "molar_mass": 18.015, "moles": 1.87}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 85 mL to 0.085 L.\n3. Compute M = 3.38 / 0.085.\nFinal: {\"answer\": 39.7647, \"unit\": \"mol/L\"}", "dedupe_signature": "a82404bbf81a6a8d59bc0e3e052acac316905310c2dee98ee1dfda5231255aa1", "difficulty": "medium", "final_answer": {"answer": 39.7647, "unit": "mol/L"}, "id": "molarity_000206_3.38_85", "license": "Apache-2.0", "prompt": "A solution contains 3.38 mol of solute in 85 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 85 mL to 0.085 L.\nCompute M = 3.38 / 0.085.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 3.38, "volume_ml": 85}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.39 y, so each step multiplies y by 1 - h*0.39.\n3. Apply that update for 5 steps and round the final state.\nFinal: {\"answer\": 9.7577, \"unit\": \"state_units\"}", "dedupe_signature": "ed7872820a31f781003c7b1e00546874d52ea953cdad07197860fb21736f4396", "difficulty": "medium", "final_answer": {"answer": 9.7577, "unit": "state_units"}, "id": "euler_decay_000207_37_0.39_0.6_5", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.39 y with y(0)=37, step size h=0.6, for 5 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.39 y, so each step multiplies y by 1 - h*0.39.\nApply that update for 5 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 37.0, "rate": 0.39, "step": 0.6, "steps": 5}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(6.7)=9.5 and f(14.4)=40.3.\n3. The interval width is 7.7.\nFinal: {\"answer\": 191.73, \"unit\": \"area_units\"}", "dedupe_signature": "09accf8f4355934240c418d23fd357429557aa8bc932758a537c9109492ca711", "difficulty": "medium", "final_answer": {"answer": 191.73, "unit": "area_units"}, "id": "trapz_linear_000208_4_-17.3_6.7_14.4", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=4x+-17.3 from x=6.7 to x=14.4. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(6.7)=9.5 and f(14.4)=40.3.\nThe interval width is 7.7.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -17.3, "slope": 4.0, "x0": 6.7, "x1": 14.4}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 1180.0 / 1000.\nFinal: {\"answer\": 1.18, \"unit\": \"kg\"}", "dedupe_signature": "5f13da74810c7d01329804ccb2bf5bcbce17e36ccedc35e2d9e992941e20cb51", "difficulty": "easy", "final_answer": {"answer": 1.18, "unit": "kg"}, "id": "unit_convert_000210_g_to_kg_1180", "license": "Apache-2.0", "prompt": "Convert 1180 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 1180.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 1180.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=20 degrees and keep the unit as newtons.\nFinal: {\"answer\": [93.9693, 34.202], \"unit\": \"N\"}", "dedupe_signature": "d6ab2bc867ae5d0f0a0077ad98c33bea56918c9075f8f0373e5ce5609a4921ac", "difficulty": "medium", "final_answer": {"answer": [93.9693, 34.202], "unit": "N"}, "id": "vector_components_000211_100_20", "license": "Apache-2.0", "prompt": "A vector has magnitude 100 N at 20 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=20 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 20, "magnitude": 100.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef threshold_flags_000214(values, threshold):\n    return [value >= threshold for value in values]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"threshold_flags_000214\"}", "dedupe_signature": "a55297952ed3b99f4b0a3630bb9329dc49f19dece4fa325dfe1a2250ba090bd0", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "threshold_flags_000214"}, "id": "code_000214_threshold_flags_000214", "license": "Apache-2.0", "prompt": "Write a Python function threshold_flags_000214(values, threshold) that returns a list of booleans showing whether each value is greater than or equal to threshold. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "threshold_flags_000214"}, "verifier": {"function": "threshold_flags_000214", "tests": ["assert threshold_flags_000214([1, 2, 3], 2) == [False, True, True]", "assert threshold_flags_000214([], 5) == []", "assert threshold_flags_000214([-1, 0], 0) == [False, True]"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 15.35 kg and a = 4.25 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 65.2375, \"unit\": \"N\"}", "dedupe_signature": "b00593e920f88109552641894c9d48b7708544c14c9d160b5bc964e3b1845577", "difficulty": "easy", "final_answer": {"answer": 65.2375, "unit": "N"}, "id": "force_000216_15.35_4.25", "license": "Apache-2.0", "prompt": "A cart has mass 15.35 kg and measured acceleration 4.25 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 15.35 kg and a = 4.25 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 4.25, "mass": 15.35}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 28.5^2 and multiply by 0.5 * 26.3.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 10681.0875, \"unit\": \"J\"}", "dedupe_signature": "adabccdd20fe4793ef7453a9f589dff3d613f1f36d0c800071420736655ec987", "difficulty": "easy", "final_answer": {"answer": 10681.0875, "unit": "J"}, "id": "ke_000217_26.3_28.5", "license": "Apache-2.0", "prompt": "A body of mass 26.3 kg moves at 28.5 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 28.5^2 and multiply by 0.5 * 26.3.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 26.3, "velocity": 28.5}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=48 degrees through the sine of 2 theta.\n3. Substitute v=9.6 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 9.343, \"unit\": \"m\"}", "dedupe_signature": "0e5c2b3418ec254bdeff5b604b599f1d6220a38fe0d0ff0e4211d621fd799525", "difficulty": "medium", "final_answer": {"answer": 9.343, "unit": "m"}, "id": "projectile_range_000218_9.6_48", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 9.6 m/s and angle 48 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=48 degrees through the sine of 2 theta.\nSubstitute v=9.6 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 48, "gravity": 9.81, "speed": 9.6}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 4.06 * 8.314 * 431 / 58.2.\nFinal: {\"answer\": 249.9714, \"unit\": \"kPa\"}", "dedupe_signature": "e028dfb2e940e8255cd9ca76c19e62d62cc3989cf206a9fe375dbc3a9a83ac9c", "difficulty": "medium", "final_answer": {"answer": 249.9714, "unit": "kPa"}, "id": "ideal_gas_000219_4.06_431_58.2", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=4.06 mol, T=431 K, and V=58.2 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 4.06 * 8.314 * 431 / 58.2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 4.06, "temp_k": 431, "volume_l": 58.2}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=121.8 V and R=83.8 ohm.\nFinal: {\"answer\": 177.0315, \"unit\": \"W\"}", "dedupe_signature": "b7c28a393ef795e08d32d20cf6b833bbb2fdbf93d33b257e332ed80f648fced3", "difficulty": "easy", "final_answer": {"answer": 177.0315, "unit": "W"}, "id": "ohm_power_000221_121.8_83.8", "license": "Apache-2.0", "prompt": "A resistor has resistance 83.8 ohm and voltage 121.8 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=121.8 V and R=83.8 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 83.8, "voltage": 121.8}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 6.05 mol * 58.44 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 353.562, \"unit\": \"g\"}", "dedupe_signature": "0ace43bf53c6168e0107fe6d378aeb21763fab281c10438e4e4b64ded8705e12", "difficulty": "medium", "final_answer": {"answer": 353.562, "unit": "g"}, "id": "stoich_mass_000223_sodium_chloride_6.05", "license": "Apache-2.0", "prompt": "A sample contains 6.05 mol of sodium chloride. Using molar mass 58.44 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 6.05 mol * 58.44 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "sodium chloride", "molar_mass": 58.44, "moles": 6.05}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 3645 mL to 3.645 L.\n3. Compute M = 2.2 / 3.645.\nFinal: {\"answer\": 0.6036, \"unit\": \"mol/L\"}", "dedupe_signature": "340acceed419a7fa2a7673f28eff334a9246cf9c41cf945aa2609f3b2996fe7a", "difficulty": "medium", "final_answer": {"answer": 0.6036, "unit": "mol/L"}, "id": "molarity_000224_2.2_3645", "license": "Apache-2.0", "prompt": "A solution contains 2.2 mol of solute in 3645 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 3645 mL to 3.645 L.\nCompute M = 2.2 / 3.645.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 2.2, "volume_ml": 3645}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.01 y, so each step multiplies y by 1 - h*0.01.\n3. Apply that update for 8 steps and round the final state.\nFinal: {\"answer\": 21.3597, \"unit\": \"state_units\"}", "dedupe_signature": "8daa1d3e920d0cdaa934f1ca2fa6ac49fa754ab818e94b0a080fe8d7a73f4dad", "difficulty": "medium", "final_answer": {"answer": 21.3597, "unit": "state_units"}, "id": "euler_decay_000225_24.5_0.01_1.7_8", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.01 y with y(0)=24.5, step size h=1.7, for 8 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.01 y, so each step multiplies y by 1 - h*0.01.\nApply that update for 8 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 24.5, "rate": 0.01, "step": 1.7, "steps": 8}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-0.8)=21.24 and f(7.7)=-6.81.\n3. The interval width is 8.5.\nFinal: {\"answer\": 61.3275, \"unit\": \"area_units\"}", "dedupe_signature": "db2d5d2431f2f34abf98c55c043463fd700d6a9ac3a7c9de38e6574a3c105e0d", "difficulty": "medium", "final_answer": {"answer": 61.3275, "unit": "area_units"}, "id": "trapz_linear_000226_-3.3_18.6_-0.8_7.7", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-3.3x+18.6 from x=-0.8 to x=7.7. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-0.8)=21.24 and f(7.7)=-6.81.\nThe interval width is 8.5.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 18.6, "slope": -3.3, "x0": -0.8, "x1": 7.7}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.16 and add it to the current value.\nFinal: {\"answer\": [-1.044, -0.964, 1.612], \"unit\": \"temperature_units\"}", "dedupe_signature": "d5929afa3f72c4aaecbe09d85fe44921dd7edd0664ff62e61cd45f55266385db", "difficulty": "hard", "final_answer": {"answer": [-1.044, -0.964, 1.612], "unit": "temperature_units"}, "id": "heat_step_000227_0.16_-0.15_-1.1_-1.7_2.3_2.0", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-0.15, right=2; current interior values are [-1.1, -1.7, 2.3]. Use r=0.16. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.16 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-1.1, -1.7, 2.3], "left": -0.15, "r": 0.16, "right": 2.0}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 6616.0 / 1000.\nFinal: {\"answer\": 6.616, \"unit\": \"kg\"}", "dedupe_signature": "16ea6b4065cb2b041d11f8dc344f35577d72aebd30b2f0a706e282249f508c33", "difficulty": "easy", "final_answer": {"answer": 6.616, "unit": "kg"}, "id": "unit_convert_000228_g_to_kg_6616", "license": "Apache-2.0", "prompt": "Convert 6616 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 6616.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 6616.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=199 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-361.1881, -124.367], \"unit\": \"N\"}", "dedupe_signature": "760070e2076b93e8803e4269556c1507921ae7251c00432005c47010d920dab6", "difficulty": "medium", "final_answer": {"answer": [-361.1881, -124.367], "unit": "N"}, "id": "vector_components_000229_382_199", "license": "Apache-2.0", "prompt": "A vector has magnitude 382 N at 199 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=199 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 199, "magnitude": 382.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-3.7, 20.5], \"unit\": \"dimensionless\"}", "dedupe_signature": "90605793f902f4a3745a6eb6f74585012a313f5a1151d2c8cba2087d462dee20", "difficulty": "medium", "final_answer": {"answer": [-3.7, 20.5], "unit": "dimensionless"}, "id": "line_two_point_000230_-16.5_-14.5_-3.7_20.5", "license": "Apache-2.0", "prompt": "A line passes through points (-16.5, 81.55) and (-14.5, 74.15). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -16.5, "x2": -14.5, "y1": 81.55000000000001, "y2": 74.15}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. m*v is momentum, not energy\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "3183c09611432a300c581f589b06621fb14a88149a694b0b650990033cc677e1", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_000231_inconsistent_1e14b074_664878", "license": "Apache-2.0", "prompt": "In instrument manual case 664878, check dimensional consistency for E = m * v. The left side has dimensions kg*m^2/s^2 and the right side has dimensions kg*m/s. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nm*v is momentum, not energy\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "E = m * v"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef finite_differences_000232(values):\n    return [values[i + 1] - values[i] for i in range(len(values) - 1)]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"finite_differences_000232\"}", "dedupe_signature": "ee5f1f46cf19289deef5116422ba961df0479a74eab32c38f23e048acafb068c", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "finite_differences_000232"}, "id": "code_000232_finite_differences_000232", "license": "Apache-2.0", "prompt": "Write a Python function finite_differences_000232(values) that returns the list of successive differences values[i+1] - values[i]. It must return [] for fewer than two values. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "finite_differences_000232"}, "verifier": {"function": "finite_differences_000232", "tests": ["assert finite_differences_000232([1, 4, 9, 16]) == [3, 5, 7]", "assert finite_differences_000232([5]) == []", "assert finite_differences_000232([]) == []"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: left_boundary, right_boundary.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"left_boundary\", \"right_boundary\"]}", "dedupe_signature": "dffc42fe120a2039d85c7fe3b20d309c3167c0c6a2bdab1743f7dce56cce3974", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["left_boundary", "right_boundary"]}, "id": "abstain_000233_left_boundary_right_boundary", "license": "Apache-2.0", "prompt": "Solve the 1D heat equation after one finite-difference step. The prompt gives r=0.28 and interior values [1.55, 1.25, -1.15], but gives no boundary values. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: left_boundary, right_boundary.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["left_boundary", "right_boundary"]}, "verifier": {"missing": ["left_boundary", "right_boundary"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 6.45 kg and a = 11.1 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 71.595, \"unit\": \"N\"}", "dedupe_signature": "40de9c4feedc01661068b08cdbdc1008ec370f37aa20896d8b0024e1d5d73550", "difficulty": "easy", "final_answer": {"answer": 71.595, "unit": "N"}, "id": "force_000234_6.45_11.1", "license": "Apache-2.0", "prompt": "A cart has mass 6.45 kg and measured acceleration 11.1 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 6.45 kg and a = 11.1 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 11.1, "mass": 6.45}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 10.15^2 and multiply by 0.5 * 26.95.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 1388.2282, \"unit\": \"J\"}", "dedupe_signature": "d40bb8a617a308d2f3bf4dd57152294a5d2dde17e20f6f283dff14c914f8cf9a", "difficulty": "easy", "final_answer": {"answer": 1388.2282, "unit": "J"}, "id": "ke_000235_26.95_10.15", "license": "Apache-2.0", "prompt": "A body of mass 26.95 kg moves at 10.15 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 10.15^2 and multiply by 0.5 * 26.95.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 26.95, "velocity": 10.15}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=64 degrees through the sine of 2 theta.\n3. Substitute v=46.7 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 175.185, \"unit\": \"m\"}", "dedupe_signature": "0f48857043296cf76e77970f27e49d19d5ec17986ca061b4c5f151f66afe685a", "difficulty": "medium", "final_answer": {"answer": 175.185, "unit": "m"}, "id": "projectile_range_000236_46.7_64", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 46.7 m/s and angle 64 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=64 degrees through the sine of 2 theta.\nSubstitute v=46.7 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 64, "gravity": 9.81, "speed": 46.7}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 4.94 * 8.314 * 449 / 10.4.\nFinal: {\"answer\": 1773.1684, \"unit\": \"kPa\"}", "dedupe_signature": "683d7c12be0f78e707185141b749fdbb63e85a03ecdef98f49d3c46045fafc1c", "difficulty": "medium", "final_answer": {"answer": 1773.1684, "unit": "kPa"}, "id": "ideal_gas_000237_4.94_449_10.4", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=4.94 mol, T=449 K, and V=10.4 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 4.94 * 8.314 * 449 / 10.4.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 4.94, "temp_k": 449, "volume_l": 10.4}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=768.5 mg, t=282 h, and T_half=60 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 29.5667, \"unit\": \"mg\"}", "dedupe_signature": "97976414fce038f8ef485124fc134fda5187286a2f3a69dd2fc3d7d5fef2530d", "difficulty": "medium", "final_answer": {"answer": 29.5667, "unit": "mg"}, "id": "half_life_000240_768.5_60_282", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 768.5 mg. Its half-life is 60 hours. How many mg remain after 282 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=768.5 mg, t=282 h, and T_half=60 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 282.0, "half_life": 60.0, "initial_amount": 768.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 6.4 mol * 58.44 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 374.016, \"unit\": \"g\"}", "dedupe_signature": "c061f64d6277217a0d142dff534bc1f265164177bc651e42791e24366e0342c8", "difficulty": "medium", "final_answer": {"answer": 374.016, "unit": "g"}, "id": "stoich_mass_000241_sodium_chloride_6.4", "license": "Apache-2.0", "prompt": "A sample contains 6.4 mol of sodium chloride. Using molar mass 58.44 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 6.4 mol * 58.44 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "sodium chloride", "molar_mass": 58.44, "moles": 6.4}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 4455 mL to 4.455 L.\n3. Compute M = 2.805 / 4.455.\nFinal: {\"answer\": 0.6296, \"unit\": \"mol/L\"}", "dedupe_signature": "b2cf4d90ccb16f1d9ebecc791c182d950e37340fa3e40ee26c5240bab99b3e9e", "difficulty": "medium", "final_answer": {"answer": 0.6296, "unit": "mol/L"}, "id": "molarity_000242_2.805_4455", "license": "Apache-2.0", "prompt": "A solution contains 2.805 mol of solute in 4455 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 4455 mL to 4.455 L.\nCompute M = 2.805 / 4.455.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 2.805, "volume_ml": 4455}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.66 y, so each step multiplies y by 1 - h*0.66.\n3. Apply that update for 11 steps and round the final state.\nFinal: {\"answer\": 0.0, \"unit\": \"state_units\"}", "dedupe_signature": "21ead411e1ed434d0686f973d59b22d32e0874a0f3d5b1ab1567a09debc88fbf", "difficulty": "medium", "final_answer": {"answer": 0.0, "unit": "state_units"}, "id": "euler_decay_000243_67_0.66_1.1_11", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.66 y with y(0)=67, step size h=1.1, for 11 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.66 y, so each step multiplies y by 1 - h*0.66.\nApply that update for 11 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 67.0, "rate": 0.66, "step": 1.1, "steps": 11}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(6.1)=-10.62 and f(13.7)=-19.74.\n3. The interval width is 7.6.\nFinal: {\"answer\": -115.368, \"unit\": \"area_units\"}", "dedupe_signature": "b813a7a5156871b5e54603ee40b9c916c3175ad7f47e8431d18cab8f9ef940ef", "difficulty": "medium", "final_answer": {"answer": -115.368, "unit": "area_units"}, "id": "trapz_linear_000244_-1.2_-3.3_6.1_13.7", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-1.2x+-3.3 from x=6.1 to x=13.7. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(6.1)=-10.62 and f(13.7)=-19.74.\nThe interval width is 7.6.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -3.3, "slope": -1.2, "x0": 6.1, "x1": 13.7}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.12 and add it to the current value.\nFinal: {\"answer\": [-0.314, 1.59, -0.828], \"unit\": \"temperature_units\"}", "dedupe_signature": "06751d68087412a17836ccaa94f028f80ecca0c56e54e86b07b86338187f8c85", "difficulty": "hard", "final_answer": {"answer": [-0.314, 1.59, -0.828], "unit": "temperature_units"}, "id": "heat_step_000245_0.12_0.85_-0.95_2.55_-1.95_2.9", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=0.85, right=2.9; current interior values are [-0.95, 2.55, -1.95]. Use r=0.12. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.12 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-0.95, 2.55, -1.95], "left": 0.85, "r": 0.12, "right": 2.9}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 29100.0 / 1000.\nFinal: {\"answer\": 29.1, \"unit\": \"kg\"}", "dedupe_signature": "b251f3505ba8e6fe7b1d9de92a3c6d0923f1f39fad7b00707e1bb4a51c7f8bef", "difficulty": "easy", "final_answer": {"answer": 29.1, "unit": "kg"}, "id": "unit_convert_000246_g_to_kg_29100", "license": "Apache-2.0", "prompt": "Convert 29100 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 29100.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 29100.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=151 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-38.4833, 21.3316], \"unit\": \"N\"}", "dedupe_signature": "8cd89370993d97bb468d7e5c1f479b3c6827cb7d5388dab2b8988bff04bde77b", "difficulty": "medium", "final_answer": {"answer": [-38.4833, 21.3316], "unit": "N"}, "id": "vector_components_000247_44_151", "license": "Apache-2.0", "prompt": "A vector has magnitude 44 N at 151 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=151 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 151, "magnitude": 44.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. lever arm times force has torque dimensions\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "f1a0bd40a74a5ee44b1e579e98db301b63293652887aa2f88f97df884a2c7bcc", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_000249_consistent_5ca82cb9_524258", "license": "Apache-2.0", "prompt": "In lab notebook case 524258, check dimensional consistency for tau = r * F. The left side has dimensions N*m and the right side has dimensions N*m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nlever arm times force has torque dimensions\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "tau = r * F"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef threshold_flags_000250(values, threshold):\n    return [value >= threshold for value in values]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"threshold_flags_000250\"}", "dedupe_signature": "98284d6ca0b6b63baee509e4897f8d8d2d51cbe49141b0e3c5f63591f06802ba", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "threshold_flags_000250"}, "id": "code_000250_threshold_flags_000250", "license": "Apache-2.0", "prompt": "Write a Python function threshold_flags_000250(values, threshold) that returns a list of booleans showing whether each value is greater than or equal to threshold. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "threshold_flags_000250"}, "verifier": {"function": "threshold_flags_000250", "tests": ["assert threshold_flags_000250([1, 2, 3], 2) == [False, True, True]", "assert threshold_flags_000250([], 5) == []", "assert threshold_flags_000250([-1, 0], 0) == [False, True]"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: left_boundary, right_boundary.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"left_boundary\", \"right_boundary\"]}", "dedupe_signature": "7191fe6d36e6237273b0eb182c326c5eecaa19d3e0b99393b7dc1b734887396a", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["left_boundary", "right_boundary"]}, "id": "abstain_000251_left_boundary_right_boundary", "license": "Apache-2.0", "prompt": "Solve the 1D heat equation after one finite-difference step. The prompt gives r=0.3 and interior values [-1.05, -0.7, 0.1], but gives no boundary values. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: left_boundary, right_boundary.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["left_boundary", "right_boundary"]}, "verifier": {"missing": ["left_boundary", "right_boundary"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 1.8 kg and a = 12.9 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 23.22, \"unit\": \"N\"}", "dedupe_signature": "e16faee25dc54ef8553e58acce1b1515983a334d4eed4b7ee2c82f71ede9bdcf", "difficulty": "easy", "final_answer": {"answer": 23.22, "unit": "N"}, "id": "force_000252_1.8_12.9", "license": "Apache-2.0", "prompt": "A cart has mass 1.8 kg and measured acceleration 12.9 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 1.8 kg and a = 12.9 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 12.9, "mass": 1.8}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 6.9^2 and multiply by 0.5 * 12.8.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 304.704, \"unit\": \"J\"}", "dedupe_signature": "eeb452560bd0c31df9fe6963f3a85afc5f9260d2e68ef071e08b2612bfdf209c", "difficulty": "easy", "final_answer": {"answer": 304.704, "unit": "J"}, "id": "ke_000253_12.8_6.9", "license": "Apache-2.0", "prompt": "A body of mass 12.8 kg moves at 6.9 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 6.9^2 and multiply by 0.5 * 12.8.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 12.8, "velocity": 6.9}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=23 degrees through the sine of 2 theta.\n3. Substitute v=41.2 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 124.4685, \"unit\": \"m\"}", "dedupe_signature": "8e81ed20edebe9895c9c48bda9558895551e97f58db2635fa41da613acc211e0", "difficulty": "medium", "final_answer": {"answer": 124.4685, "unit": "m"}, "id": "projectile_range_000254_41.2_23", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 41.2 m/s and angle 23 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=23 degrees through the sine of 2 theta.\nSubstitute v=41.2 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 23, "gravity": 9.81, "speed": 41.2}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 4.19 * 8.314 * 350 / 58.8.\nFinal: {\"answer\": 207.3551, \"unit\": \"kPa\"}", "dedupe_signature": "93e2bb232f30293a44df04720376f146788bcb20780c341ea154632d1ac7e617", "difficulty": "medium", "final_answer": {"answer": 207.3551, "unit": "kPa"}, "id": "ideal_gas_000255_4.19_350_58.8", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=4.19 mol, T=350 K, and V=58.8 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 4.19 * 8.314 * 350 / 58.8.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 4.19, "temp_k": 350, "volume_l": 58.8}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=7 V and R=124 ohm.\nFinal: {\"answer\": 0.3952, \"unit\": \"W\"}", "dedupe_signature": "caa6c4035e748a214bda87fe1749a21e080ef9ef795117631b80eaea0c8795df", "difficulty": "easy", "final_answer": {"answer": 0.3952, "unit": "W"}, "id": "ohm_power_000257_7_124", "license": "Apache-2.0", "prompt": "A resistor has resistance 124 ohm and voltage 7 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=7 V and R=124 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 124.0, "voltage": 7.0}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=856 mg, t=295.5 h, and T_half=40.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 5.4459, \"unit\": \"mg\"}", "dedupe_signature": "c2d1a0cfa510b79355f1521df6631412b4c3968636189dc29270c665b7948e6d", "difficulty": "medium", "final_answer": {"answer": 5.4459, "unit": "mg"}, "id": "half_life_000258_856_40.5_295.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 856 mg. Its half-life is 40.5 hours. How many mg remain after 295.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=856 mg, t=295.5 h, and T_half=40.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 295.5, "half_life": 40.5, "initial_amount": 856.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 4.36 mol * 100.087 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 436.3793, \"unit\": \"g\"}", "dedupe_signature": "63891c8874f8361c9ceb90194c94928b34858ee850b6e574c3165fcccdd0e72b", "difficulty": "medium", "final_answer": {"answer": 436.3793, "unit": "g"}, "id": "stoich_mass_000259_calcium_carbonate_4.36", "license": "Apache-2.0", "prompt": "A sample contains 4.36 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 4.36 mol * 100.087 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "calcium carbonate", "molar_mass": 100.087, "moles": 4.36}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 1380 mL to 1.38 L.\n3. Compute M = 3.185 / 1.38.\nFinal: {\"answer\": 2.308, \"unit\": \"mol/L\"}", "dedupe_signature": "747cb0aff3abc139108f9c2f71ba436b79745f1b0395e9302190d7ea556b2a3d", "difficulty": "medium", "final_answer": {"answer": 2.308, "unit": "mol/L"}, "id": "molarity_000260_3.185_1380", "license": "Apache-2.0", "prompt": "A solution contains 3.185 mol of solute in 1380 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 1380 mL to 1.38 L.\nCompute M = 3.185 / 1.38.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 3.185, "volume_ml": 1380}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.94 y, so each step multiplies y by 1 - h*0.94.\n3. Apply that update for 3 steps and round the final state.\nFinal: {\"answer\": -24.0132, \"unit\": \"state_units\"}", "dedupe_signature": "c1bf599555693416d29e448a3fc098b3edd241e93275b6ba69ca4e862f53316a", "difficulty": "medium", "final_answer": {"answer": -24.0132, "unit": "state_units"}, "id": "euler_decay_000261_59.5_0.94_1.85_3", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.94 y with y(0)=59.5, step size h=1.85, for 3 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.94 y, so each step multiplies y by 1 - h*0.94.\nApply that update for 3 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 59.5, "rate": 0.94, "step": 1.85, "steps": 3}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(4)=29.7 and f(8.1)=56.35.\n3. The interval width is 4.1.\nFinal: {\"answer\": 176.4025, \"unit\": \"area_units\"}", "dedupe_signature": "a16cff3faafbc213a32b73f8bc94d843b2b00c588466ced0f6e7bd04afd3ec94", "difficulty": "medium", "final_answer": {"answer": 176.4025, "unit": "area_units"}, "id": "trapz_linear_000262_6.5_3.7_4_8.1", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=6.5x+3.7 from x=4 to x=8.1. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(4)=29.7 and f(8.1)=56.35.\nThe interval width is 4.1.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 3.7, "slope": 6.5, "x0": 4.0, "x1": 8.1}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.34 and add it to the current value.\nFinal: {\"answer\": [0.76, 0.62, 0.776], \"unit\": \"temperature_units\"}", "dedupe_signature": "0e514c1fdf51d51512212ee9ab44fe0f81098cf7b97dacc0627b6bc0bc4ee357", "difficulty": "hard", "final_answer": {"answer": [0.76, 0.62, 0.776], "unit": "temperature_units"}, "id": "heat_step_000263_0.34_-0.05_1.95_0.45_-0.55_2.35", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-0.05, right=2.35; current interior values are [1.95, 0.45, -0.55]. Use r=0.34. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.34 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [1.95, 0.45, -0.55], "left": -0.05, "r": 0.34, "right": 2.35}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 100 centimeters in one meter.\n2. Apply the conversion factor directly to the given value.\n3. Compute 3459.5 / 100.\nFinal: {\"answer\": 34.595, \"unit\": \"m\"}", "dedupe_signature": "20c16f8b5ccb0912959d71a78c9e45b76912fdbe1a044ff4feafdfc9408f6143", "difficulty": "easy", "final_answer": {"answer": 34.595, "unit": "m"}, "id": "unit_convert_000264_cm_to_m_3459.5", "license": "Apache-2.0", "prompt": "Convert 3459.5 cm to m. Return the converted value with unit.", "reasoning_trace": "There are 100 centimeters in one meter.\nApply the conversion factor directly to the given value.\nCompute 3459.5 / 100.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 3459.5}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-8.3, -3.5], \"unit\": \"dimensionless\"}", "dedupe_signature": "e2f080f851f2c08fa2cd50c11737b49e3f7c27bde083eb57c0e87e358acc07ab", "difficulty": "medium", "final_answer": {"answer": [-8.3, -3.5], "unit": "dimensionless"}, "id": "line_two_point_000266_-2.25_3.75_-8.3_-3.5", "license": "Apache-2.0", "prompt": "A line passes through points (-2.25, 15.175) and (3.75, -34.625). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -2.25, "x2": 3.75, "y1": 15.175, "y2": -34.625}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. m*v is momentum, not energy\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "68b1c695848f010a68f4726fa6f59731f724ccf16a6e9bad453050de71876c3d", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_000267_inconsistent_1e14b074_27109", "license": "Apache-2.0", "prompt": "In model card equation case 27109, check dimensional consistency for E = m * v. The left side has dimensions kg*m^2/s^2 and the right side has dimensions kg*m/s. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nm*v is momentum, not energy\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "E = m * v"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: required_fields, allowed_transformations.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"required_fields\", \"allowed_transformations\"]}", "dedupe_signature": "a9af82b23820eefd4a7d02e9a8a26e9da72c36a8741e9afa8af4c32c88990b4f", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["required_fields", "allowed_transformations"]}, "id": "abstain_000269_required_fields_allowed_transformations", "license": "Apache-2.0", "prompt": "Write a sanitizer for valid billing invoice records in release 979709, but the prompt does not state which fields are required or which transformations are allowed. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: required_fields, allowed_transformations.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["required_fields", "allowed_transformations"]}, "verifier": {"missing": ["required_fields", "allowed_transformations"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 16.95 kg and a = 11.45 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 194.0775, \"unit\": \"N\"}", "dedupe_signature": "44a8ed844a1c50a1514b25cd3b1be98307b1ab86a0ae357fb8c65cc860dc3276", "difficulty": "easy", "final_answer": {"answer": 194.0775, "unit": "N"}, "id": "force_000270_16.95_11.45", "license": "Apache-2.0", "prompt": "A cart has mass 16.95 kg and measured acceleration 11.45 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 16.95 kg and a = 11.45 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 11.45, "mass": 16.95}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 25.1^2 and multiply by 0.5 * 29.9.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 9418.6495, \"unit\": \"J\"}", "dedupe_signature": "a2f4e7306604259d07b659ffb744b586146ec658854a487f35a768fcb4ebf758", "difficulty": "easy", "final_answer": {"answer": 9418.6495, "unit": "J"}, "id": "ke_000271_29.9_25.1", "license": "Apache-2.0", "prompt": "A body of mass 29.9 kg moves at 25.1 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 25.1^2 and multiply by 0.5 * 29.9.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 29.9, "velocity": 25.1}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=71 degrees through the sine of 2 theta.\n3. Substitute v=61.6 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 238.1411, \"unit\": \"m\"}", "dedupe_signature": "c7d7b30d6c48914deaa05da07ba7686a77b6b34ea856a24a36d400496198d47c", "difficulty": "medium", "final_answer": {"answer": 238.1411, "unit": "m"}, "id": "projectile_range_000272_61.6_71", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 61.6 m/s and angle 71 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=71 degrees through the sine of 2 theta.\nSubstitute v=61.6 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 71, "gravity": 9.81, "speed": 61.6}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 0.51 * 8.314 * 392 / 111.5.\nFinal: {\"answer\": 14.907, \"unit\": \"kPa\"}", "dedupe_signature": "0e57be11450e9439439e3fc1e1a994cb5ead5e7d89e8e0b3dd57c374fd7dcf48", "difficulty": "medium", "final_answer": {"answer": 14.907, "unit": "kPa"}, "id": "ideal_gas_000273_0.51_392_111.5", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=0.51 mol, T=392 K, and V=111.5 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 0.51 * 8.314 * 392 / 111.5.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 0.51, "temp_k": 392, "volume_l": 111.5}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1300 * 0.565 * 95.\nFinal: {\"answer\": 69777.5, \"unit\": \"J\"}", "dedupe_signature": "27dd9abe467339d9b2ebe09cbc269cb7613ff88f7b466ffe7b34dcff87a23ddd", "difficulty": "easy", "final_answer": {"answer": 69777.5, "unit": "J"}, "id": "heat_q_000274_1300_0.565_95", "license": "Apache-2.0", "prompt": "A 1300 g sample has specific heat 0.565 J/(g*K). How much heat is needed to raise its temperature by 95 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1300 * 0.565 * 95.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 95, "heat_capacity": 0.565, "mass_g": 1300}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=128.2 V and R=44.7 ohm.\nFinal: {\"answer\": 367.6787, \"unit\": \"W\"}", "dedupe_signature": "a8916eba66cae4474eef4f20377d720ef43930350d6640e4bed94571fc535030", "difficulty": "easy", "final_answer": {"answer": 367.6787, "unit": "W"}, "id": "ohm_power_000275_128.2_44.7", "license": "Apache-2.0", "prompt": "A resistor has resistance 44.7 ohm and voltage 128.2 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=128.2 V and R=44.7 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 44.7, "voltage": 128.2}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=108 mg, t=356.5 h, and T_half=18.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 0.0002, \"unit\": \"mg\"}", "dedupe_signature": "ad3a8d8bb752377a6c6c50d7a223dc0c3e43d3b59bb943343597120ef5e67942", "difficulty": "medium", "final_answer": {"answer": 0.0002, "unit": "mg"}, "id": "half_life_000276_108_18.5_356.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 108 mg. Its half-life is 18.5 hours. How many mg remain after 356.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=108 mg, t=356.5 h, and T_half=18.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 356.5, "half_life": 18.5, "initial_amount": 108.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 3.81 mol * 44.01 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 167.6781, \"unit\": \"g\"}", "dedupe_signature": "2b1f6fbd44371a4b7ed43a030bfe0a1b5e24d2d5578d4a44dda58f9a00cd95cb", "difficulty": "medium", "final_answer": {"answer": 167.6781, "unit": "g"}, "id": "stoich_mass_000277_carbon_dioxide_3.81", "license": "Apache-2.0", "prompt": "A sample contains 3.81 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 3.81 mol * 44.01 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "carbon dioxide", "molar_mass": 44.01, "moles": 3.81}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 235 mL to 0.235 L.\n3. Compute M = 0.06 / 0.235.\nFinal: {\"answer\": 0.2553, \"unit\": \"mol/L\"}", "dedupe_signature": "94f60e85043a1609020297f696a5bdf4cfb89a1b67cd4b729f90b73b17870e90", "difficulty": "medium", "final_answer": {"answer": 0.2553, "unit": "mol/L"}, "id": "molarity_000278_0.06_235", "license": "Apache-2.0", "prompt": "A solution contains 0.06 mol of solute in 235 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 235 mL to 0.235 L.\nCompute M = 0.06 / 0.235.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 0.06, "volume_ml": 235}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.69 y, so each step multiplies y by 1 - h*0.69.\n3. Apply that update for 12 steps and round the final state.\nFinal: {\"answer\": 0.5891, \"unit\": \"state_units\"}", "dedupe_signature": "314587d8c13c092fce2f01d9c7765fedab8c70430903a2c874e2926f39011c76", "difficulty": "medium", "final_answer": {"answer": 0.5891, "unit": "state_units"}, "id": "euler_decay_000279_3.5_0.69_0.2_12", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.69 y with y(0)=3.5, step size h=0.2, for 12 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.69 y, so each step multiplies y by 1 - h*0.69.\nApply that update for 12 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 3.5, "rate": 0.69, "step": 0.2, "steps": 12}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-9.7)=-9.75 and f(-4.9)=-2.55.\n3. The interval width is 4.8.\nFinal: {\"answer\": -29.52, \"unit\": \"area_units\"}", "dedupe_signature": "8173078aef6b0063d1111a94f49594e27f56cab2abe60f7b876907b4b67de604", "difficulty": "medium", "final_answer": {"answer": -29.52, "unit": "area_units"}, "id": "trapz_linear_000280_1.5_4.8_-9.7_-4.9", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=1.5x+4.8 from x=-9.7 to x=-4.9. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-9.7)=-9.75 and f(-4.9)=-2.55.\nThe interval width is 4.8.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 4.8, "slope": 1.5, "x0": -9.7, "x1": -4.8999999999999995}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.36 and add it to the current value.\nFinal: {\"answer\": [0.148, 0.614, 0.566], \"unit\": \"temperature_units\"}", "dedupe_signature": "70157f8fd3ad26d5c91ac6ae2d0526d9cf95de14f68c4e937c889ca1f7656899", "difficulty": "hard", "final_answer": {"answer": [0.148, 0.614, 0.566], "unit": "temperature_units"}, "id": "heat_step_000281_0.36_-1.6_1.75_0.65_-0.55_1.35", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-1.6, right=1.35; current interior values are [1.75, 0.65, -0.55]. Use r=0.36. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.36 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [1.75, 0.65, -0.55], "left": -1.6, "r": 0.36, "right": 1.35}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 100 centimeters in one meter.\n2. Apply the conversion factor directly to the given value.\n3. Compute 664.0 / 100.\nFinal: {\"answer\": 6.64, \"unit\": \"m\"}", "dedupe_signature": "b203a68a598cbb0787580df6160a2b7b1e68604f561f0db3afef591074be5152", "difficulty": "easy", "final_answer": {"answer": 6.64, "unit": "m"}, "id": "unit_convert_000282_cm_to_m_664", "license": "Apache-2.0", "prompt": "Convert 664 cm to m. Return the converted value with unit.", "reasoning_trace": "There are 100 centimeters in one meter.\nApply the conversion factor directly to the given value.\nCompute 664.0 / 100.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 664.0}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-5.45, -2.25], \"unit\": \"dimensionless\"}", "dedupe_signature": "2855d0543be7b702c152a057d04f9d6f1d407aee6be4519f2e8014a2bfa8278f", "difficulty": "medium", "final_answer": {"answer": [-5.45, -2.25], "unit": "dimensionless"}, "id": "line_two_point_000284_-20_-11_-5.45_-2.25", "license": "Apache-2.0", "prompt": "A line passes through points (-20, 106.75) and (-11, 57.7). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -20.0, "x2": -11.0, "y1": 106.75, "y2": 57.7}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef weighted_sum_000286(values, weights):\n    if len(values) != len(weights):\n        raise ValueError('length mismatch')\n    return sum(value * weight for value, weight in zip(values, weights))\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"weighted_sum_000286\"}", "dedupe_signature": "11224e676c4491ceab176d382d0c6217c1eca0e670eff4c1175a745665c4b511", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "weighted_sum_000286"}, "id": "code_000286_weighted_sum_000286", "license": "Apache-2.0", "prompt": "Write a Python function weighted_sum_000286(values, weights) that returns sum(value*weight). Raise ValueError when the two inputs have different lengths. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "weighted_sum_000286"}, "verifier": {"function": "weighted_sum_000286", "tests": ["assert weighted_sum_000286([2, 3], [4, 5]) == 23", "assert weighted_sum_000286([], []) == 0", "try:\n    weighted_sum_000286([1], [1, 2])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: rate_constant, number_of_steps.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"rate_constant\", \"number_of_steps\"]}", "dedupe_signature": "bdb3e984bd96b785784682b72f3463e8fd29df8a7afe7abb1f791c4515e97c7f", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["rate_constant", "number_of_steps"]}, "id": "abstain_000287_rate_constant_number_of_steps", "license": "Apache-2.0", "prompt": "Use explicit Euler for dy/dt = -k y. The prompt gives y(0)=20.5 and h=0.15, but omits both k and the number of steps. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: rate_constant, number_of_steps.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["rate_constant", "number_of_steps"]}, "verifier": {"missing": ["rate_constant", "number_of_steps"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 14.6 kg and a = 4.3 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 62.78, \"unit\": \"N\"}", "dedupe_signature": "09900152f8e120753bc1ffc7a7ef8517425599db0f6c58198371653c5050e95e", "difficulty": "easy", "final_answer": {"answer": 62.78, "unit": "N"}, "id": "force_000288_14.6_4.3", "license": "Apache-2.0", "prompt": "A cart has mass 14.6 kg and measured acceleration 4.3 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 14.6 kg and a = 4.3 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 4.3, "mass": 14.6}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 2.34 * 8.314 * 412 / 96.8.\nFinal: {\"answer\": 82.8033, \"unit\": \"kPa\"}", "dedupe_signature": "1299a7d2c179a6f23c46ab002be5b887557531b947000362ff1bd635f33b543a", "difficulty": "medium", "final_answer": {"answer": 82.8033, "unit": "kPa"}, "id": "ideal_gas_000291_2.34_412_96.8", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=2.34 mol, T=412 K, and V=96.8 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 2.34 * 8.314 * 412 / 96.8.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 2.34, "temp_k": 412, "volume_l": 96.8}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1490 * 1.8 * 6.\nFinal: {\"answer\": 16092.0, \"unit\": \"J\"}", "dedupe_signature": "de68067aca428372405391ffefbb444df99263a152ee7b872b6e98bf07771f1c", "difficulty": "easy", "final_answer": {"answer": 16092.0, "unit": "J"}, "id": "heat_q_000292_1490_1.8_6", "license": "Apache-2.0", "prompt": "A 1490 g sample has specific heat 1.8 J/(g*K). How much heat is needed to raise its temperature by 6 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1490 * 1.8 * 6.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 6, "heat_capacity": 1.8, "mass_g": 1490}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=71.7 V and R=112.6 ohm.\nFinal: {\"answer\": 45.6562, \"unit\": \"W\"}", "dedupe_signature": "76e88f290a4ecd4b0e8121c7f8a5e79dd54f95eccb6062d73b98aac349bd3b04", "difficulty": "easy", "final_answer": {"answer": 45.6562, "unit": "W"}, "id": "ohm_power_000293_71.7_112.6", "license": "Apache-2.0", "prompt": "A resistor has resistance 112.6 ohm and voltage 71.7 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=71.7 V and R=112.6 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 112.6, "voltage": 71.7}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=304.5 mg, t=150.5 h, and T_half=60 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 53.5185, \"unit\": \"mg\"}", "dedupe_signature": "f28594c6ef54b2fcfe1605a3414b69b22c5ec2f44fb65af902ab0cdcfabf6798", "difficulty": "medium", "final_answer": {"answer": 53.5185, "unit": "mg"}, "id": "half_life_000294_304.5_60_150.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 304.5 mg. Its half-life is 60 hours. How many mg remain after 150.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=304.5 mg, t=150.5 h, and T_half=60 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 150.5, "half_life": 60.0, "initial_amount": 304.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 6.86 mol * 44.01 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 301.9086, \"unit\": \"g\"}", "dedupe_signature": "1aebb711a7aee5f910e646bd272755b0ebe6dddcb07f6d35791b9c2969928249", "difficulty": "medium", "final_answer": {"answer": 301.9086, "unit": "g"}, "id": "stoich_mass_000295_carbon_dioxide_6.86", "license": "Apache-2.0", "prompt": "A sample contains 6.86 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 6.86 mol * 44.01 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "carbon dioxide", "molar_mass": 44.01, "moles": 6.86}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.58 y, so each step multiplies y by 1 - h*0.58.\n3. Apply that update for 3 steps and round the final state.\nFinal: {\"answer\": 0.9047, \"unit\": \"state_units\"}", "dedupe_signature": "da47813906703e5ae9669e4f62b868b1aa5dc194abe83aeb517582e69b68c745", "difficulty": "medium", "final_answer": {"answer": 0.9047, "unit": "state_units"}, "id": "euler_decay_000297_24.5_0.58_1.15_3", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.58 y with y(0)=24.5, step size h=1.15, for 3 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.58 y, so each step multiplies y by 1 - h*0.58.\nApply that update for 3 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 24.5, "rate": 0.58, "step": 1.15, "steps": 3}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-5.2)=-43.44 and f(3.5)=14.85.\n3. The interval width is 8.7.\nFinal: {\"answer\": -124.3665, \"unit\": \"area_units\"}", "dedupe_signature": "4ca4a00febaec0d9a30c38a20033fcaccf0c64e1d9e9dbc2b9c6561e13f92a09", "difficulty": "medium", "final_answer": {"answer": -124.3665, "unit": "area_units"}, "id": "trapz_linear_000298_6.7_-8.6_-5.2_3.5", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=6.7x+-8.6 from x=-5.2 to x=3.5. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-5.2)=-43.44 and f(3.5)=14.85.\nThe interval width is 8.7.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -8.6, "slope": 6.7, "x0": -5.2, "x1": 3.499999999999999}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.3 and add it to the current value.\nFinal: {\"answer\": [0.09, 0.505, 0.715], \"unit\": \"temperature_units\"}", "dedupe_signature": "fc95290dec6491fe7735c60a5e0ee50ffb29fbfdf5703b97e29a2f5949e4be15", "difficulty": "hard", "final_answer": {"answer": [0.09, 0.505, 0.715], "unit": "temperature_units"}, "id": "heat_step_000299_0.3_-1.5_1.05_0.4_0.1_1.85", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-1.5, right=1.85; current interior values are [1.05, 0.4, 0.1]. Use r=0.3. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.3 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [1.05, 0.4, 0.1], "left": -1.5, "r": 0.3, "right": 1.85}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 22119.0 / 1000.\nFinal: {\"answer\": 22.119, \"unit\": \"kg\"}", "dedupe_signature": "d610c1b420339f608f1cff4e6ba5752301d4736373c83b30b5ad4865c31eba55", "difficulty": "easy", "final_answer": {"answer": 22.119, "unit": "kg"}, "id": "unit_convert_000300_g_to_kg_22119", "license": "Apache-2.0", "prompt": "Convert 22119 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 22119.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 22119.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=148 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-355.7562, 222.3011], \"unit\": \"N\"}", "dedupe_signature": "7f62974b44c12275e3bd4c0669f524aacf298f58fcd5988e731bb88de244f046", "difficulty": "medium", "final_answer": {"answer": [-355.7562, 222.3011], "unit": "N"}, "id": "vector_components_000301_419.5_148", "license": "Apache-2.0", "prompt": "A vector has magnitude 419.5 N at 148 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=148 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 148, "magnitude": 419.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [8.8, -24.75], \"unit\": \"dimensionless\"}", "dedupe_signature": "93fae5eadc6d47160a0b7a700d7f730df1280b305445a8db4b06d13351d6e5b4", "difficulty": "medium", "final_answer": {"answer": [8.8, -24.75], "unit": "dimensionless"}, "id": "line_two_point_000302_-7.25_-4.5_8.8_-24.75", "license": "Apache-2.0", "prompt": "A line passes through points (-7.25, -88.55) and (-4.5, -64.35). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -7.25, "x2": -4.5, "y1": -88.55000000000001, "y2": -64.35}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. velocity divided by time is acceleration\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "d4516bded55045431e507d612c94b439f807d88e9eaa7d558d6210d2ac8765b9", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_000303_inconsistent_c1271127_655693", "license": "Apache-2.0", "prompt": "In quality-control check case 655693, check dimensional consistency for x = v / t. The left side has dimensions m and the right side has dimensions m/s^2. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nvelocity divided by time is acceleration\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "x = v / t"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef pairwise_ratios_000304(numerators, denominators):\n    if len(numerators) != len(denominators):\n        raise ValueError('length mismatch')\n    out = []\n    for numerator, denominator in zip(numerators, denominators):\n        if denominator == 0:\n            raise ValueError('zero denominator')\n        out.append(numerator / denominator)\n    return out\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"pairwise_ratios_000304\"}", "dedupe_signature": "26999618391a309cc3180c2b4c47cddf330794b3fa67c05ef3d446d675546c4b", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "pairwise_ratios_000304"}, "id": "code_000304_pairwise_ratios_000304", "license": "Apache-2.0", "prompt": "Write a Python function pairwise_ratios_000304(numerators, denominators) that returns a list of n/d values. Raise ValueError if lengths differ or any denominator is zero. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "pairwise_ratios_000304"}, "verifier": {"function": "pairwise_ratios_000304", "tests": ["assert pairwise_ratios_000304([2, 9], [4, 3]) == [0.5, 3.0]", "try:\n    pairwise_ratios_000304([1], [0])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass", "try:\n    pairwise_ratios_000304([1, 2], [1])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: volume.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"volume\"]}", "dedupe_signature": "f3b9969591b1dafb20ef16522409679205efd7f36277092c0192a4e9def07afa", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["volume"]}, "id": "abstain_000305_volume", "license": "Apache-2.0", "prompt": "Compute pressure from the ideal gas law. The prompt gives n=5.97 mol and T=347 K, but does not give volume. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: volume.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["volume"]}, "verifier": {"missing": ["volume"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 10.6^2 and multiply by 0.5 * 20.65.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 1160.117, \"unit\": \"J\"}", "dedupe_signature": "898e47eef75294882bafa0db71c8b9c4953462449842e904f93477c352704a57", "difficulty": "easy", "final_answer": {"answer": 1160.117, "unit": "J"}, "id": "ke_000307_20.65_10.6", "license": "Apache-2.0", "prompt": "A body of mass 20.65 kg moves at 10.6 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 10.6^2 and multiply by 0.5 * 20.65.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 20.65, "velocity": 10.6}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=59 degrees through the sine of 2 theta.\n3. Substitute v=28.5 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 73.1064, \"unit\": \"m\"}", "dedupe_signature": "8162b0d047de2341ee03da4849812899a585c761ec4d318292e19cf01c83dbcf", "difficulty": "medium", "final_answer": {"answer": 73.1064, "unit": "m"}, "id": "projectile_range_000308_28.5_59", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 28.5 m/s and angle 59 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=59 degrees through the sine of 2 theta.\nSubstitute v=28.5 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 59, "gravity": 9.81, "speed": 28.5}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 5.9 * 8.314 * 444 / 74.5.\nFinal: {\"answer\": 292.3403, \"unit\": \"kPa\"}", "dedupe_signature": "e84bae30fe3c2fef0525159ca67ac76bc74161dada568355d1d4cabb1902f617", "difficulty": "medium", "final_answer": {"answer": 292.3403, "unit": "kPa"}, "id": "ideal_gas_000309_5.9_444_74.5", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=5.9 mol, T=444 K, and V=74.5 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 5.9 * 8.314 * 444 / 74.5.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 5.9, "temp_k": 444, "volume_l": 74.5}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 455 * 4.665 * 74.\nFinal: {\"answer\": 157070.55, \"unit\": \"J\"}", "dedupe_signature": "25dbb5629dc6c2d2f46663eb30678542f3d6ab64931c4ea0b6b05875ff494bc1", "difficulty": "easy", "final_answer": {"answer": 157070.55, "unit": "J"}, "id": "heat_q_000310_455_4.665_74", "license": "Apache-2.0", "prompt": "A 455 g sample has specific heat 4.665 J/(g*K). How much heat is needed to raise its temperature by 74 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 455 * 4.665 * 74.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 74, "heat_capacity": 4.665, "mass_g": 455}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=50.7 V and R=150.1 ohm.\nFinal: {\"answer\": 17.1252, \"unit\": \"W\"}", "dedupe_signature": "21a712d3493853496414e8fc131249fcb691d8d17bf1ccbfa9208392bf4a17b7", "difficulty": "easy", "final_answer": {"answer": 17.1252, "unit": "W"}, "id": "ohm_power_000311_50.7_150.1", "license": "Apache-2.0", "prompt": "A resistor has resistance 150.1 ohm and voltage 50.7 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=50.7 V and R=150.1 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 150.1, "voltage": 50.7}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=240.5 mg, t=10.5 h, and T_half=78 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 219.0745, \"unit\": \"mg\"}", "dedupe_signature": "2ba0a4398d152daae1d332aef5ed7186f0d853460c864cebcf9471931185f173", "difficulty": "medium", "final_answer": {"answer": 219.0745, "unit": "mg"}, "id": "half_life_000312_240.5_78_10.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 240.5 mg. Its half-life is 78 hours. How many mg remain after 10.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=240.5 mg, t=10.5 h, and T_half=78 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 10.5, "half_life": 78.0, "initial_amount": 240.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 3.21 mol * 180.156 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 578.3008, \"unit\": \"g\"}", "dedupe_signature": "ceaeff9bdf0f495a8c41f348437a8465e356f8b76ae7fd031f2583993d5b4393", "difficulty": "medium", "final_answer": {"answer": 578.3008, "unit": "g"}, "id": "stoich_mass_000313_glucose_3.21", "license": "Apache-2.0", "prompt": "A sample contains 3.21 mol of glucose. Using molar mass 180.156 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 3.21 mol * 180.156 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "glucose", "molar_mass": 180.156, "moles": 3.21}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 1375 mL to 1.375 L.\n3. Compute M = 2.05 / 1.375.\nFinal: {\"answer\": 1.4909, \"unit\": \"mol/L\"}", "dedupe_signature": "8db87578d59b364f2459a71aab5b5248d51adeef996e776fc6640ea78fcc0996", "difficulty": "medium", "final_answer": {"answer": 1.4909, "unit": "mol/L"}, "id": "molarity_000314_2.05_1375", "license": "Apache-2.0", "prompt": "A solution contains 2.05 mol of solute in 1375 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 1375 mL to 1.375 L.\nCompute M = 2.05 / 1.375.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 2.05, "volume_ml": 1375}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(3.4)=34.14 and f(8.3)=56.68.\n3. The interval width is 4.9.\nFinal: {\"answer\": 222.509, \"unit\": \"area_units\"}", "dedupe_signature": "fb70279924cd22f9caeb9daa9841cb7e96b8fa94299d8f18c3208ff3afb4761c", "difficulty": "medium", "final_answer": {"answer": 222.509, "unit": "area_units"}, "id": "trapz_linear_000316_4.6_18.5_3.4_8.3", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=4.6x+18.5 from x=3.4 to x=8.3. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(3.4)=34.14 and f(8.3)=56.68.\nThe interval width is 4.9.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 18.5, "slope": 4.6, "x0": 3.4, "x1": 8.3}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.22 and add it to the current value.\nFinal: {\"answer\": [-0.827, -1.509, -0.784], \"unit\": \"temperature_units\"}", "dedupe_signature": "0c6ac27e8134931e232df4c79742685a26747e1f339243a8ea9f9440720a492b", "difficulty": "hard", "final_answer": {"answer": [-0.827, -1.509, -0.784], "unit": "temperature_units"}, "id": "heat_step_000317_0.22_2.8_-1.85_-1.85_-0.3_-0.95", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=2.8, right=-0.95; current interior values are [-1.85, -1.85, -0.3]. Use r=0.22. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.22 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-1.85, -1.85, -0.3], "left": 2.8, "r": 0.22, "right": -0.95}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=292 degrees and keep the unit as newtons.\nFinal: {\"answer\": [51.3211, -127.0242], \"unit\": \"N\"}", "dedupe_signature": "12849e9920404ceeb2e58a84835137020a778a62084284dc0ee1525a72a39261", "difficulty": "medium", "final_answer": {"answer": [51.3211, -127.0242], "unit": "N"}, "id": "vector_components_000319_137_292", "license": "Apache-2.0", "prompt": "A vector has magnitude 137 N at 292 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=292 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 292, "magnitude": 137.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-9.5, 23.75], \"unit\": \"dimensionless\"}", "dedupe_signature": "c1f1fd1de1859eed5cb219093316855b03fadb09629e1267c0ca45fc796e0e12", "difficulty": "medium", "final_answer": {"answer": [-9.5, 23.75], "unit": "dimensionless"}, "id": "line_two_point_000320_4.75_17.75_-9.5_23.75", "license": "Apache-2.0", "prompt": "A line passes through points (4.75, -21.375) and (17.75, -144.875). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 4.75, "x2": 17.75, "y1": -21.375, "y2": -144.875}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef center_values_000322(values):\n    if not values:\n        raise ValueError('center_values requires at least one value')\n    mean = sum(values) / len(values)\n    return [value - mean for value in values]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"center_values_000322\"}", "dedupe_signature": "fc57360a82d9cc2eb78ded053ec5fa5106547c6e286672c96566e84c16976a63", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "center_values_000322"}, "id": "code_000322_center_values_000322", "license": "Apache-2.0", "prompt": "Write a Python function center_values_000322(values) that subtracts the arithmetic mean from each value and returns a new list. Raise ValueError for an empty input. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "center_values_000322"}, "verifier": {"function": "center_values_000322", "tests": ["out = center_values_000322([1, 2, 3]); assert out == [-1, 0, 1]", "assert center_values_000322([5]) == [0]", "try:\n    center_values_000322([])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: rate_constant, number_of_steps.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"rate_constant\", \"number_of_steps\"]}", "dedupe_signature": "4406a66f13219f415e07a85cb7ceba3d5a0fa42e6878f49a15afdf6bf72386e3", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["rate_constant", "number_of_steps"]}, "id": "abstain_000323_rate_constant_number_of_steps", "license": "Apache-2.0", "prompt": "Use explicit Euler for dy/dt = -k y. The prompt gives y(0)=23.5 and h=0.7, but omits both k and the number of steps. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: rate_constant, number_of_steps.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["rate_constant", "number_of_steps"]}, "verifier": {"missing": ["rate_constant", "number_of_steps"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 4.3^2 and multiply by 0.5 * 21.9.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 202.4655, \"unit\": \"J\"}", "dedupe_signature": "46ed047ffa2ab982847c03eac507c6698d12f11ae9842cc8300efe97b7627fcd", "difficulty": "easy", "final_answer": {"answer": 202.4655, "unit": "J"}, "id": "ke_000325_21.9_4.3", "license": "Apache-2.0", "prompt": "A body of mass 21.9 kg moves at 4.3 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 4.3^2 and multiply by 0.5 * 21.9.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 21.9, "velocity": 4.3}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=80 degrees through the sine of 2 theta.\n3. Substitute v=49.6 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 85.7721, \"unit\": \"m\"}", "dedupe_signature": "a2dafce3659fb360973480accbb07f92a4105cf803c82aaf89654e310c746581", "difficulty": "medium", "final_answer": {"answer": 85.7721, "unit": "m"}, "id": "projectile_range_000326_49.6_80", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 49.6 m/s and angle 80 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=80 degrees through the sine of 2 theta.\nSubstitute v=49.6 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 80, "gravity": 9.81, "speed": 49.6}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 0.52 * 8.314 * 379 / 118.1.\nFinal: {\"answer\": 13.874, \"unit\": \"kPa\"}", "dedupe_signature": "f4d7c22b2decc8e59a22051ea054035701ad93d061b0736d256288d4c5f08b6a", "difficulty": "medium", "final_answer": {"answer": 13.874, "unit": "kPa"}, "id": "ideal_gas_000327_0.52_379_118.1", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=0.52 mol, T=379 K, and V=118.1 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 0.52 * 8.314 * 379 / 118.1.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 0.52, "temp_k": 379, "volume_l": 118.1}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1700 * 1.245 * 63.\nFinal: {\"answer\": 133339.5, \"unit\": \"J\"}", "dedupe_signature": "a0292873ff2332d24de906992159b090608b6d217dd07425349285066a7215b3", "difficulty": "easy", "final_answer": {"answer": 133339.5, "unit": "J"}, "id": "heat_q_000328_1700_1.245_63", "license": "Apache-2.0", "prompt": "A 1700 g sample has specific heat 1.245 J/(g*K). How much heat is needed to raise its temperature by 63 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1700 * 1.245 * 63.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 63, "heat_capacity": 1.245, "mass_g": 1700}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=294.5 mg, t=52 h, and T_half=16 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 30.9555, \"unit\": \"mg\"}", "dedupe_signature": "bc6680bff7a4f956e4e864295943bc52907228fb647e3395dc5581b33411ab59", "difficulty": "medium", "final_answer": {"answer": 30.9555, "unit": "mg"}, "id": "half_life_000330_294.5_16_52", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 294.5 mg. Its half-life is 16 hours. How many mg remain after 52 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=294.5 mg, t=52 h, and T_half=16 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 52.0, "half_life": 16.0, "initial_amount": 294.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 5.69 mol * 18.015 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 102.5054, \"unit\": \"g\"}", "dedupe_signature": "55ccafe8c3d3b0f4cb5c01c8dfee083aeb4bde7d1440abc654b858ab5a8c32e8", "difficulty": "medium", "final_answer": {"answer": 102.5054, "unit": "g"}, "id": "stoich_mass_000331_water_5.69", "license": "Apache-2.0", "prompt": "A sample contains 5.69 mol of water. Using molar mass 18.015 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 5.69 mol * 18.015 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "water", "molar_mass": 18.015, "moles": 5.69}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 3410 mL to 3.41 L.\n3. Compute M = 3.07 / 3.41.\nFinal: {\"answer\": 0.9003, \"unit\": \"mol/L\"}", "dedupe_signature": "51db641711641af9922855660b7a3cdb6a616889e3198c1ccb4ce51ae71c97c6", "difficulty": "medium", "final_answer": {"answer": 0.9003, "unit": "mol/L"}, "id": "molarity_000332_3.07_3410", "license": "Apache-2.0", "prompt": "A solution contains 3.07 mol of solute in 3410 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 3410 mL to 3.41 L.\nCompute M = 3.07 / 3.41.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 3.07, "volume_ml": 3410}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.81 y, so each step multiplies y by 1 - h*0.81.\n3. Apply that update for 9 steps and round the final state.\nFinal: {\"answer\": 20.7251, \"unit\": \"state_units\"}", "dedupe_signature": "745164d604b244365e28d985f336b3a0e35301ae470239f16e3266b2cae72f4f", "difficulty": "medium", "final_answer": {"answer": 20.7251, "unit": "state_units"}, "id": "euler_decay_000333_66.5_0.81_0.15_9", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.81 y with y(0)=66.5, step size h=0.15, for 9 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.81 y, so each step multiplies y by 1 - h*0.81.\nApply that update for 9 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 66.5, "rate": 0.81, "step": 0.15, "steps": 9}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.12 and add it to the current value.\nFinal: {\"answer\": [0.648, 2.034, 0.53], \"unit\": \"temperature_units\"}", "dedupe_signature": "599ef91ff373c30e95ef10672ee7efa1440aebc1473da00c93356126567a555c", "difficulty": "hard", "final_answer": {"answer": [0.648, 2.034, 0.53], "unit": "temperature_units"}, "id": "heat_step_000335_0.12_0.0_0.45_2.55_0.35_-0.35", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=0, right=-0.35; current interior values are [0.45, 2.55, 0.35]. Use r=0.12. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.12 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [0.45, 2.55, 0.35], "left": 0.0, "r": 0.12, "right": -0.35}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=125 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-138.8055, 198.2348], \"unit\": \"N\"}", "dedupe_signature": "9c5ff9aeef27406c5a84a5501d8402b0a67bd326a2dff772b5bb5674365e04ac", "difficulty": "medium", "final_answer": {"answer": [-138.8055, 198.2348], "unit": "N"}, "id": "vector_components_000337_242_125", "license": "Apache-2.0", "prompt": "A vector has magnitude 242 N at 125 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=125 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 125, "magnitude": 242.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-3.4, -29.75], \"unit\": \"dimensionless\"}", "dedupe_signature": "4e301fde147f50f4523e6bd2f2c3d9898027eaa7dc44d30cad01d98f26db022f", "difficulty": "medium", "final_answer": {"answer": [-3.4, -29.75], "unit": "dimensionless"}, "id": "line_two_point_000338_-16.5_-9.5_-3.4_-29.75", "license": "Apache-2.0", "prompt": "A line passes through points (-16.5, 26.35) and (-9.5, 2.55). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -16.5, "x2": -9.5, "y1": 26.35, "y2": 2.549999999999997}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. coulomb per second is ampere\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "52df2c4e876dac03af69f7abdc724152eb9a0adcc9cab784ad0160354a5a35c0", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_000339_consistent_8b38953d_938328", "license": "Apache-2.0", "prompt": "In student derivation case 938328, check dimensional consistency for I = Q / t. The left side has dimensions A and the right side has dimensions A. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\ncoulomb per second is ampere\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "I = Q / t"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef normalize_000340(values):\n    total = sum(values)\n    if total == 0:\n        raise ValueError('cannot normalize zero-sum values')\n    return [v / total for v in values]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"normalize_000340\"}", "dedupe_signature": "26e8d5e21c21f7147f56e14b5ea693458224c274f7d189bb686f1d9fc8d9a2a5", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "normalize_000340"}, "id": "code_000340_normalize_000340", "license": "Apache-2.0", "prompt": "Write a Python function normalize_000340(values) that returns a new list whose values sum to 1. Raise ValueError if the sum is zero. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "normalize_000340"}, "verifier": {"function": "normalize_000340", "tests": ["out = normalize_000340([2, 3, 5]); assert len(out) == 3", "assert abs(sum(normalize_000340([2, 3, 5])) - 1.0) < 1e-12", "assert normalize_000340([1, 1]) == [0.5, 0.5]", "try:\n    normalize_000340([1, -1])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: rate_constant, number_of_steps.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"rate_constant\", \"number_of_steps\"]}", "dedupe_signature": "be57d2770586f7de4e553b42f1d0ac639e9d5c9dde14fd33a922c82430d391f3", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["rate_constant", "number_of_steps"]}, "id": "abstain_000341_rate_constant_number_of_steps", "license": "Apache-2.0", "prompt": "Use explicit Euler for dy/dt = -k y. The prompt gives y(0)=11.5 and h=1.65, but omits both k and the number of steps. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: rate_constant, number_of_steps.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["rate_constant", "number_of_steps"]}, "verifier": {"missing": ["rate_constant", "number_of_steps"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 17.5 kg and a = 3.8 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 66.5, \"unit\": \"N\"}", "dedupe_signature": "234b482539f2bf2b58aa48d6ff30f9c09f76796a09c16c08bc592ad6088e05ed", "difficulty": "easy", "final_answer": {"answer": 66.5, "unit": "N"}, "id": "force_000342_17.5_3.8", "license": "Apache-2.0", "prompt": "A cart has mass 17.5 kg and measured acceleration 3.8 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 17.5 kg and a = 3.8 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 3.8, "mass": 17.5}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 43.25^2 and multiply by 0.5 * 7.5.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 7014.6094, \"unit\": \"J\"}", "dedupe_signature": "0f4fddb55aae8a8c6a6e6ac6496266b9727eb80d14c4d516ce2533d6e11b213b", "difficulty": "easy", "final_answer": {"answer": 7014.6094, "unit": "J"}, "id": "ke_000343_7.5_43.25", "license": "Apache-2.0", "prompt": "A body of mass 7.5 kg moves at 43.25 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 43.25^2 and multiply by 0.5 * 7.5.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 7.5, "velocity": 43.25}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=56 degrees through the sine of 2 theta.\n3. Substitute v=52.5 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 260.5046, \"unit\": \"m\"}", "dedupe_signature": "82cf9ddf6dcef4a6d90f706217007b476def9bfeefa244cdaa2a3eb71941e2be", "difficulty": "medium", "final_answer": {"answer": 260.5046, "unit": "m"}, "id": "projectile_range_000344_52.5_56", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 52.5 m/s and angle 56 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=56 degrees through the sine of 2 theta.\nSubstitute v=52.5 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 56, "gravity": 9.81, "speed": 52.5}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 3.23 * 8.314 * 602 / 50.7.\nFinal: {\"answer\": 318.8608, \"unit\": \"kPa\"}", "dedupe_signature": "fdcf388d9ef069f3c58fd593bbce497cf88c8f61d74a1e9ac9952549878dc674", "difficulty": "medium", "final_answer": {"answer": 318.8608, "unit": "kPa"}, "id": "ideal_gas_000345_3.23_602_50.7", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=3.23 mol, T=602 K, and V=50.7 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 3.23 * 8.314 * 602 / 50.7.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 3.23, "temp_k": 602, "volume_l": 50.7}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1495 * 3.77 * 90.\nFinal: {\"answer\": 507253.5, \"unit\": \"J\"}", "dedupe_signature": "d41bc8c0080a1eebfd543613843055d6805127d56b970753905bc016e60b5581", "difficulty": "easy", "final_answer": {"answer": 507253.5, "unit": "J"}, "id": "heat_q_000346_1495_3.77_90", "license": "Apache-2.0", "prompt": "A 1495 g sample has specific heat 3.77 J/(g*K). How much heat is needed to raise its temperature by 90 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1495 * 3.77 * 90.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 90, "heat_capacity": 3.77, "mass_g": 1495}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=80.5 V and R=1.2 ohm.\nFinal: {\"answer\": 5400.2083, \"unit\": \"W\"}", "dedupe_signature": "8479be912dbf656b70d651053899524b51f1b4b723b848a761fffc4e5441bfb0", "difficulty": "easy", "final_answer": {"answer": 5400.2083, "unit": "W"}, "id": "ohm_power_000347_80.5_1.2", "license": "Apache-2.0", "prompt": "A resistor has resistance 1.2 ohm and voltage 80.5 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=80.5 V and R=1.2 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 1.2, "voltage": 80.5}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=470 mg, t=181 h, and T_half=26 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 3.7711, \"unit\": \"mg\"}", "dedupe_signature": "66a3cccc4f7f29d7e2d7a7528399b9e4c9018af895004d84619f6067a96e8ce7", "difficulty": "medium", "final_answer": {"answer": 3.7711, "unit": "mg"}, "id": "half_life_000348_470_26_181", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 470 mg. Its half-life is 26 hours. How many mg remain after 181 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=470 mg, t=181 h, and T_half=26 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 181.0, "half_life": 26.0, "initial_amount": 470.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 0.94 mol * 58.44 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 54.9336, \"unit\": \"g\"}", "dedupe_signature": "fe33c683e63e330a672e60751724b1f8d4fc6e083c049793d30a6063b6cba3f8", "difficulty": "medium", "final_answer": {"answer": 54.9336, "unit": "g"}, "id": "stoich_mass_000349_sodium_chloride_0.94", "license": "Apache-2.0", "prompt": "A sample contains 0.94 mol of sodium chloride. Using molar mass 58.44 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 0.94 mol * 58.44 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "sodium chloride", "molar_mass": 58.44, "moles": 0.94}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.89 y, so each step multiplies y by 1 - h*0.89.\n3. Apply that update for 7 steps and round the final state.\nFinal: {\"answer\": 0.2577, \"unit\": \"state_units\"}", "dedupe_signature": "3b6dd56855968d3cd76289c45b1c76b9c0b79e335e9726b95da222cb5674d35a", "difficulty": "medium", "final_answer": {"answer": 0.2577, "unit": "state_units"}, "id": "euler_decay_000351_54_0.89_0.6_7", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.89 y with y(0)=54, step size h=0.6, for 7 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.89 y, so each step multiplies y by 1 - h*0.89.\nApply that update for 7 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 54.0, "rate": 0.89, "step": 0.6, "steps": 7}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(8.3)=-57.81 and f(10.4)=-69.78.\n3. The interval width is 2.1.\nFinal: {\"answer\": -133.9695, \"unit\": \"area_units\"}", "dedupe_signature": "c162b815043aa29a8f74f9a9638e2cdc8e31fb7646b9218900d8351f46eace72", "difficulty": "medium", "final_answer": {"answer": -133.9695, "unit": "area_units"}, "id": "trapz_linear_000352_-5.7_-10.5_8.3_10.4", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-5.7x+-10.5 from x=8.3 to x=10.4. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(8.3)=-57.81 and f(10.4)=-69.78.\nThe interval width is 2.1.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -10.5, "slope": -5.7, "x0": 8.3, "x1": 10.4}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.28 and add it to the current value.\nFinal: {\"answer\": [0.108, -0.118, -0.232], \"unit\": \"temperature_units\"}", "dedupe_signature": "074ef7451a92c5380663f6e87bed5394cffdd0a16c73a61b31dce61faf5a68cf", "difficulty": "hard", "final_answer": {"answer": [0.108, -0.118, -0.232], "unit": "temperature_units"}, "id": "heat_step_000353_0.28_2.0_-1.95_1.45_-0.75_-1.1", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=2, right=-1.1; current interior values are [-1.95, 1.45, -0.75]. Use r=0.28. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.28 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-1.95, 1.45, -0.75], "left": 2.0, "r": 0.28, "right": -1.1}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=147 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-288.5027, 187.3558], \"unit\": \"N\"}", "dedupe_signature": "d17d2d4ee99101388b81806c89173a232127092ed2cd296b9d925c81b1177742", "difficulty": "medium", "final_answer": {"answer": [-288.5027, 187.3558], "unit": "N"}, "id": "vector_components_000355_344_147", "license": "Apache-2.0", "prompt": "A vector has magnitude 344 N at 147 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=147 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 147, "magnitude": 344.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-0.2, 21.0], \"unit\": \"dimensionless\"}", "dedupe_signature": "0fe1991cb27a8a3fb534e8b3c4dd746b7bec3c65139fda3ff67542c6a7fc53b6", "difficulty": "medium", "final_answer": {"answer": [-0.2, 21.0], "unit": "dimensionless"}, "id": "line_two_point_000356_8.25_9_-0.2_21", "license": "Apache-2.0", "prompt": "A line passes through points (8.25, 19.35) and (9, 19.2). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 8.25, "x2": 9.0, "y1": 19.35, "y2": 19.2}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. amount times volume is not concentration\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "d0c05ec652b9a36b6f323d934376d4884e092337924a03b98317d4498838b64f", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_000357_inconsistent_74ac0b02_406659", "license": "Apache-2.0", "prompt": "In lab notebook case 406659, check dimensional consistency for C = n * V. The left side has dimensions mol/L and the right side has dimensions mol*L. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\namount times volume is not concentration\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "C = n * V"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef running_total_000358(values):\n    total = 0\n    out = []\n    for value in values:\n        total += value\n        out.append(total)\n    return out\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"running_total_000358\"}", "dedupe_signature": "5be8d6360c2f8caf40ecd2ce28ade276e081905a96842c7146fbb693b8d465f0", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "running_total_000358"}, "id": "code_000358_running_total_000358", "license": "Apache-2.0", "prompt": "Write a Python function running_total_000358(values) that returns cumulative sums as a new list. It must not mutate the input list. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "running_total_000358"}, "verifier": {"function": "running_total_000358", "tests": ["assert running_total_000358([1, 2, 3]) == [1, 3, 6]", "xs = [4, -1, 2]; assert running_total_000358(xs) == [4, 3, 5] and xs == [4, -1, 2]", "assert running_total_000358([]) == []"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: rate_constant, number_of_steps.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"rate_constant\", \"number_of_steps\"]}", "dedupe_signature": "201db1611441323da146a1933f637c4fc038b654cd5f0f1badb720233e5c0eed", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["rate_constant", "number_of_steps"]}, "id": "abstain_000359_rate_constant_number_of_steps", "license": "Apache-2.0", "prompt": "Use explicit Euler for dy/dt = -k y. The prompt gives y(0)=44 and h=0.45, but omits both k and the number of steps. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: rate_constant, number_of_steps.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["rate_constant", "number_of_steps"]}, "verifier": {"missing": ["rate_constant", "number_of_steps"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 8.25 kg and a = 13.45 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 110.9625, \"unit\": \"N\"}", "dedupe_signature": "c365b84e62b8b12089ef93d04af2cda561339ec58e38969e82f831da80932342", "difficulty": "easy", "final_answer": {"answer": 110.9625, "unit": "N"}, "id": "force_000360_8.25_13.45", "license": "Apache-2.0", "prompt": "A cart has mass 8.25 kg and measured acceleration 13.45 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 8.25 kg and a = 13.45 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 13.45, "mass": 8.25}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=36 degrees through the sine of 2 theta.\n3. Substitute v=30.1 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 87.8355, \"unit\": \"m\"}", "dedupe_signature": "f36764e40761d58e59f6104e93ba6bf0d79fab3ea08fa04140cd55782e4adcd5", "difficulty": "medium", "final_answer": {"answer": 87.8355, "unit": "m"}, "id": "projectile_range_000362_30.1_36", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 30.1 m/s and angle 36 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=36 degrees through the sine of 2 theta.\nSubstitute v=30.1 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 36, "gravity": 9.81, "speed": 30.1}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 5.01 * 8.314 * 242 / 119.0.\nFinal: {\"answer\": 84.7064, \"unit\": \"kPa\"}", "dedupe_signature": "226beb823be662e3317dcc1b1dd8980f0c0fb8247eb38adfb29d35d0b2cbb5b7", "difficulty": "medium", "final_answer": {"answer": 84.7064, "unit": "kPa"}, "id": "ideal_gas_000363_5.01_242_119.0", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=5.01 mol, T=242 K, and V=119.0 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 5.01 * 8.314 * 242 / 119.0.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 5.01, "temp_k": 242, "volume_l": 119.0}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=206.5 V and R=163.4 ohm.\nFinal: {\"answer\": 260.9685, \"unit\": \"W\"}", "dedupe_signature": "09af20a14ebf09cba7b66af1fb38e4ddf79c427f0c046c460954fbec8954f3c1", "difficulty": "easy", "final_answer": {"answer": 260.9685, "unit": "W"}, "id": "ohm_power_000365_206.5_163.4", "license": "Apache-2.0", "prompt": "A resistor has resistance 163.4 ohm and voltage 206.5 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=206.5 V and R=163.4 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 163.4, "voltage": 206.5}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=326.5 mg, t=35.5 h, and T_half=77 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 237.1901, \"unit\": \"mg\"}", "dedupe_signature": "2a50c457f35b928dcf65f2469042d8e0ff284da1d35b9c5ac14be845e40151b1", "difficulty": "medium", "final_answer": {"answer": 237.1901, "unit": "mg"}, "id": "half_life_000366_326.5_77_35.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 326.5 mg. Its half-life is 77 hours. How many mg remain after 35.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=326.5 mg, t=35.5 h, and T_half=77 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 35.5, "half_life": 77.0, "initial_amount": 326.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 2.57 mol * 18.015 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 46.2985, \"unit\": \"g\"}", "dedupe_signature": "e331e9840c8811177e0dd5c93e37e5b9f8bf1942345544962e2cdb5134b8be8d", "difficulty": "medium", "final_answer": {"answer": 46.2985, "unit": "g"}, "id": "stoich_mass_000367_water_2.57", "license": "Apache-2.0", "prompt": "A sample contains 2.57 mol of water. Using molar mass 18.015 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 2.57 mol * 18.015 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "water", "molar_mass": 18.015, "moles": 2.57}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 2455 mL to 2.455 L.\n3. Compute M = 3.795 / 2.455.\nFinal: {\"answer\": 1.5458, \"unit\": \"mol/L\"}", "dedupe_signature": "642a2f1d9fe0da1b94561a61e3ed1cc0da02240b956a1eecc9a59ade3be74165", "difficulty": "medium", "final_answer": {"answer": 1.5458, "unit": "mol/L"}, "id": "molarity_000368_3.795_2455", "license": "Apache-2.0", "prompt": "A solution contains 3.795 mol of solute in 2455 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 2455 mL to 2.455 L.\nCompute M = 3.795 / 2.455.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 3.795, "volume_ml": 2455}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.64 y, so each step multiplies y by 1 - h*0.64.\n3. Apply that update for 11 steps and round the final state.\nFinal: {\"answer\": 28.2612, \"unit\": \"state_units\"}", "dedupe_signature": "c50bd732b3a162b1b2e7e0fe800b4459bd50fa9c5786eb5fce21aee2551cac11", "difficulty": "medium", "final_answer": {"answer": 28.2612, "unit": "state_units"}, "id": "euler_decay_000369_58.5_0.64_0.1_11", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.64 y with y(0)=58.5, step size h=0.1, for 11 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.64 y, so each step multiplies y by 1 - h*0.64.\nApply that update for 11 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 58.5, "rate": 0.64, "step": 0.1, "steps": 11}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(5.7)=19.81 and f(10.3)=44.19.\n3. The interval width is 4.6.\nFinal: {\"answer\": 147.2, \"unit\": \"area_units\"}", "dedupe_signature": "d566675334aacd10ce2991de8b61c4cc6bed98cd7a6959aaaa1e481b8e6d0f08", "difficulty": "medium", "final_answer": {"answer": 147.2, "unit": "area_units"}, "id": "trapz_linear_000370_5.3_-10.4_5.7_10.3", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=5.3x+-10.4 from x=5.7 to x=10.3. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(5.7)=19.81 and f(10.3)=44.19.\nThe interval width is 4.6.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -10.4, "slope": 5.3, "x0": 5.7, "x1": 10.3}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.38 and add it to the current value.\nFinal: {\"answer\": [1.387, 1.911, 1.344], \"unit\": \"temperature_units\"}", "dedupe_signature": "fd0bacdae1fa6ef027bab4b620e1d32cb0c76985a4f4f3868ead4fc739fb3f5b", "difficulty": "hard", "final_answer": {"answer": [1.387, 1.911, 1.344], "unit": "temperature_units"}, "id": "heat_step_000371_0.38_1.25_2.85_0.6_1.8_1.8", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.25, right=1.8; current interior values are [2.85, 0.6, 1.8]. Use r=0.38. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.38 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [2.85, 0.6, 1.8], "left": 1.25, "r": 0.38, "right": 1.8}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kelvin equals Celsius plus 273.15.\n2. Apply the conversion factor directly to the given value.\n3. Compute 212.5 + 273.15.\nFinal: {\"answer\": 485.65, \"unit\": \"K\"}", "dedupe_signature": "41a4a5aa5bd4b09604a54484d5bd3ff338f2099d199147ceea58c0f7fe0b652b", "difficulty": "easy", "final_answer": {"answer": 485.65, "unit": "K"}, "id": "unit_convert_000372_c_to_k_212.5", "license": "Apache-2.0", "prompt": "Convert 212.5 degC to K. Return the converted value with unit.", "reasoning_trace": "Kelvin equals Celsius plus 273.15.\nApply the conversion factor directly to the given value.\nCompute 212.5 + 273.15.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 212.5}, "verifier": {"formula": "value + 273.15", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-3.7, 28.25], \"unit\": \"dimensionless\"}", "dedupe_signature": "50ba4c9545b7edbbed80223942aef34d4727dfa5ce676aa35c0c4b66a767439e", "difficulty": "medium", "final_answer": {"answer": [-3.7, 28.25], "unit": "dimensionless"}, "id": "line_two_point_000374_-1_8.5_-3.7_28.25", "license": "Apache-2.0", "prompt": "A line passes through points (-1, 31.95) and (8.5, -3.2). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -1.0, "x2": 8.5, "y1": 31.95, "y2": -3.200000000000003}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef safe_mean_000376(values):\n    if not values:\n        raise ValueError('safe_mean requires at least one value')\n    return sum(values) / len(values)\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"safe_mean_000376\"}", "dedupe_signature": "4dbada16f2d66c312d817eaf927aeecb989cd02cb80ed521302d9030ab33ec65", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "safe_mean_000376"}, "id": "code_000376_safe_mean_000376", "license": "Apache-2.0", "prompt": "Write a Python function safe_mean_000376(values) that returns the arithmetic mean. It must raise ValueError for an empty input and must not mutate the input list. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "safe_mean_000376"}, "verifier": {"function": "safe_mean_000376", "tests": ["assert safe_mean_000376([2, 4, 6]) == 4", "xs = [1, 2, 3]; assert safe_mean_000376(xs) == 2 and xs == [1, 2, 3]", "try:\n    safe_mean_000376([])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: recurrence, objective, tie_breaking_rule.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"recurrence\", \"objective\", \"tie_breaking_rule\"]}", "dedupe_signature": "87b767410f8246a3a1f8f4a56034d76f4cba9246addc7ed1e1c45f4c89acbd66", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["recurrence", "objective", "tie_breaking_rule"]}, "id": "abstain_000377_recurrence_objective_tie_breaking_rule", "license": "Apache-2.0", "prompt": "Write a dynamic-programming solver for a routing scoring problem with 4091 items and budget 73190, but the recurrence, objective, and tie-breaking rule are all absent. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: recurrence, objective, tie_breaking_rule.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["recurrence", "objective", "tie_breaking_rule"]}, "verifier": {"missing": ["recurrence", "objective", "tie_breaking_rule"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 14 kg and a = 2.15 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 30.1, \"unit\": \"N\"}", "dedupe_signature": "ef48afdb25f1f3cedf0498dc35a4ea3b3f7b522555dd229bc27834ff2d5c95d7", "difficulty": "easy", "final_answer": {"answer": 30.1, "unit": "N"}, "id": "force_000378_14_2.15", "license": "Apache-2.0", "prompt": "A cart has mass 14 kg and measured acceleration 2.15 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 14 kg and a = 2.15 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 2.15, "mass": 14.0}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 43.5^2 and multiply by 0.5 * 18.8.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 17787.15, \"unit\": \"J\"}", "dedupe_signature": "48cc74ce4cb81e5667fbdb3be3f8a283733ab0cbc2ac9588fda6ea9e8b2dfb90", "difficulty": "easy", "final_answer": {"answer": 17787.15, "unit": "J"}, "id": "ke_000379_18.8_43.5", "license": "Apache-2.0", "prompt": "A body of mass 18.8 kg moves at 43.5 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 43.5^2 and multiply by 0.5 * 18.8.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 18.8, "velocity": 43.5}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=71 degrees through the sine of 2 theta.\n3. Substitute v=80.5 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 406.6912, \"unit\": \"m\"}", "dedupe_signature": "9edf1d1a214d1182a244083deb32cff847d6b305b7c8b3783c46b38b91de066f", "difficulty": "medium", "final_answer": {"answer": 406.6912, "unit": "m"}, "id": "projectile_range_000380_80.5_71", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 80.5 m/s and angle 71 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=71 degrees through the sine of 2 theta.\nSubstitute v=80.5 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 71, "gravity": 9.81, "speed": 80.5}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 105 * 3.47 * 79.\nFinal: {\"answer\": 28783.65, \"unit\": \"J\"}", "dedupe_signature": "61433632ef31577085a7500db7102e6c48972c1032d24e683dfe78b4737602a1", "difficulty": "easy", "final_answer": {"answer": 28783.65, "unit": "J"}, "id": "heat_q_000382_105_3.47_79", "license": "Apache-2.0", "prompt": "A 105 g sample has specific heat 3.47 J/(g*K). How much heat is needed to raise its temperature by 79 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 105 * 3.47 * 79.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 79, "heat_capacity": 3.47, "mass_g": 105}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=119.6 V and R=62.8 ohm.\nFinal: {\"answer\": 227.7732, \"unit\": \"W\"}", "dedupe_signature": "4c59dd4974d8da5d306a84ad918c973b9b6802e808a2a1cb78ca0f6e4de6dd4e", "difficulty": "easy", "final_answer": {"answer": 227.7732, "unit": "W"}, "id": "ohm_power_000383_119.6_62.8", "license": "Apache-2.0", "prompt": "A resistor has resistance 62.8 ohm and voltage 119.6 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=119.6 V and R=62.8 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 62.8, "voltage": 119.6}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=938.5 mg, t=276 h, and T_half=95.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 126.6024, \"unit\": \"mg\"}", "dedupe_signature": "c3ebb397325c93e63966d5c9be2c7416449e392997fb0d0687e2599adbc5ffc0", "difficulty": "medium", "final_answer": {"answer": 126.6024, "unit": "mg"}, "id": "half_life_000384_938.5_95.5_276", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 938.5 mg. Its half-life is 95.5 hours. How many mg remain after 276 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=938.5 mg, t=276 h, and T_half=95.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 276.0, "half_life": 95.5, "initial_amount": 938.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 3.61 mol * 100.087 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 361.3141, \"unit\": \"g\"}", "dedupe_signature": "4ead6e9e9edadf33609fbff2dfdf20ce1b7e99f11de914bba329702815543ee3", "difficulty": "medium", "final_answer": {"answer": 361.3141, "unit": "g"}, "id": "stoich_mass_000385_calcium_carbonate_3.61", "license": "Apache-2.0", "prompt": "A sample contains 3.61 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 3.61 mol * 100.087 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "calcium carbonate", "molar_mass": 100.087, "moles": 3.61}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 4865 mL to 4.865 L.\n3. Compute M = 1.74 / 4.865.\nFinal: {\"answer\": 0.3577, \"unit\": \"mol/L\"}", "dedupe_signature": "68425511506cc7a10a2a91e5a4b2e328e8b8c46d33c54508b599246892aa7c32", "difficulty": "medium", "final_answer": {"answer": 0.3577, "unit": "mol/L"}, "id": "molarity_000386_1.74_4865", "license": "Apache-2.0", "prompt": "A solution contains 1.74 mol of solute in 4865 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 4865 mL to 4.865 L.\nCompute M = 1.74 / 4.865.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 1.74, "volume_ml": 4865}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.74 y, so each step multiplies y by 1 - h*0.74.\n3. Apply that update for 3 steps and round the final state.\nFinal: {\"answer\": 17.2919, \"unit\": \"state_units\"}", "dedupe_signature": "ebb311272060734fa0e35e1fc211d47c4b567a681336a3edaea88ca1cfbfa20b", "difficulty": "medium", "final_answer": {"answer": 17.2919, "unit": "state_units"}, "id": "euler_decay_000387_42.5_0.74_0.35_3", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.74 y with y(0)=42.5, step size h=0.35, for 3 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.74 y, so each step multiplies y by 1 - h*0.74.\nApply that update for 3 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 42.5, "rate": 0.74, "step": 0.35, "steps": 3}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-4.1)=35.44 and f(3.3)=-4.52.\n3. The interval width is 7.4.\nFinal: {\"answer\": 114.404, \"unit\": \"area_units\"}", "dedupe_signature": "48025a25e1e8f799ea5b3b041c86fa1cbe422cc1f80f234eec91380078b310c8", "difficulty": "medium", "final_answer": {"answer": 114.404, "unit": "area_units"}, "id": "trapz_linear_000388_-5.4_13.3_-4.1_3.3", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-5.4x+13.3 from x=-4.1 to x=3.3. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-4.1)=35.44 and f(3.3)=-4.52.\nThe interval width is 7.4.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 13.3, "slope": -5.4, "x0": -4.1, "x1": 3.3000000000000007}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 100 centimeters in one meter.\n2. Apply the conversion factor directly to the given value.\n3. Compute 1136.0 / 100.\nFinal: {\"answer\": 11.36, \"unit\": \"m\"}", "dedupe_signature": "df702e4de5c2eaad7dadfd60c62ce7575e851887413c38677e5c9f9ac33ccea7", "difficulty": "easy", "final_answer": {"answer": 11.36, "unit": "m"}, "id": "unit_convert_000390_cm_to_m_1136", "license": "Apache-2.0", "prompt": "Convert 1136 cm to m. Return the converted value with unit.", "reasoning_trace": "There are 100 centimeters in one meter.\nApply the conversion factor directly to the given value.\nCompute 1136.0 / 100.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 1136.0}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=278 degrees and keep the unit as newtons.\nFinal: {\"answer\": [52.0507, -370.3603], \"unit\": \"N\"}", "dedupe_signature": "367322171046d9374f96da9fa44896954468d59b5b1c2e05a1f9a8afc21a718d", "difficulty": "medium", "final_answer": {"answer": [52.0507, -370.3603], "unit": "N"}, "id": "vector_components_000391_374_278", "license": "Apache-2.0", "prompt": "A vector has magnitude 374 N at 278 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=278 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 278, "magnitude": 374.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-9.85, 22.75], \"unit\": \"dimensionless\"}", "dedupe_signature": "5c3f4e9bb2866a1fc3fa008a0fb2f2d5eb90b93bcb275342ab3d89e326d79213", "difficulty": "medium", "final_answer": {"answer": [-9.85, 22.75], "unit": "dimensionless"}, "id": "line_two_point_000392_-10.5_0.5_-9.85_22.75", "license": "Apache-2.0", "prompt": "A line passes through points (-10.5, 126.175) and (0.5, 17.825). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -10.5, "x2": 0.5, "y1": 126.175, "y2": 17.825}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. coulomb per second is ampere\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "abbabb4d98cccb55a8cc8829e0cd1656e4768969a86234798e4959660f93434b", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_000393_consistent_8b38953d_858087", "license": "Apache-2.0", "prompt": "In sensor calibration case 858087, check dimensional consistency for I = Q / t. The left side has dimensions A and the right side has dimensions A. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\ncoulomb per second is ampere\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "I = Q / t"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef running_total_000394(values):\n    total = 0\n    out = []\n    for value in values:\n        total += value\n        out.append(total)\n    return out\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"running_total_000394\"}", "dedupe_signature": "1964afd1fbdc71e848e5a36ed375bc8aea8d886d20f678c448bf39cc6a35bb5e", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "running_total_000394"}, "id": "code_000394_running_total_000394", "license": "Apache-2.0", "prompt": "Write a Python function running_total_000394(values) that returns cumulative sums as a new list. It must not mutate the input list. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "running_total_000394"}, "verifier": {"function": "running_total_000394", "tests": ["assert running_total_000394([1, 2, 3]) == [1, 3, 6]", "xs = [4, -1, 2]; assert running_total_000394(xs) == [4, 3, 5] and xs == [4, -1, 2]", "assert running_total_000394([]) == []"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 10.05 kg and a = 2.05 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 20.6025, \"unit\": \"N\"}", "dedupe_signature": "d405033eec4780fd4ab0bbbb6d650a15d454953e3a8a30de1f39007ba29719ea", "difficulty": "easy", "final_answer": {"answer": 20.6025, "unit": "N"}, "id": "force_000396_10.05_2.05", "license": "Apache-2.0", "prompt": "A cart has mass 10.05 kg and measured acceleration 2.05 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 10.05 kg and a = 2.05 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 2.05, "mass": 10.05}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 13.35^2 and multiply by 0.5 * 27.6.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 2459.4705, \"unit\": \"J\"}", "dedupe_signature": "620daeb2f9cca889404887c5cd423e9c7a1d2a1eda8e3e187872060ad5eeddaa", "difficulty": "easy", "final_answer": {"answer": 2459.4705, "unit": "J"}, "id": "ke_000397_27.6_13.35", "license": "Apache-2.0", "prompt": "A body of mass 27.6 kg moves at 13.35 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 13.35^2 and multiply by 0.5 * 27.6.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 27.6, "velocity": 13.35}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=13 degrees through the sine of 2 theta.\n3. Substitute v=52.4 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 122.6974, \"unit\": \"m\"}", "dedupe_signature": "8c51d2fc2503c0431f6992e2cd752544317447e96e034854e9f00efebe6c6ed4", "difficulty": "medium", "final_answer": {"answer": 122.6974, "unit": "m"}, "id": "projectile_range_000398_52.4_13", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 52.4 m/s and angle 13 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=13 degrees through the sine of 2 theta.\nSubstitute v=52.4 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 13, "gravity": 9.81, "speed": 52.4}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1035 * 1.28 * 6.\nFinal: {\"answer\": 7948.8, \"unit\": \"J\"}", "dedupe_signature": "2208b143c92e21841b7acc85ecef714adc98a33927ff4f2d3a11fc9fe24b4423", "difficulty": "easy", "final_answer": {"answer": 7948.8, "unit": "J"}, "id": "heat_q_000400_1035_1.28_6", "license": "Apache-2.0", "prompt": "A 1035 g sample has specific heat 1.28 J/(g*K). How much heat is needed to raise its temperature by 6 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1035 * 1.28 * 6.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 6, "heat_capacity": 1.28, "mass_g": 1035}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=136.5 V and R=178.2 ohm.\nFinal: {\"answer\": 104.5581, \"unit\": \"W\"}", "dedupe_signature": "c40f50aedf71925b2bfe7e2ebb9827174617bf73cee5848bde1ec3c7cec1498e", "difficulty": "easy", "final_answer": {"answer": 104.5581, "unit": "W"}, "id": "ohm_power_000401_136.5_178.2", "license": "Apache-2.0", "prompt": "A resistor has resistance 178.2 ohm and voltage 136.5 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=136.5 V and R=178.2 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 178.2, "voltage": 136.5}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 1.65 mol * 180.156 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 297.2574, \"unit\": \"g\"}", "dedupe_signature": "1948cfddc3480e4587ee1ba134c6c212910f7ef882e41c6ff741347f4dd1b803", "difficulty": "medium", "final_answer": {"answer": 297.2574, "unit": "g"}, "id": "stoich_mass_000403_glucose_1.65", "license": "Apache-2.0", "prompt": "A sample contains 1.65 mol of glucose. Using molar mass 180.156 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 1.65 mol * 180.156 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "glucose", "molar_mass": 180.156, "moles": 1.65}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.03 y, so each step multiplies y by 1 - h*0.03.\n3. Apply that update for 12 steps and round the final state.\nFinal: {\"answer\": 19.5668, \"unit\": \"state_units\"}", "dedupe_signature": "377b7d86edd6d9b9e97ae7ad3ca195078e16aaa43d32d5c8e8d08380cb87a10f", "difficulty": "medium", "final_answer": {"answer": 19.5668, "unit": "state_units"}, "id": "euler_decay_000405_34_0.03_1.5_12", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.03 y with y(0)=34, step size h=1.5, for 12 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.03 y, so each step multiplies y by 1 - h*0.03.\nApply that update for 12 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 34.0, "rate": 0.03, "step": 1.5, "steps": 12}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(4.7)=32.78 and f(8.5)=45.7.\n3. The interval width is 3.8.\nFinal: {\"answer\": 149.112, \"unit\": \"area_units\"}", "dedupe_signature": "0bab4723a21de7413398794a19b0db8398c5419b16b2ef5f2213178f94ca3bd4", "difficulty": "medium", "final_answer": {"answer": 149.112, "unit": "area_units"}, "id": "trapz_linear_000406_3.4_16.8_4.7_8.5", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=3.4x+16.8 from x=4.7 to x=8.5. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(4.7)=32.78 and f(8.5)=45.7.\nThe interval width is 3.8.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 16.8, "slope": 3.4, "x0": 4.7, "x1": 8.5}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.32 and add it to the current value.\nFinal: {\"answer\": [-0.82, -0.06, 1.044], \"unit\": \"temperature_units\"}", "dedupe_signature": "89f032394593815ac4c6ed06afc8add1d4f38ec325cddb5015ef4602982fe47c", "difficulty": "hard", "final_answer": {"answer": [-0.82, -0.06, 1.044], "unit": "temperature_units"}, "id": "heat_step_000407_0.32_-1.55_-1.7_0.9_0.5_1.8", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-1.55, right=1.8; current interior values are [-1.7, 0.9, 0.5]. Use r=0.32. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.32 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-1.7, 0.9, 0.5], "left": -1.55, "r": 0.32, "right": 1.8}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=139 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-101.1311, 87.9119], \"unit\": \"N\"}", "dedupe_signature": "10c6d56e0b45820bcc8a73357155ea5aa72ea3d9a92e45ceda63215d9afc9e43", "difficulty": "medium", "final_answer": {"answer": [-101.1311, 87.9119], "unit": "N"}, "id": "vector_components_000409_134_139", "license": "Apache-2.0", "prompt": "A vector has magnitude 134 N at 139 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=139 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 139, "magnitude": 134.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-0.4, 6.25], \"unit\": \"dimensionless\"}", "dedupe_signature": "529f123fb146977ca5e70b95480b1c97fcd8317e3f6fd7d55830f49bc96edbc5", "difficulty": "medium", "final_answer": {"answer": [-0.4, 6.25], "unit": "dimensionless"}, "id": "line_two_point_000410_0.25_14.25_-0.4_6.25", "license": "Apache-2.0", "prompt": "A line passes through points (0.25, 6.15) and (14.25, 0.55). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 0.25, "x2": 14.25, "y1": 6.15, "y2": 0.5499999999999998}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\nimport math\n\ndef unit_vector_000412(x, y):\n    norm = math.hypot(x, y)\n    if norm == 0:\n        raise ValueError('zero vector has no direction')\n    return (x / norm, y / norm)\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"unit_vector_000412\"}", "dedupe_signature": "5b486f5ce9f3383b846f90a31707cb7f95615dd0615d59f9cdfee31b5b65253a", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "unit_vector_000412"}, "id": "code_000412_unit_vector_000412", "license": "Apache-2.0", "prompt": "Write a Python function unit_vector_000412(x, y) that returns the 2D unit vector as a tuple. Raise ValueError for the zero vector. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "unit_vector_000412"}, "verifier": {"function": "unit_vector_000412", "tests": ["ux, uy = unit_vector_000412(3, 4); assert abs(ux - 0.6) < 1e-12 and abs(uy - 0.8) < 1e-12", "assert unit_vector_000412(0, 5) == (0, 1)", "try:\n    unit_vector_000412(0, 0)\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: rate_constant, number_of_steps.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"rate_constant\", \"number_of_steps\"]}", "dedupe_signature": "e21c24dbd59b52123b9585dc9c7911a24d157a1b5b06744385d1db4fc59a013b", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["rate_constant", "number_of_steps"]}, "id": "abstain_000413_rate_constant_number_of_steps", "license": "Apache-2.0", "prompt": "Use explicit Euler for dy/dt = -k y. The prompt gives y(0)=5.5 and h=0.8, but omits both k and the number of steps. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: rate_constant, number_of_steps.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["rate_constant", "number_of_steps"]}, "verifier": {"missing": ["rate_constant", "number_of_steps"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 8.1^2 and multiply by 0.5 * 13.15.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 431.3858, \"unit\": \"J\"}", "dedupe_signature": "b613816cd40740c1f01df2e4c1f2ddbcd5cdd9c417c6b6da78530034c0b3e71c", "difficulty": "easy", "final_answer": {"answer": 431.3858, "unit": "J"}, "id": "ke_000415_13.15_8.1", "license": "Apache-2.0", "prompt": "A body of mass 13.15 kg moves at 8.1 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 8.1^2 and multiply by 0.5 * 13.15.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 13.15, "velocity": 8.1}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=16 degrees through the sine of 2 theta.\n3. Substitute v=13.7 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 10.1387, \"unit\": \"m\"}", "dedupe_signature": "60c84be61d7b7a430b45d9fb7f80a79342e8746e8d6e4f48b762742907619a10", "difficulty": "medium", "final_answer": {"answer": 10.1387, "unit": "m"}, "id": "projectile_range_000416_13.7_16", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 13.7 m/s and angle 16 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=16 degrees through the sine of 2 theta.\nSubstitute v=13.7 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 16, "gravity": 9.81, "speed": 13.7}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 1.08 * 8.314 * 497 / 86.1.\nFinal: {\"answer\": 51.8307, \"unit\": \"kPa\"}", "dedupe_signature": "54f9ef08df345f38832357f3322b70b31e3c0b1195ff4f8363d1eb035a9e0248", "difficulty": "medium", "final_answer": {"answer": 51.8307, "unit": "kPa"}, "id": "ideal_gas_000417_1.08_497_86.1", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=1.08 mol, T=497 K, and V=86.1 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 1.08 * 8.314 * 497 / 86.1.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 1.08, "temp_k": 497, "volume_l": 86.1}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 960 * 3.03 * 109.\nFinal: {\"answer\": 317059.2, \"unit\": \"J\"}", "dedupe_signature": "6bbfb6249f5fd5224cb7c980759e0bcb1b4d0f9c8438a8836cdb2f238cc3bf22", "difficulty": "easy", "final_answer": {"answer": 317059.2, "unit": "J"}, "id": "heat_q_000418_960_3.03_109", "license": "Apache-2.0", "prompt": "A 960 g sample has specific heat 3.03 J/(g*K). How much heat is needed to raise its temperature by 109 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 960 * 3.03 * 109.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 109, "heat_capacity": 3.03, "mass_g": 960}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=196.6 V and R=98.4 ohm.\nFinal: {\"answer\": 392.8004, \"unit\": \"W\"}", "dedupe_signature": "73de0860a39ea860b45e227665681d05b089413978949ec13e1954fe01d91b4c", "difficulty": "easy", "final_answer": {"answer": 392.8004, "unit": "W"}, "id": "ohm_power_000419_196.6_98.4", "license": "Apache-2.0", "prompt": "A resistor has resistance 98.4 ohm and voltage 196.6 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=196.6 V and R=98.4 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 98.4, "voltage": 196.6}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 6.71 mol * 44.01 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 295.3071, \"unit\": \"g\"}", "dedupe_signature": "988a8a4ba1abb59ca1ffe7e52b47fc60caff2df54945cd57e8cd05dac4c55bd8", "difficulty": "medium", "final_answer": {"answer": 295.3071, "unit": "g"}, "id": "stoich_mass_000421_carbon_dioxide_6.71", "license": "Apache-2.0", "prompt": "A sample contains 6.71 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 6.71 mol * 44.01 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "carbon dioxide", "molar_mass": 44.01, "moles": 6.71}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 2530 mL to 2.53 L.\n3. Compute M = 4.085 / 2.53.\nFinal: {\"answer\": 1.6146, \"unit\": \"mol/L\"}", "dedupe_signature": "4197e8b0c1b234fdf75a0728e3bf1a5f32ce0a306304643061980265e8aae654", "difficulty": "medium", "final_answer": {"answer": 1.6146, "unit": "mol/L"}, "id": "molarity_000422_4.085_2530", "license": "Apache-2.0", "prompt": "A solution contains 4.085 mol of solute in 2530 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 2530 mL to 2.53 L.\nCompute M = 4.085 / 2.53.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 4.085, "volume_ml": 2530}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.68 y, so each step multiplies y by 1 - h*0.68.\n3. Apply that update for 4 steps and round the final state.\nFinal: {\"answer\": 7.4923, \"unit\": \"state_units\"}", "dedupe_signature": "3b919bc8a0443035047d6ed9143c16b4db9a7a955c69ee1398f2083a872a6e12", "difficulty": "medium", "final_answer": {"answer": 7.4923, "unit": "state_units"}, "id": "euler_decay_000423_61_0.68_0.6_4", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.68 y with y(0)=61, step size h=0.6, for 4 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.68 y, so each step multiplies y by 1 - h*0.68.\nApply that update for 4 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 61.0, "rate": 0.68, "step": 0.6, "steps": 4}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.18 and add it to the current value.\nFinal: {\"answer\": [0.25, 0.125, -0.294], \"unit\": \"temperature_units\"}", "dedupe_signature": "e95908d7ee665e078d1923031f4f56d2175523ae2a6d43555ecda578be24061c", "difficulty": "hard", "final_answer": {"answer": [0.25, 0.125, -0.294], "unit": "temperature_units"}, "id": "heat_step_000425_0.18_2.9_-0.65_0.8_-1.5_2.9", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=2.9, right=2.9; current interior values are [-0.65, 0.8, -1.5]. Use r=0.18. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.18 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-0.65, 0.8, -1.5], "left": 2.9, "r": 0.18, "right": 2.9}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 100 centimeters in one meter.\n2. Apply the conversion factor directly to the given value.\n3. Compute 3391.0 / 100.\nFinal: {\"answer\": 33.91, \"unit\": \"m\"}", "dedupe_signature": "c870ed935b6cc8e53081f72a005670f25b5e0f4b975d3ef309856823375f0b6a", "difficulty": "easy", "final_answer": {"answer": 33.91, "unit": "m"}, "id": "unit_convert_000426_cm_to_m_3391", "license": "Apache-2.0", "prompt": "Convert 3391 cm to m. Return the converted value with unit.", "reasoning_trace": "There are 100 centimeters in one meter.\nApply the conversion factor directly to the given value.\nCompute 3391.0 / 100.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 3391.0}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=284 degrees and keep the unit as newtons.\nFinal: {\"answer\": [76.6892, -307.5837], \"unit\": \"N\"}", "dedupe_signature": "52fcefa773eb8b93b6a760ea282429699535f79cd1aea4d0f92302836183daf0", "difficulty": "medium", "final_answer": {"answer": [76.6892, -307.5837], "unit": "N"}, "id": "vector_components_000427_317_284", "license": "Apache-2.0", "prompt": "A vector has magnitude 317 N at 284 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=284 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 284, "magnitude": 317.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [7.6, 0.75], \"unit\": \"dimensionless\"}", "dedupe_signature": "7daa4d93fb25295de6cc9ae090ce27410d6d1a01211701290b89a9e5bbf4c2f7", "difficulty": "medium", "final_answer": {"answer": [7.6, 0.75], "unit": "dimensionless"}, "id": "line_two_point_000428_8_15.5_7.6_0.75", "license": "Apache-2.0", "prompt": "A line passes through points (8, 61.55) and (15.5, 118.55). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 8.0, "x2": 15.5, "y1": 61.55, "y2": 118.55}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef threshold_flags_000430(values, threshold):\n    return [value >= threshold for value in values]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"threshold_flags_000430\"}", "dedupe_signature": "118c4c4ed042d5ee8cd6a6458d443d6aa9ff7ada6b9bbc7575fd54147b62e3d4", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "threshold_flags_000430"}, "id": "code_000430_threshold_flags_000430", "license": "Apache-2.0", "prompt": "Write a Python function threshold_flags_000430(values, threshold) that returns a list of booleans showing whether each value is greater than or equal to threshold. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "threshold_flags_000430"}, "verifier": {"function": "threshold_flags_000430", "tests": ["assert threshold_flags_000430([1, 2, 3], 2) == [False, True, True]", "assert threshold_flags_000430([], 5) == []", "assert threshold_flags_000430([-1, 0], 0) == [False, True]"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 18.15^2 and multiply by 0.5 * 7.75.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 1276.5122, \"unit\": \"J\"}", "dedupe_signature": "2c22baf3b69bf8aa82d51528688dfb074cbc229fa825c0ec4f5fa86595484cd8", "difficulty": "easy", "final_answer": {"answer": 1276.5122, "unit": "J"}, "id": "ke_000433_7.75_18.15", "license": "Apache-2.0", "prompt": "A body of mass 7.75 kg moves at 18.15 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 18.15^2 and multiply by 0.5 * 7.75.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 7.75, "velocity": 18.15}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=10 degrees through the sine of 2 theta.\n3. Substitute v=67.8 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 160.2662, \"unit\": \"m\"}", "dedupe_signature": "c04009e322dfed26d009238318ffb0cab200b0bb41a760e4ef2ef848153292fa", "difficulty": "medium", "final_answer": {"answer": 160.2662, "unit": "m"}, "id": "projectile_range_000434_67.8_10", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 67.8 m/s and angle 10 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=10 degrees through the sine of 2 theta.\nSubstitute v=67.8 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 10, "gravity": 9.81, "speed": 67.8}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 2.31 * 8.314 * 367 / 22.2.\nFinal: {\"answer\": 317.4937, \"unit\": \"kPa\"}", "dedupe_signature": "fc487e27576503e3dd4c8eab8dc02017012aa4ef92cef94f871700e9624de477", "difficulty": "medium", "final_answer": {"answer": 317.4937, "unit": "kPa"}, "id": "ideal_gas_000435_2.31_367_22.2", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=2.31 mol, T=367 K, and V=22.2 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 2.31 * 8.314 * 367 / 22.2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 2.31, "temp_k": 367, "volume_l": 22.2}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1205 * 4.735 * 45.\nFinal: {\"answer\": 256755.375, \"unit\": \"J\"}", "dedupe_signature": "f5453765807880af081ec63ceeec296d291640cfe35bf6425c9e20a94d7316d7", "difficulty": "easy", "final_answer": {"answer": 256755.375, "unit": "J"}, "id": "heat_q_000436_1205_4.735_45", "license": "Apache-2.0", "prompt": "A 1205 g sample has specific heat 4.735 J/(g*K). How much heat is needed to raise its temperature by 45 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1205 * 4.735 * 45.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 45, "heat_capacity": 4.735, "mass_g": 1205}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=172.5 V and R=106.2 ohm.\nFinal: {\"answer\": 280.1907, \"unit\": \"W\"}", "dedupe_signature": "85858abfa1c4cbea9d0c3a903c055ff6b693d96ad640f05f746c4d0362dca20d", "difficulty": "easy", "final_answer": {"answer": 280.1907, "unit": "W"}, "id": "ohm_power_000437_172.5_106.2", "license": "Apache-2.0", "prompt": "A resistor has resistance 106.2 ohm and voltage 172.5 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=172.5 V and R=106.2 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 106.2, "voltage": 172.5}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=793.5 mg, t=255.5 h, and T_half=52 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 26.3298, \"unit\": \"mg\"}", "dedupe_signature": "8f2564e20ce7eab06027f2d57adffdc6f81548106abc5758af99af847350f54a", "difficulty": "medium", "final_answer": {"answer": 26.3298, "unit": "mg"}, "id": "half_life_000438_793.5_52_255.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 793.5 mg. Its half-life is 52 hours. How many mg remain after 255.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=793.5 mg, t=255.5 h, and T_half=52 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 255.5, "half_life": 52.0, "initial_amount": 793.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 4.07 mol * 18.015 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 73.3211, \"unit\": \"g\"}", "dedupe_signature": "18c4c349f86bf5cbe7bc1ae47b603f5d1f133bdaa89b57f05273ddc870061301", "difficulty": "medium", "final_answer": {"answer": 73.3211, "unit": "g"}, "id": "stoich_mass_000439_water_4.07", "license": "Apache-2.0", "prompt": "A sample contains 4.07 mol of water. Using molar mass 18.015 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 4.07 mol * 18.015 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "water", "molar_mass": 18.015, "moles": 4.07}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.38 y, so each step multiplies y by 1 - h*0.38.\n3. Apply that update for 8 steps and round the final state.\nFinal: {\"answer\": 0.0395, \"unit\": \"state_units\"}", "dedupe_signature": "237a240f69bf6aff1a71cdb9c4bae0f5fa61c8a6bdf138a028bc3ad4a0db8bdc", "difficulty": "medium", "final_answer": {"answer": 0.0395, "unit": "state_units"}, "id": "euler_decay_000441_3_0.38_1.1_8", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.38 y with y(0)=3, step size h=1.1, for 8 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.38 y, so each step multiplies y by 1 - h*0.38.\nApply that update for 8 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 3.0, "rate": 0.38, "step": 1.1, "steps": 8}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-1.3)=-15.53 and f(5.1)=-21.29.\n3. The interval width is 6.4.\nFinal: {\"answer\": -117.824, \"unit\": \"area_units\"}", "dedupe_signature": "1ce8bc9984f470b7784ebca9b7b60bf42b03cd298b0c8ba25f9c7c3c61e1fbf3", "difficulty": "medium", "final_answer": {"answer": -117.824, "unit": "area_units"}, "id": "trapz_linear_000442_-0.9_-16.7_-1.3_5.1", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-0.9x+-16.7 from x=-1.3 to x=5.1. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-1.3)=-15.53 and f(5.1)=-21.29.\nThe interval width is 6.4.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -16.7, "slope": -0.9, "x0": -1.3, "x1": 5.1000000000000005}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.22 and add it to the current value.\nFinal: {\"answer\": [1.515, 1.728, 0.496], \"unit\": \"temperature_units\"}", "dedupe_signature": "2c94db5f3692db57713418f4c4126fb9b9f31d530dd2367f1af9934392c544b6", "difficulty": "hard", "final_answer": {"answer": [1.515, 1.728, 0.496], "unit": "temperature_units"}, "id": "heat_step_000443_0.22_1.15_1.35_2.3_0.65_-1.7", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.15, right=-1.7; current interior values are [1.35, 2.3, 0.65]. Use r=0.22. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.22 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [1.35, 2.3, 0.65], "left": 1.15, "r": 0.22, "right": -1.7}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [7.55, 7.75], \"unit\": \"dimensionless\"}", "dedupe_signature": "c6139c6d431bcd25537177ab91db4088c29cb1871f29d9ed5898507d0680bf76", "difficulty": "medium", "final_answer": {"answer": [7.55, 7.75], "unit": "dimensionless"}, "id": "line_two_point_000446_-18_-11.75_7.55_7.75", "license": "Apache-2.0", "prompt": "A line passes through points (-18, -128.15) and (-11.75, -80.9625). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -18.0, "x2": -11.75, "y1": -128.15, "y2": -80.96249999999999}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. grams cancel with J/(g*K), and kelvin cancels, leaving joules\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "8a58db18ef040e879812c6f6b90ebdae7786eb0e8eb5b13f495aa5c4a25eca7f", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_000447_consistent_4153435f_50710", "license": "Apache-2.0", "prompt": "In model card equation case 50710, check dimensional consistency for Q = m * c * DeltaT. The left side has dimensions J and the right side has dimensions J. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\ngrams cancel with J/(g*K), and kelvin cancels, leaving joules\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "Q = m * c * DeltaT"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\nimport math\n\ndef unit_vector_000448(x, y):\n    norm = math.hypot(x, y)\n    if norm == 0:\n        raise ValueError('zero vector has no direction')\n    return (x / norm, y / norm)\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"unit_vector_000448\"}", "dedupe_signature": "663ff65e8ce5059afdc758a92bcfc73c85ed2f74aaf55d1256875d978aede138", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "unit_vector_000448"}, "id": "code_000448_unit_vector_000448", "license": "Apache-2.0", "prompt": "Write a Python function unit_vector_000448(x, y) that returns the 2D unit vector as a tuple. Raise ValueError for the zero vector. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "unit_vector_000448"}, "verifier": {"function": "unit_vector_000448", "tests": ["ux, uy = unit_vector_000448(3, 4); assert abs(ux - 0.6) < 1e-12 and abs(uy - 0.8) < 1e-12", "assert unit_vector_000448(0, 5) == (0, 1)", "try:\n    unit_vector_000448(0, 0)\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: launch_angle_or_vertical_velocity.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"launch_angle_or_vertical_velocity\"]}", "dedupe_signature": "72b620c386dbf4a5eb2cb952efcb3715c43cbf3bb91bc7bc740c6fbf168178f7", "difficulty": "easy", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["launch_angle_or_vertical_velocity"]}, "id": "abstain_000449_launch_angle_or_vertical_velocity", "license": "Apache-2.0", "prompt": "Compute projectile range on level ground. The prompt gives initial speed 12 m/s but does not give launch angle or vertical velocity. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: launch_angle_or_vertical_velocity.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["launch_angle_or_vertical_velocity"]}, "verifier": {"missing": ["launch_angle_or_vertical_velocity"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 0.85 kg and a = 10.5 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 8.925, \"unit\": \"N\"}", "dedupe_signature": "bafc9e99b9d2abad5b18f2edf1e0398fa6c9a33754c9518698d92b2ab5cbd8e7", "difficulty": "easy", "final_answer": {"answer": 8.925, "unit": "N"}, "id": "force_000450_0.85_10.5", "license": "Apache-2.0", "prompt": "A cart has mass 0.85 kg and measured acceleration 10.5 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 0.85 kg and a = 10.5 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 10.5, "mass": 0.85}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 3.25^2 and multiply by 0.5 * 7.15.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 37.7609, \"unit\": \"J\"}", "dedupe_signature": "6a37f3274a47560ffe2b1568cc054ca53dc198dc87300abf668f22106ededea4", "difficulty": "easy", "final_answer": {"answer": 37.7609, "unit": "J"}, "id": "ke_000451_7.15_3.25", "license": "Apache-2.0", "prompt": "A body of mass 7.15 kg moves at 3.25 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 3.25^2 and multiply by 0.5 * 7.15.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 7.15, "velocity": 3.25}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=21 degrees through the sine of 2 theta.\n3. Substitute v=63.1 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 271.5818, \"unit\": \"m\"}", "dedupe_signature": "6e619ed0a239a46deb1428b83abb5b950a8568819e8bd4ee6370257416b3ba89", "difficulty": "medium", "final_answer": {"answer": 271.5818, "unit": "m"}, "id": "projectile_range_000452_63.1_21", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 63.1 m/s and angle 21 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=21 degrees through the sine of 2 theta.\nSubstitute v=63.1 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 21, "gravity": 9.81, "speed": 63.1}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 2.56 * 8.314 * 565 / 101.9.\nFinal: {\"answer\": 118.0115, \"unit\": \"kPa\"}", "dedupe_signature": "227f789bb4be26990f829cd2c3a74ce7b8ddc0122c68b59264219cf6fd3642b9", "difficulty": "medium", "final_answer": {"answer": 118.0115, "unit": "kPa"}, "id": "ideal_gas_000453_2.56_565_101.9", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=2.56 mol, T=565 K, and V=101.9 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 2.56 * 8.314 * 565 / 101.9.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 2.56, "temp_k": 565, "volume_l": 101.9}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1900 * 2.72 * 46.\nFinal: {\"answer\": 237728.0, \"unit\": \"J\"}", "dedupe_signature": "0a173ddff9d90fa22be3d077a330dff48ce8812d2defd679032f7b9ab834bc97", "difficulty": "easy", "final_answer": {"answer": 237728.0, "unit": "J"}, "id": "heat_q_000454_1900_2.72_46", "license": "Apache-2.0", "prompt": "A 1900 g sample has specific heat 2.72 J/(g*K). How much heat is needed to raise its temperature by 46 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1900 * 2.72 * 46.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 46, "heat_capacity": 2.72, "mass_g": 1900}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=25.2 V and R=88.2 ohm.\nFinal: {\"answer\": 7.2, \"unit\": \"W\"}", "dedupe_signature": "dac74517f174778112fa32c17edb887e66d43507a955b347d3ac249032032667", "difficulty": "easy", "final_answer": {"answer": 7.2, "unit": "W"}, "id": "ohm_power_000455_25.2_88.2", "license": "Apache-2.0", "prompt": "A resistor has resistance 88.2 ohm and voltage 25.2 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=25.2 V and R=88.2 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 88.2, "voltage": 25.2}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=627 mg, t=44 h, and T_half=45.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 320.7463, \"unit\": \"mg\"}", "dedupe_signature": "dcf601f933f48256c4d9fc857df25031ff32480858ea437b59f6557fa0ab855e", "difficulty": "medium", "final_answer": {"answer": 320.7463, "unit": "mg"}, "id": "half_life_000456_627_45.5_44", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 627 mg. Its half-life is 45.5 hours. How many mg remain after 44 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=627 mg, t=44 h, and T_half=45.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 44.0, "half_life": 45.5, "initial_amount": 627.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 5.92 mol * 44.01 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 260.5392, \"unit\": \"g\"}", "dedupe_signature": "4fe92ea6ed0d19ec666692b07820cb31060432567986d145c2bcfb43e69ea3cf", "difficulty": "medium", "final_answer": {"answer": 260.5392, "unit": "g"}, "id": "stoich_mass_000457_carbon_dioxide_5.92", "license": "Apache-2.0", "prompt": "A sample contains 5.92 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 5.92 mol * 44.01 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "carbon dioxide", "molar_mass": 44.01, "moles": 5.92}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 315 mL to 0.315 L.\n3. Compute M = 4.165 / 0.315.\nFinal: {\"answer\": 13.2222, \"unit\": \"mol/L\"}", "dedupe_signature": "176ac4eb76bd3046f9cc9c9cfb5a317208da668c5b23284ec6ea96fd84d4ff3c", "difficulty": "medium", "final_answer": {"answer": 13.2222, "unit": "mol/L"}, "id": "molarity_000458_4.165_315", "license": "Apache-2.0", "prompt": "A solution contains 4.165 mol of solute in 315 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 315 mL to 0.315 L.\nCompute M = 4.165 / 0.315.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 4.165, "volume_ml": 315}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.85 y, so each step multiplies y by 1 - h*0.85.\n3. Apply that update for 8 steps and round the final state.\nFinal: {\"answer\": 0.0022, \"unit\": \"state_units\"}", "dedupe_signature": "d28e1854a48a4673867e94e139c77d0027fac0524133db3e1cd89b110094f824", "difficulty": "medium", "final_answer": {"answer": 0.0022, "unit": "state_units"}, "id": "euler_decay_000459_21_0.85_1.55_8", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.85 y with y(0)=21, step size h=1.55, for 8 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.85 y, so each step multiplies y by 1 - h*0.85.\nApply that update for 8 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 21.0, "rate": 0.85, "step": 1.55, "steps": 8}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-9.7)=-49.16 and f(-4.4)=-29.02.\n3. The interval width is 5.3.\nFinal: {\"answer\": -207.177, \"unit\": \"area_units\"}", "dedupe_signature": "ddd2b9893d92af88745ad34aaf9d8678adeef8eeb265515729c6d2abc418aeff", "difficulty": "medium", "final_answer": {"answer": -207.177, "unit": "area_units"}, "id": "trapz_linear_000460_3.8_-12.3_-9.7_-4.4", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=3.8x+-12.3 from x=-9.7 to x=-4.4. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-9.7)=-49.16 and f(-4.4)=-29.02.\nThe interval width is 5.3.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -12.3, "slope": 3.8, "x0": -9.7, "x1": -4.3999999999999995}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.46 and add it to the current value.\nFinal: {\"answer\": [-1.45, 1.175, -0.3], \"unit\": \"temperature_units\"}", "dedupe_signature": "68179f163fd2cb258e464dd7e77b33c48d3aa3fd1d125e999533e53425a187f1", "difficulty": "hard", "final_answer": {"answer": [-1.45, 1.175, -0.3], "unit": "temperature_units"}, "id": "heat_step_000461_0.46_-1.8_2.0_-1.7_0.85_0.9", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-1.8, right=0.9; current interior values are [2.0, -1.7, 0.85]. Use r=0.46. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.46 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [2.0, -1.7, 0.85], "left": -1.8, "r": 0.46, "right": 0.9}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 100 centimeters in one meter.\n2. Apply the conversion factor directly to the given value.\n3. Compute 2086.5 / 100.\nFinal: {\"answer\": 20.865, \"unit\": \"m\"}", "dedupe_signature": "2bbb4e79786b4ad04f4e7371953a39b29e8a7d759ff999d3a0ef74f6b51894cc", "difficulty": "easy", "final_answer": {"answer": 20.865, "unit": "m"}, "id": "unit_convert_000462_cm_to_m_2086.5", "license": "Apache-2.0", "prompt": "Convert 2086.5 cm to m. Return the converted value with unit.", "reasoning_trace": "There are 100 centimeters in one meter.\nApply the conversion factor directly to the given value.\nCompute 2086.5 / 100.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 2086.5}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=71 degrees and keep the unit as newtons.\nFinal: {\"answer\": [34.9986, 101.6432], \"unit\": \"N\"}", "dedupe_signature": "ee3bd42752e7ac7ef3d107a5acd992cc88e41aa26932fa7fe322cc554add57b9", "difficulty": "medium", "final_answer": {"answer": [34.9986, 101.6432], "unit": "N"}, "id": "vector_components_000463_107.5_71", "license": "Apache-2.0", "prompt": "A vector has magnitude 107.5 N at 71 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=71 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 71, "magnitude": 107.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. energy divided by length is force, not spring constant\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "61bf7d08faff37ace11bb18c7ff88d90e2861891ec4a9a9c1e49c6a0514f7c78", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_000465_inconsistent_56040f5d_680133", "license": "Apache-2.0", "prompt": "In sensor calibration case 680133, check dimensional consistency for k = E / x. The left side has dimensions N/m and the right side has dimensions J/m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nenergy divided by length is force, not spring constant\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "k = E / x"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: left_boundary, right_boundary.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"left_boundary\", \"right_boundary\"]}", "dedupe_signature": "dda3a77acdc55a0cd8e358b87fd4d09842f045177430bd841308c52e8b27270f", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["left_boundary", "right_boundary"]}, "id": "abstain_000467_left_boundary_right_boundary", "license": "Apache-2.0", "prompt": "Solve the 1D heat equation after one finite-difference step. The prompt gives r=0.08 and interior values [-1.3, 2.55, -0.45], but gives no boundary values. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: left_boundary, right_boundary.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["left_boundary", "right_boundary"]}, "verifier": {"missing": ["left_boundary", "right_boundary"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 23.55^2 and multiply by 0.5 * 15.95.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 4422.9549, \"unit\": \"J\"}", "dedupe_signature": "d49a66531e984b910f549bd1c8aac62386aca90460788d1f6bed56add1584ac0", "difficulty": "easy", "final_answer": {"answer": 4422.9549, "unit": "J"}, "id": "ke_000469_15.95_23.55", "license": "Apache-2.0", "prompt": "A body of mass 15.95 kg moves at 23.55 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 23.55^2 and multiply by 0.5 * 15.95.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 15.95, "velocity": 23.55}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=24 degrees through the sine of 2 theta.\n3. Substitute v=56.1 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 238.4131, \"unit\": \"m\"}", "dedupe_signature": "336732a63126681bd2b26a4ea1371bb53301e26181baa3b5fb7987a52e2a6235", "difficulty": "medium", "final_answer": {"answer": 238.4131, "unit": "m"}, "id": "projectile_range_000470_56.1_24", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 56.1 m/s and angle 24 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=24 degrees through the sine of 2 theta.\nSubstitute v=56.1 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 24, "gravity": 9.81, "speed": 56.1}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 5.05 * 8.314 * 509 / 74.8.\nFinal: {\"answer\": 285.7048, \"unit\": \"kPa\"}", "dedupe_signature": "9df5f5c97bcdcff7a705f1f2afcf31d7b00a1846bd4486574ce66d4728668b16", "difficulty": "medium", "final_answer": {"answer": 285.7048, "unit": "kPa"}, "id": "ideal_gas_000471_5.05_509_74.8", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=5.05 mol, T=509 K, and V=74.8 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 5.05 * 8.314 * 509 / 74.8.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 5.05, "temp_k": 509, "volume_l": 74.8}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=51.6 V and R=78.4 ohm.\nFinal: {\"answer\": 33.9612, \"unit\": \"W\"}", "dedupe_signature": "8abde219d3fb2f5bdaaba5c65bb156d0da1a38bf505cfcfc46817c9657460f31", "difficulty": "easy", "final_answer": {"answer": 33.9612, "unit": "W"}, "id": "ohm_power_000473_51.6_78.4", "license": "Apache-2.0", "prompt": "A resistor has resistance 78.4 ohm and voltage 51.6 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=51.6 V and R=78.4 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 78.4, "voltage": 51.6}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 3.29 mol * 58.44 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 192.2676, \"unit\": \"g\"}", "dedupe_signature": "b589b4b361b49e02b23b726ccc19667bb416d8d38e8047364796d24d492741b3", "difficulty": "medium", "final_answer": {"answer": 192.2676, "unit": "g"}, "id": "stoich_mass_000475_sodium_chloride_3.29", "license": "Apache-2.0", "prompt": "A sample contains 3.29 mol of sodium chloride. Using molar mass 58.44 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 3.29 mol * 58.44 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "sodium chloride", "molar_mass": 58.44, "moles": 3.29}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.01 y, so each step multiplies y by 1 - h*0.01.\n3. Apply that update for 7 steps and round the final state.\nFinal: {\"answer\": 42.9333, \"unit\": \"state_units\"}", "dedupe_signature": "341f3bd6e41bd29038da0b5bedb3e558ba88387f222fa6580c9c7f8fc3ac72a8", "difficulty": "medium", "final_answer": {"answer": 42.9333, "unit": "state_units"}, "id": "euler_decay_000477_44_0.01_0.35_7", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.01 y with y(0)=44, step size h=0.35, for 7 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.01 y, so each step multiplies y by 1 - h*0.01.\nApply that update for 7 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 44.0, "rate": 0.01, "step": 0.35, "steps": 7}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-6.5)=49.9 and f(0.6)=8.72.\n3. The interval width is 7.1.\nFinal: {\"answer\": 208.101, \"unit\": \"area_units\"}", "dedupe_signature": "61cfc5bdeeac54d09398a3645a4f8483f272bee5beca2a107aade8818d9fdc92", "difficulty": "medium", "final_answer": {"answer": 208.101, "unit": "area_units"}, "id": "trapz_linear_000478_-5.8_12.2_-6.5_0.6", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-5.8x+12.2 from x=-6.5 to x=0.6. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-6.5)=49.9 and f(0.6)=8.72.\nThe interval width is 7.1.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 12.2, "slope": -5.8, "x0": -6.5, "x1": 0.5999999999999996}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.46 and add it to the current value.\nFinal: {\"answer\": [0.386, 0.225, 2.294], \"unit\": \"temperature_units\"}", "dedupe_signature": "b5d281001e3167a165241101cb75bc72d651534e01d69cca51b3cee9e15565b0", "difficulty": "hard", "final_answer": {"answer": [0.386, 0.225, 2.294], "unit": "temperature_units"}, "id": "heat_step_000479_0.46_-1.05_-0.35_1.95_0.5_2.95", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-1.05, right=2.95; current interior values are [-0.35, 1.95, 0.5]. Use r=0.46. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.46 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-0.35, 1.95, 0.5], "left": -1.05, "r": 0.46, "right": 2.95}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 100 centimeters in one meter.\n2. Apply the conversion factor directly to the given value.\n3. Compute 4547.0 / 100.\nFinal: {\"answer\": 45.47, \"unit\": \"m\"}", "dedupe_signature": "0dc54cea076f3b85b7ea15f96d3cc108711b3af2896e2536714b3d598bb83d61", "difficulty": "easy", "final_answer": {"answer": 45.47, "unit": "m"}, "id": "unit_convert_000480_cm_to_m_4547", "license": "Apache-2.0", "prompt": "Convert 4547 cm to m. Return the converted value with unit.", "reasoning_trace": "There are 100 centimeters in one meter.\nApply the conversion factor directly to the given value.\nCompute 4547.0 / 100.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 4547.0}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=56 degrees and keep the unit as newtons.\nFinal: {\"answer\": [75.491, 111.9201], \"unit\": \"N\"}", "dedupe_signature": "cc19eac48bcecf6d53b9e5e5f64e5cad0510a488d6c5a3a94de304ca7a594249", "difficulty": "medium", "final_answer": {"answer": [75.491, 111.9201], "unit": "N"}, "id": "vector_components_000481_135_56", "license": "Apache-2.0", "prompt": "A vector has magnitude 135 N at 56 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=56 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 56, "magnitude": 135.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-2.05, -25.75], \"unit\": \"dimensionless\"}", "dedupe_signature": "1761d5c0c2453a43e09a665465cde6dfdcbb0efa17c8dea1d691c9591ca90f90", "difficulty": "medium", "final_answer": {"answer": [-2.05, -25.75], "unit": "dimensionless"}, "id": "line_two_point_000482_-10.75_-6.5_-2.05_-25.75", "license": "Apache-2.0", "prompt": "A line passes through points (-10.75, -3.7125) and (-6.5, -12.425). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -10.75, "x2": -6.5, "y1": -3.712500000000002, "y2": -12.425}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. mass times acceleration has newton dimensions\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "baf76d111f8167bfaaa38de7bd2a19a9ee6c44e65bed66c09b8183732bc98fd5", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_000483_consistent_03f5e041_472590", "license": "Apache-2.0", "prompt": "In student derivation case 472590, check dimensional consistency for F = m * a. The left side has dimensions kg*m/s^2 and the right side has dimensions kg*m/s^2. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nmass times acceleration has newton dimensions\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "F = m * a"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef finite_differences_000484(values):\n    return [values[i + 1] - values[i] for i in range(len(values) - 1)]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"finite_differences_000484\"}", "dedupe_signature": "520d16e041477380af14acd003f8d672fc0652067153ad923ddfc0cb62ffd338", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "finite_differences_000484"}, "id": "code_000484_finite_differences_000484", "license": "Apache-2.0", "prompt": "Write a Python function finite_differences_000484(values) that returns the list of successive differences values[i+1] - values[i]. It must return [] for fewer than two values. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "finite_differences_000484"}, "verifier": {"function": "finite_differences_000484", "tests": ["assert finite_differences_000484([1, 4, 9, 16]) == [3, 5, 7]", "assert finite_differences_000484([5]) == []", "assert finite_differences_000484([]) == []"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: target_schema, valid_examples.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"target_schema\", \"valid_examples\"]}", "dedupe_signature": "c3b7826d66a6fdeeeda7cbbe260d92b09485847256343fff5863c466254bf1e0", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["target_schema", "valid_examples"]}, "id": "abstain_000485_target_schema_valid_examples", "license": "Apache-2.0", "prompt": "Write a parser that converts each mobile invoice record from batch 246070 into the correct schema, but the prompt does not include the target schema or examples. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: target_schema, valid_examples.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["target_schema", "valid_examples"]}, "verifier": {"missing": ["target_schema", "valid_examples"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 10.5 kg and a = 12.5 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 131.25, \"unit\": \"N\"}", "dedupe_signature": "c6d0941eff1fdbd406757004e1479fc13f1a4ac586187bd0d16be6fb588f1bd3", "difficulty": "easy", "final_answer": {"answer": 131.25, "unit": "N"}, "id": "force_000486_10.5_12.5", "license": "Apache-2.0", "prompt": "A cart has mass 10.5 kg and measured acceleration 12.5 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 10.5 kg and a = 12.5 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 12.5, "mass": 10.5}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 5.65^2 and multiply by 0.5 * 27.4.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 437.3383, \"unit\": \"J\"}", "dedupe_signature": "48cd929fb62a594e879402b434ecbafb54e637008ee54e1c2a48f8d803df95e3", "difficulty": "easy", "final_answer": {"answer": 437.3383, "unit": "J"}, "id": "ke_000487_27.4_5.65", "license": "Apache-2.0", "prompt": "A body of mass 27.4 kg moves at 5.65 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 5.65^2 and multiply by 0.5 * 27.4.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 27.4, "velocity": 5.65}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=39 degrees through the sine of 2 theta.\n3. Substitute v=24.7 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 60.8316, \"unit\": \"m\"}", "dedupe_signature": "7cf5f995c4cb82ee704f4d078ea366c6c0b2cead67704e36858282be12ae9af7", "difficulty": "medium", "final_answer": {"answer": 60.8316, "unit": "m"}, "id": "projectile_range_000488_24.7_39", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 24.7 m/s and angle 39 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=39 degrees through the sine of 2 theta.\nSubstitute v=24.7 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 39, "gravity": 9.81, "speed": 24.7}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 1.16 * 8.314 * 585 / 38.3.\nFinal: {\"answer\": 147.3076, \"unit\": \"kPa\"}", "dedupe_signature": "35d78e93daf106e87955b4e9d405d95a1424971d81ba593d9c2597f0cbb5e849", "difficulty": "medium", "final_answer": {"answer": 147.3076, "unit": "kPa"}, "id": "ideal_gas_000489_1.16_585_38.3", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=1.16 mol, T=585 K, and V=38.3 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 1.16 * 8.314 * 585 / 38.3.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 1.16, "temp_k": 585, "volume_l": 38.3}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 380 * 4.035 * 91.\nFinal: {\"answer\": 139530.3, \"unit\": \"J\"}", "dedupe_signature": "c50683cd2d481ed8182a6de3499c5f58385c4265d43a73a0f7c1ce1e124dfffa", "difficulty": "easy", "final_answer": {"answer": 139530.3, "unit": "J"}, "id": "heat_q_000490_380_4.035_91", "license": "Apache-2.0", "prompt": "A 380 g sample has specific heat 4.035 J/(g*K). How much heat is needed to raise its temperature by 91 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 380 * 4.035 * 91.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 91, "heat_capacity": 4.035, "mass_g": 380}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=66.8 V and R=95.8 ohm.\nFinal: {\"answer\": 46.5787, \"unit\": \"W\"}", "dedupe_signature": "aa33d4a90cc189c3486f9aa2f8db7f366281545bdda3c27f5bb81bc8d63c0d09", "difficulty": "easy", "final_answer": {"answer": 46.5787, "unit": "W"}, "id": "ohm_power_000491_66.8_95.8", "license": "Apache-2.0", "prompt": "A resistor has resistance 95.8 ohm and voltage 66.8 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=66.8 V and R=95.8 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 95.8, "voltage": 66.8}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=680.5 mg, t=46 h, and T_half=30.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 239.23, \"unit\": \"mg\"}", "dedupe_signature": "0be578df1a391431e8d3eecbeeda976a43e8e571cc4ff6e8de28cef1e3f81a36", "difficulty": "medium", "final_answer": {"answer": 239.23, "unit": "mg"}, "id": "half_life_000492_680.5_30.5_46", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 680.5 mg. Its half-life is 30.5 hours. How many mg remain after 46 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=680.5 mg, t=46 h, and T_half=30.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 46.0, "half_life": 30.5, "initial_amount": 680.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 7.56 mol * 58.44 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 441.8064, \"unit\": \"g\"}", "dedupe_signature": "ead39fe3893c8fe417e21efbe107ffcf71f18682fef16487812a9512e802a0ed", "difficulty": "medium", "final_answer": {"answer": 441.8064, "unit": "g"}, "id": "stoich_mass_000493_sodium_chloride_7.56", "license": "Apache-2.0", "prompt": "A sample contains 7.56 mol of sodium chloride. Using molar mass 58.44 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 7.56 mol * 58.44 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "sodium chloride", "molar_mass": 58.44, "moles": 7.56}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 4610 mL to 4.61 L.\n3. Compute M = 3.805 / 4.61.\nFinal: {\"answer\": 0.8254, \"unit\": \"mol/L\"}", "dedupe_signature": "1cd8c6a714753a69a013a1d3eb64eea319525d3192aaff8471b90ac08a8b48ae", "difficulty": "medium", "final_answer": {"answer": 0.8254, "unit": "mol/L"}, "id": "molarity_000494_3.805_4610", "license": "Apache-2.0", "prompt": "A solution contains 3.805 mol of solute in 4610 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 4610 mL to 4.61 L.\nCompute M = 3.805 / 4.61.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 3.805, "volume_ml": 4610}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.41 y, so each step multiplies y by 1 - h*0.41.\n3. Apply that update for 12 steps and round the final state.\nFinal: {\"answer\": 18.3283, \"unit\": \"state_units\"}", "dedupe_signature": "19d03d7cc4dd54da5c52c5c9986d44829420b9aee981114ac348c14b1c8c9422", "difficulty": "medium", "final_answer": {"answer": 18.3283, "unit": "state_units"}, "id": "euler_decay_000495_23.5_0.41_0.05_12", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.41 y with y(0)=23.5, step size h=0.05, for 12 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.41 y, so each step multiplies y by 1 - h*0.41.\nApply that update for 12 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 23.5, "rate": 0.41, "step": 0.05, "steps": 12}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.38 and add it to the current value.\nFinal: {\"answer\": [-0.182, 0.406, 0.647], \"unit\": \"temperature_units\"}", "dedupe_signature": "04bb2c0259557e1412c7b8553149eaac4fa3e5819a150d689af54795117d0382", "difficulty": "hard", "final_answer": {"answer": [-0.182, 0.406, 0.647], "unit": "temperature_units"}, "id": "heat_step_000497_0.38_-0.3_1.3_-1.0_0.4_2.45", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-0.3, right=2.45; current interior values are [1.3, -1.0, 0.4]. Use r=0.38. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.38 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [1.3, -1.0, 0.4], "left": -0.3, "r": 0.38, "right": 2.45}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kelvin equals Celsius plus 273.15.\n2. Apply the conversion factor directly to the given value.\n3. Compute 242.0 + 273.15.\nFinal: {\"answer\": 515.15, \"unit\": \"K\"}", "dedupe_signature": "0150439ef7e812640a0a61a605accbf4404a4aafe898ee8a387013a3c98bc0dd", "difficulty": "easy", "final_answer": {"answer": 515.15, "unit": "K"}, "id": "unit_convert_000498_c_to_k_242", "license": "Apache-2.0", "prompt": "Convert 242 degC to K. Return the converted value with unit.", "reasoning_trace": "Kelvin equals Celsius plus 273.15.\nApply the conversion factor directly to the given value.\nCompute 242.0 + 273.15.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 242.0}, "verifier": {"formula": "value + 273.15", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=114 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-110.0223, 247.114], \"unit\": \"N\"}", "dedupe_signature": "0c8dd8533c9c01f9fe1941b92c3b7a5a567e321c1252e450898e9cd9570ec7f7", "difficulty": "medium", "final_answer": {"answer": [-110.0223, 247.114], "unit": "N"}, "id": "vector_components_000499_270.5_114", "license": "Apache-2.0", "prompt": "A vector has magnitude 270.5 N at 114 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=114 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 114, "magnitude": 270.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [6.3, -27.0], \"unit\": \"dimensionless\"}", "dedupe_signature": "c13d49ade55198975d5f8bc80f02a24cd2d7230568b4c933bb5af423e2851d48", "difficulty": "medium", "final_answer": {"answer": [6.3, -27.0], "unit": "dimensionless"}, "id": "line_two_point_000500_10.75_25.75_6.3_-27", "license": "Apache-2.0", "prompt": "A line passes through points (10.75, 40.725) and (25.75, 135.225). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 10.75, "x2": 25.75, "y1": 40.724999999999994, "y2": 135.225}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. lever arm times force has torque dimensions\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "9a23677e5c9abca2dec47f69d62eeb838366971e449761784fff475b5bc5a253", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_000501_consistent_5ca82cb9_183617", "license": "Apache-2.0", "prompt": "In simulation spec case 183617, check dimensional consistency for tau = r * F. The left side has dimensions N*m and the right side has dimensions N*m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nlever arm times force has torque dimensions\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "tau = r * F"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef weighted_sum_000502(values, weights):\n    if len(values) != len(weights):\n        raise ValueError('length mismatch')\n    return sum(value * weight for value, weight in zip(values, weights))\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"weighted_sum_000502\"}", "dedupe_signature": "8d78fc10517a2fb6cf49db9faa24796badae00585c334454c90f1f35173cac0c", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "weighted_sum_000502"}, "id": "code_000502_weighted_sum_000502", "license": "Apache-2.0", "prompt": "Write a Python function weighted_sum_000502(values, weights) that returns sum(value*weight). Raise ValueError when the two inputs have different lengths. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "weighted_sum_000502"}, "verifier": {"function": "weighted_sum_000502", "tests": ["assert weighted_sum_000502([2, 3], [4, 5]) == 23", "assert weighted_sum_000502([], []) == 0", "try:\n    weighted_sum_000502([1], [1, 2])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: volume.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"volume\"]}", "dedupe_signature": "a1f998784de762fde49882e04307083e67d952dce72a99b4f8a878cf6cae5220", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["volume"]}, "id": "abstain_000503_volume", "license": "Apache-2.0", "prompt": "Compute pressure from the ideal gas law. The prompt gives n=1.39 mol and T=562 K, but does not give volume. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: volume.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["volume"]}, "verifier": {"missing": ["volume"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=27 degrees through the sine of 2 theta.\n3. Substitute v=51.1 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 215.3428, \"unit\": \"m\"}", "dedupe_signature": "fb7c529ec5766d19ab7523e0ab2ea6e3eefbed929a0275285fa10be9a9931391", "difficulty": "medium", "final_answer": {"answer": 215.3428, "unit": "m"}, "id": "projectile_range_000506_51.1_27", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 51.1 m/s and angle 27 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=27 degrees through the sine of 2 theta.\nSubstitute v=51.1 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 27, "gravity": 9.81, "speed": 51.1}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 3.71 * 8.314 * 440 / 76.9.\nFinal: {\"answer\": 176.486, \"unit\": \"kPa\"}", "dedupe_signature": "5cc21befbc2aed8ecff5f9044e38e811d4e16261b0cb85cfabf4c1d053a6bd67", "difficulty": "medium", "final_answer": {"answer": 176.486, "unit": "kPa"}, "id": "ideal_gas_000507_3.71_440_76.9", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=3.71 mol, T=440 K, and V=76.9 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 3.71 * 8.314 * 440 / 76.9.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 3.71, "temp_k": 440, "volume_l": 76.9}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=15.8 V and R=190.8 ohm.\nFinal: {\"answer\": 1.3084, \"unit\": \"W\"}", "dedupe_signature": "1c79b3ece874279d6f0bbf7f7ebb6d929961b24814071523604bc8d95301fe65", "difficulty": "easy", "final_answer": {"answer": 1.3084, "unit": "W"}, "id": "ohm_power_000509_15.8_190.8", "license": "Apache-2.0", "prompt": "A resistor has resistance 190.8 ohm and voltage 15.8 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=15.8 V and R=190.8 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 190.8, "voltage": 15.8}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 1.46 mol * 180.156 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 263.0278, \"unit\": \"g\"}", "dedupe_signature": "c7198cafb551ef4c72e35d6bb5b397cb1183a28da296c46343a741ed261f64f4", "difficulty": "medium", "final_answer": {"answer": 263.0278, "unit": "g"}, "id": "stoich_mass_000511_glucose_1.46", "license": "Apache-2.0", "prompt": "A sample contains 1.46 mol of glucose. Using molar mass 180.156 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 1.46 mol * 180.156 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "glucose", "molar_mass": 180.156, "moles": 1.46}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 2235 mL to 2.235 L.\n3. Compute M = 0.605 / 2.235.\nFinal: {\"answer\": 0.2707, \"unit\": \"mol/L\"}", "dedupe_signature": "0c2c571818cf9ee28f50539a94841bc9dfeabe366676b5b92f5798b8277c367d", "difficulty": "medium", "final_answer": {"answer": 0.2707, "unit": "mol/L"}, "id": "molarity_000512_0.605_2235", "license": "Apache-2.0", "prompt": "A solution contains 0.605 mol of solute in 2235 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 2235 mL to 2.235 L.\nCompute M = 0.605 / 2.235.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 0.605, "volume_ml": 2235}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.19 y, so each step multiplies y by 1 - h*0.19.\n3. Apply that update for 5 steps and round the final state.\nFinal: {\"answer\": 52.8725, \"unit\": \"state_units\"}", "dedupe_signature": "99bc270b4e648532aae3d9e4fffea7253107d6f1d20e0082a5cca3fddcc37761", "difficulty": "medium", "final_answer": {"answer": 52.8725, "unit": "state_units"}, "id": "euler_decay_000513_78.5_0.19_0.4_5", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.19 y with y(0)=78.5, step size h=0.4, for 5 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.19 y, so each step multiplies y by 1 - h*0.19.\nApply that update for 5 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 78.5, "rate": 0.19, "step": 0.4, "steps": 5}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 36983.0 / 1000.\nFinal: {\"answer\": 36.983, \"unit\": \"kg\"}", "dedupe_signature": "e3c1597014a24aaf7e89edbdbc5ba79aa729cd43387c9d1334bdde703138c5d0", "difficulty": "easy", "final_answer": {"answer": 36.983, "unit": "kg"}, "id": "unit_convert_000516_g_to_kg_36983", "license": "Apache-2.0", "prompt": "Convert 36983 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 36983.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 36983.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-9.3, -18.0], \"unit\": \"dimensionless\"}", "dedupe_signature": "ad120b588110b657332ed7e22eb9677da59ff2119c32b5031c2455bef89cf7ef", "difficulty": "medium", "final_answer": {"answer": [-9.3, -18.0], "unit": "dimensionless"}, "id": "line_two_point_000518_-15_-4_-9.3_-18", "license": "Apache-2.0", "prompt": "A line passes through points (-15, 121.5) and (-4, 19.2). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -15.0, "x2": -4.0, "y1": 121.5, "y2": 19.200000000000003}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. m*v is momentum, not energy\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "75b723455c81a656c4d8cff0c1a0f5bb0c75b157178b616aef6e1e14a1cb6010", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_000519_inconsistent_1e14b074_585139", "license": "Apache-2.0", "prompt": "In model card equation case 585139, check dimensional consistency for E = m * v. The left side has dimensions kg*m^2/s^2 and the right side has dimensions kg*m/s. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nm*v is momentum, not energy\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "E = m * v"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef center_values_000520(values):\n    if not values:\n        raise ValueError('center_values requires at least one value')\n    mean = sum(values) / len(values)\n    return [value - mean for value in values]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"center_values_000520\"}", "dedupe_signature": "3e8dfb2ee9cf03d81a7835a316ccbd9a372bb2dea4e77367c85d4eda6af2d4e3", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "center_values_000520"}, "id": "code_000520_center_values_000520", "license": "Apache-2.0", "prompt": "Write a Python function center_values_000520(values) that subtracts the arithmetic mean from each value and returns a new list. Raise ValueError for an empty input. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "center_values_000520"}, "verifier": {"function": "center_values_000520", "tests": ["out = center_values_000520([1, 2, 3]); assert out == [-1, 0, 1]", "assert center_values_000520([5]) == [0]", "try:\n    center_values_000520([])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: volume.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"volume\"]}", "dedupe_signature": "b038285b080a002cfac5e0f75757682617fd9946d668caa5da47ab79351bfba2", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["volume"]}, "id": "abstain_000521_volume", "license": "Apache-2.0", "prompt": "Compute pressure from the ideal gas law. The prompt gives n=4.06 mol and T=594 K, but does not give volume. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: volume.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["volume"]}, "verifier": {"missing": ["volume"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 23.65 kg and a = 14.7 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 347.655, \"unit\": \"N\"}", "dedupe_signature": "dd75fdcc6d6f1f38b9b1933aa57c0382a80ee509262357e9ec6c6486a90c52f2", "difficulty": "easy", "final_answer": {"answer": 347.655, "unit": "N"}, "id": "force_000522_23.65_14.7", "license": "Apache-2.0", "prompt": "A cart has mass 23.65 kg and measured acceleration 14.7 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 23.65 kg and a = 14.7 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 14.7, "mass": 23.65}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=17 degrees through the sine of 2 theta.\n3. Substitute v=20.6 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 24.1895, \"unit\": \"m\"}", "dedupe_signature": "3e94f1da9c0cbba8d2c6289367c60871095dc6bd58bef1adc68ff54626692d46", "difficulty": "medium", "final_answer": {"answer": 24.1895, "unit": "m"}, "id": "projectile_range_000524_20.6_17", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 20.6 m/s and angle 17 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=17 degrees through the sine of 2 theta.\nSubstitute v=20.6 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 17, "gravity": 9.81, "speed": 20.6}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 3.71 * 8.314 * 327 / 72.8.\nFinal: {\"answer\": 138.548, \"unit\": \"kPa\"}", "dedupe_signature": "dc399b2f79003ab6d42702aad0859eaa4b7ab964944b2d41f47ba40cad7aeddf", "difficulty": "medium", "final_answer": {"answer": 138.548, "unit": "kPa"}, "id": "ideal_gas_000525_3.71_327_72.8", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=3.71 mol, T=327 K, and V=72.8 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 3.71 * 8.314 * 327 / 72.8.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 3.71, "temp_k": 327, "volume_l": 72.8}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1765 * 2.22 * 20.\nFinal: {\"answer\": 78366.0, \"unit\": \"J\"}", "dedupe_signature": "afc803e0913fd594130e16f1a22939b87107e8a74a77f336949ee078e02613fa", "difficulty": "easy", "final_answer": {"answer": 78366.0, "unit": "J"}, "id": "heat_q_000526_1765_2.22_20", "license": "Apache-2.0", "prompt": "A 1765 g sample has specific heat 2.22 J/(g*K). How much heat is needed to raise its temperature by 20 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1765 * 2.22 * 20.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 20, "heat_capacity": 2.22, "mass_g": 1765}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=109 V and R=128.1 ohm.\nFinal: {\"answer\": 92.7479, \"unit\": \"W\"}", "dedupe_signature": "708b3fe70cbff0f773a32495beb415363756c4a12e68e113edbc367da8cdbfe3", "difficulty": "easy", "final_answer": {"answer": 92.7479, "unit": "W"}, "id": "ohm_power_000527_109_128.1", "license": "Apache-2.0", "prompt": "A resistor has resistance 128.1 ohm and voltage 109 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=109 V and R=128.1 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 128.1, "voltage": 109.0}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 4.35 mol * 180.156 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 783.6786, \"unit\": \"g\"}", "dedupe_signature": "cd0025b63aad6a1f52743d494a71d1c40f515ddb493986382c778c21f897c70a", "difficulty": "medium", "final_answer": {"answer": 783.6786, "unit": "g"}, "id": "stoich_mass_000529_glucose_4.35", "license": "Apache-2.0", "prompt": "A sample contains 4.35 mol of glucose. Using molar mass 180.156 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 4.35 mol * 180.156 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "glucose", "molar_mass": 180.156, "moles": 4.35}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 1220 mL to 1.22 L.\n3. Compute M = 2.53 / 1.22.\nFinal: {\"answer\": 2.0738, \"unit\": \"mol/L\"}", "dedupe_signature": "20d10eb71c38fb33ad95ac1813d879a92891451f24d54683abed5b6afaa2420a", "difficulty": "medium", "final_answer": {"answer": 2.0738, "unit": "mol/L"}, "id": "molarity_000530_2.53_1220", "license": "Apache-2.0", "prompt": "A solution contains 2.53 mol of solute in 1220 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 1220 mL to 1.22 L.\nCompute M = 2.53 / 1.22.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 2.53, "volume_ml": 1220}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.41 y, so each step multiplies y by 1 - h*0.41.\n3. Apply that update for 8 steps and round the final state.\nFinal: {\"answer\": 3.1073, \"unit\": \"state_units\"}", "dedupe_signature": "b393ac6798a6c1155d765b441fe815f5a2c1cbd05734e6d1df6462017e43156e", "difficulty": "medium", "final_answer": {"answer": 3.1073, "unit": "state_units"}, "id": "euler_decay_000531_24_0.41_0.55_8", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.41 y with y(0)=24, step size h=0.55, for 8 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.41 y, so each step multiplies y by 1 - h*0.41.\nApply that update for 8 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 24.0, "rate": 0.41, "step": 0.55, "steps": 8}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-6.1)=6.55 and f(3.1)=-7.25.\n3. The interval width is 9.2.\nFinal: {\"answer\": -3.22, \"unit\": \"area_units\"}", "dedupe_signature": "5660bce8bf30ac33f1db67a3d6d0f7d565dea985963a080203895aba2dac2e42", "difficulty": "medium", "final_answer": {"answer": -3.22, "unit": "area_units"}, "id": "trapz_linear_000532_-1.5_-2.6_-6.1_3.1", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-1.5x+-2.6 from x=-6.1 to x=3.1. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-6.1)=6.55 and f(3.1)=-7.25.\nThe interval width is 9.2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -2.6, "slope": -1.5, "x0": -6.1, "x1": 3.0999999999999996}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kelvin equals Celsius plus 273.15.\n2. Apply the conversion factor directly to the given value.\n3. Compute 191.5 + 273.15.\nFinal: {\"answer\": 464.65, \"unit\": \"K\"}", "dedupe_signature": "b0df9116d29819a09c8c49ccc41539f7bb0ccf0235da187f00f8a910d6fbec49", "difficulty": "easy", "final_answer": {"answer": 464.65, "unit": "K"}, "id": "unit_convert_000534_c_to_k_191.5", "license": "Apache-2.0", "prompt": "Convert 191.5 degC to K. Return the converted value with unit.", "reasoning_trace": "Kelvin equals Celsius plus 273.15.\nApply the conversion factor directly to the given value.\nCompute 191.5 + 273.15.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 191.5}, "verifier": {"formula": "value + 273.15", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=326 degrees and keep the unit as newtons.\nFinal: {\"answer\": [39.3793, -26.5617], \"unit\": \"N\"}", "dedupe_signature": "122289347c1a38685e0cbe45ef0fbaa8dc34a3edcf20d8ec1857afa35a73ee01", "difficulty": "medium", "final_answer": {"answer": [39.3793, -26.5617], "unit": "N"}, "id": "vector_components_000535_47.5_326", "license": "Apache-2.0", "prompt": "A vector has magnitude 47.5 N at 326 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=326 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 326, "magnitude": 47.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [5.85, -2.25], \"unit\": \"dimensionless\"}", "dedupe_signature": "da07120a2e853c39e4417cc21c29f86622434766a880cde69f678633b7d67c71", "difficulty": "medium", "final_answer": {"answer": [5.85, -2.25], "unit": "dimensionless"}, "id": "line_two_point_000536_-1.75_4.25_5.85_-2.25", "license": "Apache-2.0", "prompt": "A line passes through points (-1.75, -12.4875) and (4.25, 22.6125). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -1.75, "x2": 4.25, "y1": -12.487499999999999, "y2": 22.612499999999997}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. coulomb per second is ampere\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "a0e3ccf8ac75dbe2eb4371882f33c9322117f8ba12f087917da9da86040856cb", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_000537_consistent_8b38953d_821933", "license": "Apache-2.0", "prompt": "In sensor calibration case 821933, check dimensional consistency for I = Q / t. The left side has dimensions A and the right side has dimensions A. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\ncoulomb per second is ampere\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "I = Q / t"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: launch_angle_or_vertical_velocity.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"launch_angle_or_vertical_velocity\"]}", "dedupe_signature": "06c079e0e5abb8acdd0cd37e6743b2309633ca48b2dd1d508cad979a89993a38", "difficulty": "easy", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["launch_angle_or_vertical_velocity"]}, "id": "abstain_000539_launch_angle_or_vertical_velocity", "license": "Apache-2.0", "prompt": "Compute projectile range on level ground. The prompt gives initial speed 71.6 m/s but does not give launch angle or vertical velocity. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: launch_angle_or_vertical_velocity.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["launch_angle_or_vertical_velocity"]}, "verifier": {"missing": ["launch_angle_or_vertical_velocity"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 4.75 kg and a = 13.7 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 65.075, \"unit\": \"N\"}", "dedupe_signature": "2ed98616159139fd88912e74c918c339e1067a3d5d0a135bac09f60333ae2883", "difficulty": "easy", "final_answer": {"answer": 65.075, "unit": "N"}, "id": "force_000540_4.75_13.7", "license": "Apache-2.0", "prompt": "A cart has mass 4.75 kg and measured acceleration 13.7 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 4.75 kg and a = 13.7 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 13.7, "mass": 4.75}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 30.9^2 and multiply by 0.5 * 8.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 3819.24, \"unit\": \"J\"}", "dedupe_signature": "5f9da37f22e012994d3ae8a6193215a0b14a8dde0197a8616265e4d8ca9ce2fb", "difficulty": "easy", "final_answer": {"answer": 3819.24, "unit": "J"}, "id": "ke_000541_8_30.9", "license": "Apache-2.0", "prompt": "A body of mass 8 kg moves at 30.9 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 30.9^2 and multiply by 0.5 * 8.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 8.0, "velocity": 30.9}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=79 degrees through the sine of 2 theta.\n3. Substitute v=70.8 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 191.4137, \"unit\": \"m\"}", "dedupe_signature": "ce73b4b3588af71a13fd77731e4767d8b69d212946ff7b555b6dff4e2bb89f7c", "difficulty": "medium", "final_answer": {"answer": 191.4137, "unit": "m"}, "id": "projectile_range_000542_70.8_79", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 70.8 m/s and angle 79 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=79 degrees through the sine of 2 theta.\nSubstitute v=70.8 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 79, "gravity": 9.81, "speed": 70.8}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1025 * 4.785 * 63.\nFinal: {\"answer\": 308991.375, \"unit\": \"J\"}", "dedupe_signature": "f706baabf6ff35fab68f5c41197f895287fce4a647af6bc03f7369d058e63d67", "difficulty": "easy", "final_answer": {"answer": 308991.375, "unit": "J"}, "id": "heat_q_000544_1025_4.785_63", "license": "Apache-2.0", "prompt": "A 1025 g sample has specific heat 4.785 J/(g*K). How much heat is needed to raise its temperature by 63 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1025 * 4.785 * 63.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 63, "heat_capacity": 4.785, "mass_g": 1025}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=289 mg, t=238.5 h, and T_half=30 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 1.1687, \"unit\": \"mg\"}", "dedupe_signature": "c5b531eba8b6de5063145b4b6f5b8cfc1a22e42aa044ed5fc25032237b459184", "difficulty": "medium", "final_answer": {"answer": 1.1687, "unit": "mg"}, "id": "half_life_000546_289_30_238.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 289 mg. Its half-life is 30 hours. How many mg remain after 238.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=289 mg, t=238.5 h, and T_half=30 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 238.5, "half_life": 30.0, "initial_amount": 289.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 3545 mL to 3.545 L.\n3. Compute M = 1.35 / 3.545.\nFinal: {\"answer\": 0.3808, \"unit\": \"mol/L\"}", "dedupe_signature": "a10462d72d3b188163b00197b5520baf0a9def954c3b5bafb2ba0a386a2989ce", "difficulty": "medium", "final_answer": {"answer": 0.3808, "unit": "mol/L"}, "id": "molarity_000548_1.35_3545", "license": "Apache-2.0", "prompt": "A solution contains 1.35 mol of solute in 3545 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 3545 mL to 3.545 L.\nCompute M = 1.35 / 3.545.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 1.35, "volume_ml": 3545}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.14 y, so each step multiplies y by 1 - h*0.14.\n3. Apply that update for 11 steps and round the final state.\nFinal: {\"answer\": 2.6963, \"unit\": \"state_units\"}", "dedupe_signature": "9a240a509ccfaf14d9a68dc33201b7317b513682b82f450cba3d6a901ca3d2f7", "difficulty": "medium", "final_answer": {"answer": 2.6963, "unit": "state_units"}, "id": "euler_decay_000549_15.5_0.14_1.05_11", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.14 y with y(0)=15.5, step size h=1.05, for 11 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.14 y, so each step multiplies y by 1 - h*0.14.\nApply that update for 11 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 15.5, "rate": 0.14, "step": 1.05, "steps": 11}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(1.3)=-1.49 and f(7.3)=8.71.\n3. The interval width is 6.\nFinal: {\"answer\": 21.66, \"unit\": \"area_units\"}", "dedupe_signature": "8cfb4d72e8f5b31e50e9b16e257691ec31bbf6826fe9bd8f2dab74bb69576e17", "difficulty": "medium", "final_answer": {"answer": 21.66, "unit": "area_units"}, "id": "trapz_linear_000550_1.7_-3.7_1.3_7.3", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=1.7x+-3.7 from x=1.3 to x=7.3. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(1.3)=-1.49 and f(7.3)=8.71.\nThe interval width is 6.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -3.7, "slope": 1.7, "x0": 1.3, "x1": 7.3}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.34 and add it to the current value.\nFinal: {\"answer\": [1.079, 1.137, 1.335], \"unit\": \"temperature_units\"}", "dedupe_signature": "baddd05e9f16c55e3b2aa84eb9478306df8f95c9557624c82b46f36e84051d52", "difficulty": "hard", "final_answer": {"answer": [1.079, 1.137, 1.335], "unit": "temperature_units"}, "id": "heat_step_000551_0.34_0.1_0.45_2.65_0.4_0.9", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=0.1, right=0.9; current interior values are [0.45, 2.65, 0.4]. Use r=0.34. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.34 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [0.45, 2.65, 0.4], "left": 0.1, "r": 0.34, "right": 0.9}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kelvin equals Celsius plus 273.15.\n2. Apply the conversion factor directly to the given value.\n3. Compute -42.5 + 273.15.\nFinal: {\"answer\": 230.65, \"unit\": \"K\"}", "dedupe_signature": "498c098e56f1e99fa750a59a50dacf86a0b075897e0eb9ca6e4229aa597b25b0", "difficulty": "easy", "final_answer": {"answer": 230.65, "unit": "K"}, "id": "unit_convert_000552_c_to_k_-42.5", "license": "Apache-2.0", "prompt": "Convert -42.5 degC to K. Return the converted value with unit.", "reasoning_trace": "Kelvin equals Celsius plus 273.15.\nApply the conversion factor directly to the given value.\nCompute -42.5 + 273.15.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": -42.5}, "verifier": {"formula": "value + 273.15", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=258 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-17.9844, -84.6098], \"unit\": \"N\"}", "dedupe_signature": "28adfad38e8fb0de3eb51e03d4ba38db73c73c3897994d2ee594213d54851c4a", "difficulty": "medium", "final_answer": {"answer": [-17.9844, -84.6098], "unit": "N"}, "id": "vector_components_000553_86.5_258", "license": "Apache-2.0", "prompt": "A vector has magnitude 86.5 N at 258 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=258 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 258, "magnitude": 86.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [4.65, 10.25], \"unit\": \"dimensionless\"}", "dedupe_signature": "f398fc101de4b57e10d68b6fdd96278511b435831d5f82308ada16bf6a9fbb25", "difficulty": "medium", "final_answer": {"answer": [4.65, 10.25], "unit": "dimensionless"}, "id": "line_two_point_000554_18.75_27.75_4.65_10.25", "license": "Apache-2.0", "prompt": "A line passes through points (18.75, 97.4375) and (27.75, 139.288). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 18.75, "x2": 27.75, "y1": 97.4375, "y2": 139.28750000000002}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. amount times volume is not concentration\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "c28daae63b8dbe9607283ba8ee3a119db41f04d53029d960ebaf30843051c0e9", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_000555_inconsistent_74ac0b02_15775", "license": "Apache-2.0", "prompt": "In student derivation case 15775, check dimensional consistency for C = n * V. The left side has dimensions mol/L and the right side has dimensions mol*L. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\namount times volume is not concentration\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "C = n * V"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: rate_constant, number_of_steps.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"rate_constant\", \"number_of_steps\"]}", "dedupe_signature": "a4c70b67afad2ed3246ed1203ea5d250cef111795de0c26f38559995dfcdbd76", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["rate_constant", "number_of_steps"]}, "id": "abstain_000557_rate_constant_number_of_steps", "license": "Apache-2.0", "prompt": "Use explicit Euler for dy/dt = -k y. The prompt gives y(0)=37 and h=0.15, but omits both k and the number of steps. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: rate_constant, number_of_steps.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["rate_constant", "number_of_steps"]}, "verifier": {"missing": ["rate_constant", "number_of_steps"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 8.8 kg and a = 13.45 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 118.36, \"unit\": \"N\"}", "dedupe_signature": "7057f5927041770eaa77c34a152789c678af9c45ec7fed6a6daf5380104d56a7", "difficulty": "easy", "final_answer": {"answer": 118.36, "unit": "N"}, "id": "force_000558_8.8_13.45", "license": "Apache-2.0", "prompt": "A cart has mass 8.8 kg and measured acceleration 13.45 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 8.8 kg and a = 13.45 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 13.45, "mass": 8.8}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 6.15^2 and multiply by 0.5 * 21.25.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 401.8641, \"unit\": \"J\"}", "dedupe_signature": "2f757c4ed080f47d9e391e6c6168212fcfa409a6aa1074fb4d518128a524bd19", "difficulty": "easy", "final_answer": {"answer": 401.8641, "unit": "J"}, "id": "ke_000559_21.25_6.15", "license": "Apache-2.0", "prompt": "A body of mass 21.25 kg moves at 6.15 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 6.15^2 and multiply by 0.5 * 21.25.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 21.25, "velocity": 6.15}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=75 degrees through the sine of 2 theta.\n3. Substitute v=60.5 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 186.5571, \"unit\": \"m\"}", "dedupe_signature": "36f8245691073d94e82e85fdba87767ea584d1e9a8cb035afa0e23a84074d5b6", "difficulty": "medium", "final_answer": {"answer": 186.5571, "unit": "m"}, "id": "projectile_range_000560_60.5_75", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 60.5 m/s and angle 75 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=75 degrees through the sine of 2 theta.\nSubstitute v=60.5 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 75, "gravity": 9.81, "speed": 60.5}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 1.45 * 8.314 * 485 / 20.7.\nFinal: {\"answer\": 282.4551, \"unit\": \"kPa\"}", "dedupe_signature": "3fe8dfb367c1b75f171d8498d33977131c3eedec7393cb8a3bdb730376f93dc1", "difficulty": "medium", "final_answer": {"answer": 282.4551, "unit": "kPa"}, "id": "ideal_gas_000561_1.45_485_20.7", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=1.45 mol, T=485 K, and V=20.7 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 1.45 * 8.314 * 485 / 20.7.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 1.45, "temp_k": 485, "volume_l": 20.7}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=207.9 V and R=98.3 ohm.\nFinal: {\"answer\": 439.699, \"unit\": \"W\"}", "dedupe_signature": "4f34d2e0ccae0d80209350394e25ede4c17ddd913c93f0dc46cfc7218946912c", "difficulty": "easy", "final_answer": {"answer": 439.699, "unit": "W"}, "id": "ohm_power_000563_207.9_98.3", "license": "Apache-2.0", "prompt": "A resistor has resistance 98.3 ohm and voltage 207.9 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=207.9 V and R=98.3 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 98.3, "voltage": 207.9}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=981 mg, t=19.5 h, and T_half=34.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 663.0124, \"unit\": \"mg\"}", "dedupe_signature": "b66f6aa551cad09d178764e487cf2abdd6abc100f2289533df8c00da6911103c", "difficulty": "medium", "final_answer": {"answer": 663.0124, "unit": "mg"}, "id": "half_life_000564_981_34.5_19.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 981 mg. Its half-life is 34.5 hours. How many mg remain after 19.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=981 mg, t=19.5 h, and T_half=34.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 19.5, "half_life": 34.5, "initial_amount": 981.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 1470 mL to 1.47 L.\n3. Compute M = 3.2 / 1.47.\nFinal: {\"answer\": 2.1769, \"unit\": \"mol/L\"}", "dedupe_signature": "759a4c08ae9e0b163cee78afbcc47fd34a9e38f275c2562b4081be57e15fac2b", "difficulty": "medium", "final_answer": {"answer": 2.1769, "unit": "mol/L"}, "id": "molarity_000566_3.2_1470", "license": "Apache-2.0", "prompt": "A solution contains 3.2 mol of solute in 1470 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 1470 mL to 1.47 L.\nCompute M = 3.2 / 1.47.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 3.2, "volume_ml": 1470}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.58 y, so each step multiplies y by 1 - h*0.58.\n3. Apply that update for 12 steps and round the final state.\nFinal: {\"answer\": 0.0002, \"unit\": \"state_units\"}", "dedupe_signature": "cb33aac231933ddefc15221900836381ce61eeae57d1d86f10306747102afb48", "difficulty": "medium", "final_answer": {"answer": 0.0002, "unit": "state_units"}, "id": "euler_decay_000567_6.5_0.58_1_12", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.58 y with y(0)=6.5, step size h=1, for 12 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.58 y, so each step multiplies y by 1 - h*0.58.\nApply that update for 12 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 6.5, "rate": 0.58, "step": 1.0, "steps": 12}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-2.5)=-13.8 and f(4)=-13.8.\n3. The interval width is 6.5.\nFinal: {\"answer\": -89.7, \"unit\": \"area_units\"}", "dedupe_signature": "bed2b5c334a62cb5015e39afcccf511eae1f2e17f55306b94799c870f2af4545", "difficulty": "medium", "final_answer": {"answer": -89.7, "unit": "area_units"}, "id": "trapz_linear_000568_0_-13.8_-2.5_4", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=0x+-13.8 from x=-2.5 to x=4. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-2.5)=-13.8 and f(4)=-13.8.\nThe interval width is 6.5.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -13.8, "slope": 0.0, "x0": -2.5, "x1": 4.0}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.3 and add it to the current value.\nFinal: {\"answer\": [1.075, 0.595, 0.055], \"unit\": \"temperature_units\"}", "dedupe_signature": "68c4960834ddc2b5a5a052545a7f93ec6ce2929c9a84dd4c4bb0835c6632755a", "difficulty": "hard", "final_answer": {"answer": [1.075, 0.595, 0.055], "unit": "temperature_units"}, "id": "heat_step_000569_0.3_1.9_0.85_0.55_0.4_-0.9", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.9, right=-0.9; current interior values are [0.85, 0.55, 0.4]. Use r=0.3. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.3 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [0.85, 0.55, 0.4], "left": 1.9, "r": 0.3, "right": -0.9}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 45429.0 / 1000.\nFinal: {\"answer\": 45.429, \"unit\": \"kg\"}", "dedupe_signature": "3319c7f09c02cc9d029999b903dc524cc997514c02284f7ef429e17382365599", "difficulty": "easy", "final_answer": {"answer": 45.429, "unit": "kg"}, "id": "unit_convert_000570_g_to_kg_45429", "license": "Apache-2.0", "prompt": "Convert 45429 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 45429.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 45429.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=221 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-339.9967, -295.5546], \"unit\": \"N\"}", "dedupe_signature": "d4ea3f2fb6fafee935af751dd4f6743398a1e7a488b85df761af9dda9663dca4", "difficulty": "medium", "final_answer": {"answer": [-339.9967, -295.5546], "unit": "N"}, "id": "vector_components_000571_450.5_221", "license": "Apache-2.0", "prompt": "A vector has magnitude 450.5 N at 221 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=221 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 221, "magnitude": 450.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-1.6, 21.25], \"unit\": \"dimensionless\"}", "dedupe_signature": "928342ba6868cb2258735cfaca3001f4b014b3c519cea8bf74c2540a69ca475e", "difficulty": "medium", "final_answer": {"answer": [-1.6, 21.25], "unit": "dimensionless"}, "id": "line_two_point_000572_16_16.75_-1.6_21.25", "license": "Apache-2.0", "prompt": "A line passes through points (16, -4.35) and (16.75, -5.55). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 16.0, "x2": 16.75, "y1": -4.350000000000001, "y2": -5.550000000000001}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. amount times volume is not concentration\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "00bf1ab346d73464409d18a14bf831b4938928866c4db84b0ed3126805568e04", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_000573_inconsistent_74ac0b02_406756", "license": "Apache-2.0", "prompt": "In field worksheet case 406756, check dimensional consistency for C = n * V. The left side has dimensions mol/L and the right side has dimensions mol*L. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\namount times volume is not concentration\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "C = n * V"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef weighted_sum_000574(values, weights):\n    if len(values) != len(weights):\n        raise ValueError('length mismatch')\n    return sum(value * weight for value, weight in zip(values, weights))\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"weighted_sum_000574\"}", "dedupe_signature": "926cc709b60b85eeff287de0e8849ecf589de20940cb6b6ce7c243d5961ced63", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "weighted_sum_000574"}, "id": "code_000574_weighted_sum_000574", "license": "Apache-2.0", "prompt": "Write a Python function weighted_sum_000574(values, weights) that returns sum(value*weight). Raise ValueError when the two inputs have different lengths. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "weighted_sum_000574"}, "verifier": {"function": "weighted_sum_000574", "tests": ["assert weighted_sum_000574([2, 3], [4, 5]) == 23", "assert weighted_sum_000574([], []) == 0", "try:\n    weighted_sum_000574([1], [1, 2])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: volume.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"volume\"]}", "dedupe_signature": "9af183aa6a0d55be7f6276253e9cfcb394111c5594e41ef9d3a942def516e518", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["volume"]}, "id": "abstain_000575_volume", "license": "Apache-2.0", "prompt": "Compute pressure from the ideal gas law. The prompt gives n=1.92 mol and T=251 K, but does not give volume. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: volume.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["volume"]}, "verifier": {"missing": ["volume"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 10.65 kg and a = 12.3 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 130.995, \"unit\": \"N\"}", "dedupe_signature": "b17b4d124f2037a48f6544da1bfc60a8c8e4f942fa719b36b9bbc3b73ad89910", "difficulty": "easy", "final_answer": {"answer": 130.995, "unit": "N"}, "id": "force_000576_10.65_12.3", "license": "Apache-2.0", "prompt": "A cart has mass 10.65 kg and measured acceleration 12.3 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 10.65 kg and a = 12.3 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 12.3, "mass": 10.65}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 25.3^2 and multiply by 0.5 * 8.85.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 2832.3983, \"unit\": \"J\"}", "dedupe_signature": "d9a772660bb104595f5b5e547ff038a4273f17b8481e3de5833eb1fa0562c5ed", "difficulty": "easy", "final_answer": {"answer": 2832.3983, "unit": "J"}, "id": "ke_000577_8.85_25.3", "license": "Apache-2.0", "prompt": "A body of mass 8.85 kg moves at 25.3 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 25.3^2 and multiply by 0.5 * 8.85.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 8.85, "velocity": 25.3}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=55 degrees through the sine of 2 theta.\n3. Substitute v=31.3 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 93.8438, \"unit\": \"m\"}", "dedupe_signature": "f845e6f4f14cf60c9e1eeece57e7f55d5703bd77231573b51308a9d3762ab5d8", "difficulty": "medium", "final_answer": {"answer": 93.8438, "unit": "m"}, "id": "projectile_range_000578_31.3_55", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 31.3 m/s and angle 55 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=55 degrees through the sine of 2 theta.\nSubstitute v=31.3 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 55, "gravity": 9.81, "speed": 31.3}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 0.48 * 8.314 * 597 / 46.0.\nFinal: {\"answer\": 51.7926, \"unit\": \"kPa\"}", "dedupe_signature": "2be48cf222a1d2c7e2a63f050838ebefbdb3df4f5ccf6072d06257466f069e37", "difficulty": "medium", "final_answer": {"answer": 51.7926, "unit": "kPa"}, "id": "ideal_gas_000579_0.48_597_46.0", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=0.48 mol, T=597 K, and V=46.0 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 0.48 * 8.314 * 597 / 46.0.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 0.48, "temp_k": 597, "volume_l": 46.0}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=24.9 V and R=32.3 ohm.\nFinal: {\"answer\": 19.1954, \"unit\": \"W\"}", "dedupe_signature": "d135ce9c7cd4335d6a17852f85d6b64885deff6a3cd19903fd8e06be1ac66e65", "difficulty": "easy", "final_answer": {"answer": 19.1954, "unit": "W"}, "id": "ohm_power_000581_24.9_32.3", "license": "Apache-2.0", "prompt": "A resistor has resistance 32.3 ohm and voltage 24.9 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=24.9 V and R=32.3 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 32.3, "voltage": 24.9}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 7.67 mol * 180.156 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 1381.7965, \"unit\": \"g\"}", "dedupe_signature": "37806d9d60197ba5d7f07ce3872408944481e845b40444a189f3ff8e89427bb5", "difficulty": "medium", "final_answer": {"answer": 1381.7965, "unit": "g"}, "id": "stoich_mass_000583_glucose_7.67", "license": "Apache-2.0", "prompt": "A sample contains 7.67 mol of glucose. Using molar mass 180.156 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 7.67 mol * 180.156 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "glucose", "molar_mass": 180.156, "moles": 7.67}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 3975 mL to 3.975 L.\n3. Compute M = 4.6 / 3.975.\nFinal: {\"answer\": 1.1572, \"unit\": \"mol/L\"}", "dedupe_signature": "f3085c74115d28c5cb385f552a7a1b989aa610d457e03e7e55ec067558f0ecba", "difficulty": "medium", "final_answer": {"answer": 1.1572, "unit": "mol/L"}, "id": "molarity_000584_4.6_3975", "license": "Apache-2.0", "prompt": "A solution contains 4.6 mol of solute in 3975 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 3975 mL to 3.975 L.\nCompute M = 4.6 / 3.975.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 4.6, "volume_ml": 3975}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.21 y, so each step multiplies y by 1 - h*0.21.\n3. Apply that update for 10 steps and round the final state.\nFinal: {\"answer\": 1.6676, \"unit\": \"state_units\"}", "dedupe_signature": "e1b1d2208fb6843df71d796942dbe418f0fda4a78e2152f45616239ad8fbc1d5", "difficulty": "medium", "final_answer": {"answer": 1.6676, "unit": "state_units"}, "id": "euler_decay_000585_4.5_0.21_0.45_10", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.21 y with y(0)=4.5, step size h=0.45, for 10 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.21 y, so each step multiplies y by 1 - h*0.21.\nApply that update for 10 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 4.5, "rate": 0.21, "step": 0.45, "steps": 10}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(9.3)=24.33 and f(13.7)=42.37.\n3. The interval width is 4.4.\nFinal: {\"answer\": 146.74, \"unit\": \"area_units\"}", "dedupe_signature": "3563d996898ec96bbfbf1d44db83eba7cee43e2f0a6cb9fa417faad7cc0732cc", "difficulty": "medium", "final_answer": {"answer": 146.74, "unit": "area_units"}, "id": "trapz_linear_000586_4.1_-13.8_9.3_13.7", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=4.1x+-13.8 from x=9.3 to x=13.7. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(9.3)=24.33 and f(13.7)=42.37.\nThe interval width is 4.4.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -13.8, "slope": 4.1, "x0": 9.3, "x1": 13.700000000000001}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.42 and add it to the current value.\nFinal: {\"answer\": [0.387, 0.789, 1.556], \"unit\": \"temperature_units\"}", "dedupe_signature": "485207a01bda278f90de9aa50f0c476aca23efebfaba160a42c8b02371ae2abb", "difficulty": "hard", "final_answer": {"answer": [0.387, 0.789, 1.556], "unit": "temperature_units"}, "id": "heat_step_000587_0.42_-1.3_1.5_1.65_-0.25_2.15", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-1.3, right=2.15; current interior values are [1.5, 1.65, -0.25]. Use r=0.42. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.42 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [1.5, 1.65, -0.25], "left": -1.3, "r": 0.42, "right": 2.15}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 100 centimeters in one meter.\n2. Apply the conversion factor directly to the given value.\n3. Compute 1114.0 / 100.\nFinal: {\"answer\": 11.14, \"unit\": \"m\"}", "dedupe_signature": "98913c245559ca91d9d9acfdd736cdc967b75bcf1b16d3b79214d167b9fec48c", "difficulty": "easy", "final_answer": {"answer": 11.14, "unit": "m"}, "id": "unit_convert_000588_cm_to_m_1114", "license": "Apache-2.0", "prompt": "Convert 1114 cm to m. Return the converted value with unit.", "reasoning_trace": "There are 100 centimeters in one meter.\nApply the conversion factor directly to the given value.\nCompute 1114.0 / 100.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 1114.0}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=14 degrees and keep the unit as newtons.\nFinal: {\"answer\": [374.5342, 93.3819], \"unit\": \"N\"}", "dedupe_signature": "3b59504df76bc00b9d0bf9da141b4a90ea369ea20996b9f14e9de2ca88cc87de", "difficulty": "medium", "final_answer": {"answer": [374.5342, 93.3819], "unit": "N"}, "id": "vector_components_000589_386_14", "license": "Apache-2.0", "prompt": "A vector has magnitude 386 N at 14 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=14 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 14, "magnitude": 386.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [8.9, -5.75], \"unit\": \"dimensionless\"}", "dedupe_signature": "0d53ac1a2329ffc901548f80cda1252424b365c1ff6d711303d4f3a95c2d212a", "difficulty": "medium", "final_answer": {"answer": [8.9, -5.75], "unit": "dimensionless"}, "id": "line_two_point_000590_-14_-6.75_8.9_-5.75", "license": "Apache-2.0", "prompt": "A line passes through points (-14, -130.35) and (-6.75, -65.825). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -14.0, "x2": -6.75, "y1": -130.35000000000002, "y2": -65.825}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. density times acceleration times height gives kg/(m*s^2), or pascal\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "7f3093a6cd416ef3e77e92a32ea40bcd89400eeeeb6e1c74fa7cc0b5f2e2b040", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_000591_consistent_b7d3eed1_478330", "license": "Apache-2.0", "prompt": "In field worksheet case 478330, check dimensional consistency for p = rho * g * h. The left side has dimensions Pa and the right side has dimensions Pa. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\ndensity times acceleration times height gives kg/(m*s^2), or pascal\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "p = rho * g * h"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef weighted_sum_000592(values, weights):\n    if len(values) != len(weights):\n        raise ValueError('length mismatch')\n    return sum(value * weight for value, weight in zip(values, weights))\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"weighted_sum_000592\"}", "dedupe_signature": "3cefab444ce4abc517adda48234e974fc0005038018bda40589c8d2df52505a4", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "weighted_sum_000592"}, "id": "code_000592_weighted_sum_000592", "license": "Apache-2.0", "prompt": "Write a Python function weighted_sum_000592(values, weights) that returns sum(value*weight). Raise ValueError when the two inputs have different lengths. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "weighted_sum_000592"}, "verifier": {"function": "weighted_sum_000592", "tests": ["assert weighted_sum_000592([2, 3], [4, 5]) == 23", "assert weighted_sum_000592([], []) == 0", "try:\n    weighted_sum_000592([1], [1, 2])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: required_fields, allowed_transformations.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"required_fields\", \"allowed_transformations\"]}", "dedupe_signature": "422bcdb2f0cf0ac0ffc1594261135b7e2e7e1f57925c8e202d2684e7fcc7b65e", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["required_fields", "allowed_transformations"]}, "id": "abstain_000593_required_fields_allowed_transformations", "license": "Apache-2.0", "prompt": "Write a sanitizer for valid billing survey records in release 692532, but the prompt does not state which fields are required or which transformations are allowed. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: required_fields, allowed_transformations.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["required_fields", "allowed_transformations"]}, "verifier": {"missing": ["required_fields", "allowed_transformations"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 20.45 kg and a = 3.35 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 68.5075, \"unit\": \"N\"}", "dedupe_signature": "757af32b73cf4ab1e011f0dabdc6d1520bafb7d8502f13505abaf4252c7adc2f", "difficulty": "easy", "final_answer": {"answer": 68.5075, "unit": "N"}, "id": "force_000594_20.45_3.35", "license": "Apache-2.0", "prompt": "A cart has mass 20.45 kg and measured acceleration 3.35 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 20.45 kg and a = 3.35 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 3.35, "mass": 20.45}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 41^2 and multiply by 0.5 * 10.7.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 8993.35, \"unit\": \"J\"}", "dedupe_signature": "0aabcbc082c7173016b3f705316c42a4167e6f3790a6666fc5557ea281acb25a", "difficulty": "easy", "final_answer": {"answer": 8993.35, "unit": "J"}, "id": "ke_000595_10.7_41", "license": "Apache-2.0", "prompt": "A body of mass 10.7 kg moves at 41 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 41^2 and multiply by 0.5 * 10.7.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 10.7, "velocity": 41.0}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=153.5 V and R=117.8 ohm.\nFinal: {\"answer\": 200.0191, \"unit\": \"W\"}", "dedupe_signature": "d3afe8e20d0ca29c7a3c85a78a51197f1cbc0cb6f31ac00f4003f9daf7a401f5", "difficulty": "easy", "final_answer": {"answer": 200.0191, "unit": "W"}, "id": "ohm_power_000599_153.5_117.8", "license": "Apache-2.0", "prompt": "A resistor has resistance 117.8 ohm and voltage 153.5 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=153.5 V and R=117.8 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 117.8, "voltage": 153.5}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=573 mg, t=135 h, and T_half=20 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 5.3236, \"unit\": \"mg\"}", "dedupe_signature": "d0d63adb06e8c322fcc20df82ad09955c5443e45bcf9171241d0f01f6fa584b5", "difficulty": "medium", "final_answer": {"answer": 5.3236, "unit": "mg"}, "id": "half_life_000600_573_20_135", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 573 mg. Its half-life is 20 hours. How many mg remain after 135 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=573 mg, t=135 h, and T_half=20 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 135.0, "half_life": 20.0, "initial_amount": 573.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.36 y, so each step multiplies y by 1 - h*0.36.\n3. Apply that update for 10 steps and round the final state.\nFinal: {\"answer\": 23.247, \"unit\": \"state_units\"}", "dedupe_signature": "8cc4b8045a75f6496b9635f4525bf49c018912faaaa56b9632509baec77ae25d", "difficulty": "medium", "final_answer": {"answer": 23.247, "unit": "state_units"}, "id": "euler_decay_000603_40.5_0.36_0.15_10", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.36 y with y(0)=40.5, step size h=0.15, for 10 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.36 y, so each step multiplies y by 1 - h*0.36.\nApply that update for 10 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 40.5, "rate": 0.36, "step": 0.15, "steps": 10}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(9.2)=7.96 and f(10.4)=8.32.\n3. The interval width is 1.2.\nFinal: {\"answer\": 9.768, \"unit\": \"area_units\"}", "dedupe_signature": "ff2327fd5d9cdbb5d4cd74a3f7e71b1214a65d289ba7adcc807732a1b52442c4", "difficulty": "medium", "final_answer": {"answer": 9.768, "unit": "area_units"}, "id": "trapz_linear_000604_0.3_5.2_9.2_10.4", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=0.3x+5.2 from x=9.2 to x=10.4. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(9.2)=7.96 and f(10.4)=8.32.\nThe interval width is 1.2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 5.2, "slope": 0.3, "x0": 9.2, "x1": 10.399999999999999}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.22 and add it to the current value.\nFinal: {\"answer\": [1.565, 1.53, -0.039], \"unit\": \"temperature_units\"}", "dedupe_signature": "2fbc15ed697b61cc8d0ab598ff9806f540ac4047e736a45e390b7f4430984970", "difficulty": "hard", "final_answer": {"answer": [1.565, 1.53, -0.039], "unit": "temperature_units"}, "id": "heat_step_000605_0.22_2.1_0.85_2.85_-1.15_-0.1", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=2.1, right=-0.1; current interior values are [0.85, 2.85, -1.15]. Use r=0.22. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.22 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [0.85, 2.85, -1.15], "left": 2.1, "r": 0.22, "right": -0.1}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 46123.0 / 1000.\nFinal: {\"answer\": 46.123, \"unit\": \"kg\"}", "dedupe_signature": "5a33246ad26e2667d51a13470bb34a885e45eeb70cef7f186312cbd10850413f", "difficulty": "easy", "final_answer": {"answer": 46.123, "unit": "kg"}, "id": "unit_convert_000606_g_to_kg_46123", "license": "Apache-2.0", "prompt": "Convert 46123 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 46123.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 46123.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=342 degrees and keep the unit as newtons.\nFinal: {\"answer\": [132.6724, -43.1079], \"unit\": \"N\"}", "dedupe_signature": "627c5d0931e74a9c460a7579c551efe3394e51478ac736a614f17f8f51300d09", "difficulty": "medium", "final_answer": {"answer": [132.6724, -43.1079], "unit": "N"}, "id": "vector_components_000607_139.5_342", "license": "Apache-2.0", "prompt": "A vector has magnitude 139.5 N at 342 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=342 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 342, "magnitude": 139.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-7.15, -17.25], \"unit\": \"dimensionless\"}", "dedupe_signature": "ad05216a238d400921b5c800d8064ef9740a1e15383b1a2d22e65934cf4dd99f", "difficulty": "medium", "final_answer": {"answer": [-7.15, -17.25], "unit": "dimensionless"}, "id": "line_two_point_000608_14.75_25.75_-7.15_-17.25", "license": "Apache-2.0", "prompt": "A line passes through points (14.75, -122.713) and (25.75, -201.363). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 14.75, "x2": 25.75, "y1": -122.7125, "y2": -201.3625}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. m*v is momentum, not energy\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "55747f11915ad2097d75e7fa994bc5402ba0507f8f82d4614827fa1379649f7e", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_000609_inconsistent_1e14b074_902761", "license": "Apache-2.0", "prompt": "In model card equation case 902761, check dimensional consistency for E = m * v. The left side has dimensions kg*m^2/s^2 and the right side has dimensions kg*m/s. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nm*v is momentum, not energy\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "E = m * v"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: volume.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"volume\"]}", "dedupe_signature": "f45e21cb63da828ec07f2e366905afa4f62db4de4ffd26e9ef232d58341c139f", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["volume"]}, "id": "abstain_000611_volume", "license": "Apache-2.0", "prompt": "Compute pressure from the ideal gas law. The prompt gives n=3.19 mol and T=309 K, but does not give volume. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: volume.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["volume"]}, "verifier": {"missing": ["volume"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 0.8 kg and a = 5.65 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 4.52, \"unit\": \"N\"}", "dedupe_signature": "ad50aaf57389c84f6eecbf64730bdc9b09ba7cb9a8094277a571218089ad2d7c", "difficulty": "easy", "final_answer": {"answer": 4.52, "unit": "N"}, "id": "force_000612_0.8_5.65", "license": "Apache-2.0", "prompt": "A cart has mass 0.8 kg and measured acceleration 5.65 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 0.8 kg and a = 5.65 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 5.65, "mass": 0.8}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 35.3^2 and multiply by 0.5 * 1.85.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 1152.6332, \"unit\": \"J\"}", "dedupe_signature": "4c92fffc2a1c765aca3f634b2a842439cc24381e43d0d5af86909957903397c7", "difficulty": "easy", "final_answer": {"answer": 1152.6332, "unit": "J"}, "id": "ke_000613_1.85_35.3", "license": "Apache-2.0", "prompt": "A body of mass 1.85 kg moves at 35.3 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 35.3^2 and multiply by 0.5 * 1.85.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 1.85, "velocity": 35.3}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=79 degrees through the sine of 2 theta.\n3. Substitute v=58.4 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 130.2363, \"unit\": \"m\"}", "dedupe_signature": "326881e7afbd328f6c33e2690a2c09e3bd7a0ea5fbf38ca848eaa95aa93249bc", "difficulty": "medium", "final_answer": {"answer": 130.2363, "unit": "m"}, "id": "projectile_range_000614_58.4_79", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 58.4 m/s and angle 79 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=79 degrees through the sine of 2 theta.\nSubstitute v=58.4 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 79, "gravity": 9.81, "speed": 58.4}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 2.43 * 8.314 * 330 / 52.8.\nFinal: {\"answer\": 126.2689, \"unit\": \"kPa\"}", "dedupe_signature": "b935c8e6c711372072882b2d6251246e80c1ccfd704ea386801e7c7f9b525055", "difficulty": "medium", "final_answer": {"answer": 126.2689, "unit": "kPa"}, "id": "ideal_gas_000615_2.43_330_52.8", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=2.43 mol, T=330 K, and V=52.8 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 2.43 * 8.314 * 330 / 52.8.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 2.43, "temp_k": 330, "volume_l": 52.8}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 820 * 3.23 * 91.\nFinal: {\"answer\": 241022.6, \"unit\": \"J\"}", "dedupe_signature": "89b325aad1d609c37ac66639ba9ce996d35bf578447f76b8e31ed0c532a37158", "difficulty": "easy", "final_answer": {"answer": 241022.6, "unit": "J"}, "id": "heat_q_000616_820_3.23_91", "license": "Apache-2.0", "prompt": "A 820 g sample has specific heat 3.23 J/(g*K). How much heat is needed to raise its temperature by 91 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 820 * 3.23 * 91.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 91, "heat_capacity": 3.23, "mass_g": 820}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=93.2 V and R=160.6 ohm.\nFinal: {\"answer\": 54.0862, \"unit\": \"W\"}", "dedupe_signature": "e7799c667796d70699bf62f1b4676c842b7dd453ecdad16fb257a7e40a700ff9", "difficulty": "easy", "final_answer": {"answer": 54.0862, "unit": "W"}, "id": "ohm_power_000617_93.2_160.6", "license": "Apache-2.0", "prompt": "A resistor has resistance 160.6 ohm and voltage 93.2 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=93.2 V and R=160.6 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 160.6, "voltage": 93.2}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=469.5 mg, t=279 h, and T_half=24 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 0.1486, \"unit\": \"mg\"}", "dedupe_signature": "560d811f1d274803566bc7e9e4c86f3bb6181f5fa42931faf64507782f589b6e", "difficulty": "medium", "final_answer": {"answer": 0.1486, "unit": "mg"}, "id": "half_life_000618_469.5_24_279", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 469.5 mg. Its half-life is 24 hours. How many mg remain after 279 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=469.5 mg, t=279 h, and T_half=24 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 279.0, "half_life": 24.0, "initial_amount": 469.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 6.38 mol * 18.015 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 114.9357, \"unit\": \"g\"}", "dedupe_signature": "bf2b83f8d2635a4c96258cc1438dc72ffd50e0b516fdfd1913d24a3b6c8cc983", "difficulty": "medium", "final_answer": {"answer": 114.9357, "unit": "g"}, "id": "stoich_mass_000619_water_6.38", "license": "Apache-2.0", "prompt": "A sample contains 6.38 mol of water. Using molar mass 18.015 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 6.38 mol * 18.015 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "water", "molar_mass": 18.015, "moles": 6.38}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 4775 mL to 4.775 L.\n3. Compute M = 4.15 / 4.775.\nFinal: {\"answer\": 0.8691, \"unit\": \"mol/L\"}", "dedupe_signature": "701adc386d09e3682865985e370ea51af9fdb666f67dcc040fef12b1ac92cbfd", "difficulty": "medium", "final_answer": {"answer": 0.8691, "unit": "mol/L"}, "id": "molarity_000620_4.15_4775", "license": "Apache-2.0", "prompt": "A solution contains 4.15 mol of solute in 4775 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 4775 mL to 4.775 L.\nCompute M = 4.15 / 4.775.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 4.15, "volume_ml": 4775}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.58 y, so each step multiplies y by 1 - h*0.58.\n3. Apply that update for 3 steps and round the final state.\nFinal: {\"answer\": 5.4333, \"unit\": \"state_units\"}", "dedupe_signature": "60e8e778c5005d6bca3a7878d50da29d28c7de3c13d726ff6639e25584a13d6a", "difficulty": "medium", "final_answer": {"answer": 5.4333, "unit": "state_units"}, "id": "euler_decay_000621_6.5_0.58_0.1_3", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.58 y with y(0)=6.5, step size h=0.1, for 3 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.58 y, so each step multiplies y by 1 - h*0.58.\nApply that update for 3 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 6.5, "rate": 0.58, "step": 0.1, "steps": 3}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(8.6)=18 and f(16.1)=29.25.\n3. The interval width is 7.5.\nFinal: {\"answer\": 177.1875, \"unit\": \"area_units\"}", "dedupe_signature": "eca0d37bf9afc6d63241faec7c7d992a3a0737d43a7c98e7071e722ad5109ef8", "difficulty": "medium", "final_answer": {"answer": 177.1875, "unit": "area_units"}, "id": "trapz_linear_000622_1.5_5.1_8.6_16.1", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=1.5x+5.1 from x=8.6 to x=16.1. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(8.6)=18 and f(16.1)=29.25.\nThe interval width is 7.5.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 5.1, "slope": 1.5, "x0": 8.6, "x1": 16.1}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.1 and add it to the current value.\nFinal: {\"answer\": [-1.34, 0.71, -0.885], \"unit\": \"temperature_units\"}", "dedupe_signature": "f8d7adbef8d6387f63eaff88bd09928d7baff8c6932037625a7ebcbb3344e39b", "difficulty": "hard", "final_answer": {"answer": [-1.34, 0.71, -0.885], "unit": "temperature_units"}, "id": "heat_step_000623_0.1_0.1_-1.85_1.3_-1.45_1.45", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=0.1, right=1.45; current interior values are [-1.85, 1.3, -1.45]. Use r=0.1. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.1 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-1.85, 1.3, -1.45], "left": 0.1, "r": 0.1, "right": 1.45}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=254 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-4.8237, -16.8221], \"unit\": \"N\"}", "dedupe_signature": "761d3163a985fc09b959912f23350d6151bb1f9893629390bd0274254b5bd710", "difficulty": "medium", "final_answer": {"answer": [-4.8237, -16.8221], "unit": "N"}, "id": "vector_components_000625_17.5_254", "license": "Apache-2.0", "prompt": "A vector has magnitude 17.5 N at 254 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=254 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 254, "magnitude": 17.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef safe_mean_000628(values):\n    if not values:\n        raise ValueError('safe_mean requires at least one value')\n    return sum(values) / len(values)\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"safe_mean_000628\"}", "dedupe_signature": "ca59e6948232aee66db40826534aaed05116bf59b39f4e6667c5e411ea0cc7ad", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "safe_mean_000628"}, "id": "code_000628_safe_mean_000628", "license": "Apache-2.0", "prompt": "Write a Python function safe_mean_000628(values) that returns the arithmetic mean. It must raise ValueError for an empty input and must not mutate the input list. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "safe_mean_000628"}, "verifier": {"function": "safe_mean_000628", "tests": ["assert safe_mean_000628([2, 4, 6]) == 4", "xs = [1, 2, 3]; assert safe_mean_000628(xs) == 2 and xs == [1, 2, 3]", "try:\n    safe_mean_000628([])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 13.65 kg and a = 7.95 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 108.5175, \"unit\": \"N\"}", "dedupe_signature": "5ab24ec1b7e0b7e63d53e6a229dabe5a172097c0dd2921a58856026dd1f5bd8c", "difficulty": "easy", "final_answer": {"answer": 108.5175, "unit": "N"}, "id": "force_000630_13.65_7.95", "license": "Apache-2.0", "prompt": "A cart has mass 13.65 kg and measured acceleration 7.95 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 13.65 kg and a = 7.95 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 7.95, "mass": 13.65}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 5.35^2 and multiply by 0.5 * 15.7.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 224.6866, \"unit\": \"J\"}", "dedupe_signature": "6a2442af5d1fc54857320f916b28ab595d0b51bddb1682546859d31858694661", "difficulty": "easy", "final_answer": {"answer": 224.6866, "unit": "J"}, "id": "ke_000631_15.7_5.35", "license": "Apache-2.0", "prompt": "A body of mass 15.7 kg moves at 5.35 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 5.35^2 and multiply by 0.5 * 15.7.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 15.7, "velocity": 5.35}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=35 degrees through the sine of 2 theta.\n3. Substitute v=67 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 429.998, \"unit\": \"m\"}", "dedupe_signature": "419640ea3cda1e7e835e93df52b40bb003c0e6fe4b44bcb3ca984bf868cd264e", "difficulty": "medium", "final_answer": {"answer": 429.998, "unit": "m"}, "id": "projectile_range_000632_67_35", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 67 m/s and angle 35 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=35 degrees through the sine of 2 theta.\nSubstitute v=67 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 35, "gravity": 9.81, "speed": 67.0}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 0.9 * 8.314 * 584 / 39.5.\nFinal: {\"answer\": 110.6288, \"unit\": \"kPa\"}", "dedupe_signature": "253d7844d50932824556a0cd937c29f0d8664672e6c35679172d545066e6b8b5", "difficulty": "medium", "final_answer": {"answer": 110.6288, "unit": "kPa"}, "id": "ideal_gas_000633_0.9_584_39.5", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=0.9 mol, T=584 K, and V=39.5 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 0.9 * 8.314 * 584 / 39.5.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 0.9, "temp_k": 584, "volume_l": 39.5}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1850 * 3.585 * 71.\nFinal: {\"answer\": 470889.75, \"unit\": \"J\"}", "dedupe_signature": "0864118cfbc312c8434b0e676713fdb40e4e9f6b3eabc7655b76dc65729bdf8e", "difficulty": "easy", "final_answer": {"answer": 470889.75, "unit": "J"}, "id": "heat_q_000634_1850_3.585_71", "license": "Apache-2.0", "prompt": "A 1850 g sample has specific heat 3.585 J/(g*K). How much heat is needed to raise its temperature by 71 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1850 * 3.585 * 71.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 71, "heat_capacity": 3.585, "mass_g": 1850}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=234.9 V and R=29 ohm.\nFinal: {\"answer\": 1902.69, \"unit\": \"W\"}", "dedupe_signature": "f15a5f7be6861ebb9fc3ff2cb98439454481b3337958b39b6031a770d382136a", "difficulty": "easy", "final_answer": {"answer": 1902.69, "unit": "W"}, "id": "ohm_power_000635_234.9_29", "license": "Apache-2.0", "prompt": "A resistor has resistance 29 ohm and voltage 234.9 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=234.9 V and R=29 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 29.0, "voltage": 234.9}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=913 mg, t=183 h, and T_half=16.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 0.4186, \"unit\": \"mg\"}", "dedupe_signature": "a76da6db6f11679231bdd905c19d8818b9be2b9575299e698b092ffc55856855", "difficulty": "medium", "final_answer": {"answer": 0.4186, "unit": "mg"}, "id": "half_life_000636_913_16.5_183", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 913 mg. Its half-life is 16.5 hours. How many mg remain after 183 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=913 mg, t=183 h, and T_half=16.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 183.0, "half_life": 16.5, "initial_amount": 913.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 7.46 mol * 44.01 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 328.3146, \"unit\": \"g\"}", "dedupe_signature": "86973ef9e083f8d21a74cd005c1983da78e16e4138a9eb17f78bc2c7c1f126f1", "difficulty": "medium", "final_answer": {"answer": 328.3146, "unit": "g"}, "id": "stoich_mass_000637_carbon_dioxide_7.46", "license": "Apache-2.0", "prompt": "A sample contains 7.46 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 7.46 mol * 44.01 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "carbon dioxide", "molar_mass": 44.01, "moles": 7.46}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 1885 mL to 1.885 L.\n3. Compute M = 2.54 / 1.885.\nFinal: {\"answer\": 1.3475, \"unit\": \"mol/L\"}", "dedupe_signature": "e6c8735fdc191098aaf2e3ed226025d955c5d7cdec855bf253f5e90f280ee2cd", "difficulty": "medium", "final_answer": {"answer": 1.3475, "unit": "mol/L"}, "id": "molarity_000638_2.54_1885", "license": "Apache-2.0", "prompt": "A solution contains 2.54 mol of solute in 1885 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 1885 mL to 1.885 L.\nCompute M = 2.54 / 1.885.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 2.54, "volume_ml": 1885}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.13 y, so each step multiplies y by 1 - h*0.13.\n3. Apply that update for 7 steps and round the final state.\nFinal: {\"answer\": 7.7194, \"unit\": \"state_units\"}", "dedupe_signature": "9cdb325dba10fbbde11c1a940df2694cb17023f844fe4bf963e0bf748a868e03", "difficulty": "medium", "final_answer": {"answer": 7.7194, "unit": "state_units"}, "id": "euler_decay_000639_31.5_0.13_1.4_7", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.13 y with y(0)=31.5, step size h=1.4, for 7 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.13 y, so each step multiplies y by 1 - h*0.13.\nApply that update for 7 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 31.5, "rate": 0.13, "step": 1.4, "steps": 7}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.34 and add it to the current value.\nFinal: {\"answer\": [0.172, 1.044, 0.354], \"unit\": \"temperature_units\"}", "dedupe_signature": "02e88cc9ee586627ec51eaa19fedb655a1b680ba171fe1bb54a9becd2fb09c28", "difficulty": "hard", "final_answer": {"answer": [0.172, 1.044, 0.354], "unit": "temperature_units"}, "id": "heat_step_000641_0.34_0.1_-0.1_0.5_2.7_-2.0", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=0.1, right=-2; current interior values are [-0.1, 0.5, 2.7]. Use r=0.34. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.34 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-0.1, 0.5, 2.7], "left": 0.1, "r": 0.34, "right": -2.0}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 100 centimeters in one meter.\n2. Apply the conversion factor directly to the given value.\n3. Compute 1296.5 / 100.\nFinal: {\"answer\": 12.965, \"unit\": \"m\"}", "dedupe_signature": "a9535d9e638999432e4e724e6e796a319c5e244105da01f9c1e92351a3433603", "difficulty": "easy", "final_answer": {"answer": 12.965, "unit": "m"}, "id": "unit_convert_000642_cm_to_m_1296.5", "license": "Apache-2.0", "prompt": "Convert 1296.5 cm to m. Return the converted value with unit.", "reasoning_trace": "There are 100 centimeters in one meter.\nApply the conversion factor directly to the given value.\nCompute 1296.5 / 100.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 1296.5}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=355 degrees and keep the unit as newtons.\nFinal: {\"answer\": [264.9878, -23.1834], \"unit\": \"N\"}", "dedupe_signature": "4b748e084b5cc27ea50de7154a93889f289f38f6c8bd2de103225c336323acd4", "difficulty": "medium", "final_answer": {"answer": [264.9878, -23.1834], "unit": "N"}, "id": "vector_components_000643_266_355", "license": "Apache-2.0", "prompt": "A vector has magnitude 266 N at 355 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=355 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 355, "magnitude": 266.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [8.75, -7.25], \"unit\": \"dimensionless\"}", "dedupe_signature": "ed267dd34f4fee226c4c6bd75ce27e1252a9d55f8a0e2e756ffb66199b787cf0", "difficulty": "medium", "final_answer": {"answer": [8.75, -7.25], "unit": "dimensionless"}, "id": "line_two_point_000644_-14.25_-3.75_8.75_-7.25", "license": "Apache-2.0", "prompt": "A line passes through points (-14.25, -131.938) and (-3.75, -40.0625). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -14.25, "x2": -3.75, "y1": -131.9375, "y2": -40.0625}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. grams cancel with J/(g*K), and kelvin cancels, leaving joules\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "c604116100736f97c8bb6a489d09b8836bf38c79ca5694c4b26312a96a593769", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_000645_consistent_4153435f_572039", "license": "Apache-2.0", "prompt": "In model card equation case 572039, check dimensional consistency for Q = m * c * DeltaT. The left side has dimensions J and the right side has dimensions J. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\ngrams cancel with J/(g*K), and kelvin cancels, leaving joules\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "Q = m * c * DeltaT"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef center_values_000646(values):\n    if not values:\n        raise ValueError('center_values requires at least one value')\n    mean = sum(values) / len(values)\n    return [value - mean for value in values]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"center_values_000646\"}", "dedupe_signature": "346978e7abcd760a4115455d15365c20100b2585a475c86223383ce09041815e", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "center_values_000646"}, "id": "code_000646_center_values_000646", "license": "Apache-2.0", "prompt": "Write a Python function center_values_000646(values) that subtracts the arithmetic mean from each value and returns a new list. Raise ValueError for an empty input. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "center_values_000646"}, "verifier": {"function": "center_values_000646", "tests": ["out = center_values_000646([1, 2, 3]); assert out == [-1, 0, 1]", "assert center_values_000646([5]) == [0]", "try:\n    center_values_000646([])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 31.1^2 and multiply by 0.5 * 19.2.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 9285.216, \"unit\": \"J\"}", "dedupe_signature": "d42ee6f7506b33fc067edbb43569f9e66de90aa227e877c5959661662e29d603", "difficulty": "easy", "final_answer": {"answer": 9285.216, "unit": "J"}, "id": "ke_000649_19.2_31.1", "license": "Apache-2.0", "prompt": "A body of mass 19.2 kg moves at 31.1 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 31.1^2 and multiply by 0.5 * 19.2.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 19.2, "velocity": 31.1}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=59 degrees through the sine of 2 theta.\n3. Substitute v=21.6 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 41.9927, \"unit\": \"m\"}", "dedupe_signature": "83826adb93f5ab041cbe63f68ffb68be4a95be6d128f44447fa7f30d4b725d1e", "difficulty": "medium", "final_answer": {"answer": 41.9927, "unit": "m"}, "id": "projectile_range_000650_21.6_59", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 21.6 m/s and angle 59 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=59 degrees through the sine of 2 theta.\nSubstitute v=21.6 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 59, "gravity": 9.81, "speed": 21.6}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 5.63 * 8.314 * 277 / 15.3.\nFinal: {\"answer\": 847.4357, \"unit\": \"kPa\"}", "dedupe_signature": "0a6a675660178841eb3b12703a8f87948ae38c693ff322b40634571bee59077d", "difficulty": "medium", "final_answer": {"answer": 847.4357, "unit": "kPa"}, "id": "ideal_gas_000651_5.63_277_15.3", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=5.63 mol, T=277 K, and V=15.3 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 5.63 * 8.314 * 277 / 15.3.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 5.63, "temp_k": 277, "volume_l": 15.3}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1755 * 1.69 * 11.\nFinal: {\"answer\": 32625.45, \"unit\": \"J\"}", "dedupe_signature": "db1bbec57da86b795095855f8b07ce1c27d3fc8dc9c2c7df4806a823b6eb5ff8", "difficulty": "easy", "final_answer": {"answer": 32625.45, "unit": "J"}, "id": "heat_q_000652_1755_1.69_11", "license": "Apache-2.0", "prompt": "A 1755 g sample has specific heat 1.69 J/(g*K). How much heat is needed to raise its temperature by 11 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1755 * 1.69 * 11.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 11, "heat_capacity": 1.69, "mass_g": 1755}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=120.9 V and R=188.2 ohm.\nFinal: {\"answer\": 77.6664, \"unit\": \"W\"}", "dedupe_signature": "3536dc1f22ea580bed28fd93b8052d8e1b11e435c8a4e3941f5a1af466c873a4", "difficulty": "easy", "final_answer": {"answer": 77.6664, "unit": "W"}, "id": "ohm_power_000653_120.9_188.2", "license": "Apache-2.0", "prompt": "A resistor has resistance 188.2 ohm and voltage 120.9 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=120.9 V and R=188.2 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 188.2, "voltage": 120.9}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 7.61 mol * 100.087 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 761.6621, \"unit\": \"g\"}", "dedupe_signature": "21c6a4f6832618ba427c185210f8db88c0588cd184259ace6c9ff8258657f91e", "difficulty": "medium", "final_answer": {"answer": 761.6621, "unit": "g"}, "id": "stoich_mass_000655_calcium_carbonate_7.61", "license": "Apache-2.0", "prompt": "A sample contains 7.61 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 7.61 mol * 100.087 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "calcium carbonate", "molar_mass": 100.087, "moles": 7.61}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 3490 mL to 3.49 L.\n3. Compute M = 3.84 / 3.49.\nFinal: {\"answer\": 1.1003, \"unit\": \"mol/L\"}", "dedupe_signature": "f0cd0c4739d9b1f07ac87189ac49f92af2fc3a09bc508efa59674cb90473b78e", "difficulty": "medium", "final_answer": {"answer": 1.1003, "unit": "mol/L"}, "id": "molarity_000656_3.84_3490", "license": "Apache-2.0", "prompt": "A solution contains 3.84 mol of solute in 3490 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 3490 mL to 3.49 L.\nCompute M = 3.84 / 3.49.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 3.84, "volume_ml": 3490}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-6.3)=5.91 and f(-3.9)=4.23.\n3. The interval width is 2.4.\nFinal: {\"answer\": 12.168, \"unit\": \"area_units\"}", "dedupe_signature": "097af686d146486f5e55fee95450b2c5c14bf7a7a5839343a8cae157c49e60ed", "difficulty": "medium", "final_answer": {"answer": 12.168, "unit": "area_units"}, "id": "trapz_linear_000658_-0.7_1.5_-6.3_-3.9", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-0.7x+1.5 from x=-6.3 to x=-3.9. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-6.3)=5.91 and f(-3.9)=4.23.\nThe interval width is 2.4.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 1.5, "slope": -0.7, "x0": -6.3, "x1": -3.9}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.42 and add it to the current value.\nFinal: {\"answer\": [0.719, 0.763, 0.767], \"unit\": \"temperature_units\"}", "dedupe_signature": "282d6f5b29ace81755226d69b059e357227b6f75ec8726a79f453efb04e64ecf", "difficulty": "hard", "final_answer": {"answer": [0.719, 0.763, 0.767], "unit": "temperature_units"}, "id": "heat_step_000659_0.42_-0.8_2.0_1.75_-0.85_0.4", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-0.8, right=0.4; current interior values are [2.0, 1.75, -0.85]. Use r=0.42. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.42 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [2.0, 1.75, -0.85], "left": -0.8, "r": 0.42, "right": 0.4}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 28676.0 / 1000.\nFinal: {\"answer\": 28.676, \"unit\": \"kg\"}", "dedupe_signature": "bf5d711b5398ebf4bd864f57ac6fbcc58559f3a4a8ac470a79f934709b41dea3", "difficulty": "easy", "final_answer": {"answer": 28.676, "unit": "kg"}, "id": "unit_convert_000660_g_to_kg_28676", "license": "Apache-2.0", "prompt": "Convert 28676 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 28676.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 28676.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=92 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-4.2752, 122.4254], \"unit\": \"N\"}", "dedupe_signature": "e5e6cf00b7cce8bd116d91a99be6e00a7f15e39e047dcecfb598d54f7af5099a", "difficulty": "medium", "final_answer": {"answer": [-4.2752, 122.4254], "unit": "N"}, "id": "vector_components_000661_122.5_92", "license": "Apache-2.0", "prompt": "A vector has magnitude 122.5 N at 92 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=92 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 92, "magnitude": 122.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-3.4, -28.25], \"unit\": \"dimensionless\"}", "dedupe_signature": "23b0a7c5ad00abd13a000bf4990d5128cb8c01937eb7aadaa13199dc280abd1e", "difficulty": "medium", "final_answer": {"answer": [-3.4, -28.25], "unit": "dimensionless"}, "id": "line_two_point_000662_-5.75_5_-3.4_-28.25", "license": "Apache-2.0", "prompt": "A line passes through points (-5.75, -8.7) and (5, -45.25). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -5.75, "x2": 5.0, "y1": -8.7, "y2": -45.25}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef weighted_sum_000664(values, weights):\n    if len(values) != len(weights):\n        raise ValueError('length mismatch')\n    return sum(value * weight for value, weight in zip(values, weights))\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"weighted_sum_000664\"}", "dedupe_signature": "60dc55833af085a274b71851a78ed030a9b75d1f559cb5f95f4fab0acef3c7cc", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "weighted_sum_000664"}, "id": "code_000664_weighted_sum_000664", "license": "Apache-2.0", "prompt": "Write a Python function weighted_sum_000664(values, weights) that returns sum(value*weight). Raise ValueError when the two inputs have different lengths. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "weighted_sum_000664"}, "verifier": {"function": "weighted_sum_000664", "tests": ["assert weighted_sum_000664([2, 3], [4, 5]) == 23", "assert weighted_sum_000664([], []) == 0", "try:\n    weighted_sum_000664([1], [1, 2])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: launch_angle_or_vertical_velocity.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"launch_angle_or_vertical_velocity\"]}", "dedupe_signature": "e25d48c53cdd26d731094bb97979410700fbbee5188e520a0fa805fbabe28ced", "difficulty": "easy", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["launch_angle_or_vertical_velocity"]}, "id": "abstain_000665_launch_angle_or_vertical_velocity", "license": "Apache-2.0", "prompt": "Compute projectile range on level ground. The prompt gives initial speed 77.9 m/s but does not give launch angle or vertical velocity. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: launch_angle_or_vertical_velocity.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["launch_angle_or_vertical_velocity"]}, "verifier": {"missing": ["launch_angle_or_vertical_velocity"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 14.35 kg and a = 4.45 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 63.8575, \"unit\": \"N\"}", "dedupe_signature": "e1f2839e4697c83d00aec0381456efb734cd4e5314206cc89446f4b0a1ec5ac7", "difficulty": "easy", "final_answer": {"answer": 63.8575, "unit": "N"}, "id": "force_000666_14.35_4.45", "license": "Apache-2.0", "prompt": "A cart has mass 14.35 kg and measured acceleration 4.45 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 14.35 kg and a = 4.45 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 4.45, "mass": 14.35}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 19.3^2 and multiply by 0.5 * 16.35.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 3045.1058, \"unit\": \"J\"}", "dedupe_signature": "0cd306f589e734af27219f62d5a6cfb27279fbdc13a4d725abdf11658f1da417", "difficulty": "easy", "final_answer": {"answer": 3045.1058, "unit": "J"}, "id": "ke_000667_16.35_19.3", "license": "Apache-2.0", "prompt": "A body of mass 16.35 kg moves at 19.3 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 19.3^2 and multiply by 0.5 * 16.35.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 16.35, "velocity": 19.3}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=71 degrees through the sine of 2 theta.\n3. Substitute v=7.7 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 3.721, \"unit\": \"m\"}", "dedupe_signature": "c8e0ea3e0d32b3dd7c3e4b4fe326d6eb3542c171b880ce482720218185574c92", "difficulty": "medium", "final_answer": {"answer": 3.721, "unit": "m"}, "id": "projectile_range_000668_7.7_71", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 7.7 m/s and angle 71 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=71 degrees through the sine of 2 theta.\nSubstitute v=7.7 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 71, "gravity": 9.81, "speed": 7.7}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 1.02 * 8.314 * 253 / 105.5.\nFinal: {\"answer\": 20.3366, \"unit\": \"kPa\"}", "dedupe_signature": "967c22015d94d3f943a0098ea40b4b2a49fc4ffd2e765b6fa1d9d8622dd9f533", "difficulty": "medium", "final_answer": {"answer": 20.3366, "unit": "kPa"}, "id": "ideal_gas_000669_1.02_253_105.5", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=1.02 mol, T=253 K, and V=105.5 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 1.02 * 8.314 * 253 / 105.5.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 1.02, "temp_k": 253, "volume_l": 105.5}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1240 * 1.09 * 71.\nFinal: {\"answer\": 95963.6, \"unit\": \"J\"}", "dedupe_signature": "d061aeeb871ca0c069903c6c6eb270b0e503ffbe4e814dda151bac56c41cdf00", "difficulty": "easy", "final_answer": {"answer": 95963.6, "unit": "J"}, "id": "heat_q_000670_1240_1.09_71", "license": "Apache-2.0", "prompt": "A 1240 g sample has specific heat 1.09 J/(g*K). How much heat is needed to raise its temperature by 71 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1240 * 1.09 * 71.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 71, "heat_capacity": 1.09, "mass_g": 1240}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=77 V and R=153 ohm.\nFinal: {\"answer\": 38.7516, \"unit\": \"W\"}", "dedupe_signature": "14b3ee50675b4682e4183154d63f19cd15c3e90fc4ef95626d545e147bb5c9e8", "difficulty": "easy", "final_answer": {"answer": 38.7516, "unit": "W"}, "id": "ohm_power_000671_77_153", "license": "Apache-2.0", "prompt": "A resistor has resistance 153 ohm and voltage 77 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=77 V and R=153 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 153.0, "voltage": 77.0}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=913.5 mg, t=349.5 h, and T_half=55 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 11.1635, \"unit\": \"mg\"}", "dedupe_signature": "efbb7c3c6e0a3b097e6ac41dcc450603729f31fb4ea5cc3854f5a25e9e82a397", "difficulty": "medium", "final_answer": {"answer": 11.1635, "unit": "mg"}, "id": "half_life_000672_913.5_55_349.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 913.5 mg. Its half-life is 55 hours. How many mg remain after 349.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=913.5 mg, t=349.5 h, and T_half=55 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 349.5, "half_life": 55.0, "initial_amount": 913.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 3.6 mol * 18.015 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 64.854, \"unit\": \"g\"}", "dedupe_signature": "92498d6d423f30fdb5c3b20e035d4318e865697c49835cb4b44cdba85f5835e7", "difficulty": "medium", "final_answer": {"answer": 64.854, "unit": "g"}, "id": "stoich_mass_000673_water_3.6", "license": "Apache-2.0", "prompt": "A sample contains 3.6 mol of water. Using molar mass 18.015 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 3.6 mol * 18.015 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "water", "molar_mass": 18.015, "moles": 3.6}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 400 mL to 0.4 L.\n3. Compute M = 3.705 / 0.4.\nFinal: {\"answer\": 9.2625, \"unit\": \"mol/L\"}", "dedupe_signature": "3a8307a73f0f59c9b337fb9c0cb425bba7d85cb9022c0141eb0cc49ee5285906", "difficulty": "medium", "final_answer": {"answer": 9.2625, "unit": "mol/L"}, "id": "molarity_000674_3.705_400", "license": "Apache-2.0", "prompt": "A solution contains 3.705 mol of solute in 400 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 400 mL to 0.4 L.\nCompute M = 3.705 / 0.4.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 3.705, "volume_ml": 400}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(1.5)=-19 and f(7.4)=-29.62.\n3. The interval width is 5.9.\nFinal: {\"answer\": -143.429, \"unit\": \"area_units\"}", "dedupe_signature": "42fc203d057c3772028955e864474896220f7eda0056d0af517b61cdba6c019c", "difficulty": "medium", "final_answer": {"answer": -143.429, "unit": "area_units"}, "id": "trapz_linear_000676_-1.8_-16.3_1.5_7.4", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-1.8x+-16.3 from x=1.5 to x=7.4. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(1.5)=-19 and f(7.4)=-29.62.\nThe interval width is 5.9.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -16.3, "slope": -1.8, "x0": 1.5, "x1": 7.4}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.3 and add it to the current value.\nFinal: {\"answer\": [0.695, 0.73, 0.395], \"unit\": \"temperature_units\"}", "dedupe_signature": "60ad8c6bec3f06812d0b979501413417a16a9b3a880da4c0451be0a7bf21e31d", "difficulty": "hard", "final_answer": {"answer": [0.695, 0.73, 0.395], "unit": "temperature_units"}, "id": "heat_step_000677_0.3_1.5_0.65_-0.05_1.85_-1.1", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.5, right=-1.1; current interior values are [0.65, -0.05, 1.85]. Use r=0.3. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.3 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [0.65, -0.05, 1.85], "left": 1.5, "r": 0.3, "right": -1.1}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 29889.0 / 1000.\nFinal: {\"answer\": 29.889, \"unit\": \"kg\"}", "dedupe_signature": "58051c3291148013d19fd943f5a3fbda63856fc2a4041197f92a6b9bce0bbf1d", "difficulty": "easy", "final_answer": {"answer": 29.889, "unit": "kg"}, "id": "unit_convert_000678_g_to_kg_29889", "license": "Apache-2.0", "prompt": "Convert 29889 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 29889.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 29889.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=153 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-40.9863, 20.8836], \"unit\": \"N\"}", "dedupe_signature": "094df13ec1722ea495ce77f89d0e5bd3315463b154a8bd137e4a8673934bc0f4", "difficulty": "medium", "final_answer": {"answer": [-40.9863, 20.8836], "unit": "N"}, "id": "vector_components_000679_46_153", "license": "Apache-2.0", "prompt": "A vector has magnitude 46 N at 153 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=153 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 153, "magnitude": 46.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-3.55, -7.0], \"unit\": \"dimensionless\"}", "dedupe_signature": "6be320ea0ed036923a4c06922191e54387497d6116da573e804bc6552cdcb11b", "difficulty": "medium", "final_answer": {"answer": [-3.55, -7.0], "unit": "dimensionless"}, "id": "line_two_point_000680_-15_-12.75_-3.55_-7", "license": "Apache-2.0", "prompt": "A line passes through points (-15, 46.25) and (-12.75, 38.2625). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -15.0, "x2": -12.75, "y1": 46.25, "y2": 38.262499999999996}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. density times acceleration times height gives kg/(m*s^2), or pascal\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "c54aeb8e17920694881cbf3fb4efb850dedfb2821257363050ff0e75eee270be", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_000681_consistent_b7d3eed1_684771", "license": "Apache-2.0", "prompt": "In sensor calibration case 684771, check dimensional consistency for p = rho * g * h. The left side has dimensions Pa and the right side has dimensions Pa. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\ndensity times acceleration times height gives kg/(m*s^2), or pascal\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "p = rho * g * h"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef safe_mean_000682(values):\n    if not values:\n        raise ValueError('safe_mean requires at least one value')\n    return sum(values) / len(values)\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"safe_mean_000682\"}", "dedupe_signature": "d92de027f21937b1c91f014bc011eb7592c3c840715db4b256922b847e7dcc43", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "safe_mean_000682"}, "id": "code_000682_safe_mean_000682", "license": "Apache-2.0", "prompt": "Write a Python function safe_mean_000682(values) that returns the arithmetic mean. It must raise ValueError for an empty input and must not mutate the input list. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "safe_mean_000682"}, "verifier": {"function": "safe_mean_000682", "tests": ["assert safe_mean_000682([2, 4, 6]) == 4", "xs = [1, 2, 3]; assert safe_mean_000682(xs) == 2 and xs == [1, 2, 3]", "try:\n    safe_mean_000682([])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: volume.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"volume\"]}", "dedupe_signature": "769e769e58d8b8600626e5cb451e9521b39436a5d0381f91a019eb890de4b6f9", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["volume"]}, "id": "abstain_000683_volume", "license": "Apache-2.0", "prompt": "Compute pressure from the ideal gas law. The prompt gives n=4.35 mol and T=505 K, but does not give volume. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: volume.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["volume"]}, "verifier": {"missing": ["volume"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 26.95^2 and multiply by 0.5 * 13.75.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 4993.3297, \"unit\": \"J\"}", "dedupe_signature": "9e51c6084c49649986f72ace3fd9266ec19fd51794ed24fae87ce6d230607563", "difficulty": "easy", "final_answer": {"answer": 4993.3297, "unit": "J"}, "id": "ke_000685_13.75_26.95", "license": "Apache-2.0", "prompt": "A body of mass 13.75 kg moves at 26.95 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 26.95^2 and multiply by 0.5 * 13.75.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 13.75, "velocity": 26.95}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 2.17 * 8.314 * 584 / 68.5.\nFinal: {\"answer\": 153.8126, \"unit\": \"kPa\"}", "dedupe_signature": "5c010952b6df21eb0a115bac6e7572b64f3554cafdcdeea4c30bdf719d76c2c9", "difficulty": "medium", "final_answer": {"answer": 153.8126, "unit": "kPa"}, "id": "ideal_gas_000687_2.17_584_68.5", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=2.17 mol, T=584 K, and V=68.5 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 2.17 * 8.314 * 584 / 68.5.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 2.17, "temp_k": 584, "volume_l": 68.5}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 740 * 2.175 * 48.\nFinal: {\"answer\": 77256.0, \"unit\": \"J\"}", "dedupe_signature": "53d0cc7249bcdcb77c6d5c0e1589af0719fa72891580516c84b3fabd1f59b29a", "difficulty": "easy", "final_answer": {"answer": 77256.0, "unit": "J"}, "id": "heat_q_000688_740_2.175_48", "license": "Apache-2.0", "prompt": "A 740 g sample has specific heat 2.175 J/(g*K). How much heat is needed to raise its temperature by 48 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 740 * 2.175 * 48.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 48, "heat_capacity": 2.175, "mass_g": 740}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=56.3 V and R=196.5 ohm.\nFinal: {\"answer\": 16.1307, \"unit\": \"W\"}", "dedupe_signature": "f041a046e31342df82b3417bd7ebbf5e8c3d06cf466a1dd6e0f708cc69d27ac5", "difficulty": "easy", "final_answer": {"answer": 16.1307, "unit": "W"}, "id": "ohm_power_000689_56.3_196.5", "license": "Apache-2.0", "prompt": "A resistor has resistance 196.5 ohm and voltage 56.3 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=56.3 V and R=196.5 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 196.5, "voltage": 56.3}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=65 mg, t=97 h, and T_half=21 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 2.6451, \"unit\": \"mg\"}", "dedupe_signature": "70e1c8e146718058f7724b17fadde5f931612dde4f1dc1b08b0b9e360f10dfdc", "difficulty": "medium", "final_answer": {"answer": 2.6451, "unit": "mg"}, "id": "half_life_000690_65_21_97", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 65 mg. Its half-life is 21 hours. How many mg remain after 97 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=65 mg, t=97 h, and T_half=21 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 97.0, "half_life": 21.0, "initial_amount": 65.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 2.08 mol * 100.087 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 208.181, \"unit\": \"g\"}", "dedupe_signature": "4b2ef33aaa075ecfd977c983a5614d938519a901dd0fae5ce319ca9c310a173d", "difficulty": "medium", "final_answer": {"answer": 208.181, "unit": "g"}, "id": "stoich_mass_000691_calcium_carbonate_2.08", "license": "Apache-2.0", "prompt": "A sample contains 2.08 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 2.08 mol * 100.087 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "calcium carbonate", "molar_mass": 100.087, "moles": 2.08}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 3230 mL to 3.23 L.\n3. Compute M = 4.465 / 3.23.\nFinal: {\"answer\": 1.3824, \"unit\": \"mol/L\"}", "dedupe_signature": "5021ca5a8db11a138a0e3a50e263b6a3d3e4accf8acaeb8bfc762778e2c64c92", "difficulty": "medium", "final_answer": {"answer": 1.3824, "unit": "mol/L"}, "id": "molarity_000692_4.465_3230", "license": "Apache-2.0", "prompt": "A solution contains 4.465 mol of solute in 3230 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 3230 mL to 3.23 L.\nCompute M = 4.465 / 3.23.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 4.465, "volume_ml": 3230}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.32 y, so each step multiplies y by 1 - h*0.32.\n3. Apply that update for 2 steps and round the final state.\nFinal: {\"answer\": 4.7629, \"unit\": \"state_units\"}", "dedupe_signature": "8489d76f18bbec908193cccd5ba912a0163ce55331ce177d57450289f2e9a26e", "difficulty": "medium", "final_answer": {"answer": 4.7629, "unit": "state_units"}, "id": "euler_decay_000693_20_0.32_1.6_2", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.32 y with y(0)=20, step size h=1.6, for 2 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.32 y, so each step multiplies y by 1 - h*0.32.\nApply that update for 2 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 20.0, "rate": 0.32, "step": 1.6, "steps": 2}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.16 and add it to the current value.\nFinal: {\"answer\": [1.186, -1.348, -1.664], \"unit\": \"temperature_units\"}", "dedupe_signature": "c322f03d64a2905a9bb5e282fb1a67ab9ab52a0b13fd97b3c66d6c2eda055ef4", "difficulty": "hard", "final_answer": {"answer": [1.186, -1.348, -1.664], "unit": "temperature_units"}, "id": "heat_step_000695_0.16_2.3_1.65_-1.9_-2.0_0.0", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=2.3, right=0; current interior values are [1.65, -1.9, -2.0]. Use r=0.16. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.16 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [1.65, -1.9, -2.0], "left": 2.3, "r": 0.16, "right": 0.0}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 11209.0 / 1000.\nFinal: {\"answer\": 11.209, \"unit\": \"kg\"}", "dedupe_signature": "c947abbead3ca167473ab79c3c97a549056bb128b41e131bedbeaa075af578c2", "difficulty": "easy", "final_answer": {"answer": 11.209, "unit": "kg"}, "id": "unit_convert_000696_g_to_kg_11209", "license": "Apache-2.0", "prompt": "Convert 11209 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 11209.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 11209.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=307 degrees and keep the unit as newtons.\nFinal: {\"answer\": [157.0737, -208.4439], \"unit\": \"N\"}", "dedupe_signature": "0f51a0de34c5b1351c3d89c1d0ae34f87456e9fb7e93b51ff908d9abadfed236", "difficulty": "medium", "final_answer": {"answer": [157.0737, -208.4439], "unit": "N"}, "id": "vector_components_000697_261_307", "license": "Apache-2.0", "prompt": "A vector has magnitude 261 N at 307 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=307 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 307, "magnitude": 261.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [7.65, 19.5], \"unit\": \"dimensionless\"}", "dedupe_signature": "9d9d832bb2b98c30d600adf2a1cb7000fe9d76806a4734ecd74bba1a75051688", "difficulty": "medium", "final_answer": {"answer": [7.65, 19.5], "unit": "dimensionless"}, "id": "line_two_point_000698_4_6.25_7.65_19.5", "license": "Apache-2.0", "prompt": "A line passes through points (4, 50.1) and (6.25, 67.3125). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 4.0, "x2": 6.25, "y1": 50.1, "y2": 67.3125}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. amount times volume is not concentration\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "9ea1e4f368bc0ff26e75555d302dbc9b6cba9204a5c976f1131fc2e6156f9689", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_000699_inconsistent_74ac0b02_238444", "license": "Apache-2.0", "prompt": "In sensor calibration case 238444, check dimensional consistency for C = n * V. The left side has dimensions mol/L and the right side has dimensions mol*L. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\namount times volume is not concentration\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "C = n * V"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef center_values_000700(values):\n    if not values:\n        raise ValueError('center_values requires at least one value')\n    mean = sum(values) / len(values)\n    return [value - mean for value in values]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"center_values_000700\"}", "dedupe_signature": "78b9e83e034ffb97e1f2ae38d9178e8de721d3d9da01c0cdd690b7ed66596699", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "center_values_000700"}, "id": "code_000700_center_values_000700", "license": "Apache-2.0", "prompt": "Write a Python function center_values_000700(values) that subtracts the arithmetic mean from each value and returns a new list. Raise ValueError for an empty input. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "center_values_000700"}, "verifier": {"function": "center_values_000700", "tests": ["out = center_values_000700([1, 2, 3]); assert out == [-1, 0, 1]", "assert center_values_000700([5]) == [0]", "try:\n    center_values_000700([])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: required_fields, allowed_transformations.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"required_fields\", \"allowed_transformations\"]}", "dedupe_signature": "85f65eabd2f61b92f2969146b9ca4c865b307011bf62e5230cb2c140168d040c", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["required_fields", "allowed_transformations"]}, "id": "abstain_000701_required_fields_allowed_transformations", "license": "Apache-2.0", "prompt": "Write a sanitizer for valid laboratory survey records in release 252549, but the prompt does not state which fields are required or which transformations are allowed. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: required_fields, allowed_transformations.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["required_fields", "allowed_transformations"]}, "verifier": {"missing": ["required_fields", "allowed_transformations"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 40.25^2 and multiply by 0.5 * 28.5.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 23085.8906, \"unit\": \"J\"}", "dedupe_signature": "aa1bbbba499b47ecd7616c545113f6b5ea77b96fa5ce07c44619322e5136ce37", "difficulty": "easy", "final_answer": {"answer": 23085.8906, "unit": "J"}, "id": "ke_000703_28.5_40.25", "license": "Apache-2.0", "prompt": "A body of mass 28.5 kg moves at 40.25 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 40.25^2 and multiply by 0.5 * 28.5.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 28.5, "velocity": 40.25}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=37 degrees through the sine of 2 theta.\n3. Substitute v=8.2 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 6.5887, \"unit\": \"m\"}", "dedupe_signature": "dee0df2f0afdbb2f5bc81627f415cc1b9890f564a1444a4885e40e21df9e1d9c", "difficulty": "medium", "final_answer": {"answer": 6.5887, "unit": "m"}, "id": "projectile_range_000704_8.2_37", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 8.2 m/s and angle 37 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=37 degrees through the sine of 2 theta.\nSubstitute v=8.2 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 37, "gravity": 9.81, "speed": 8.2}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 2.3 * 8.314 * 383 / 88.7.\nFinal: {\"answer\": 82.5682, \"unit\": \"kPa\"}", "dedupe_signature": "506641eaf9d7ebf481adf0078c49e39072b2d48bd8338688fd905b7f3acdf451", "difficulty": "medium", "final_answer": {"answer": 82.5682, "unit": "kPa"}, "id": "ideal_gas_000705_2.3_383_88.7", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=2.3 mol, T=383 K, and V=88.7 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 2.3 * 8.314 * 383 / 88.7.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 2.3, "temp_k": 383, "volume_l": 88.7}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1030 * 1.13 * 5.\nFinal: {\"answer\": 5819.5, \"unit\": \"J\"}", "dedupe_signature": "b8aa8fd4f4600f62c718a0ee282ea162095be2cbf1be957a604db419d611ed4f", "difficulty": "easy", "final_answer": {"answer": 5819.5, "unit": "J"}, "id": "heat_q_000706_1030_1.13_5", "license": "Apache-2.0", "prompt": "A 1030 g sample has specific heat 1.13 J/(g*K). How much heat is needed to raise its temperature by 5 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1030 * 1.13 * 5.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 5, "heat_capacity": 1.13, "mass_g": 1030}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=856 mg, t=98 h, and T_half=80.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 368.1311, \"unit\": \"mg\"}", "dedupe_signature": "830cbc6053071f61ded5d282d8ca1a77231dc28f2e4969dc3d560057b0dec9b9", "difficulty": "medium", "final_answer": {"answer": 368.1311, "unit": "mg"}, "id": "half_life_000708_856_80.5_98", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 856 mg. Its half-life is 80.5 hours. How many mg remain after 98 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=856 mg, t=98 h, and T_half=80.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 98.0, "half_life": 80.5, "initial_amount": 856.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 3.38 mol * 58.44 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 197.5272, \"unit\": \"g\"}", "dedupe_signature": "aad7bdb0dcebf955f029e3d51a2f2fa2476d36c7e949f94b6878dc1d04b58867", "difficulty": "medium", "final_answer": {"answer": 197.5272, "unit": "g"}, "id": "stoich_mass_000709_sodium_chloride_3.38", "license": "Apache-2.0", "prompt": "A sample contains 3.38 mol of sodium chloride. Using molar mass 58.44 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 3.38 mol * 58.44 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "sodium chloride", "molar_mass": 58.44, "moles": 3.38}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.54 y, so each step multiplies y by 1 - h*0.54.\n3. Apply that update for 10 steps and round the final state.\nFinal: {\"answer\": 0.0071, \"unit\": \"state_units\"}", "dedupe_signature": "19043d8817a040cd1898cb26e1308bf1301f7f6481fcc367d746919b22227f6f", "difficulty": "medium", "final_answer": {"answer": 0.0071, "unit": "state_units"}, "id": "euler_decay_000711_9.5_0.54_0.95_10", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.54 y with y(0)=9.5, step size h=0.95, for 10 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.54 y, so each step multiplies y by 1 - h*0.54.\nApply that update for 10 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 9.5, "rate": 0.54, "step": 0.95, "steps": 10}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(1.1)=-8.13 and f(5.4)=20.68.\n3. The interval width is 4.3.\nFinal: {\"answer\": 26.9825, \"unit\": \"area_units\"}", "dedupe_signature": "5b9da73ebb143c18293097d3a52fe4cbff4935992bcd0f6e074dadae26255040", "difficulty": "medium", "final_answer": {"answer": 26.9825, "unit": "area_units"}, "id": "trapz_linear_000712_6.7_-15.5_1.1_5.4", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=6.7x+-15.5 from x=1.1 to x=5.4. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(1.1)=-8.13 and f(5.4)=20.68.\nThe interval width is 4.3.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -15.5, "slope": 6.7, "x0": 1.1, "x1": 5.4}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 100 centimeters in one meter.\n2. Apply the conversion factor directly to the given value.\n3. Compute 338.0 / 100.\nFinal: {\"answer\": 3.38, \"unit\": \"m\"}", "dedupe_signature": "99d8413041e049a8cb938c2a03589c88d509d1b854130331228d06e3d94729bd", "difficulty": "easy", "final_answer": {"answer": 3.38, "unit": "m"}, "id": "unit_convert_000714_cm_to_m_338", "license": "Apache-2.0", "prompt": "Convert 338 cm to m. Return the converted value with unit.", "reasoning_trace": "There are 100 centimeters in one meter.\nApply the conversion factor directly to the given value.\nCompute 338.0 / 100.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 338.0}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=128 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-211.7875, 271.0757], \"unit\": \"N\"}", "dedupe_signature": "6e69173b06a64c8500029ebd27b24d290439ab440000c6df70a96a4ed506de54", "difficulty": "medium", "final_answer": {"answer": [-211.7875, 271.0757], "unit": "N"}, "id": "vector_components_000715_344_128", "license": "Apache-2.0", "prompt": "A vector has magnitude 344 N at 128 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=128 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 128, "magnitude": 344.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-8.25, 16.5], \"unit\": \"dimensionless\"}", "dedupe_signature": "6cdbfe5b493efcac0e71089c0951a169259e1a777f0aefd506ab1a3b32f56697", "difficulty": "medium", "final_answer": {"answer": [-8.25, 16.5], "unit": "dimensionless"}, "id": "line_two_point_000716_13_19.75_-8.25_16.5", "license": "Apache-2.0", "prompt": "A line passes through points (13, -90.75) and (19.75, -146.438). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 13.0, "x2": 19.75, "y1": -90.75, "y2": -146.4375}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. amount times volume is not concentration\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "546187b5d7d3372bd706c5578b35b825d7e1b4d6282ba72215fd336c3e1c5141", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_000717_inconsistent_74ac0b02_454466", "license": "Apache-2.0", "prompt": "In sensor calibration case 454466, check dimensional consistency for C = n * V. The left side has dimensions mol/L and the right side has dimensions mol*L. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\namount times volume is not concentration\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "C = n * V"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef threshold_flags_000718(values, threshold):\n    return [value >= threshold for value in values]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"threshold_flags_000718\"}", "dedupe_signature": "84a1dda3ff24f4180996380a009844ee9d9592f513d71a2ede14795412ff0a0a", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "threshold_flags_000718"}, "id": "code_000718_threshold_flags_000718", "license": "Apache-2.0", "prompt": "Write a Python function threshold_flags_000718(values, threshold) that returns a list of booleans showing whether each value is greater than or equal to threshold. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "threshold_flags_000718"}, "verifier": {"function": "threshold_flags_000718", "tests": ["assert threshold_flags_000718([1, 2, 3], 2) == [False, True, True]", "assert threshold_flags_000718([], 5) == []", "assert threshold_flags_000718([-1, 0], 0) == [False, True]"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: left_boundary, right_boundary.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"left_boundary\", \"right_boundary\"]}", "dedupe_signature": "67128cdff5fd29c32cf4266cd5e8dc7d374ef233caa3a46f67f980b0e6fb7022", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["left_boundary", "right_boundary"]}, "id": "abstain_000719_left_boundary_right_boundary", "license": "Apache-2.0", "prompt": "Solve the 1D heat equation after one finite-difference step. The prompt gives r=0.08 and interior values [0.55, 1.85, -1.0], but gives no boundary values. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: left_boundary, right_boundary.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["left_boundary", "right_boundary"]}, "verifier": {"missing": ["left_boundary", "right_boundary"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 24.25 kg and a = 10 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 242.5, \"unit\": \"N\"}", "dedupe_signature": "af15df1fad1591bd8b84ebbb0b3c2d693f3e961efbad273270d08d0ba48f3735", "difficulty": "easy", "final_answer": {"answer": 242.5, "unit": "N"}, "id": "force_000720_24.25_10", "license": "Apache-2.0", "prompt": "A cart has mass 24.25 kg and measured acceleration 10 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 24.25 kg and a = 10 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 10.0, "mass": 24.25}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 15.75^2 and multiply by 0.5 * 15.15.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 1879.0734, \"unit\": \"J\"}", "dedupe_signature": "5290e41b99f7963c981623a63adde771d111c19eb3dcb16b1e73229ec43efda4", "difficulty": "easy", "final_answer": {"answer": 1879.0734, "unit": "J"}, "id": "ke_000721_15.15_15.75", "license": "Apache-2.0", "prompt": "A body of mass 15.15 kg moves at 15.75 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 15.75^2 and multiply by 0.5 * 15.15.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 15.15, "velocity": 15.75}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 6 * 8.314 * 426 / 10.7.\nFinal: {\"answer\": 1986.0359, \"unit\": \"kPa\"}", "dedupe_signature": "7cabc39f9e3f743ce4ffd40f6cd5c4d19428cd9219f61a4eb53b670637ef2d67", "difficulty": "medium", "final_answer": {"answer": 1986.0359, "unit": "kPa"}, "id": "ideal_gas_000723_6_426_10.7", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=6 mol, T=426 K, and V=10.7 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 6 * 8.314 * 426 / 10.7.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 6.0, "temp_k": 426, "volume_l": 10.7}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 765 * 4.225 * 21.\nFinal: {\"answer\": 67874.625, \"unit\": \"J\"}", "dedupe_signature": "a8cbaff88502afc76462f0119d0971f9b87e62fd9042973d89bb8d2501f57afa", "difficulty": "easy", "final_answer": {"answer": 67874.625, "unit": "J"}, "id": "heat_q_000724_765_4.225_21", "license": "Apache-2.0", "prompt": "A 765 g sample has specific heat 4.225 J/(g*K). How much heat is needed to raise its temperature by 21 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 765 * 4.225 * 21.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 21, "heat_capacity": 4.225, "mass_g": 765}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=179.9 V and R=131.6 ohm.\nFinal: {\"answer\": 245.9271, \"unit\": \"W\"}", "dedupe_signature": "08292f50a0be56d3fe468e0d8e1773d14173d9b5f6d88d3f14e5760a2fa19862", "difficulty": "easy", "final_answer": {"answer": 245.9271, "unit": "W"}, "id": "ohm_power_000725_179.9_131.6", "license": "Apache-2.0", "prompt": "A resistor has resistance 131.6 ohm and voltage 179.9 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=179.9 V and R=131.6 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 131.6, "voltage": 179.9}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=892 mg, t=360 h, and T_half=110.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 93.2467, \"unit\": \"mg\"}", "dedupe_signature": "58b686f69a6002149d21b3537e4a1412babc00e2e4b723fde05bcc05b96cd29b", "difficulty": "medium", "final_answer": {"answer": 93.2467, "unit": "mg"}, "id": "half_life_000726_892_110.5_360", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 892 mg. Its half-life is 110.5 hours. How many mg remain after 360 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=892 mg, t=360 h, and T_half=110.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 360.0, "half_life": 110.5, "initial_amount": 892.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 1.84 mol * 18.015 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 33.1476, \"unit\": \"g\"}", "dedupe_signature": "f68b30aafe558864c825c1eaaabf939198e770a32ea090786d94900b4170f507", "difficulty": "medium", "final_answer": {"answer": 33.1476, "unit": "g"}, "id": "stoich_mass_000727_water_1.84", "license": "Apache-2.0", "prompt": "A sample contains 1.84 mol of water. Using molar mass 18.015 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 1.84 mol * 18.015 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "water", "molar_mass": 18.015, "moles": 1.84}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 1825 mL to 1.825 L.\n3. Compute M = 1.045 / 1.825.\nFinal: {\"answer\": 0.5726, \"unit\": \"mol/L\"}", "dedupe_signature": "b5be3714f299c8abb2db020d744a9f02aa00a8b7b48f3e479a0eaf00ed39e337", "difficulty": "medium", "final_answer": {"answer": 0.5726, "unit": "mol/L"}, "id": "molarity_000728_1.045_1825", "license": "Apache-2.0", "prompt": "A solution contains 1.045 mol of solute in 1825 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 1825 mL to 1.825 L.\nCompute M = 1.045 / 1.825.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 1.045, "volume_ml": 1825}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(1.5)=0.7 and f(9.9)=7.42.\n3. The interval width is 8.4.\nFinal: {\"answer\": 34.104, \"unit\": \"area_units\"}", "dedupe_signature": "2500cd767c6a47aed699b647f537cbb59d0c9dae040199fb6865520af8163bab", "difficulty": "medium", "final_answer": {"answer": 34.104, "unit": "area_units"}, "id": "trapz_linear_000730_0.8_-0.5_1.5_9.9", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=0.8x+-0.5 from x=1.5 to x=9.9. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(1.5)=0.7 and f(9.9)=7.42.\nThe interval width is 8.4.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -0.5, "slope": 0.8, "x0": 1.5, "x1": 9.9}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.38 and add it to the current value.\nFinal: {\"answer\": [0.227, 0.468, -0.544], \"unit\": \"temperature_units\"}", "dedupe_signature": "f0072271d000a8641f54a04cf74f8cd65b251e5a7dcb5ab1647d89d2c0098bef", "difficulty": "hard", "final_answer": {"answer": [0.227, 0.468, -0.544], "unit": "temperature_units"}, "id": "heat_step_000731_0.38_2.1_0.55_-1.85_1.85_-0.75", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=2.1, right=-0.75; current interior values are [0.55, -1.85, 1.85]. Use r=0.38. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.38 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [0.55, -1.85, 1.85], "left": 2.1, "r": 0.38, "right": -0.75}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 44331.0 / 1000.\nFinal: {\"answer\": 44.331, \"unit\": \"kg\"}", "dedupe_signature": "5ddfec2e3313c22d8b22e26d3ec1ef90496bbc19305ff06261598253cbeab0f7", "difficulty": "easy", "final_answer": {"answer": 44.331, "unit": "kg"}, "id": "unit_convert_000732_g_to_kg_44331", "license": "Apache-2.0", "prompt": "Convert 44331 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 44331.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 44331.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=95 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-31.2889, 357.6339], \"unit\": \"N\"}", "dedupe_signature": "523871d192a2b6dba47747debf5070d05e12124895c4c865e496e5b5a805f543", "difficulty": "medium", "final_answer": {"answer": [-31.2889, 357.6339], "unit": "N"}, "id": "vector_components_000733_359_95", "license": "Apache-2.0", "prompt": "A vector has magnitude 359 N at 95 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=95 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 95, "magnitude": 359.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [5.5, -12.5], \"unit\": \"dimensionless\"}", "dedupe_signature": "d7bb93114f2888ae2d872f81c6a3adc6b051b72eeccfaf12aaf17a89aa6a2679", "difficulty": "medium", "final_answer": {"answer": [5.5, -12.5], "unit": "dimensionless"}, "id": "line_two_point_000734_7.25_17.25_5.5_-12.5", "license": "Apache-2.0", "prompt": "A line passes through points (7.25, 27.375) and (17.25, 82.375). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 7.25, "x2": 17.25, "y1": 27.375, "y2": 82.375}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. density times acceleration times height gives kg/(m*s^2), or pascal\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "64b511c8c32fee307c351102194f66eaff5e416cad8b515e41a5bbac44dce777", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_000735_consistent_b7d3eed1_948981", "license": "Apache-2.0", "prompt": "In lab notebook case 948981, check dimensional consistency for p = rho * g * h. The left side has dimensions Pa and the right side has dimensions Pa. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\ndensity times acceleration times height gives kg/(m*s^2), or pascal\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "p = rho * g * h"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef weighted_sum_000736(values, weights):\n    if len(values) != len(weights):\n        raise ValueError('length mismatch')\n    return sum(value * weight for value, weight in zip(values, weights))\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"weighted_sum_000736\"}", "dedupe_signature": "6b7ff6673d11eaad64166a845e1faf7d1b14e029a2ac6641420e78cf4fbdce7d", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "weighted_sum_000736"}, "id": "code_000736_weighted_sum_000736", "license": "Apache-2.0", "prompt": "Write a Python function weighted_sum_000736(values, weights) that returns sum(value*weight). Raise ValueError when the two inputs have different lengths. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "weighted_sum_000736"}, "verifier": {"function": "weighted_sum_000736", "tests": ["assert weighted_sum_000736([2, 3], [4, 5]) == 23", "assert weighted_sum_000736([], []) == 0", "try:\n    weighted_sum_000736([1], [1, 2])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: rate_constant, number_of_steps.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"rate_constant\", \"number_of_steps\"]}", "dedupe_signature": "8e1977f733cc982587acb33a6d3741f4b7dc00c5989a50fea1e70d2f48c29e54", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["rate_constant", "number_of_steps"]}, "id": "abstain_000737_rate_constant_number_of_steps", "license": "Apache-2.0", "prompt": "Use explicit Euler for dy/dt = -k y. The prompt gives y(0)=9.5 and h=0.8, but omits both k and the number of steps. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: rate_constant, number_of_steps.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["rate_constant", "number_of_steps"]}, "verifier": {"missing": ["rate_constant", "number_of_steps"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 17.65 kg and a = 4.7 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 82.955, \"unit\": \"N\"}", "dedupe_signature": "aed6625ad958512da919104ad77eaec54e9ddce647fbc40eadf29108673b12c9", "difficulty": "easy", "final_answer": {"answer": 82.955, "unit": "N"}, "id": "force_000738_17.65_4.7", "license": "Apache-2.0", "prompt": "A cart has mass 17.65 kg and measured acceleration 4.7 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 17.65 kg and a = 4.7 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 4.7, "mass": 17.65}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 18.95^2 and multiply by 0.5 * 8.25.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 1481.2978, \"unit\": \"J\"}", "dedupe_signature": "bb7389b22ddc1f3d30a6f9eab23ef95e2cf9db8b092c382c46ee574b6c1ea44a", "difficulty": "easy", "final_answer": {"answer": 1481.2978, "unit": "J"}, "id": "ke_000739_8.25_18.95", "license": "Apache-2.0", "prompt": "A body of mass 8.25 kg moves at 18.95 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 18.95^2 and multiply by 0.5 * 8.25.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 8.25, "velocity": 18.95}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=77 degrees through the sine of 2 theta.\n3. Substitute v=52.1 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 121.2965, \"unit\": \"m\"}", "dedupe_signature": "6011ede80b22c2f6ffac7d3759df40c20fb621dd6651f0f79d3eddfa20b87a18", "difficulty": "medium", "final_answer": {"answer": 121.2965, "unit": "m"}, "id": "projectile_range_000740_52.1_77", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 52.1 m/s and angle 77 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=77 degrees through the sine of 2 theta.\nSubstitute v=52.1 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 77, "gravity": 9.81, "speed": 52.1}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 3.56 * 8.314 * 267 / 103.1.\nFinal: {\"answer\": 76.6501, \"unit\": \"kPa\"}", "dedupe_signature": "40a47a5977e71d8b418708184b8217e1e664f35ac85d4f59b88c8a157c915529", "difficulty": "medium", "final_answer": {"answer": 76.6501, "unit": "kPa"}, "id": "ideal_gas_000741_3.56_267_103.1", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=3.56 mol, T=267 K, and V=103.1 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 3.56 * 8.314 * 267 / 103.1.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 3.56, "temp_k": 267, "volume_l": 103.1}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 715 * 3.62 * 12.\nFinal: {\"answer\": 31059.6, \"unit\": \"J\"}", "dedupe_signature": "82f63fa75234a2216c543fd15d8735e1e1a23f84fe7d384418c4e0e5466b557d", "difficulty": "easy", "final_answer": {"answer": 31059.6, "unit": "J"}, "id": "heat_q_000742_715_3.62_12", "license": "Apache-2.0", "prompt": "A 715 g sample has specific heat 3.62 J/(g*K). How much heat is needed to raise its temperature by 12 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 715 * 3.62 * 12.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 12, "heat_capacity": 3.62, "mass_g": 715}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 0.97 mol * 44.01 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 42.6897, \"unit\": \"g\"}", "dedupe_signature": "6b945b35a32dd781ba0dd27d91412e333bb80d0deefc1e665aeb4b7dce9f19c6", "difficulty": "medium", "final_answer": {"answer": 42.6897, "unit": "g"}, "id": "stoich_mass_000745_carbon_dioxide_0.97", "license": "Apache-2.0", "prompt": "A sample contains 0.97 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 0.97 mol * 44.01 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "carbon dioxide", "molar_mass": 44.01, "moles": 0.97}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 3625 mL to 3.625 L.\n3. Compute M = 3.845 / 3.625.\nFinal: {\"answer\": 1.0607, \"unit\": \"mol/L\"}", "dedupe_signature": "d05e461030e7c82dc71aab309cb5d8163971a724ef5afec97e66e9b7817e746d", "difficulty": "medium", "final_answer": {"answer": 1.0607, "unit": "mol/L"}, "id": "molarity_000746_3.845_3625", "license": "Apache-2.0", "prompt": "A solution contains 3.845 mol of solute in 3625 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 3625 mL to 3.625 L.\nCompute M = 3.845 / 3.625.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 3.845, "volume_ml": 3625}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.63 y, so each step multiplies y by 1 - h*0.63.\n3. Apply that update for 4 steps and round the final state.\nFinal: {\"answer\": 2.1277, \"unit\": \"state_units\"}", "dedupe_signature": "9cbf7d6f9012057a9bf9a8296ad23ff4f3449543032b68c50e1da013ee217280", "difficulty": "medium", "final_answer": {"answer": 2.1277, "unit": "state_units"}, "id": "euler_decay_000747_17.5_0.63_0.65_4", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.63 y with y(0)=17.5, step size h=0.65, for 4 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.63 y, so each step multiplies y by 1 - h*0.63.\nApply that update for 4 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 17.5, "rate": 0.63, "step": 0.65, "steps": 4}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(3.2)=37.52 and f(10.9)=88.34.\n3. The interval width is 7.7.\nFinal: {\"answer\": 484.561, \"unit\": \"area_units\"}", "dedupe_signature": "8a9ea483f07f51927330ac7a50dcd38f2b34692cf5f6c0a846bdec65b698c6ef", "difficulty": "medium", "final_answer": {"answer": 484.561, "unit": "area_units"}, "id": "trapz_linear_000748_6.6_16.4_3.2_10.9", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=6.6x+16.4 from x=3.2 to x=10.9. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(3.2)=37.52 and f(10.9)=88.34.\nThe interval width is 7.7.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 16.4, "slope": 6.6, "x0": 3.2, "x1": 10.9}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.46 and add it to the current value.\nFinal: {\"answer\": [-0.114, 0.129, -0.525], \"unit\": \"temperature_units\"}", "dedupe_signature": "78e7dde0c9657cae448192ea4b2849b2c1a97941f969ff1e6c3814f0143f0f6c", "difficulty": "hard", "final_answer": {"answer": [-0.114, 0.129, -0.525], "unit": "temperature_units"}, "id": "heat_step_000749_0.46_0.1_0.3_-0.4_0.05_-0.75", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=0.1, right=-0.75; current interior values are [0.3, -0.4, 0.05]. Use r=0.46. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.46 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [0.3, -0.4, 0.05], "left": 0.1, "r": 0.46, "right": -0.75}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 100 centimeters in one meter.\n2. Apply the conversion factor directly to the given value.\n3. Compute 2642.0 / 100.\nFinal: {\"answer\": 26.42, \"unit\": \"m\"}", "dedupe_signature": "93104e5b016f6eff78cd0692a47940937a3ad2a8b046da92719c76c669ca83a5", "difficulty": "easy", "final_answer": {"answer": 26.42, "unit": "m"}, "id": "unit_convert_000750_cm_to_m_2642", "license": "Apache-2.0", "prompt": "Convert 2642 cm to m. Return the converted value with unit.", "reasoning_trace": "There are 100 centimeters in one meter.\nApply the conversion factor directly to the given value.\nCompute 2642.0 / 100.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 2642.0}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=158 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-41.2597, 16.67], \"unit\": \"N\"}", "dedupe_signature": "78e219162a3103db9ddf7354fed0a26cf89e93bec491db2dced7744f828d5f51", "difficulty": "medium", "final_answer": {"answer": [-41.2597, 16.67], "unit": "N"}, "id": "vector_components_000751_44.5_158", "license": "Apache-2.0", "prompt": "A vector has magnitude 44.5 N at 158 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=158 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 158, "magnitude": 44.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-7.1, -13.25], \"unit\": \"dimensionless\"}", "dedupe_signature": "a4cb48da8212144a9e6cf0122956d78ea334dba6a4ed8a743ca9a177dc2d9d6d", "difficulty": "medium", "final_answer": {"answer": [-7.1, -13.25], "unit": "dimensionless"}, "id": "line_two_point_000752_4.5_14_-7.1_-13.25", "license": "Apache-2.0", "prompt": "A line passes through points (4.5, -45.2) and (14, -112.65). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 4.5, "x2": 14.0, "y1": -45.2, "y2": -112.64999999999999}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. velocity times time gives distance, not acceleration\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "cc22247d5ff1f41020ec0af0c92b202cf3c8f4a7ae49d063edd3310bc194195c", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_000753_inconsistent_7481c798_486049", "license": "Apache-2.0", "prompt": "In lab notebook case 486049, check dimensional consistency for a = v * t. The left side has dimensions m/s^2 and the right side has dimensions m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nvelocity times time gives distance, not acceleration\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "a = v * t"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef safe_mean_000754(values):\n    if not values:\n        raise ValueError('safe_mean requires at least one value')\n    return sum(values) / len(values)\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"safe_mean_000754\"}", "dedupe_signature": "f51da3310a1d356ad6a440611940f3b7d5c2f644d0cd3763f0296f5aef8f2127", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "safe_mean_000754"}, "id": "code_000754_safe_mean_000754", "license": "Apache-2.0", "prompt": "Write a Python function safe_mean_000754(values) that returns the arithmetic mean. It must raise ValueError for an empty input and must not mutate the input list. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "safe_mean_000754"}, "verifier": {"function": "safe_mean_000754", "tests": ["assert safe_mean_000754([2, 4, 6]) == 4", "xs = [1, 2, 3]; assert safe_mean_000754(xs) == 2 and xs == [1, 2, 3]", "try:\n    safe_mean_000754([])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 20.55 kg and a = 13.9 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 285.645, \"unit\": \"N\"}", "dedupe_signature": "4c067eb2d00f6fe1577ed452f239875588142f98b1ec582c3645afb7a56a7db5", "difficulty": "easy", "final_answer": {"answer": 285.645, "unit": "N"}, "id": "force_000756_20.55_13.9", "license": "Apache-2.0", "prompt": "A cart has mass 20.55 kg and measured acceleration 13.9 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 20.55 kg and a = 13.9 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 13.9, "mass": 20.55}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 17.55^2 and multiply by 0.5 * 10.05.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 1547.7126, \"unit\": \"J\"}", "dedupe_signature": "4b631564772525ff6551edea644397de045c3ebd8c2b74f5e6c2c6262fe05a22", "difficulty": "easy", "final_answer": {"answer": 1547.7126, "unit": "J"}, "id": "ke_000757_10.05_17.55", "license": "Apache-2.0", "prompt": "A body of mass 10.05 kg moves at 17.55 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 17.55^2 and multiply by 0.5 * 10.05.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 10.05, "velocity": 17.55}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=30 degrees through the sine of 2 theta.\n3. Substitute v=82.6 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 602.3123, \"unit\": \"m\"}", "dedupe_signature": "9451344dc2c4c8b9dc560952a7a5be8e0946ce506a6fd04a9b491e94b522537a", "difficulty": "medium", "final_answer": {"answer": 602.3123, "unit": "m"}, "id": "projectile_range_000758_82.6_30", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 82.6 m/s and angle 30 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=30 degrees through the sine of 2 theta.\nSubstitute v=82.6 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 30, "gravity": 9.81, "speed": 82.6}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1075 * 4.055 * 5.\nFinal: {\"answer\": 21795.625, \"unit\": \"J\"}", "dedupe_signature": "25970b9815492c62535afda54e78b6499ed4d90cdd7a601c85a1d36fc020a837", "difficulty": "easy", "final_answer": {"answer": 21795.625, "unit": "J"}, "id": "heat_q_000760_1075_4.055_5", "license": "Apache-2.0", "prompt": "A 1075 g sample has specific heat 4.055 J/(g*K). How much heat is needed to raise its temperature by 5 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1075 * 4.055 * 5.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 5, "heat_capacity": 4.055, "mass_g": 1075}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=57.2 V and R=23 ohm.\nFinal: {\"answer\": 142.2539, \"unit\": \"W\"}", "dedupe_signature": "d8bfb0743756ead29c7e232d3c1bfd45b03b070484c59827e830eaa989243318", "difficulty": "easy", "final_answer": {"answer": 142.2539, "unit": "W"}, "id": "ohm_power_000761_57.2_23", "license": "Apache-2.0", "prompt": "A resistor has resistance 23 ohm and voltage 57.2 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=57.2 V and R=23 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 23.0, "voltage": 57.2}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=279 mg, t=189.5 h, and T_half=96 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 71.0205, \"unit\": \"mg\"}", "dedupe_signature": "1d72dda1c82b422322c5b9b5a4e5d133d5f02197e8cb5a215da8498e6d714d2c", "difficulty": "medium", "final_answer": {"answer": 71.0205, "unit": "mg"}, "id": "half_life_000762_279_96_189.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 279 mg. Its half-life is 96 hours. How many mg remain after 189.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=279 mg, t=189.5 h, and T_half=96 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 189.5, "half_life": 96.0, "initial_amount": 279.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 6.8 mol * 180.156 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 1225.0608, \"unit\": \"g\"}", "dedupe_signature": "61177e2e24cf6d99f8f32f094b598685ae28088f6ec60ac55449a03ec80f5bf4", "difficulty": "medium", "final_answer": {"answer": 1225.0608, "unit": "g"}, "id": "stoich_mass_000763_glucose_6.8", "license": "Apache-2.0", "prompt": "A sample contains 6.8 mol of glucose. Using molar mass 180.156 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 6.8 mol * 180.156 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "glucose", "molar_mass": 180.156, "moles": 6.8}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 2215 mL to 2.215 L.\n3. Compute M = 3.9 / 2.215.\nFinal: {\"answer\": 1.7607, \"unit\": \"mol/L\"}", "dedupe_signature": "928d2f3b299779926abb8622230a72d9998c563241814610a6689d4b66375e23", "difficulty": "medium", "final_answer": {"answer": 1.7607, "unit": "mol/L"}, "id": "molarity_000764_3.9_2215", "license": "Apache-2.0", "prompt": "A solution contains 3.9 mol of solute in 2215 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 2215 mL to 2.215 L.\nCompute M = 3.9 / 2.215.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 3.9, "volume_ml": 2215}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(5.4)=-48.58 and f(15.3)=-114.91.\n3. The interval width is 9.9.\nFinal: {\"answer\": -809.2755, \"unit\": \"area_units\"}", "dedupe_signature": "4e429f9b43038bc380ed2241590e1cf3e22b0394d762ca5be6ec2eeb47498611", "difficulty": "medium", "final_answer": {"answer": -809.2755, "unit": "area_units"}, "id": "trapz_linear_000766_-6.7_-12.4_5.4_15.3", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-6.7x+-12.4 from x=5.4 to x=15.3. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(5.4)=-48.58 and f(15.3)=-114.91.\nThe interval width is 9.9.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -12.4, "slope": -6.7, "x0": 5.4, "x1": 15.3}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [0.7, 6.5], \"unit\": \"dimensionless\"}", "dedupe_signature": "5cff98ff2110b07eb896a8dee16c79f00014d805db1bd8b75d6b5e776940d045", "difficulty": "medium", "final_answer": {"answer": [0.7, 6.5], "unit": "dimensionless"}, "id": "line_two_point_000770_-1.5_0.75_0.7_6.5", "license": "Apache-2.0", "prompt": "A line passes through points (-1.5, 5.45) and (0.75, 7.025). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -1.5, "x2": 0.75, "y1": 5.45, "y2": 7.025}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. amount times volume is not concentration\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "67a500962d7e0097f9ee11370ed6e49aa2d2f601b88bc5715557ebd5d7d6fca7", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_000771_inconsistent_74ac0b02_447082", "license": "Apache-2.0", "prompt": "In field worksheet case 447082, check dimensional consistency for C = n * V. The left side has dimensions mol/L and the right side has dimensions mol*L. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\namount times volume is not concentration\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "C = n * V"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: target_schema, valid_examples.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"target_schema\", \"valid_examples\"]}", "dedupe_signature": "d0d955dbd5b340cadde425df93cdff84d6cebfedd2a7751a10bd05e5a4df680f", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["target_schema", "valid_examples"]}, "id": "abstain_000773_target_schema_valid_examples", "license": "Apache-2.0", "prompt": "Write a parser that converts each warehouse experiment record from batch 690725 into the correct schema, but the prompt does not include the target schema or examples. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: target_schema, valid_examples.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["target_schema", "valid_examples"]}, "verifier": {"missing": ["target_schema", "valid_examples"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 13.6 kg and a = 5.15 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 70.04, \"unit\": \"N\"}", "dedupe_signature": "6f8e216ea0f2402027702cf4cf158f60afe53ee1ff30e26cfec5ccf564bcfc6a", "difficulty": "easy", "final_answer": {"answer": 70.04, "unit": "N"}, "id": "force_000774_13.6_5.15", "license": "Apache-2.0", "prompt": "A cart has mass 13.6 kg and measured acceleration 5.15 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 13.6 kg and a = 5.15 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 5.15, "mass": 13.6}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 33.65^2 and multiply by 0.5 * 3.4.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 1924.9482, \"unit\": \"J\"}", "dedupe_signature": "fed62f6501ece464743d0ce2bcdd66f321b23a752eb8400b7296373f732b1f7b", "difficulty": "easy", "final_answer": {"answer": 1924.9482, "unit": "J"}, "id": "ke_000775_3.4_33.65", "license": "Apache-2.0", "prompt": "A body of mass 3.4 kg moves at 33.65 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 33.65^2 and multiply by 0.5 * 3.4.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 3.4, "velocity": 33.65}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=21 degrees through the sine of 2 theta.\n3. Substitute v=70 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 334.2243, \"unit\": \"m\"}", "dedupe_signature": "6541dcbf2eb9668c3152b7f086fc1305e6beb91e1e1e4de8c819da7825b01af4", "difficulty": "medium", "final_answer": {"answer": 334.2243, "unit": "m"}, "id": "projectile_range_000776_70_21", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 70 m/s and angle 21 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=21 degrees through the sine of 2 theta.\nSubstitute v=70 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 21, "gravity": 9.81, "speed": 70.0}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 2.15 * 8.314 * 524 / 22.4.\nFinal: {\"answer\": 418.1497, \"unit\": \"kPa\"}", "dedupe_signature": "46d7cc75f1a84fa14f88d39692fb773b3d4a48811d644ee7aa8576273ba9eb39", "difficulty": "medium", "final_answer": {"answer": 418.1497, "unit": "kPa"}, "id": "ideal_gas_000777_2.15_524_22.4", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=2.15 mol, T=524 K, and V=22.4 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 2.15 * 8.314 * 524 / 22.4.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 2.15, "temp_k": 524, "volume_l": 22.4}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=11.1 V and R=46.2 ohm.\nFinal: {\"answer\": 2.6669, \"unit\": \"W\"}", "dedupe_signature": "44a5abb1ac8f6f9437fe968116db11645a12630c95c0136723136feb5f429a67", "difficulty": "easy", "final_answer": {"answer": 2.6669, "unit": "W"}, "id": "ohm_power_000779_11.1_46.2", "license": "Apache-2.0", "prompt": "A resistor has resistance 46.2 ohm and voltage 11.1 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=11.1 V and R=46.2 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 46.2, "voltage": 11.1}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 7.75 mol * 58.44 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 452.91, \"unit\": \"g\"}", "dedupe_signature": "45940d6e2f366663fb714fc75416ada7990708391089ba5de35be88c5b387eb3", "difficulty": "medium", "final_answer": {"answer": 452.91, "unit": "g"}, "id": "stoich_mass_000781_sodium_chloride_7.75", "license": "Apache-2.0", "prompt": "A sample contains 7.75 mol of sodium chloride. Using molar mass 58.44 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 7.75 mol * 58.44 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "sodium chloride", "molar_mass": 58.44, "moles": 7.75}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 2550 mL to 2.55 L.\n3. Compute M = 4.92 / 2.55.\nFinal: {\"answer\": 1.9294, \"unit\": \"mol/L\"}", "dedupe_signature": "a8ff745e70acdf460c123aa64dd176208604a6ae8cc85af45115be83d43a770d", "difficulty": "medium", "final_answer": {"answer": 1.9294, "unit": "mol/L"}, "id": "molarity_000782_4.92_2550", "license": "Apache-2.0", "prompt": "A solution contains 4.92 mol of solute in 2550 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 2550 mL to 2.55 L.\nCompute M = 4.92 / 2.55.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 4.92, "volume_ml": 2550}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.12 y, so each step multiplies y by 1 - h*0.12.\n3. Apply that update for 7 steps and round the final state.\nFinal: {\"answer\": 2.8415, \"unit\": \"state_units\"}", "dedupe_signature": "2e0f0660c9d6008ce0c13462c695e5d26eeffdd16cac4d4ee71d56c46ea7566b", "difficulty": "medium", "final_answer": {"answer": 2.8415, "unit": "state_units"}, "id": "euler_decay_000783_12_0.12_1.55_7", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.12 y with y(0)=12, step size h=1.55, for 7 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.12 y, so each step multiplies y by 1 - h*0.12.\nApply that update for 7 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 12.0, "rate": 0.12, "step": 1.55, "steps": 7}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-6)=-19.5 and f(0)=-2.7.\n3. The interval width is 6.\nFinal: {\"answer\": -66.6, \"unit\": \"area_units\"}", "dedupe_signature": "1dd066cfb7450b13bce915daefc43f530d65cb8a907f0560a6c12b48d05de532", "difficulty": "medium", "final_answer": {"answer": -66.6, "unit": "area_units"}, "id": "trapz_linear_000784_2.8_-2.7_-6_0", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=2.8x+-2.7 from x=-6 to x=0. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-6)=-19.5 and f(0)=-2.7.\nThe interval width is 6.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -2.7, "slope": 2.8, "x0": -6.0, "x1": 0.0}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.26 and add it to the current value.\nFinal: {\"answer\": [1.038, 1.574, 1.456], \"unit\": \"temperature_units\"}", "dedupe_signature": "f91192a66fde054c6f38b17e0cf719e74b047387acd0a80260eb45fadff234c0", "difficulty": "hard", "final_answer": {"answer": [1.038, 1.574, 1.456], "unit": "temperature_units"}, "id": "heat_step_000785_0.26_-0.2_0.7_2.9_0.0_2.7", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-0.2, right=2.7; current interior values are [0.7, 2.9, 0.0]. Use r=0.26. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.26 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [0.7, 2.9, 0.0], "left": -0.2, "r": 0.26, "right": 2.7}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 100 centimeters in one meter.\n2. Apply the conversion factor directly to the given value.\n3. Compute 1736.0 / 100.\nFinal: {\"answer\": 17.36, \"unit\": \"m\"}", "dedupe_signature": "e28cab577762f4955926745cec12a32aebe787048dc201325a979a6e1695be11", "difficulty": "easy", "final_answer": {"answer": 17.36, "unit": "m"}, "id": "unit_convert_000786_cm_to_m_1736", "license": "Apache-2.0", "prompt": "Convert 1736 cm to m. Return the converted value with unit.", "reasoning_trace": "There are 100 centimeters in one meter.\nApply the conversion factor directly to the given value.\nCompute 1736.0 / 100.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 1736.0}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=97 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-27.969, 227.7893], \"unit\": \"N\"}", "dedupe_signature": "dcd77c7a7ea8f484041ec3cf08c5483bbf0cdb159c9c78e748f1cadcdd7d8852", "difficulty": "medium", "final_answer": {"answer": [-27.969, 227.7893], "unit": "N"}, "id": "vector_components_000787_229.5_97", "license": "Apache-2.0", "prompt": "A vector has magnitude 229.5 N at 97 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=97 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 97, "magnitude": 229.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [1.55, 14.25], \"unit\": \"dimensionless\"}", "dedupe_signature": "2b48412f251bb2220493a651dac02d65f170d63e072511c96a5314f4c1e1b0fc", "difficulty": "medium", "final_answer": {"answer": [1.55, 14.25], "unit": "dimensionless"}, "id": "line_two_point_000788_-5_0.25_1.55_14.25", "license": "Apache-2.0", "prompt": "A line passes through points (-5, 6.5) and (0.25, 14.6375). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -5.0, "x2": 0.25, "y1": 6.5, "y2": 14.6375}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. m*v is momentum, not energy\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "04a849250bdb05fec1bc661d7d63347dc7c3402c69085b59749ddbce0bd89ce2", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_000789_inconsistent_1e14b074_799179", "license": "Apache-2.0", "prompt": "In instrument manual case 799179, check dimensional consistency for E = m * v. The left side has dimensions kg*m^2/s^2 and the right side has dimensions kg*m/s. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nm*v is momentum, not energy\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "E = m * v"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef weighted_sum_000790(values, weights):\n    if len(values) != len(weights):\n        raise ValueError('length mismatch')\n    return sum(value * weight for value, weight in zip(values, weights))\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"weighted_sum_000790\"}", "dedupe_signature": "64554d9464781216ef86ef95455c52f024b3ca58d55a72980d215ce11b353521", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "weighted_sum_000790"}, "id": "code_000790_weighted_sum_000790", "license": "Apache-2.0", "prompt": "Write a Python function weighted_sum_000790(values, weights) that returns sum(value*weight). Raise ValueError when the two inputs have different lengths. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "weighted_sum_000790"}, "verifier": {"function": "weighted_sum_000790", "tests": ["assert weighted_sum_000790([2, 3], [4, 5]) == 23", "assert weighted_sum_000790([], []) == 0", "try:\n    weighted_sum_000790([1], [1, 2])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 42.6^2 and multiply by 0.5 * 2.6.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 2359.188, \"unit\": \"J\"}", "dedupe_signature": "9a9bc6a3f93efa6aceca07f6845c63ec16f3ddeac3f9a5b43c8ea0db21edfeaf", "difficulty": "easy", "final_answer": {"answer": 2359.188, "unit": "J"}, "id": "ke_000793_2.6_42.6", "license": "Apache-2.0", "prompt": "A body of mass 2.6 kg moves at 42.6 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 42.6^2 and multiply by 0.5 * 2.6.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 2.6, "velocity": 42.6}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=80 degrees through the sine of 2 theta.\n3. Substitute v=22.9 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 18.2833, \"unit\": \"m\"}", "dedupe_signature": "7529e03d32981a05a8618dc2c544208c36f450d55572eff936fa0f6ecf039e6d", "difficulty": "medium", "final_answer": {"answer": 18.2833, "unit": "m"}, "id": "projectile_range_000794_22.9_80", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 22.9 m/s and angle 80 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=80 degrees through the sine of 2 theta.\nSubstitute v=22.9 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 80, "gravity": 9.81, "speed": 22.9}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 0.53 * 8.314 * 309 / 21.5.\nFinal: {\"answer\": 63.3295, \"unit\": \"kPa\"}", "dedupe_signature": "7b19531ed62bb8b49150cd0c7c72fd861a6d9b87e715a4eb247d2de87bc4a8bc", "difficulty": "medium", "final_answer": {"answer": 63.3295, "unit": "kPa"}, "id": "ideal_gas_000795_0.53_309_21.5", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=0.53 mol, T=309 K, and V=21.5 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 0.53 * 8.314 * 309 / 21.5.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 0.53, "temp_k": 309, "volume_l": 21.5}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1085 * 3.83 * 108.\nFinal: {\"answer\": 448799.4, \"unit\": \"J\"}", "dedupe_signature": "a7774e3f703121e35a80fb2ac45f3d7e38e082336bc098eac8d245b05aff62a1", "difficulty": "easy", "final_answer": {"answer": 448799.4, "unit": "J"}, "id": "heat_q_000796_1085_3.83_108", "license": "Apache-2.0", "prompt": "A 1085 g sample has specific heat 3.83 J/(g*K). How much heat is needed to raise its temperature by 108 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1085 * 3.83 * 108.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 108, "heat_capacity": 3.83, "mass_g": 1085}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=79.8 V and R=62.5 ohm.\nFinal: {\"answer\": 101.8886, \"unit\": \"W\"}", "dedupe_signature": "befb088efaec46923f6afb589362b45ae6f6abe3c8f81705f4c517ea352ff1cd", "difficulty": "easy", "final_answer": {"answer": 101.8886, "unit": "W"}, "id": "ohm_power_000797_79.8_62.5", "license": "Apache-2.0", "prompt": "A resistor has resistance 62.5 ohm and voltage 79.8 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=79.8 V and R=62.5 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 62.5, "voltage": 79.8}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=977 mg, t=201 h, and T_half=90 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 207.7755, \"unit\": \"mg\"}", "dedupe_signature": "da28fe3ff0b32ee72d40c58cf09c8862353ebe3526dc767876031411c4cb6cfb", "difficulty": "medium", "final_answer": {"answer": 207.7755, "unit": "mg"}, "id": "half_life_000798_977_90_201", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 977 mg. Its half-life is 90 hours. How many mg remain after 201 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=977 mg, t=201 h, and T_half=90 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 201.0, "half_life": 90.0, "initial_amount": 977.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 2150 mL to 2.15 L.\n3. Compute M = 1.59 / 2.15.\nFinal: {\"answer\": 0.7395, \"unit\": \"mol/L\"}", "dedupe_signature": "0cd355f6671aaa0f6b3592f4ab98e892d28265a48e369ed18b2b5eb1dd45288e", "difficulty": "medium", "final_answer": {"answer": 0.7395, "unit": "mol/L"}, "id": "molarity_000800_1.59_2150", "license": "Apache-2.0", "prompt": "A solution contains 1.59 mol of solute in 2150 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 2150 mL to 2.15 L.\nCompute M = 1.59 / 2.15.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 1.59, "volume_ml": 2150}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.32 y, so each step multiplies y by 1 - h*0.32.\n3. Apply that update for 6 steps and round the final state.\nFinal: {\"answer\": 0.1038, \"unit\": \"state_units\"}", "dedupe_signature": "cadc31eb80d185af661856786c8f53762cea885aac721a869d19cfa3481f1723", "difficulty": "medium", "final_answer": {"answer": 0.1038, "unit": "state_units"}, "id": "euler_decay_000801_22.5_0.32_1.85_6", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.32 y with y(0)=22.5, step size h=1.85, for 6 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.32 y, so each step multiplies y by 1 - h*0.32.\nApply that update for 6 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 22.5, "rate": 0.32, "step": 1.85, "steps": 6}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(1)=17.6 and f(2.1)=24.97.\n3. The interval width is 1.1.\nFinal: {\"answer\": 23.4135, \"unit\": \"area_units\"}", "dedupe_signature": "7a01ae89c0690302619f832bff45214debec75eb30309484c82a7fbba17c3152", "difficulty": "medium", "final_answer": {"answer": 23.4135, "unit": "area_units"}, "id": "trapz_linear_000802_6.7_10.9_1_2.1", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=6.7x+10.9 from x=1 to x=2.1. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(1)=17.6 and f(2.1)=24.97.\nThe interval width is 1.1.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 10.9, "slope": 6.7, "x0": 1.0, "x1": 2.1}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.4 and add it to the current value.\nFinal: {\"answer\": [0.25, -0.4, 0.68], \"unit\": \"temperature_units\"}", "dedupe_signature": "063fbc45dd10165d939c904c4717bc2b468296ad7f89d089a18967d50f29edcb", "difficulty": "hard", "final_answer": {"answer": [0.25, -0.4, 0.68], "unit": "temperature_units"}, "id": "heat_step_000803_0.4_0.25_-1.05_0.9_-0.4_1.0", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=0.25, right=1; current interior values are [-1.05, 0.9, -0.4]. Use r=0.4. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.4 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-1.05, 0.9, -0.4], "left": 0.25, "r": 0.4, "right": 1.0}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=1 degrees and keep the unit as newtons.\nFinal: {\"answer\": [64.9901, 1.1344], \"unit\": \"N\"}", "dedupe_signature": "0115a38209ca1acf531c4ff185e90990390d5c4a2b63cfe87e7b20054d8002d7", "difficulty": "medium", "final_answer": {"answer": [64.9901, 1.1344], "unit": "N"}, "id": "vector_components_000805_65_1", "license": "Apache-2.0", "prompt": "A vector has magnitude 65 N at 1 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=1 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 1, "magnitude": 65.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [7.4, 14.5], \"unit\": \"dimensionless\"}", "dedupe_signature": "3f7345b8b7f36dd5c0bd9d06c540202d6672fb103a34ffd37542c5613da1ab13", "difficulty": "medium", "final_answer": {"answer": [7.4, 14.5], "unit": "dimensionless"}, "id": "line_two_point_000806_-3_9_7.4_14.5", "license": "Apache-2.0", "prompt": "A line passes through points (-3, -7.7) and (9, 81.1). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -3.0, "x2": 9.0, "y1": -7.700000000000003, "y2": 81.10000000000001}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. volt squared divided by ohm is watt\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "a5176fbf12aaeda547322a5fad7cd932983cd46a56f795643b7efd8729ec54c3", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_000807_consistent_82e93f3d_593813", "license": "Apache-2.0", "prompt": "In simulation spec case 593813, check dimensional consistency for P = V^2 / R. The left side has dimensions W and the right side has dimensions W. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nvolt squared divided by ohm is watt\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "P = V^2 / R"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef normalize_000808(values):\n    total = sum(values)\n    if total == 0:\n        raise ValueError('cannot normalize zero-sum values')\n    return [v / total for v in values]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"normalize_000808\"}", "dedupe_signature": "9e84043c12b05f628d703f85ea0b8f14ac7eb5bbb6f1bd73c30507270735423d", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "normalize_000808"}, "id": "code_000808_normalize_000808", "license": "Apache-2.0", "prompt": "Write a Python function normalize_000808(values) that returns a new list whose values sum to 1. Raise ValueError if the sum is zero. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "normalize_000808"}, "verifier": {"function": "normalize_000808", "tests": ["out = normalize_000808([2, 3, 5]); assert len(out) == 3", "assert abs(sum(normalize_000808([2, 3, 5])) - 1.0) < 1e-12", "assert normalize_000808([1, 1]) == [0.5, 0.5]", "try:\n    normalize_000808([1, -1])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: launch_angle_or_vertical_velocity.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"launch_angle_or_vertical_velocity\"]}", "dedupe_signature": "dc6d8cd30bf29d088882376b09f522f9eb27c6def00aa8e91e72f28a5c432675", "difficulty": "easy", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["launch_angle_or_vertical_velocity"]}, "id": "abstain_000809_launch_angle_or_vertical_velocity", "license": "Apache-2.0", "prompt": "Compute projectile range on level ground. The prompt gives initial speed 38.8 m/s but does not give launch angle or vertical velocity. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: launch_angle_or_vertical_velocity.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["launch_angle_or_vertical_velocity"]}, "verifier": {"missing": ["launch_angle_or_vertical_velocity"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 22.4 kg and a = 10.8 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 241.92, \"unit\": \"N\"}", "dedupe_signature": "29187cc04cba2a25be03976f147d0e106a5c0c55e40f328507b56ad07eff7e8a", "difficulty": "easy", "final_answer": {"answer": 241.92, "unit": "N"}, "id": "force_000810_22.4_10.8", "license": "Apache-2.0", "prompt": "A cart has mass 22.4 kg and measured acceleration 10.8 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 22.4 kg and a = 10.8 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 10.8, "mass": 22.4}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 43.75^2 and multiply by 0.5 * 24.7.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 23638.6719, \"unit\": \"J\"}", "dedupe_signature": "a28cefadd55a627e19da014d317e7a58a9b570e9d7069f98b70801b4aeb16361", "difficulty": "easy", "final_answer": {"answer": 23638.6719, "unit": "J"}, "id": "ke_000811_24.7_43.75", "license": "Apache-2.0", "prompt": "A body of mass 24.7 kg moves at 43.75 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 43.75^2 and multiply by 0.5 * 24.7.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 24.7, "velocity": 43.75}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=43 degrees through the sine of 2 theta.\n3. Substitute v=35.4 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 127.4319, \"unit\": \"m\"}", "dedupe_signature": "e7ca5bf6de6ba5f8d44cf3d034657c3d57f05b3b8639302bfa3f967297ee2dfd", "difficulty": "medium", "final_answer": {"answer": 127.4319, "unit": "m"}, "id": "projectile_range_000812_35.4_43", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 35.4 m/s and angle 43 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=43 degrees through the sine of 2 theta.\nSubstitute v=35.4 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 43, "gravity": 9.81, "speed": 35.4}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=92.6 V and R=60.7 ohm.\nFinal: {\"answer\": 141.2646, \"unit\": \"W\"}", "dedupe_signature": "dc9d54d56fbfc722716ddd4401d3a0a446e7e09a6c410fff7d9ef151706c1f96", "difficulty": "easy", "final_answer": {"answer": 141.2646, "unit": "W"}, "id": "ohm_power_000815_92.6_60.7", "license": "Apache-2.0", "prompt": "A resistor has resistance 60.7 ohm and voltage 92.6 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=92.6 V and R=60.7 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 60.7, "voltage": 92.6}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=555.5 mg, t=23.5 h, and T_half=2 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 0.1613, \"unit\": \"mg\"}", "dedupe_signature": "9d70039e7222f685a4007aa79a4f15b5ac058fc53f90912ccc87209bdbfd5bdd", "difficulty": "medium", "final_answer": {"answer": 0.1613, "unit": "mg"}, "id": "half_life_000816_555.5_2_23.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 555.5 mg. Its half-life is 2 hours. How many mg remain after 23.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=555.5 mg, t=23.5 h, and T_half=2 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 23.5, "half_life": 2.0, "initial_amount": 555.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 3.51 mol * 180.156 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 632.3476, \"unit\": \"g\"}", "dedupe_signature": "ec2f56171d609e707b16fe21dc8eaf90f9e9efde8e9dccf7fcfca1cc1477cfe3", "difficulty": "medium", "final_answer": {"answer": 632.3476, "unit": "g"}, "id": "stoich_mass_000817_glucose_3.51", "license": "Apache-2.0", "prompt": "A sample contains 3.51 mol of glucose. Using molar mass 180.156 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 3.51 mol * 180.156 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "glucose", "molar_mass": 180.156, "moles": 3.51}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.51 y, so each step multiplies y by 1 - h*0.51.\n3. Apply that update for 6 steps and round the final state.\nFinal: {\"answer\": 0.0, \"unit\": \"state_units\"}", "dedupe_signature": "cb0c27897582797c38404133c5b49df40c4444e341a073705adba22934b0c1c2", "difficulty": "medium", "final_answer": {"answer": 0.0, "unit": "state_units"}, "id": "euler_decay_000819_9.5_0.51_1.75_6", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.51 y with y(0)=9.5, step size h=1.75, for 6 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.51 y, so each step multiplies y by 1 - h*0.51.\nApply that update for 6 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 9.5, "rate": 0.51, "step": 1.75, "steps": 6}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 100 centimeters in one meter.\n2. Apply the conversion factor directly to the given value.\n3. Compute 2523.5 / 100.\nFinal: {\"answer\": 25.235, \"unit\": \"m\"}", "dedupe_signature": "041e43f7a8d9849b88fe64e4535d4db49b5bf9703f74c2cf2047940f76bcdc34", "difficulty": "easy", "final_answer": {"answer": 25.235, "unit": "m"}, "id": "unit_convert_000822_cm_to_m_2523.5", "license": "Apache-2.0", "prompt": "Convert 2523.5 cm to m. Return the converted value with unit.", "reasoning_trace": "There are 100 centimeters in one meter.\nApply the conversion factor directly to the given value.\nCompute 2523.5 / 100.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 2523.5}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-0.05, 4.75], \"unit\": \"dimensionless\"}", "dedupe_signature": "35e7e457e283f413089433786b3f47c4f9748647bc25a3d91fe6d82c1842a2f3", "difficulty": "medium", "final_answer": {"answer": [-0.05, 4.75], "unit": "dimensionless"}, "id": "line_two_point_000824_4_16_-0.05_4.75", "license": "Apache-2.0", "prompt": "A line passes through points (4, 4.55) and (16, 3.95). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 4.0, "x2": 16.0, "y1": 4.55, "y2": 3.95}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 22.7 kg and a = 3.75 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 85.125, \"unit\": \"N\"}", "dedupe_signature": "a8410f0fee5478fc4320d3b06a19f646c2b0a471553df4cd269cabd29962e5a4", "difficulty": "easy", "final_answer": {"answer": 85.125, "unit": "N"}, "id": "force_000828_22.7_3.75", "license": "Apache-2.0", "prompt": "A cart has mass 22.7 kg and measured acceleration 3.75 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 22.7 kg and a = 3.75 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 3.75, "mass": 22.7}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 24.6^2 and multiply by 0.5 * 25.7.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 7776.306, \"unit\": \"J\"}", "dedupe_signature": "3893ae2939a3d84f76552c1e0c3fa95d4e02e975f2bf35ce2a94dea264e54928", "difficulty": "easy", "final_answer": {"answer": 7776.306, "unit": "J"}, "id": "ke_000829_25.7_24.6", "license": "Apache-2.0", "prompt": "A body of mass 25.7 kg moves at 24.6 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 24.6^2 and multiply by 0.5 * 25.7.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 25.7, "velocity": 24.6}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 3.47 * 8.314 * 293 / 17.1.\nFinal: {\"answer\": 494.3232, \"unit\": \"kPa\"}", "dedupe_signature": "0cb981d8354300d4f8c7d6145d6aa20c86aa69f3c297dac2ee34570ce8a6a479", "difficulty": "medium", "final_answer": {"answer": 494.3232, "unit": "kPa"}, "id": "ideal_gas_000831_3.47_293_17.1", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=3.47 mol, T=293 K, and V=17.1 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 3.47 * 8.314 * 293 / 17.1.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 3.47, "temp_k": 293, "volume_l": 17.1}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=108 V and R=57.4 ohm.\nFinal: {\"answer\": 203.2056, \"unit\": \"W\"}", "dedupe_signature": "dfbbec3097e3a8c525ce6e4a94e845eadeea6bb91fc6a393ea82a0f7de779d19", "difficulty": "easy", "final_answer": {"answer": 203.2056, "unit": "W"}, "id": "ohm_power_000833_108_57.4", "license": "Apache-2.0", "prompt": "A resistor has resistance 57.4 ohm and voltage 108 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=108 V and R=57.4 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 57.4, "voltage": 108.0}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=26.5 mg, t=110 h, and T_half=24 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 1.1054, \"unit\": \"mg\"}", "dedupe_signature": "5cc15a82b9d7cf2647f7e28d7930542c3b5cb350622fc51a3ff2d16ec7886a3b", "difficulty": "medium", "final_answer": {"answer": 1.1054, "unit": "mg"}, "id": "half_life_000834_26.5_24_110", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 26.5 mg. Its half-life is 24 hours. How many mg remain after 110 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=26.5 mg, t=110 h, and T_half=24 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 110.0, "half_life": 24.0, "initial_amount": 26.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 1.12 mol * 58.44 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 65.4528, \"unit\": \"g\"}", "dedupe_signature": "5d4ff69b84abd50bfadbe88376ae1d7957c5f0a495ad83cf770a97faf4a84543", "difficulty": "medium", "final_answer": {"answer": 65.4528, "unit": "g"}, "id": "stoich_mass_000835_sodium_chloride_1.12", "license": "Apache-2.0", "prompt": "A sample contains 1.12 mol of sodium chloride. Using molar mass 58.44 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 1.12 mol * 58.44 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "sodium chloride", "molar_mass": 58.44, "moles": 1.12}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 2565 mL to 2.565 L.\n3. Compute M = 4.375 / 2.565.\nFinal: {\"answer\": 1.7057, \"unit\": \"mol/L\"}", "dedupe_signature": "be3e7357b5a2199d5bbcf5be041616433620d82532c61e2f584f7e974a2803e5", "difficulty": "medium", "final_answer": {"answer": 1.7057, "unit": "mol/L"}, "id": "molarity_000836_4.375_2565", "license": "Apache-2.0", "prompt": "A solution contains 4.375 mol of solute in 2565 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 2565 mL to 2.565 L.\nCompute M = 4.375 / 2.565.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 4.375, "volume_ml": 2565}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.03 y, so each step multiplies y by 1 - h*0.03.\n3. Apply that update for 6 steps and round the final state.\nFinal: {\"answer\": 0.8804, \"unit\": \"state_units\"}", "dedupe_signature": "634446386ef81d07b4b1b84639b50a5d7f7c1f28329ec184538fddb246ac8cf0", "difficulty": "medium", "final_answer": {"answer": 0.8804, "unit": "state_units"}, "id": "euler_decay_000837_1_0.03_0.7_6", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.03 y with y(0)=1, step size h=0.7, for 6 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.03 y, so each step multiplies y by 1 - h*0.03.\nApply that update for 6 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 1.0, "rate": 0.03, "step": 0.7, "steps": 6}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-6)=9.4 and f(2.7)=5.92.\n3. The interval width is 8.7.\nFinal: {\"answer\": 66.642, \"unit\": \"area_units\"}", "dedupe_signature": "4101f8d58a8e19b9c938381b5e9ba2ad29c8abe0ca109abb8b0221d37fc722a2", "difficulty": "medium", "final_answer": {"answer": 66.642, "unit": "area_units"}, "id": "trapz_linear_000838_-0.4_7_-6_2.7", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-0.4x+7 from x=-6 to x=2.7. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-6)=9.4 and f(2.7)=5.92.\nThe interval width is 8.7.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 7.0, "slope": -0.4, "x0": -6.0, "x1": 2.6999999999999993}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.4 and add it to the current value.\nFinal: {\"answer\": [0.26, 0.56, -0.08], \"unit\": \"temperature_units\"}", "dedupe_signature": "2d11f0d3fd2b7d62a0f00382802ee2cb906df20e3f9290d736af35f15daa85fa", "difficulty": "hard", "final_answer": {"answer": [0.26, 0.56, -0.08], "unit": "temperature_units"}, "id": "heat_step_000839_0.4_2.45_0.4_-2.0_2.0_0.8", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=2.45, right=0.8; current interior values are [0.4, -2.0, 2.0]. Use r=0.4. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.4 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [0.4, -2.0, 2.0], "left": 2.45, "r": 0.4, "right": 0.8}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=63 degrees and keep the unit as newtons.\nFinal: {\"answer\": [182.2772, 357.7391], \"unit\": \"N\"}", "dedupe_signature": "388fce2dfe2e54937221ceb69615ec71962581f7bdc9e4b4e95d7757430094bb", "difficulty": "medium", "final_answer": {"answer": [182.2772, 357.7391], "unit": "N"}, "id": "vector_components_000841_401.5_63", "license": "Apache-2.0", "prompt": "A vector has magnitude 401.5 N at 63 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=63 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 63, "magnitude": 401.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [5.15, -10.25], \"unit\": \"dimensionless\"}", "dedupe_signature": "c88e1d500aa3ceec93813aa52cc8d4629db66c560c90a23fcf9f418a3c69f2f3", "difficulty": "medium", "final_answer": {"answer": [5.15, -10.25], "unit": "dimensionless"}, "id": "line_two_point_000842_1.5_2.25_5.15_-10.25", "license": "Apache-2.0", "prompt": "A line passes through points (1.5, -2.525) and (2.25, 1.3375). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 1.5, "x2": 2.25, "y1": -2.5249999999999995, "y2": 1.3375000000000004}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: volume.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"volume\"]}", "dedupe_signature": "d5b27260804e7ebce0c8f29e4814e27434ae30085586bbd645cf4cd2844447ca", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["volume"]}, "id": "abstain_000845_volume", "license": "Apache-2.0", "prompt": "Compute pressure from the ideal gas law. The prompt gives n=3.51 mol and T=531 K, but does not give volume. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: volume.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["volume"]}, "verifier": {"missing": ["volume"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 1.05 kg and a = 0.25 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 0.2625, \"unit\": \"N\"}", "dedupe_signature": "742a85b0c493afe95ad8be32d8c109d6ed8d3b90e56a1d4c1de6409af83fdf73", "difficulty": "easy", "final_answer": {"answer": 0.2625, "unit": "N"}, "id": "force_000846_1.05_0.25", "license": "Apache-2.0", "prompt": "A cart has mass 1.05 kg and measured acceleration 0.25 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 1.05 kg and a = 0.25 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 0.25, "mass": 1.05}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 32.45^2 and multiply by 0.5 * 27.9.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 14689.3849, \"unit\": \"J\"}", "dedupe_signature": "6868df3050779eaee8cd090248f08645d54d41b2ef2b0239a5c0d069c0b8dc0f", "difficulty": "easy", "final_answer": {"answer": 14689.3849, "unit": "J"}, "id": "ke_000847_27.9_32.45", "license": "Apache-2.0", "prompt": "A body of mass 27.9 kg moves at 32.45 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 32.45^2 and multiply by 0.5 * 27.9.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 27.9, "velocity": 32.45}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=48 degrees through the sine of 2 theta.\n3. Substitute v=71.8 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 522.6299, \"unit\": \"m\"}", "dedupe_signature": "4c4b45e68b0eeb0689994a198aef873aa87e1a24f6a8e4ac636f9d60aa847d4d", "difficulty": "medium", "final_answer": {"answer": 522.6299, "unit": "m"}, "id": "projectile_range_000848_71.8_48", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 71.8 m/s and angle 48 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=48 degrees through the sine of 2 theta.\nSubstitute v=71.8 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 48, "gravity": 9.81, "speed": 71.8}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 4.78 * 8.314 * 359 / 117.5.\nFinal: {\"answer\": 121.4212, \"unit\": \"kPa\"}", "dedupe_signature": "d9622c5a418a50b8268da70303cd0572f667ffa6cbae42e15a575e29873bbc78", "difficulty": "medium", "final_answer": {"answer": 121.4212, "unit": "kPa"}, "id": "ideal_gas_000849_4.78_359_117.5", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=4.78 mol, T=359 K, and V=117.5 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 4.78 * 8.314 * 359 / 117.5.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 4.78, "temp_k": 359, "volume_l": 117.5}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 540 * 0.525 * 81.\nFinal: {\"answer\": 22963.5, \"unit\": \"J\"}", "dedupe_signature": "c58a1efbc8add425a8bffa30a9e29a43bd5c5257e8d1d3a19a6fb9dd1b48e4c0", "difficulty": "easy", "final_answer": {"answer": 22963.5, "unit": "J"}, "id": "heat_q_000850_540_0.525_81", "license": "Apache-2.0", "prompt": "A 540 g sample has specific heat 0.525 J/(g*K). How much heat is needed to raise its temperature by 81 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 540 * 0.525 * 81.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 81, "heat_capacity": 0.525, "mass_g": 540}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=195.3 V and R=173.9 ohm.\nFinal: {\"answer\": 219.3335, \"unit\": \"W\"}", "dedupe_signature": "6e9e392015b36c84427f26fcb3f25d4300e44ade2a9badfd61d31a757435f540", "difficulty": "easy", "final_answer": {"answer": 219.3335, "unit": "W"}, "id": "ohm_power_000851_195.3_173.9", "license": "Apache-2.0", "prompt": "A resistor has resistance 173.9 ohm and voltage 195.3 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=195.3 V and R=173.9 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 173.9, "voltage": 195.3}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=598 mg, t=302 h, and T_half=6 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 0.0, \"unit\": \"mg\"}", "dedupe_signature": "d99b76c94fb90a65e0041fedcc7a10f8cf837e8b37ca7467efcfea3a02f41fe6", "difficulty": "medium", "final_answer": {"answer": 0.0, "unit": "mg"}, "id": "half_life_000852_598_6_302", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 598 mg. Its half-life is 6 hours. How many mg remain after 302 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=598 mg, t=302 h, and T_half=6 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 302.0, "half_life": 6.0, "initial_amount": 598.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 2.12 mol * 180.156 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 381.9307, \"unit\": \"g\"}", "dedupe_signature": "3eda6448f8585da4ee625e139b28058c19c50e36610a5b600c6a45987d8b93d0", "difficulty": "medium", "final_answer": {"answer": 381.9307, "unit": "g"}, "id": "stoich_mass_000853_glucose_2.12", "license": "Apache-2.0", "prompt": "A sample contains 2.12 mol of glucose. Using molar mass 180.156 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 2.12 mol * 180.156 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "glucose", "molar_mass": 180.156, "moles": 2.12}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 4160 mL to 4.16 L.\n3. Compute M = 4.085 / 4.16.\nFinal: {\"answer\": 0.982, \"unit\": \"mol/L\"}", "dedupe_signature": "19db07f356ec016305f2226fea1445adce39b0399966ea305eac10c0d04d2a7a", "difficulty": "medium", "final_answer": {"answer": 0.982, "unit": "mol/L"}, "id": "molarity_000854_4.085_4160", "license": "Apache-2.0", "prompt": "A solution contains 4.085 mol of solute in 4160 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 4160 mL to 4.16 L.\nCompute M = 4.085 / 4.16.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 4.085, "volume_ml": 4160}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.08 y, so each step multiplies y by 1 - h*0.08.\n3. Apply that update for 12 steps and round the final state.\nFinal: {\"answer\": 14.3235, \"unit\": \"state_units\"}", "dedupe_signature": "7d8978d60105e916ec3ad39e9e5b4deb5e1e648fbb084bb86bbc638ac07a71fa", "difficulty": "medium", "final_answer": {"answer": 14.3235, "unit": "state_units"}, "id": "euler_decay_000855_53.5_0.08_1.3_12", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.08 y with y(0)=53.5, step size h=1.3, for 12 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.08 y, so each step multiplies y by 1 - h*0.08.\nApply that update for 12 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 53.5, "rate": 0.08, "step": 1.3, "steps": 12}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. amount times volume is not concentration\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "b8b231523bc857f87226a0e6dee9530d1ba086f5b80319400252369b0e9abc48", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_000861_inconsistent_74ac0b02_222640", "license": "Apache-2.0", "prompt": "In instrument manual case 222640, check dimensional consistency for C = n * V. The left side has dimensions mol/L and the right side has dimensions mol*L. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\namount times volume is not concentration\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "C = n * V"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef weighted_sum_000862(values, weights):\n    if len(values) != len(weights):\n        raise ValueError('length mismatch')\n    return sum(value * weight for value, weight in zip(values, weights))\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"weighted_sum_000862\"}", "dedupe_signature": "fa3b14810184ad3a3b925028c44d0a40acb8c8603f44231bd4eb8ce9e74767bd", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "weighted_sum_000862"}, "id": "code_000862_weighted_sum_000862", "license": "Apache-2.0", "prompt": "Write a Python function weighted_sum_000862(values, weights) that returns sum(value*weight). Raise ValueError when the two inputs have different lengths. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "weighted_sum_000862"}, "verifier": {"function": "weighted_sum_000862", "tests": ["assert weighted_sum_000862([2, 3], [4, 5]) == 23", "assert weighted_sum_000862([], []) == 0", "try:\n    weighted_sum_000862([1], [1, 2])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: launch_angle_or_vertical_velocity.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"launch_angle_or_vertical_velocity\"]}", "dedupe_signature": "9c10b700d6299d2f3aa12f7238225f9fb7de9b74fdbbb84c8ab3b03e44a9d2af", "difficulty": "easy", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["launch_angle_or_vertical_velocity"]}, "id": "abstain_000863_launch_angle_or_vertical_velocity", "license": "Apache-2.0", "prompt": "Compute projectile range on level ground. The prompt gives initial speed 65 m/s but does not give launch angle or vertical velocity. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: launch_angle_or_vertical_velocity.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["launch_angle_or_vertical_velocity"]}, "verifier": {"missing": ["launch_angle_or_vertical_velocity"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 9.75 kg and a = 1.45 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 14.1375, \"unit\": \"N\"}", "dedupe_signature": "f323226bcd465955df3573073cda2e9811b32e2f93c3c5fb645d6d97a700c22b", "difficulty": "easy", "final_answer": {"answer": 14.1375, "unit": "N"}, "id": "force_000864_9.75_1.45", "license": "Apache-2.0", "prompt": "A cart has mass 9.75 kg and measured acceleration 1.45 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 9.75 kg and a = 1.45 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 1.45, "mass": 9.75}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 3.3^2 and multiply by 0.5 * 25.05.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 136.3972, \"unit\": \"J\"}", "dedupe_signature": "61a9efe72332bb65a3e216283df3d257c0ea6048a0ec6f6a2c32dd3022bf7728", "difficulty": "easy", "final_answer": {"answer": 136.3972, "unit": "J"}, "id": "ke_000865_25.05_3.3", "license": "Apache-2.0", "prompt": "A body of mass 25.05 kg moves at 3.3 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 3.3^2 and multiply by 0.5 * 25.05.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 25.05, "velocity": 3.3}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=21 degrees through the sine of 2 theta.\n3. Substitute v=18.8 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 24.1078, \"unit\": \"m\"}", "dedupe_signature": "8e1a2eb848ecc8c0eb9b1521a9f9e3c5d5403006f5880c672749c1c30d783f16", "difficulty": "medium", "final_answer": {"answer": 24.1078, "unit": "m"}, "id": "projectile_range_000866_18.8_21", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 18.8 m/s and angle 21 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=21 degrees through the sine of 2 theta.\nSubstitute v=18.8 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 21, "gravity": 9.81, "speed": 18.8}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 3.97 * 8.314 * 256 / 72.2.\nFinal: {\"answer\": 117.0316, \"unit\": \"kPa\"}", "dedupe_signature": "5300afeea190c7107d68c3d420380dcf8208b50983e146c2b55409b0dbb58398", "difficulty": "medium", "final_answer": {"answer": 117.0316, "unit": "kPa"}, "id": "ideal_gas_000867_3.97_256_72.2", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=3.97 mol, T=256 K, and V=72.2 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 3.97 * 8.314 * 256 / 72.2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 3.97, "temp_k": 256, "volume_l": 72.2}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 640 * 0.81 * 80.\nFinal: {\"answer\": 41472.0, \"unit\": \"J\"}", "dedupe_signature": "a2f94ad50a626166194ef2a837c54f8f4ae45448c6130392e48184727a94f75a", "difficulty": "easy", "final_answer": {"answer": 41472.0, "unit": "J"}, "id": "heat_q_000868_640_0.81_80", "license": "Apache-2.0", "prompt": "A 640 g sample has specific heat 0.81 J/(g*K). How much heat is needed to raise its temperature by 80 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 640 * 0.81 * 80.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 80, "heat_capacity": 0.81, "mass_g": 640}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=56.1 V and R=124.8 ohm.\nFinal: {\"answer\": 25.218, \"unit\": \"W\"}", "dedupe_signature": "537c7fa9c1314873e6fff35dc588c64df83bcbbbdecebed7a3e1fdc46da2dba7", "difficulty": "easy", "final_answer": {"answer": 25.218, "unit": "W"}, "id": "ohm_power_000869_56.1_124.8", "license": "Apache-2.0", "prompt": "A resistor has resistance 124.8 ohm and voltage 56.1 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=56.1 V and R=124.8 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 124.8, "voltage": 56.1}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=176 mg, t=23.5 h, and T_half=25.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 92.9165, \"unit\": \"mg\"}", "dedupe_signature": "57bd9b23e51ef40c0febc9244cc9f41f1247255408542b63e84335dcd6075106", "difficulty": "medium", "final_answer": {"answer": 92.9165, "unit": "mg"}, "id": "half_life_000870_176_25.5_23.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 176 mg. Its half-life is 25.5 hours. How many mg remain after 23.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=176 mg, t=23.5 h, and T_half=25.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 23.5, "half_life": 25.5, "initial_amount": 176.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 5.93 mol * 18.015 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 106.8289, \"unit\": \"g\"}", "dedupe_signature": "a8d953b9b8916ec6e66994a8de6294f957701d9a53d4529de1e1a3dc67097c29", "difficulty": "medium", "final_answer": {"answer": 106.8289, "unit": "g"}, "id": "stoich_mass_000871_water_5.93", "license": "Apache-2.0", "prompt": "A sample contains 5.93 mol of water. Using molar mass 18.015 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 5.93 mol * 18.015 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "water", "molar_mass": 18.015, "moles": 5.93}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 420 mL to 0.42 L.\n3. Compute M = 0.365 / 0.42.\nFinal: {\"answer\": 0.869, \"unit\": \"mol/L\"}", "dedupe_signature": "8c4ada10a42b7517a834371dce543aa7976b18879a8c0f23dd050850dc77778b", "difficulty": "medium", "final_answer": {"answer": 0.869, "unit": "mol/L"}, "id": "molarity_000872_0.365_420", "license": "Apache-2.0", "prompt": "A solution contains 0.365 mol of solute in 420 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 420 mL to 0.42 L.\nCompute M = 0.365 / 0.42.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 0.365, "volume_ml": 420}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.94 y, so each step multiplies y by 1 - h*0.94.\n3. Apply that update for 3 steps and round the final state.\nFinal: {\"answer\": 0.1137, \"unit\": \"state_units\"}", "dedupe_signature": "c92a1e93dc066b297d650e2858c9a3eeee6e5bb0ab48c7b74cb14a8c60e7277c", "difficulty": "medium", "final_answer": {"answer": 0.1137, "unit": "state_units"}, "id": "euler_decay_000873_14_0.94_0.85_3", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.94 y with y(0)=14, step size h=0.85, for 3 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.94 y, so each step multiplies y by 1 - h*0.94.\nApply that update for 3 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 14.0, "rate": 0.94, "step": 0.85, "steps": 3}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-5.3)=-8.52 and f(-1.6)=-10.74.\n3. The interval width is 3.7.\nFinal: {\"answer\": -35.631, \"unit\": \"area_units\"}", "dedupe_signature": "222469330d42988bda77147b85de935db10975d54c10544213181aaffe687635", "difficulty": "medium", "final_answer": {"answer": -35.631, "unit": "area_units"}, "id": "trapz_linear_000874_-0.6_-11.7_-5.3_-1.6", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-0.6x+-11.7 from x=-5.3 to x=-1.6. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-5.3)=-8.52 and f(-1.6)=-10.74.\nThe interval width is 3.7.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -11.7, "slope": -0.6, "x0": -5.3, "x1": -1.5999999999999996}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.28 and add it to the current value.\nFinal: {\"answer\": [-0.782, -0.568, -0.452], \"unit\": \"temperature_units\"}", "dedupe_signature": "23fcc431e342353006580e8477aafcc21a17940c58828db259e49b7fc8670e24", "difficulty": "hard", "final_answer": {"answer": [-0.782, -0.568, -0.452], "unit": "temperature_units"}, "id": "heat_step_000875_0.28_-0.65_-2.0_1.0_-1.6_-0.1", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-0.65, right=-0.1; current interior values are [-2.0, 1.0, -1.6]. Use r=0.28. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.28 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-2.0, 1.0, -1.6], "left": -0.65, "r": 0.28, "right": -0.1}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 100 centimeters in one meter.\n2. Apply the conversion factor directly to the given value.\n3. Compute 1313.0 / 100.\nFinal: {\"answer\": 13.13, \"unit\": \"m\"}", "dedupe_signature": "ecd4bbf7d602d629695f9327f9b668c9213535ccf8c85a2eced87e9c5635940a", "difficulty": "easy", "final_answer": {"answer": 13.13, "unit": "m"}, "id": "unit_convert_000876_cm_to_m_1313", "license": "Apache-2.0", "prompt": "Convert 1313 cm to m. Return the converted value with unit.", "reasoning_trace": "There are 100 centimeters in one meter.\nApply the conversion factor directly to the given value.\nCompute 1313.0 / 100.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 1313.0}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [3.2, -0.25], \"unit\": \"dimensionless\"}", "dedupe_signature": "9f7b043fb56ea9ccd205972e1dd015d187b1be980155a8e5f82772965a81c955", "difficulty": "medium", "final_answer": {"answer": [3.2, -0.25], "unit": "dimensionless"}, "id": "line_two_point_000878_-4.5_8.5_3.2_-0.25", "license": "Apache-2.0", "prompt": "A line passes through points (-4.5, -14.65) and (8.5, 26.95). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -4.5, "x2": 8.5, "y1": -14.65, "y2": 26.950000000000003}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. amount times volume is not concentration\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "0e6cde74c754d8aa67b54548782c68ee69aed6251d47cf7d1b7cb953b2335c2b", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_000879_inconsistent_74ac0b02_691479", "license": "Apache-2.0", "prompt": "In instrument manual case 691479, check dimensional consistency for C = n * V. The left side has dimensions mol/L and the right side has dimensions mol*L. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\namount times volume is not concentration\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "C = n * V"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef weighted_sum_000880(values, weights):\n    if len(values) != len(weights):\n        raise ValueError('length mismatch')\n    return sum(value * weight for value, weight in zip(values, weights))\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"weighted_sum_000880\"}", "dedupe_signature": "d3896dcfa956cc2f0b6ec639b9092e5e8a8e5e847dc3a3b503e9336c0b3763d8", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "weighted_sum_000880"}, "id": "code_000880_weighted_sum_000880", "license": "Apache-2.0", "prompt": "Write a Python function weighted_sum_000880(values, weights) that returns sum(value*weight). Raise ValueError when the two inputs have different lengths. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "weighted_sum_000880"}, "verifier": {"function": "weighted_sum_000880", "tests": ["assert weighted_sum_000880([2, 3], [4, 5]) == 23", "assert weighted_sum_000880([], []) == 0", "try:\n    weighted_sum_000880([1], [1, 2])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: target_schema, valid_examples.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"target_schema\", \"valid_examples\"]}", "dedupe_signature": "2fb1db3669d7a99caeefb256501b5cad2f3105901f592efcabd4d5d3b4d270f4", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["target_schema", "valid_examples"]}, "id": "abstain_000881_target_schema_valid_examples", "license": "Apache-2.0", "prompt": "Write a parser that converts each billing experiment record from batch 203867 into the correct schema, but the prompt does not include the target schema or examples. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: target_schema, valid_examples.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["target_schema", "valid_examples"]}, "verifier": {"missing": ["target_schema", "valid_examples"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 22.3 kg and a = 0.6 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 13.38, \"unit\": \"N\"}", "dedupe_signature": "188750ae4216f5010b938df72f596dafb35b6e6b64cf9a4d1e408be287c439c5", "difficulty": "easy", "final_answer": {"answer": 13.38, "unit": "N"}, "id": "force_000882_22.3_0.6", "license": "Apache-2.0", "prompt": "A cart has mass 22.3 kg and measured acceleration 0.6 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 22.3 kg and a = 0.6 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 0.6, "mass": 22.3}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=45 degrees through the sine of 2 theta.\n3. Substitute v=49.2 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 246.7523, \"unit\": \"m\"}", "dedupe_signature": "0cdcf0b58ec6c543740600782d1c3262134f270577aa82c41b78c011531122bc", "difficulty": "medium", "final_answer": {"answer": 246.7523, "unit": "m"}, "id": "projectile_range_000884_49.2_45", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 49.2 m/s and angle 45 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=45 degrees through the sine of 2 theta.\nSubstitute v=49.2 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 45, "gravity": 9.81, "speed": 49.2}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 2.39 * 8.314 * 431 / 89.3.\nFinal: {\"answer\": 95.9033, \"unit\": \"kPa\"}", "dedupe_signature": "9e7267c313d8176e172005ebb5d5e3eeb9c45b90209acc32474a8a0b1adc5376", "difficulty": "medium", "final_answer": {"answer": 95.9033, "unit": "kPa"}, "id": "ideal_gas_000885_2.39_431_89.3", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=2.39 mol, T=431 K, and V=89.3 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 2.39 * 8.314 * 431 / 89.3.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 2.39, "temp_k": 431, "volume_l": 89.3}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1420 * 3.255 * 112.\nFinal: {\"answer\": 517675.2, \"unit\": \"J\"}", "dedupe_signature": "15fd980d6befaadc77b96b3a2b16916a89c37389b6db845a35567735aa1b09aa", "difficulty": "easy", "final_answer": {"answer": 517675.2, "unit": "J"}, "id": "heat_q_000886_1420_3.255_112", "license": "Apache-2.0", "prompt": "A 1420 g sample has specific heat 3.255 J/(g*K). How much heat is needed to raise its temperature by 112 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1420 * 3.255 * 112.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 112, "heat_capacity": 3.255, "mass_g": 1420}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=9.1 V and R=198.5 ohm.\nFinal: {\"answer\": 0.4172, \"unit\": \"W\"}", "dedupe_signature": "5a97bfb35e765a5d1377d8101200ca62a4d04c38cecef0e405b894940b653a5d", "difficulty": "easy", "final_answer": {"answer": 0.4172, "unit": "W"}, "id": "ohm_power_000887_9.1_198.5", "license": "Apache-2.0", "prompt": "A resistor has resistance 198.5 ohm and voltage 9.1 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=9.1 V and R=198.5 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 198.5, "voltage": 9.1}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=403.5 mg, t=143.5 h, and T_half=96 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 143.1747, \"unit\": \"mg\"}", "dedupe_signature": "352f1b7b39da3cf59e72c819bb2efa77944e0ded650595cf3154af5d75e0a7ef", "difficulty": "medium", "final_answer": {"answer": 143.1747, "unit": "mg"}, "id": "half_life_000888_403.5_96_143.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 403.5 mg. Its half-life is 96 hours. How many mg remain after 143.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=403.5 mg, t=143.5 h, and T_half=96 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 143.5, "half_life": 96.0, "initial_amount": 403.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 4525 mL to 4.525 L.\n3. Compute M = 0.295 / 4.525.\nFinal: {\"answer\": 0.0652, \"unit\": \"mol/L\"}", "dedupe_signature": "ed14b6459881bee48ff1c8dd4d6498a934a416c33c61c769d32dd693ec168abf", "difficulty": "medium", "final_answer": {"answer": 0.0652, "unit": "mol/L"}, "id": "molarity_000890_0.295_4525", "license": "Apache-2.0", "prompt": "A solution contains 0.295 mol of solute in 4525 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 4525 mL to 4.525 L.\nCompute M = 0.295 / 4.525.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 0.295, "volume_ml": 4525}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.96 y, so each step multiplies y by 1 - h*0.96.\n3. Apply that update for 7 steps and round the final state.\nFinal: {\"answer\": -0.1421, \"unit\": \"state_units\"}", "dedupe_signature": "4d9f0066c9f25054c09c53be4f9488bf787e591a00e95e5857f1d74e90917b7c", "difficulty": "medium", "final_answer": {"answer": -0.1421, "unit": "state_units"}, "id": "euler_decay_000891_44.5_0.96_1.5_7", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.96 y with y(0)=44.5, step size h=1.5, for 7 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.96 y, so each step multiplies y by 1 - h*0.96.\nApply that update for 7 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 44.5, "rate": 0.96, "step": 1.5, "steps": 7}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.04 and add it to the current value.\nFinal: {\"answer\": [2.434, -1.506, 0.83], \"unit\": \"temperature_units\"}", "dedupe_signature": "14d2ba3490e2ef4f827f7eb24177c5689151f317c73affed463804a00188a3a8", "difficulty": "hard", "final_answer": {"answer": [2.434, -1.506, 0.83], "unit": "temperature_units"}, "id": "heat_step_000893_0.04_0.55_2.7_-1.8_1.05_-1.6", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=0.55, right=-1.6; current interior values are [2.7, -1.8, 1.05]. Use r=0.04. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.04 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [2.7, -1.8, 1.05], "left": 0.55, "r": 0.04, "right": -1.6}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. lever arm times force has torque dimensions\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "bd07cf9d5d342848b72db0d3e52785351436d00cffa6d0f35287718cfe02ac90", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_000897_consistent_5ca82cb9_689724", "license": "Apache-2.0", "prompt": "In quality-control check case 689724, check dimensional consistency for tau = r * F. The left side has dimensions N*m and the right side has dimensions N*m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nlever arm times force has torque dimensions\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "tau = r * F"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef safe_mean_000898(values):\n    if not values:\n        raise ValueError('safe_mean requires at least one value')\n    return sum(values) / len(values)\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"safe_mean_000898\"}", "dedupe_signature": "3e53ff3283377f48ca4de15c26cf5c8252407d941d60bea64b60c03d5180d0ef", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "safe_mean_000898"}, "id": "code_000898_safe_mean_000898", "license": "Apache-2.0", "prompt": "Write a Python function safe_mean_000898(values) that returns the arithmetic mean. It must raise ValueError for an empty input and must not mutate the input list. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "safe_mean_000898"}, "verifier": {"function": "safe_mean_000898", "tests": ["assert safe_mean_000898([2, 4, 6]) == 4", "xs = [1, 2, 3]; assert safe_mean_000898(xs) == 2 and xs == [1, 2, 3]", "try:\n    safe_mean_000898([])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: recurrence, objective, tie_breaking_rule.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"recurrence\", \"objective\", \"tie_breaking_rule\"]}", "dedupe_signature": "db08a90462965b2fbcd084c396a65c89e92b0f0a0e75b01f93e3f1c4d181c20d", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["recurrence", "objective", "tie_breaking_rule"]}, "id": "abstain_000899_recurrence_objective_tie_breaking_rule", "license": "Apache-2.0", "prompt": "Write a dynamic-programming solver for a allocation scoring problem with 2753 items and budget 91755, but the recurrence, objective, and tie-breaking rule are all absent. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: recurrence, objective, tie_breaking_rule.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["recurrence", "objective", "tie_breaking_rule"]}, "verifier": {"missing": ["recurrence", "objective", "tie_breaking_rule"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 21.85 kg and a = 13.6 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 297.16, \"unit\": \"N\"}", "dedupe_signature": "908aee5991206d3b3b1c3a4812790972652b48b981dd8c7dc30219a340561619", "difficulty": "easy", "final_answer": {"answer": 297.16, "unit": "N"}, "id": "force_000900_21.85_13.6", "license": "Apache-2.0", "prompt": "A cart has mass 21.85 kg and measured acceleration 13.6 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 21.85 kg and a = 13.6 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 13.6, "mass": 21.85}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=39 degrees through the sine of 2 theta.\n3. Substitute v=43.6 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 189.5433, \"unit\": \"m\"}", "dedupe_signature": "213ba95320015c87432e09e357ed6375eb0ed58ab1d58fd242a9e7fda4b73f17", "difficulty": "medium", "final_answer": {"answer": 189.5433, "unit": "m"}, "id": "projectile_range_000902_43.6_39", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 43.6 m/s and angle 39 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=39 degrees through the sine of 2 theta.\nSubstitute v=43.6 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 39, "gravity": 9.81, "speed": 43.6}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1260 * 4.235 * 12.\nFinal: {\"answer\": 64033.2, \"unit\": \"J\"}", "dedupe_signature": "caae63579bbd7253ad59b4305c18bebb9c10960aab595c0b51c0aaa6dff191b3", "difficulty": "easy", "final_answer": {"answer": 64033.2, "unit": "J"}, "id": "heat_q_000904_1260_4.235_12", "license": "Apache-2.0", "prompt": "A 1260 g sample has specific heat 4.235 J/(g*K). How much heat is needed to raise its temperature by 12 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1260 * 4.235 * 12.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 12, "heat_capacity": 4.235, "mass_g": 1260}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=141.8 V and R=135.9 ohm.\nFinal: {\"answer\": 147.9561, \"unit\": \"W\"}", "dedupe_signature": "b93d0ae0d633ad1abfc641af0ed72a1efcc954b3d9346cf17641e981ea544021", "difficulty": "easy", "final_answer": {"answer": 147.9561, "unit": "W"}, "id": "ohm_power_000905_141.8_135.9", "license": "Apache-2.0", "prompt": "A resistor has resistance 135.9 ohm and voltage 141.8 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=141.8 V and R=135.9 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 135.9, "voltage": 141.8}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=21.5 mg, t=67.5 h, and T_half=108.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 13.9689, \"unit\": \"mg\"}", "dedupe_signature": "f5af5c6678e33e08955408812ce38dcf663a8b2f3c3ac52622e339288ad5ecfa", "difficulty": "medium", "final_answer": {"answer": 13.9689, "unit": "mg"}, "id": "half_life_000906_21.5_108.5_67.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 21.5 mg. Its half-life is 108.5 hours. How many mg remain after 67.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=21.5 mg, t=67.5 h, and T_half=108.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 67.5, "half_life": 108.5, "initial_amount": 21.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.4 y, so each step multiplies y by 1 - h*0.4.\n3. Apply that update for 3 steps and round the final state.\nFinal: {\"answer\": 6.1322, \"unit\": \"state_units\"}", "dedupe_signature": "4beb3839fa923e3f7caa954404cc935734214a0b87aebd7624250b438400a09f", "difficulty": "medium", "final_answer": {"answer": 6.1322, "unit": "state_units"}, "id": "euler_decay_000909_63_0.4_1.35_3", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.4 y with y(0)=63, step size h=1.35, for 3 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.4 y, so each step multiplies y by 1 - h*0.4.\nApply that update for 3 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 63.0, "rate": 0.4, "step": 1.35, "steps": 3}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-2.9)=17.19 and f(5.1)=-39.61.\n3. The interval width is 8.\nFinal: {\"answer\": -89.68, \"unit\": \"area_units\"}", "dedupe_signature": "2547705cc7740418e99271c4f5094783ca713d77d66959773161d4f9f7fce129", "difficulty": "medium", "final_answer": {"answer": -89.68, "unit": "area_units"}, "id": "trapz_linear_000910_-7.1_-3.4_-2.9_5.1", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-7.1x+-3.4 from x=-2.9 to x=5.1. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-2.9)=17.19 and f(5.1)=-39.61.\nThe interval width is 8.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -3.4, "slope": -7.1, "x0": -2.9, "x1": 5.1}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.28 and add it to the current value.\nFinal: {\"answer\": [1.592, 1.546, -0.034], \"unit\": \"temperature_units\"}", "dedupe_signature": "0bc318d30f8d620bbd7647b52aa5da130c4a10cb5ea1a597297a27647427aba1", "difficulty": "hard", "final_answer": {"answer": [1.592, 1.546, -0.034], "unit": "temperature_units"}, "id": "heat_step_000911_0.28_-1.0_2.95_2.05_-0.65_-1.15", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-1, right=-1.15; current interior values are [2.95, 2.05, -0.65]. Use r=0.28. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.28 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [2.95, 2.05, -0.65], "left": -1.0, "r": 0.28, "right": -1.15}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 24635.0 / 1000.\nFinal: {\"answer\": 24.635, \"unit\": \"kg\"}", "dedupe_signature": "94165f116d692c89028ea84b891604f021e4f14c24e1df1e09caf4b96bb8f379", "difficulty": "easy", "final_answer": {"answer": 24.635, "unit": "kg"}, "id": "unit_convert_000912_g_to_kg_24635", "license": "Apache-2.0", "prompt": "Convert 24635 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 24635.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 24635.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=243 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-113.2706, -222.3061], \"unit\": \"N\"}", "dedupe_signature": "100bdd8b90f7c61b5474f69169d4b039ac73a4fb1eb8575446698695e95cde9f", "difficulty": "medium", "final_answer": {"answer": [-113.2706, -222.3061], "unit": "N"}, "id": "vector_components_000913_249.5_243", "license": "Apache-2.0", "prompt": "A vector has magnitude 249.5 N at 243 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=243 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 243, "magnitude": 249.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-4.8, 20.75], \"unit\": \"dimensionless\"}", "dedupe_signature": "ee598f932687c7e505dc8e2f8f62071c48b3f9a70d898fb27465339c773ddf21", "difficulty": "medium", "final_answer": {"answer": [-4.8, 20.75], "unit": "dimensionless"}, "id": "line_two_point_000914_-3.5_6.5_-4.8_20.75", "license": "Apache-2.0", "prompt": "A line passes through points (-3.5, 37.55) and (6.5, -10.45). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -3.5, "x2": 6.5, "y1": 37.55, "y2": -10.45}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. volt squared divided by ohm is watt\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "10bcbfce5324e0e552a9179917d7f7272cc8528eefa1665217bca714beebd4e7", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_000915_consistent_82e93f3d_100721", "license": "Apache-2.0", "prompt": "In sensor calibration case 100721, check dimensional consistency for P = V^2 / R. The left side has dimensions W and the right side has dimensions W. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nvolt squared divided by ohm is watt\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "P = V^2 / R"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef clamp_000916(x, lo, hi):\n    if lo > hi:\n        raise ValueError('lo must be <= hi')\n    return min(max(x, lo), hi)\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"clamp_000916\"}", "dedupe_signature": "76cf9ac900f1308714df13a13fffc53dc0a820b7c73118dfdce968052f987f27", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "clamp_000916"}, "id": "code_000916_clamp_000916", "license": "Apache-2.0", "prompt": "Write a Python function clamp_000916(x, lo, hi) that clips x into the inclusive interval [lo, hi]. It must raise ValueError if lo > hi. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "clamp_000916"}, "verifier": {"function": "clamp_000916", "tests": ["assert clamp_000916(5, 0, 10) == 5", "assert clamp_000916(-2, 0, 10) == 0", "assert clamp_000916(12, 0, 10) == 10", "try:\n    clamp_000916(1, 3, 2)\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: recurrence, objective, tie_breaking_rule.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"recurrence\", \"objective\", \"tie_breaking_rule\"]}", "dedupe_signature": "76622454b0219b1bd5594dfc4f36f95f4d6f751805c0ca57317b0181fd90e8f6", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["recurrence", "objective", "tie_breaking_rule"]}, "id": "abstain_000917_recurrence_objective_tie_breaking_rule", "license": "Apache-2.0", "prompt": "Write a dynamic-programming solver for a routing scoring problem with 174 items and budget 10565, but the recurrence, objective, and tie-breaking rule are all absent. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: recurrence, objective, tie_breaking_rule.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["recurrence", "objective", "tie_breaking_rule"]}, "verifier": {"missing": ["recurrence", "objective", "tie_breaking_rule"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 19.5 kg and a = 12.25 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 238.875, \"unit\": \"N\"}", "dedupe_signature": "f46c213315c35f8affd6abcfe2fef671b3ae38f323991259db9ad5d5cc897c49", "difficulty": "easy", "final_answer": {"answer": 238.875, "unit": "N"}, "id": "force_000918_19.5_12.25", "license": "Apache-2.0", "prompt": "A cart has mass 19.5 kg and measured acceleration 12.25 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 19.5 kg and a = 12.25 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 12.25, "mass": 19.5}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 28.5^2 and multiply by 0.5 * 24.35.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 9889.1438, \"unit\": \"J\"}", "dedupe_signature": "0d64e07bd037834b3278c87ef3cba690e693e38f2ce5cce1c403e5674e80b5ac", "difficulty": "easy", "final_answer": {"answer": 9889.1438, "unit": "J"}, "id": "ke_000919_24.35_28.5", "license": "Apache-2.0", "prompt": "A body of mass 24.35 kg moves at 28.5 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 28.5^2 and multiply by 0.5 * 24.35.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 24.35, "velocity": 28.5}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=58 degrees through the sine of 2 theta.\n3. Substitute v=77 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 543.2161, \"unit\": \"m\"}", "dedupe_signature": "405f73d1e13438c2a069109008de28517c229f6c6a15691f8d62d9f20621fb99", "difficulty": "medium", "final_answer": {"answer": 543.2161, "unit": "m"}, "id": "projectile_range_000920_77_58", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 77 m/s and angle 58 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=58 degrees through the sine of 2 theta.\nSubstitute v=77 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 58, "gravity": 9.81, "speed": 77.0}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 1.27 * 8.314 * 476 / 15.2.\nFinal: {\"answer\": 330.6565, \"unit\": \"kPa\"}", "dedupe_signature": "ea2ddbf3df249604aa7278ae0264fb0a779be25a5cef0d30cfcad57a53774b30", "difficulty": "medium", "final_answer": {"answer": 330.6565, "unit": "kPa"}, "id": "ideal_gas_000921_1.27_476_15.2", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=1.27 mol, T=476 K, and V=15.2 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 1.27 * 8.314 * 476 / 15.2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 1.27, "temp_k": 476, "volume_l": 15.2}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1755 * 4.1 * 117.\nFinal: {\"answer\": 841873.5, \"unit\": \"J\"}", "dedupe_signature": "8a9abda593eac4eb391c4ba8dd8413799d510bd5b413af2aaef5329f7f34a4f6", "difficulty": "easy", "final_answer": {"answer": 841873.5, "unit": "J"}, "id": "heat_q_000922_1755_4.1_117", "license": "Apache-2.0", "prompt": "A 1755 g sample has specific heat 4.1 J/(g*K). How much heat is needed to raise its temperature by 117 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1755 * 4.1 * 117.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 117, "heat_capacity": 4.1, "mass_g": 1755}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=177.5 V and R=109.5 ohm.\nFinal: {\"answer\": 287.7283, \"unit\": \"W\"}", "dedupe_signature": "8cae01be373f981ed7db5fa074430cd1a973fd5f0c8580ba0bee9e395b4a7216", "difficulty": "easy", "final_answer": {"answer": 287.7283, "unit": "W"}, "id": "ohm_power_000923_177.5_109.5", "license": "Apache-2.0", "prompt": "A resistor has resistance 109.5 ohm and voltage 177.5 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=177.5 V and R=109.5 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 109.5, "voltage": 177.5}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 2.44 mol * 100.087 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 244.2123, \"unit\": \"g\"}", "dedupe_signature": "a3a04db24fc69ed2c86186842698a16e3ba3cab2d51cfbbbe75b00501cfb9c80", "difficulty": "medium", "final_answer": {"answer": 244.2123, "unit": "g"}, "id": "stoich_mass_000925_calcium_carbonate_2.44", "license": "Apache-2.0", "prompt": "A sample contains 2.44 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 2.44 mol * 100.087 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "calcium carbonate", "molar_mass": 100.087, "moles": 2.44}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 1860 mL to 1.86 L.\n3. Compute M = 1.76 / 1.86.\nFinal: {\"answer\": 0.9462, \"unit\": \"mol/L\"}", "dedupe_signature": "8a76bdde2c42c3e521ac2f9f90a4a016efc1d13b8747f151053e98b52d42cd66", "difficulty": "medium", "final_answer": {"answer": 0.9462, "unit": "mol/L"}, "id": "molarity_000926_1.76_1860", "license": "Apache-2.0", "prompt": "A solution contains 1.76 mol of solute in 1860 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 1860 mL to 1.86 L.\nCompute M = 1.76 / 1.86.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 1.76, "volume_ml": 1860}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.12 y, so each step multiplies y by 1 - h*0.12.\n3. Apply that update for 7 steps and round the final state.\nFinal: {\"answer\": 31.0828, \"unit\": \"state_units\"}", "dedupe_signature": "f25f9d037bc6537124ae5142858caab76bac54ec9611cbacc53b0cabc28612f2", "difficulty": "medium", "final_answer": {"answer": 31.0828, "unit": "state_units"}, "id": "euler_decay_000927_63_0.12_0.8_7", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.12 y with y(0)=63, step size h=0.8, for 7 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.12 y, so each step multiplies y by 1 - h*0.12.\nApply that update for 7 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 63.0, "rate": 0.12, "step": 0.8, "steps": 7}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-5.4)=-33.42 and f(2.4)=0.12.\n3. The interval width is 7.8.\nFinal: {\"answer\": -129.87, \"unit\": \"area_units\"}", "dedupe_signature": "41cf182f763880f4bdbddc2449cb3b7430ff89dfa2412f8b1553191cf7d11c20", "difficulty": "medium", "final_answer": {"answer": -129.87, "unit": "area_units"}, "id": "trapz_linear_000928_4.3_-10.2_-5.4_2.4", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=4.3x+-10.2 from x=-5.4 to x=2.4. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-5.4)=-33.42 and f(2.4)=0.12.\nThe interval width is 7.8.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -10.2, "slope": 4.3, "x0": -5.4, "x1": 2.3999999999999995}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.48 and add it to the current value.\nFinal: {\"answer\": [0.514, -0.054, 0.562], \"unit\": \"temperature_units\"}", "dedupe_signature": "a0cf071f67315af168a723a92ae63be4f7625a1d77ee6d878356355ebe464dbb", "difficulty": "hard", "final_answer": {"answer": [0.514, -0.054, 0.562], "unit": "temperature_units"}, "id": "heat_step_000929_0.48_1.25_-0.35_-0.15_0.25_1.3", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.25, right=1.3; current interior values are [-0.35, -0.15, 0.25]. Use r=0.48. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.48 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-0.35, -0.15, 0.25], "left": 1.25, "r": 0.48, "right": 1.3}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 27382.0 / 1000.\nFinal: {\"answer\": 27.382, \"unit\": \"kg\"}", "dedupe_signature": "2a8cea121e9cdc9c8f83f7c1a392bb8da8b0d6872992f1a4a238c888ebdaa63f", "difficulty": "easy", "final_answer": {"answer": 27.382, "unit": "kg"}, "id": "unit_convert_000930_g_to_kg_27382", "license": "Apache-2.0", "prompt": "Convert 27382 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 27382.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 27382.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [8.7, 10.75], \"unit\": \"dimensionless\"}", "dedupe_signature": "0f77a921c6d58cf458b1c0db002b06e86bb722a230d1c26cb12d03a424186550", "difficulty": "medium", "final_answer": {"answer": [8.7, 10.75], "unit": "dimensionless"}, "id": "line_two_point_000932_9.25_14.25_8.7_10.75", "license": "Apache-2.0", "prompt": "A line passes through points (9.25, 91.225) and (14.25, 134.725). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 9.25, "x2": 14.25, "y1": 91.225, "y2": 134.725}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. velocity times time gives distance, not acceleration\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "c52df2959fb53155bf9d8af339327a1ffc582c36585602610a49caaf7ea47d2f", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_000933_inconsistent_7481c798_241672", "license": "Apache-2.0", "prompt": "In simulation spec case 241672, check dimensional consistency for a = v * t. The left side has dimensions m/s^2 and the right side has dimensions m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nvelocity times time gives distance, not acceleration\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "a = v * t"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 11.8 kg and a = 9.1 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 107.38, \"unit\": \"N\"}", "dedupe_signature": "a45da01ff87c9c2aeb257f69e3e3bb2c56d5a30621379014ec54af12035977bb", "difficulty": "easy", "final_answer": {"answer": 107.38, "unit": "N"}, "id": "force_000936_11.8_9.1", "license": "Apache-2.0", "prompt": "A cart has mass 11.8 kg and measured acceleration 9.1 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 11.8 kg and a = 9.1 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 9.1, "mass": 11.8}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 29.3^2 and multiply by 0.5 * 28.4.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 12190.558, \"unit\": \"J\"}", "dedupe_signature": "ee29280f14dcf3ae9ef1618b61de4579ba4f833aacb6e150b37ee81953a616a6", "difficulty": "easy", "final_answer": {"answer": 12190.558, "unit": "J"}, "id": "ke_000937_28.4_29.3", "license": "Apache-2.0", "prompt": "A body of mass 28.4 kg moves at 29.3 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 29.3^2 and multiply by 0.5 * 28.4.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 28.4, "velocity": 29.3}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=59 degrees through the sine of 2 theta.\n3. Substitute v=42.7 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 164.1049, \"unit\": \"m\"}", "dedupe_signature": "a21e5e018179e3ea134de3923fe2f7963fbf5a8e0ddf2e2e3eb9e85db790ea3b", "difficulty": "medium", "final_answer": {"answer": 164.1049, "unit": "m"}, "id": "projectile_range_000938_42.7_59", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 42.7 m/s and angle 59 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=59 degrees through the sine of 2 theta.\nSubstitute v=42.7 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 59, "gravity": 9.81, "speed": 42.7}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 460 * 4.55 * 46.\nFinal: {\"answer\": 96278.0, \"unit\": \"J\"}", "dedupe_signature": "6a1eb8af431d15a58f9a8d8d9301bd40fb6deb26a696006de387d9d1f1c320c4", "difficulty": "easy", "final_answer": {"answer": 96278.0, "unit": "J"}, "id": "heat_q_000940_460_4.55_46", "license": "Apache-2.0", "prompt": "A 460 g sample has specific heat 4.55 J/(g*K). How much heat is needed to raise its temperature by 46 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 460 * 4.55 * 46.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 46, "heat_capacity": 4.55, "mass_g": 460}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=18.4 V and R=114.8 ohm.\nFinal: {\"answer\": 2.9491, \"unit\": \"W\"}", "dedupe_signature": "257e546a1d4f75b71d098f76ed7123991a5083aa13e0d326456f43dce9cfe012", "difficulty": "easy", "final_answer": {"answer": 2.9491, "unit": "W"}, "id": "ohm_power_000941_18.4_114.8", "license": "Apache-2.0", "prompt": "A resistor has resistance 114.8 ohm and voltage 18.4 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=18.4 V and R=114.8 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 114.8, "voltage": 18.4}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=974 mg, t=146 h, and T_half=14.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 0.9068, \"unit\": \"mg\"}", "dedupe_signature": "92e2dca859bd512934dc70ca4e3b82694cc6a1723ed3b60255d01423a04b959e", "difficulty": "medium", "final_answer": {"answer": 0.9068, "unit": "mg"}, "id": "half_life_000942_974_14.5_146", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 974 mg. Its half-life is 14.5 hours. How many mg remain after 146 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=974 mg, t=146 h, and T_half=14.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 146.0, "half_life": 14.5, "initial_amount": 974.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 7.65 mol * 58.44 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 447.066, \"unit\": \"g\"}", "dedupe_signature": "ba39e159e96ac8f660d193618bbc255a390c1ca685661f968c4e907bf4a34495", "difficulty": "medium", "final_answer": {"answer": 447.066, "unit": "g"}, "id": "stoich_mass_000943_sodium_chloride_7.65", "license": "Apache-2.0", "prompt": "A sample contains 7.65 mol of sodium chloride. Using molar mass 58.44 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 7.65 mol * 58.44 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "sodium chloride", "molar_mass": 58.44, "moles": 7.65}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 4990 mL to 4.99 L.\n3. Compute M = 0.615 / 4.99.\nFinal: {\"answer\": 0.1232, \"unit\": \"mol/L\"}", "dedupe_signature": "60238255aeeba6e7daa4107ff7635288fe89d90a00853d3c1b7a112a20fe1361", "difficulty": "medium", "final_answer": {"answer": 0.1232, "unit": "mol/L"}, "id": "molarity_000944_0.615_4990", "license": "Apache-2.0", "prompt": "A solution contains 0.615 mol of solute in 4990 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 4990 mL to 4.99 L.\nCompute M = 0.615 / 4.99.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 0.615, "volume_ml": 4990}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.52 y, so each step multiplies y by 1 - h*0.52.\n3. Apply that update for 5 steps and round the final state.\nFinal: {\"answer\": 0.0, \"unit\": \"state_units\"}", "dedupe_signature": "17c099e63bb3abb60b54ae350139cdca74f66e732383dd5e3a75d1d34ef5405c", "difficulty": "medium", "final_answer": {"answer": 0.0, "unit": "state_units"}, "id": "euler_decay_000945_3_0.52_1.75_5", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.52 y with y(0)=3, step size h=1.75, for 5 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.52 y, so each step multiplies y by 1 - h*0.52.\nApply that update for 5 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 3.0, "rate": 0.52, "step": 1.75, "steps": 5}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-0.7)=-18.27 and f(7.2)=-17.48.\n3. The interval width is 7.9.\nFinal: {\"answer\": -141.2125, \"unit\": \"area_units\"}", "dedupe_signature": "957afa2ce24e14a40fd3230dcdb23648249b24773a6f92c1fdd0f4663b3d55eb", "difficulty": "medium", "final_answer": {"answer": -141.2125, "unit": "area_units"}, "id": "trapz_linear_000946_0.1_-18.2_-0.7_7.2", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=0.1x+-18.2 from x=-0.7 to x=7.2. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-0.7)=-18.27 and f(7.2)=-17.48.\nThe interval width is 7.9.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -18.2, "slope": 0.1, "x0": -0.7, "x1": 7.2}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.24 and add it to the current value.\nFinal: {\"answer\": [1.794, 0.452, -0.27], \"unit\": \"temperature_units\"}", "dedupe_signature": "0d0bd4c2d9dc05dd40b3b854ef03c5726333cca73fbaeff9c9f4741f805b9fe7", "difficulty": "hard", "final_answer": {"answer": [1.794, 0.452, -0.27], "unit": "temperature_units"}, "id": "heat_step_000947_0.24_2.05_2.55_-0.1_-0.45_-0.05", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=2.05, right=-0.05; current interior values are [2.55, -0.1, -0.45]. Use r=0.24. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.24 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [2.55, -0.1, -0.45], "left": 2.05, "r": 0.24, "right": -0.05}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-0.6, 0.0], \"unit\": \"dimensionless\"}", "dedupe_signature": "fd6d4ceb9752fd3ad48f22c4bb712b4fe137ffa388f7f196fd41a1ba28a8d59e", "difficulty": "medium", "final_answer": {"answer": [-0.6, 0.0], "unit": "dimensionless"}, "id": "line_two_point_000950_-19.25_-9.5_-0.6_0", "license": "Apache-2.0", "prompt": "A line passes through points (-19.25, 11.55) and (-9.5, 5.7). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -19.25, "x2": -9.5, "y1": 11.549999999999999, "y2": 5.7}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. speed squared over acceleration has units of meters\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "d7debc3e0142d9c3e79c8a419b745728831606617cfa39108dc8d1798f39814d", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_000951_consistent_741d4e34_152139", "license": "Apache-2.0", "prompt": "In simulation spec case 152139, check dimensional consistency for R = v^2 * sin(theta) / g. The left side has dimensions m and the right side has dimensions m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nspeed squared over acceleration has units of meters\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "R = v^2 * sin(theta) / g"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef normalize_000952(values):\n    total = sum(values)\n    if total == 0:\n        raise ValueError('cannot normalize zero-sum values')\n    return [v / total for v in values]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"normalize_000952\"}", "dedupe_signature": "b50888b54a2c9068f1417e0732ae6ca6e2d6be8660c61bbd7d5450526b1cbcf1", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "normalize_000952"}, "id": "code_000952_normalize_000952", "license": "Apache-2.0", "prompt": "Write a Python function normalize_000952(values) that returns a new list whose values sum to 1. Raise ValueError if the sum is zero. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "normalize_000952"}, "verifier": {"function": "normalize_000952", "tests": ["out = normalize_000952([2, 3, 5]); assert len(out) == 3", "assert abs(sum(normalize_000952([2, 3, 5])) - 1.0) < 1e-12", "assert normalize_000952([1, 1]) == [0.5, 0.5]", "try:\n    normalize_000952([1, -1])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: volume.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"volume\"]}", "dedupe_signature": "6d4cb585b157b9c290df20be96564e0abfdd96fbdd00a21f29e00c5d55bc5037", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["volume"]}, "id": "abstain_000953_volume", "license": "Apache-2.0", "prompt": "Compute pressure from the ideal gas law. The prompt gives n=2.19 mol and T=283 K, but does not give volume. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: volume.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["volume"]}, "verifier": {"missing": ["volume"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 30.3^2 and multiply by 0.5 * 27.1.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 12440.1195, \"unit\": \"J\"}", "dedupe_signature": "64c8f0e91f2c8908a23dea42de73efb2737e117312f9aa3e22789feca140b548", "difficulty": "easy", "final_answer": {"answer": 12440.1195, "unit": "J"}, "id": "ke_000955_27.1_30.3", "license": "Apache-2.0", "prompt": "A body of mass 27.1 kg moves at 30.3 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 30.3^2 and multiply by 0.5 * 27.1.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 27.1, "velocity": 30.3}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=52 degrees through the sine of 2 theta.\n3. Substitute v=37.5 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 139.0906, \"unit\": \"m\"}", "dedupe_signature": "322452c9ff0264676a32b12ec3b391cd2b57b039b1faaade25226b6269478cbc", "difficulty": "medium", "final_answer": {"answer": 139.0906, "unit": "m"}, "id": "projectile_range_000956_37.5_52", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 37.5 m/s and angle 52 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=52 degrees through the sine of 2 theta.\nSubstitute v=37.5 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 52, "gravity": 9.81, "speed": 37.5}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 0.94 * 8.314 * 251 / 51.1.\nFinal: {\"answer\": 38.3876, \"unit\": \"kPa\"}", "dedupe_signature": "eb76de2ef917ee74577d134abc4705ef285c1fa2dbcfb752654ad53f1c948fca", "difficulty": "medium", "final_answer": {"answer": 38.3876, "unit": "kPa"}, "id": "ideal_gas_000957_0.94_251_51.1", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=0.94 mol, T=251 K, and V=51.1 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 0.94 * 8.314 * 251 / 51.1.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 0.94, "temp_k": 251, "volume_l": 51.1}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 75 * 2.545 * 115.\nFinal: {\"answer\": 21950.625, \"unit\": \"J\"}", "dedupe_signature": "139c48d864d70ea620c2c0ab98bf95b81873d3b3c2a6b57002097bd660a01c84", "difficulty": "easy", "final_answer": {"answer": 21950.625, "unit": "J"}, "id": "heat_q_000958_75_2.545_115", "license": "Apache-2.0", "prompt": "A 75 g sample has specific heat 2.545 J/(g*K). How much heat is needed to raise its temperature by 115 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 75 * 2.545 * 115.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 115, "heat_capacity": 2.545, "mass_g": 75}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=53 V and R=157.1 ohm.\nFinal: {\"answer\": 17.8803, \"unit\": \"W\"}", "dedupe_signature": "deef007fdd330c51ac4d1bb2a308c43757379691435358058e4ce6cd700151c1", "difficulty": "easy", "final_answer": {"answer": 17.8803, "unit": "W"}, "id": "ohm_power_000959_53_157.1", "license": "Apache-2.0", "prompt": "A resistor has resistance 157.1 ohm and voltage 53 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=53 V and R=157.1 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 157.1, "voltage": 53.0}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 4970 mL to 4.97 L.\n3. Compute M = 2.27 / 4.97.\nFinal: {\"answer\": 0.4567, \"unit\": \"mol/L\"}", "dedupe_signature": "d054bec1f3732c70aacf5ea37b7e0889a6d182ed0c8e788eae13259b242194d1", "difficulty": "medium", "final_answer": {"answer": 0.4567, "unit": "mol/L"}, "id": "molarity_000962_2.27_4970", "license": "Apache-2.0", "prompt": "A solution contains 2.27 mol of solute in 4970 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 4970 mL to 4.97 L.\nCompute M = 2.27 / 4.97.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 2.27, "volume_ml": 4970}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.67 y, so each step multiplies y by 1 - h*0.67.\n3. Apply that update for 4 steps and round the final state.\nFinal: {\"answer\": 18.4488, \"unit\": \"state_units\"}", "dedupe_signature": "bdc7bef4a0d61b2c6c3dce7c716d5558e1e912a41d825f69a7abe52df64abf75", "difficulty": "medium", "final_answer": {"answer": 18.4488, "unit": "state_units"}, "id": "euler_decay_000963_77.5_0.67_0.45_4", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.67 y with y(0)=77.5, step size h=0.45, for 4 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.67 y, so each step multiplies y by 1 - h*0.67.\nApply that update for 4 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 77.5, "rate": 0.67, "step": 0.45, "steps": 4}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-7.3)=-62.29 and f(0.8)=-11.26.\n3. The interval width is 8.1.\nFinal: {\"answer\": -297.8775, \"unit\": \"area_units\"}", "dedupe_signature": "59e5e9dd204b5769762550416b917ef0e632b3da7a8b5ddfb86b25a7d879593c", "difficulty": "medium", "final_answer": {"answer": -297.8775, "unit": "area_units"}, "id": "trapz_linear_000964_6.3_-16.3_-7.3_0.8", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=6.3x+-16.3 from x=-7.3 to x=0.8. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-7.3)=-62.29 and f(0.8)=-11.26.\nThe interval width is 8.1.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -16.3, "slope": 6.3, "x0": -7.3, "x1": 0.7999999999999998}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.32 and add it to the current value.\nFinal: {\"answer\": [0.236, 1.804, 1.964], \"unit\": \"temperature_units\"}", "dedupe_signature": "a1e507efa563a3568c222dc7945a0b13b059429612ab55e79bea0841bbb208c6", "difficulty": "hard", "final_answer": {"answer": [0.236, 1.804, 1.964], "unit": "temperature_units"}, "id": "heat_step_000965_0.32_-1.85_-0.1_2.7_2.7_0.4", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-1.85, right=0.4; current interior values are [-0.1, 2.7, 2.7]. Use r=0.32. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.32 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-0.1, 2.7, 2.7], "left": -1.85, "r": 0.32, "right": 0.4}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 100 centimeters in one meter.\n2. Apply the conversion factor directly to the given value.\n3. Compute 3818.5 / 100.\nFinal: {\"answer\": 38.185, \"unit\": \"m\"}", "dedupe_signature": "4e43036252dd6d954561c45aa942bf610f5435a78f214551409f0c6a59440456", "difficulty": "easy", "final_answer": {"answer": 38.185, "unit": "m"}, "id": "unit_convert_000966_cm_to_m_3818.5", "license": "Apache-2.0", "prompt": "Convert 3818.5 cm to m. Return the converted value with unit.", "reasoning_trace": "There are 100 centimeters in one meter.\nApply the conversion factor directly to the given value.\nCompute 3818.5 / 100.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 3818.5}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-9.25, -23.25], \"unit\": \"dimensionless\"}", "dedupe_signature": "cad5ce343746114eb2a5f5d37aa925608060ccc3e2854a6e0b0dc3a55e44d8c5", "difficulty": "medium", "final_answer": {"answer": [-9.25, -23.25], "unit": "dimensionless"}, "id": "line_two_point_000968_16_23.25_-9.25_-23.25", "license": "Apache-2.0", "prompt": "A line passes through points (16, -171.25) and (23.25, -238.312). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 16.0, "x2": 23.25, "y1": -171.25, "y2": -238.3125}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. m*v is momentum, not energy\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "9fbd1656d92f20323af0a0d494b488cc14fa49bce30959c7a9b6c0e7a5718cf9", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_000969_inconsistent_1e14b074_545993", "license": "Apache-2.0", "prompt": "In quality-control check case 545993, check dimensional consistency for E = m * v. The left side has dimensions kg*m^2/s^2 and the right side has dimensions kg*m/s. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nm*v is momentum, not energy\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "E = m * v"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef pairwise_ratios_000970(numerators, denominators):\n    if len(numerators) != len(denominators):\n        raise ValueError('length mismatch')\n    out = []\n    for numerator, denominator in zip(numerators, denominators):\n        if denominator == 0:\n            raise ValueError('zero denominator')\n        out.append(numerator / denominator)\n    return out\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"pairwise_ratios_000970\"}", "dedupe_signature": "4b75edf4ef1ca4cfcd184de509256859bab02433f778fbc96cc4d366567e89f6", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "pairwise_ratios_000970"}, "id": "code_000970_pairwise_ratios_000970", "license": "Apache-2.0", "prompt": "Write a Python function pairwise_ratios_000970(numerators, denominators) that returns a list of n/d values. Raise ValueError if lengths differ or any denominator is zero. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "pairwise_ratios_000970"}, "verifier": {"function": "pairwise_ratios_000970", "tests": ["assert pairwise_ratios_000970([2, 9], [4, 3]) == [0.5, 3.0]", "try:\n    pairwise_ratios_000970([1], [0])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass", "try:\n    pairwise_ratios_000970([1, 2], [1])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: left_boundary, right_boundary.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"left_boundary\", \"right_boundary\"]}", "dedupe_signature": "4ab915a5c74bda8bfbdf80923f3702df884bbb347b9e2b8d61ad98df63982659", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["left_boundary", "right_boundary"]}, "id": "abstain_000971_left_boundary_right_boundary", "license": "Apache-2.0", "prompt": "Solve the 1D heat equation after one finite-difference step. The prompt gives r=0.18 and interior values [0.65, 0.45, 2.15], but gives no boundary values. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: left_boundary, right_boundary.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["left_boundary", "right_boundary"]}, "verifier": {"missing": ["left_boundary", "right_boundary"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=59 degrees through the sine of 2 theta.\n3. Substitute v=12.6 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 14.2892, \"unit\": \"m\"}", "dedupe_signature": "7e9f03d9eb93d4e54184e9743dac1557b69c57a78796e7a88968a9cd192dba89", "difficulty": "medium", "final_answer": {"answer": 14.2892, "unit": "m"}, "id": "projectile_range_000974_12.6_59", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 12.6 m/s and angle 59 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=59 degrees through the sine of 2 theta.\nSubstitute v=12.6 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 59, "gravity": 9.81, "speed": 12.6}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 695 * 2.105 * 69.\nFinal: {\"answer\": 100945.275, \"unit\": \"J\"}", "dedupe_signature": "3cd71f08bd64a308a7c21f2d51c0208b72edbac99f15823d1ac6e481c9116352", "difficulty": "easy", "final_answer": {"answer": 100945.275, "unit": "J"}, "id": "heat_q_000976_695_2.105_69", "license": "Apache-2.0", "prompt": "A 695 g sample has specific heat 2.105 J/(g*K). How much heat is needed to raise its temperature by 69 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 695 * 2.105 * 69.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 69, "heat_capacity": 2.105, "mass_g": 695}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=63.6 V and R=92.8 ohm.\nFinal: {\"answer\": 43.5879, \"unit\": \"W\"}", "dedupe_signature": "47415321765cb5e99be7b1f60638a6bf9e1d718939d6d57a2f11c39603a64980", "difficulty": "easy", "final_answer": {"answer": 43.5879, "unit": "W"}, "id": "ohm_power_000977_63.6_92.8", "license": "Apache-2.0", "prompt": "A resistor has resistance 92.8 ohm and voltage 63.6 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=63.6 V and R=92.8 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 92.8, "voltage": 63.6}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=264 mg, t=263 h, and T_half=118 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 56.3202, \"unit\": \"mg\"}", "dedupe_signature": "887cbfd2a9c346e96b8c3452bf259d4adabadefc1e600af5c98d608a891ef857", "difficulty": "medium", "final_answer": {"answer": 56.3202, "unit": "mg"}, "id": "half_life_000978_264_118_263", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 264 mg. Its half-life is 118 hours. How many mg remain after 263 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=264 mg, t=263 h, and T_half=118 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 263.0, "half_life": 118.0, "initial_amount": 264.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 4.51 mol * 44.01 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 198.4851, \"unit\": \"g\"}", "dedupe_signature": "dc0c37335abdc16813583904a8add32519aea4a5c25a732d3cb2ea86edcd654e", "difficulty": "medium", "final_answer": {"answer": 198.4851, "unit": "g"}, "id": "stoich_mass_000979_carbon_dioxide_4.51", "license": "Apache-2.0", "prompt": "A sample contains 4.51 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 4.51 mol * 44.01 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "carbon dioxide", "molar_mass": 44.01, "moles": 4.51}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 4345 mL to 4.345 L.\n3. Compute M = 3.38 / 4.345.\nFinal: {\"answer\": 0.7779, \"unit\": \"mol/L\"}", "dedupe_signature": "108f60a192d17f84c904f473e9a6a8e1c3ea3dd89e3fa5efc27f568d3ad28891", "difficulty": "medium", "final_answer": {"answer": 0.7779, "unit": "mol/L"}, "id": "molarity_000980_3.38_4345", "license": "Apache-2.0", "prompt": "A solution contains 3.38 mol of solute in 4345 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 4345 mL to 4.345 L.\nCompute M = 3.38 / 4.345.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 3.38, "volume_ml": 4345}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.4 y, so each step multiplies y by 1 - h*0.4.\n3. Apply that update for 5 steps and round the final state.\nFinal: {\"answer\": 3.8725, \"unit\": \"state_units\"}", "dedupe_signature": "b10e913bd6b8193f9a4b50996eba900678529e68eee2326d43a5ec7710067ec0", "difficulty": "medium", "final_answer": {"answer": 3.8725, "unit": "state_units"}, "id": "euler_decay_000981_59_0.4_1.05_5", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.4 y with y(0)=59, step size h=1.05, for 5 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.4 y, so each step multiplies y by 1 - h*0.4.\nApply that update for 5 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 59.0, "rate": 0.4, "step": 1.05, "steps": 5}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-2.7)=-27.58 and f(5.1)=22.34.\n3. The interval width is 7.8.\nFinal: {\"answer\": -20.436, \"unit\": \"area_units\"}", "dedupe_signature": "4fac33289181f2000855ce3d22cedc40db55df9c8604990ff179fb9fd3144ede", "difficulty": "medium", "final_answer": {"answer": -20.436, "unit": "area_units"}, "id": "trapz_linear_000982_6.4_-10.3_-2.7_5.1", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=6.4x+-10.3 from x=-2.7 to x=5.1. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-2.7)=-27.58 and f(5.1)=22.34.\nThe interval width is 7.8.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -10.3, "slope": 6.4, "x0": -2.7, "x1": 5.1}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.1 and add it to the current value.\nFinal: {\"answer\": [1.37, 1.445, 1.43], \"unit\": \"temperature_units\"}", "dedupe_signature": "e4aceafdb21adc2aff6fe2946ee76bb37a96a85df94d507281eaaae8a2d9053d", "difficulty": "hard", "final_answer": {"answer": [1.37, 1.445, 1.43], "unit": "temperature_units"}, "id": "heat_step_000983_0.1_2.25_1.25_1.45_1.6_0.05", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=2.25, right=0.05; current interior values are [1.25, 1.45, 1.6]. Use r=0.1. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.1 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [1.25, 1.45, 1.6], "left": 2.25, "r": 0.1, "right": 0.05}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kelvin equals Celsius plus 273.15.\n2. Apply the conversion factor directly to the given value.\n3. Compute -54.5 + 273.15.\nFinal: {\"answer\": 218.65, \"unit\": \"K\"}", "dedupe_signature": "a479945f9bdc044edd80fba51f603b36c6bb134dc0543947c83802b207eb7631", "difficulty": "easy", "final_answer": {"answer": 218.65, "unit": "K"}, "id": "unit_convert_000984_c_to_k_-54.5", "license": "Apache-2.0", "prompt": "Convert -54.5 degC to K. Return the converted value with unit.", "reasoning_trace": "Kelvin equals Celsius plus 273.15.\nApply the conversion factor directly to the given value.\nCompute -54.5 + 273.15.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": -54.5}, "verifier": {"formula": "value + 273.15", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=159 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-440.65, 169.1497], \"unit\": \"N\"}", "dedupe_signature": "49e87dd56e20fba5e1cf7a3fbcbae5589104211b07ebc602fce51228280a0cc0", "difficulty": "medium", "final_answer": {"answer": [-440.65, 169.1497], "unit": "N"}, "id": "vector_components_000985_472_159", "license": "Apache-2.0", "prompt": "A vector has magnitude 472 N at 159 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=159 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 159, "magnitude": 472.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [2.25, 21.75], \"unit\": \"dimensionless\"}", "dedupe_signature": "fe4e6220122c646304411adf945e7fdeeaf6c53c42633a853073d5ca5a8f9f63", "difficulty": "medium", "final_answer": {"answer": [2.25, 21.75], "unit": "dimensionless"}, "id": "line_two_point_000986_-17.25_-12.75_2.25_21.75", "license": "Apache-2.0", "prompt": "A line passes through points (-17.25, -17.0625) and (-12.75, -6.9375). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -17.25, "x2": -12.75, "y1": -17.0625, "y2": -6.9375}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. velocity divided by time is acceleration\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "ac212a217ca3ddbe2a6173106f69236c9715edd50969c6b5d543161fcfd7d79c", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_000987_inconsistent_c1271127_189021", "license": "Apache-2.0", "prompt": "In model card equation case 189021, check dimensional consistency for x = v / t. The left side has dimensions m and the right side has dimensions m/s^2. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nvelocity divided by time is acceleration\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "x = v / t"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\nimport math\n\ndef unit_vector_000988(x, y):\n    norm = math.hypot(x, y)\n    if norm == 0:\n        raise ValueError('zero vector has no direction')\n    return (x / norm, y / norm)\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"unit_vector_000988\"}", "dedupe_signature": "508e1f3cc73ea405a8dd60d7b3cf200351070e4b49fe12f382cc657a7303d7bb", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "unit_vector_000988"}, "id": "code_000988_unit_vector_000988", "license": "Apache-2.0", "prompt": "Write a Python function unit_vector_000988(x, y) that returns the 2D unit vector as a tuple. Raise ValueError for the zero vector. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "unit_vector_000988"}, "verifier": {"function": "unit_vector_000988", "tests": ["ux, uy = unit_vector_000988(3, 4); assert abs(ux - 0.6) < 1e-12 and abs(uy - 0.8) < 1e-12", "assert unit_vector_000988(0, 5) == (0, 1)", "try:\n    unit_vector_000988(0, 0)\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 14.5 kg and a = 10.85 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 157.325, \"unit\": \"N\"}", "dedupe_signature": "b374c9d7d0a2cf2f7dcaf11fcc7dc976737a604fe8567d72ad1d4faff08f9165", "difficulty": "easy", "final_answer": {"answer": 157.325, "unit": "N"}, "id": "force_000990_14.5_10.85", "license": "Apache-2.0", "prompt": "A cart has mass 14.5 kg and measured acceleration 10.85 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 14.5 kg and a = 10.85 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 10.85, "mass": 14.5}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=80 degrees through the sine of 2 theta.\n3. Substitute v=50.1 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 87.5101, \"unit\": \"m\"}", "dedupe_signature": "49783e7692c83a70978046e47d65c54490e7c41909dc2b3174cb9e176ab52fd1", "difficulty": "medium", "final_answer": {"answer": 87.5101, "unit": "m"}, "id": "projectile_range_000992_50.1_80", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 50.1 m/s and angle 80 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=80 degrees through the sine of 2 theta.\nSubstitute v=50.1 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 80, "gravity": 9.81, "speed": 50.1}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 5.36 * 8.314 * 409 / 37.9.\nFinal: {\"answer\": 480.9046, \"unit\": \"kPa\"}", "dedupe_signature": "a8c4ec79e3a5b6c9836132ae47f85830f29b1aadc90b80b25dd78b5a3c4354bb", "difficulty": "medium", "final_answer": {"answer": 480.9046, "unit": "kPa"}, "id": "ideal_gas_000993_5.36_409_37.9", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=5.36 mol, T=409 K, and V=37.9 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 5.36 * 8.314 * 409 / 37.9.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 5.36, "temp_k": 409, "volume_l": 37.9}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1135 * 1.39 * 23.\nFinal: {\"answer\": 36285.95, \"unit\": \"J\"}", "dedupe_signature": "dcc78f1ee16008c20bd53ca323dd5cbe0f3c9a9806fe03778dc33a2b276e60c5", "difficulty": "easy", "final_answer": {"answer": 36285.95, "unit": "J"}, "id": "heat_q_000994_1135_1.39_23", "license": "Apache-2.0", "prompt": "A 1135 g sample has specific heat 1.39 J/(g*K). How much heat is needed to raise its temperature by 23 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1135 * 1.39 * 23.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 23, "heat_capacity": 1.39, "mass_g": 1135}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=131.3 V and R=31.8 ohm.\nFinal: {\"answer\": 542.1286, \"unit\": \"W\"}", "dedupe_signature": "f6d5b145fb913824b55a9ccec0083f7ff966469af8d8039b274a2df8896d68be", "difficulty": "easy", "final_answer": {"answer": 542.1286, "unit": "W"}, "id": "ohm_power_000995_131.3_31.8", "license": "Apache-2.0", "prompt": "A resistor has resistance 31.8 ohm and voltage 131.3 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=131.3 V and R=31.8 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 31.8, "voltage": 131.3}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=944 mg, t=343 h, and T_half=42.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 3.5114, \"unit\": \"mg\"}", "dedupe_signature": "635e9ebeea4a7bd33f30f98f7ac519e534454095df2f5028cc1dba8959f53629", "difficulty": "medium", "final_answer": {"answer": 3.5114, "unit": "mg"}, "id": "half_life_000996_944_42.5_343", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 944 mg. Its half-life is 42.5 hours. How many mg remain after 343 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=944 mg, t=343 h, and T_half=42.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 343.0, "half_life": 42.5, "initial_amount": 944.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 4020 mL to 4.02 L.\n3. Compute M = 2.91 / 4.02.\nFinal: {\"answer\": 0.7239, \"unit\": \"mol/L\"}", "dedupe_signature": "dd5c3f277fb4c1b60c5017be81716e30aa023768296bc96fa4bc154b52f91d3f", "difficulty": "medium", "final_answer": {"answer": 0.7239, "unit": "mol/L"}, "id": "molarity_000998_2.91_4020", "license": "Apache-2.0", "prompt": "A solution contains 2.91 mol of solute in 4020 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 4020 mL to 4.02 L.\nCompute M = 2.91 / 4.02.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 2.91, "volume_ml": 4020}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-4.8)=39.68 and f(-1.7)=23.87.\n3. The interval width is 3.1.\nFinal: {\"answer\": 98.5025, \"unit\": \"area_units\"}", "dedupe_signature": "4367bd498b25125b5b414f3ddf1391ff8f41b6809d6adad316c863e625c58441", "difficulty": "medium", "final_answer": {"answer": 98.5025, "unit": "area_units"}, "id": "trapz_linear_001000_-5.1_15.2_-4.8_-1.7", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-5.1x+15.2 from x=-4.8 to x=-1.7. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-4.8)=39.68 and f(-1.7)=23.87.\nThe interval width is 3.1.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 15.2, "slope": -5.1, "x0": -4.8, "x1": -1.6999999999999997}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.06 and add it to the current value.\nFinal: {\"answer\": [1.908, 0.338, 2.518], \"unit\": \"temperature_units\"}", "dedupe_signature": "213319b3157bbde82ee41b3604c81a4c1f750dddec8be0d730535d650b8f0e94", "difficulty": "hard", "final_answer": {"answer": [1.908, 0.338, 2.518], "unit": "temperature_units"}, "id": "heat_step_001001_0.06_0.95_2.1_0.05_2.8_0.85", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=0.95, right=0.85; current interior values are [2.1, 0.05, 2.8]. Use r=0.06. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.06 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [2.1, 0.05, 2.8], "left": 0.95, "r": 0.06, "right": 0.85}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 100 centimeters in one meter.\n2. Apply the conversion factor directly to the given value.\n3. Compute 1643.5 / 100.\nFinal: {\"answer\": 16.435, \"unit\": \"m\"}", "dedupe_signature": "b056db30b0991b7ab39ae75869583727f6792c4c7224e8840897fd60aef2407f", "difficulty": "easy", "final_answer": {"answer": 16.435, "unit": "m"}, "id": "unit_convert_001002_cm_to_m_1643.5", "license": "Apache-2.0", "prompt": "Convert 1643.5 cm to m. Return the converted value with unit.", "reasoning_trace": "There are 100 centimeters in one meter.\nApply the conversion factor directly to the given value.\nCompute 1643.5 / 100.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 1643.5}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=40 degrees and keep the unit as newtons.\nFinal: {\"answer\": [41.3664, 34.7105], \"unit\": \"N\"}", "dedupe_signature": "da822c806e7f77a10fc0a82405bdaaa5c486492c9aa1881c0bf9321aa058c9f8", "difficulty": "medium", "final_answer": {"answer": [41.3664, 34.7105], "unit": "N"}, "id": "vector_components_001003_54_40", "license": "Apache-2.0", "prompt": "A vector has magnitude 54 N at 40 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=40 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 40, "magnitude": 54.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-0.8, -22.0], \"unit\": \"dimensionless\"}", "dedupe_signature": "2a0e38f00e86d3577f8ffb6965b35a9b83a0b1cea996d2f2a9b018208cfd85e8", "difficulty": "medium", "final_answer": {"answer": [-0.8, -22.0], "unit": "dimensionless"}, "id": "line_two_point_001004_14.25_27.5_-0.8_-22", "license": "Apache-2.0", "prompt": "A line passes through points (14.25, -33.4) and (27.5, -44). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 14.25, "x2": 27.5, "y1": -33.4, "y2": -44.0}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. velocity times time gives distance, not acceleration\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "b329e83a0c88e11087e81a09069a386ff2fde3269f00edb0769d7bb1bb9c0600", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_001005_inconsistent_7481c798_728386", "license": "Apache-2.0", "prompt": "In field worksheet case 728386, check dimensional consistency for a = v * t. The left side has dimensions m/s^2 and the right side has dimensions m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nvelocity times time gives distance, not acceleration\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "a = v * t"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef safe_mean_001006(values):\n    if not values:\n        raise ValueError('safe_mean requires at least one value')\n    return sum(values) / len(values)\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"safe_mean_001006\"}", "dedupe_signature": "a316d93871a7671300918613bd2956070275e783b70bf265066a91f52c52e5cf", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "safe_mean_001006"}, "id": "code_001006_safe_mean_001006", "license": "Apache-2.0", "prompt": "Write a Python function safe_mean_001006(values) that returns the arithmetic mean. It must raise ValueError for an empty input and must not mutate the input list. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "safe_mean_001006"}, "verifier": {"function": "safe_mean_001006", "tests": ["assert safe_mean_001006([2, 4, 6]) == 4", "xs = [1, 2, 3]; assert safe_mean_001006(xs) == 2 and xs == [1, 2, 3]", "try:\n    safe_mean_001006([])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: required_fields, allowed_transformations.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"required_fields\", \"allowed_transformations\"]}", "dedupe_signature": "2d8a22a78a57927d98364e369a6ba2cd1549c3be1aa4598833ac778bb68e6e16", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["required_fields", "allowed_transformations"]}, "id": "abstain_001007_required_fields_allowed_transformations", "license": "Apache-2.0", "prompt": "Write a sanitizer for valid mobile invoice records in release 625555, but the prompt does not state which fields are required or which transformations are allowed. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: required_fields, allowed_transformations.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["required_fields", "allowed_transformations"]}, "verifier": {"missing": ["required_fields", "allowed_transformations"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 4.8^2 and multiply by 0.5 * 7.3.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 84.096, \"unit\": \"J\"}", "dedupe_signature": "5d0ce082d6dac8e510577486d87c6a7b4499f6ee41716476267b414b7fbc2879", "difficulty": "easy", "final_answer": {"answer": 84.096, "unit": "J"}, "id": "ke_001009_7.3_4.8", "license": "Apache-2.0", "prompt": "A body of mass 7.3 kg moves at 4.8 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 4.8^2 and multiply by 0.5 * 7.3.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 7.3, "velocity": 4.8}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=77 degrees through the sine of 2 theta.\n3. Substitute v=61.5 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 169.0142, \"unit\": \"m\"}", "dedupe_signature": "42b247eb96032a8c7d4c08ea8e0d87342198e346248ded57aa727e2da148fb79", "difficulty": "medium", "final_answer": {"answer": 169.0142, "unit": "m"}, "id": "projectile_range_001010_61.5_77", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 61.5 m/s and angle 77 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=77 degrees through the sine of 2 theta.\nSubstitute v=61.5 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 77, "gravity": 9.81, "speed": 61.5}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=113.7 V and R=120.5 ohm.\nFinal: {\"answer\": 107.2837, \"unit\": \"W\"}", "dedupe_signature": "6b00b53cb28bed556a832cf493a4edaeddef9524263bd329a9bb97bffc66e341", "difficulty": "easy", "final_answer": {"answer": 107.2837, "unit": "W"}, "id": "ohm_power_001013_113.7_120.5", "license": "Apache-2.0", "prompt": "A resistor has resistance 120.5 ohm and voltage 113.7 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=113.7 V and R=120.5 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 120.5, "voltage": 113.7}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 2130 mL to 2.13 L.\n3. Compute M = 3.82 / 2.13.\nFinal: {\"answer\": 1.7934, \"unit\": \"mol/L\"}", "dedupe_signature": "8d42596883cb7881b3f2b00b14eb7a25f9f8cca82bd966ea2fd1b16a2b296e72", "difficulty": "medium", "final_answer": {"answer": 1.7934, "unit": "mol/L"}, "id": "molarity_001016_3.82_2130", "license": "Apache-2.0", "prompt": "A solution contains 3.82 mol of solute in 2130 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 2130 mL to 2.13 L.\nCompute M = 3.82 / 2.13.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 3.82, "volume_ml": 2130}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.73 y, so each step multiplies y by 1 - h*0.73.\n3. Apply that update for 11 steps and round the final state.\nFinal: {\"answer\": 0.0, \"unit\": \"state_units\"}", "dedupe_signature": "23fc9d1c7bd92307c56cf68e5e2824f31183ca8ad3fbfe1248e09de104e0bf87", "difficulty": "medium", "final_answer": {"answer": 0.0, "unit": "state_units"}, "id": "euler_decay_001017_52.5_0.73_1.25_11", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.73 y with y(0)=52.5, step size h=1.25, for 11 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.73 y, so each step multiplies y by 1 - h*0.73.\nApply that update for 11 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 52.5, "rate": 0.73, "step": 1.25, "steps": 11}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(9.8)=60.08 and f(14.8)=93.08.\n3. The interval width is 5.\nFinal: {\"answer\": 382.9, \"unit\": \"area_units\"}", "dedupe_signature": "f5c7375644c43c95ac7838c4ee8f4c2538df6f840af3955d12ecb2d14c26eab7", "difficulty": "medium", "final_answer": {"answer": 382.9, "unit": "area_units"}, "id": "trapz_linear_001018_6.6_-4.6_9.8_14.8", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=6.6x+-4.6 from x=9.8 to x=14.8. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(9.8)=60.08 and f(14.8)=93.08.\nThe interval width is 5.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -4.6, "slope": 6.6, "x0": 9.8, "x1": 14.8}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.22 and add it to the current value.\nFinal: {\"answer\": [0.793, 1.829, 1.003], \"unit\": \"temperature_units\"}", "dedupe_signature": "ffa97204acbe7ee77ce8e9ca0dd574baa421aec5f0f7f430914c723436924a30", "difficulty": "hard", "final_answer": {"answer": [0.793, 1.829, 1.003], "unit": "temperature_units"}, "id": "heat_step_001019_0.22_-0.55_0.65_2.5_1.3_-1.25", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-0.55, right=-1.25; current interior values are [0.65, 2.5, 1.3]. Use r=0.22. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.22 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [0.65, 2.5, 1.3], "left": -0.55, "r": 0.22, "right": -1.25}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 26986.0 / 1000.\nFinal: {\"answer\": 26.986, \"unit\": \"kg\"}", "dedupe_signature": "56148bba6f820c257147c29c8843b7e85d3ff2c1b7405d4c6b81635d002c3b35", "difficulty": "easy", "final_answer": {"answer": 26.986, "unit": "kg"}, "id": "unit_convert_001020_g_to_kg_26986", "license": "Apache-2.0", "prompt": "Convert 26986 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 26986.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 26986.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=22 degrees and keep the unit as newtons.\nFinal: {\"answer\": [94.5728, 38.2099], \"unit\": \"N\"}", "dedupe_signature": "418d21b1844b2aa85caf96e238c64e4687dddd581294053826c63dddac388b00", "difficulty": "medium", "final_answer": {"answer": [94.5728, 38.2099], "unit": "N"}, "id": "vector_components_001021_102_22", "license": "Apache-2.0", "prompt": "A vector has magnitude 102 N at 22 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=22 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 22, "magnitude": 102.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-3.9, 3.5], \"unit\": \"dimensionless\"}", "dedupe_signature": "4fe0340bff38a4017db228f692cf84bb9dabac63e1c89e7de08d3ad872f5fe52", "difficulty": "medium", "final_answer": {"answer": [-3.9, 3.5], "unit": "dimensionless"}, "id": "line_two_point_001022_12.5_13_-3.9_3.5", "license": "Apache-2.0", "prompt": "A line passes through points (12.5, -45.25) and (13, -47.2). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 12.5, "x2": 13.0, "y1": -45.25, "y2": -47.199999999999996}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. speed squared over acceleration has units of meters\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "46f9325ae586132382b69e2bccce7e45c6ab22395cc24f3816d3fbcd94c65739", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_001023_consistent_741d4e34_255729", "license": "Apache-2.0", "prompt": "In simulation spec case 255729, check dimensional consistency for R = v^2 * sin(theta) / g. The left side has dimensions m and the right side has dimensions m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nspeed squared over acceleration has units of meters\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "R = v^2 * sin(theta) / g"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef normalize_001024(values):\n    total = sum(values)\n    if total == 0:\n        raise ValueError('cannot normalize zero-sum values')\n    return [v / total for v in values]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"normalize_001024\"}", "dedupe_signature": "a29b0c6d47eccc0e7a951c5dbd661cc748d81a89e223575f51c040d9dc66eb60", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "normalize_001024"}, "id": "code_001024_normalize_001024", "license": "Apache-2.0", "prompt": "Write a Python function normalize_001024(values) that returns a new list whose values sum to 1. Raise ValueError if the sum is zero. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "normalize_001024"}, "verifier": {"function": "normalize_001024", "tests": ["out = normalize_001024([2, 3, 5]); assert len(out) == 3", "assert abs(sum(normalize_001024([2, 3, 5])) - 1.0) < 1e-12", "assert normalize_001024([1, 1]) == [0.5, 0.5]", "try:\n    normalize_001024([1, -1])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: launch_angle_or_vertical_velocity.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"launch_angle_or_vertical_velocity\"]}", "dedupe_signature": "9db1c4e3a1a88398ec08cfb7c9cb8147a7bfc4ccb0ea8cd41b99c55afa73b7ed", "difficulty": "easy", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["launch_angle_or_vertical_velocity"]}, "id": "abstain_001025_launch_angle_or_vertical_velocity", "license": "Apache-2.0", "prompt": "Compute projectile range on level ground. The prompt gives initial speed 53.8 m/s but does not give launch angle or vertical velocity. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: launch_angle_or_vertical_velocity.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["launch_angle_or_vertical_velocity"]}, "verifier": {"missing": ["launch_angle_or_vertical_velocity"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 19.45 kg and a = 2.75 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 53.4875, \"unit\": \"N\"}", "dedupe_signature": "a7d0cfac063f7320fa34180c2d93f79116b9db77dea8004c5e0574c4f2993fe8", "difficulty": "easy", "final_answer": {"answer": 53.4875, "unit": "N"}, "id": "force_001026_19.45_2.75", "license": "Apache-2.0", "prompt": "A cart has mass 19.45 kg and measured acceleration 2.75 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 19.45 kg and a = 2.75 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 2.75, "mass": 19.45}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 4.2^2 and multiply by 0.5 * 22.6.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 199.332, \"unit\": \"J\"}", "dedupe_signature": "1a6bcb98594e5e72917c8f950828651e6d6b933045c2ae2e334fd0930e47996c", "difficulty": "easy", "final_answer": {"answer": 199.332, "unit": "J"}, "id": "ke_001027_22.6_4.2", "license": "Apache-2.0", "prompt": "A body of mass 22.6 kg moves at 4.2 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 4.2^2 and multiply by 0.5 * 22.6.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 22.6, "velocity": 4.2}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=71 degrees through the sine of 2 theta.\n3. Substitute v=41.1 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 106.0124, \"unit\": \"m\"}", "dedupe_signature": "efe0120b8dee51bae8436753c60a7fdd5935758282aabe882d36af02edb156b2", "difficulty": "medium", "final_answer": {"answer": 106.0124, "unit": "m"}, "id": "projectile_range_001028_41.1_71", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 41.1 m/s and angle 71 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=71 degrees through the sine of 2 theta.\nSubstitute v=41.1 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 71, "gravity": 9.81, "speed": 41.1}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 2.71 * 8.314 * 369 / 78.7.\nFinal: {\"answer\": 105.6406, \"unit\": \"kPa\"}", "dedupe_signature": "a435fbcd6c58ecb8ff451537a43e5a9409da70f4012ee15c1c7ba573f8072169", "difficulty": "medium", "final_answer": {"answer": 105.6406, "unit": "kPa"}, "id": "ideal_gas_001029_2.71_369_78.7", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=2.71 mol, T=369 K, and V=78.7 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 2.71 * 8.314 * 369 / 78.7.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 2.71, "temp_k": 369, "volume_l": 78.7}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1985 * 3.205 * 38.\nFinal: {\"answer\": 241753.15, \"unit\": \"J\"}", "dedupe_signature": "ae4bdddd30932ff978046530cca41037be8e5f565a13c31f864232a3235d0b0f", "difficulty": "easy", "final_answer": {"answer": 241753.15, "unit": "J"}, "id": "heat_q_001030_1985_3.205_38", "license": "Apache-2.0", "prompt": "A 1985 g sample has specific heat 3.205 J/(g*K). How much heat is needed to raise its temperature by 38 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1985 * 3.205 * 38.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 38, "heat_capacity": 3.205, "mass_g": 1985}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=236.4 V and R=99 ohm.\nFinal: {\"answer\": 564.4945, \"unit\": \"W\"}", "dedupe_signature": "63812b48cd400985de7305c234903d86cf6b5229bf9e59f881a72d03eaa287be", "difficulty": "easy", "final_answer": {"answer": 564.4945, "unit": "W"}, "id": "ohm_power_001031_236.4_99", "license": "Apache-2.0", "prompt": "A resistor has resistance 99 ohm and voltage 236.4 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=236.4 V and R=99 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 99.0, "voltage": 236.4}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=85.5 mg, t=204 h, and T_half=119 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 26.0564, \"unit\": \"mg\"}", "dedupe_signature": "87a83be0cd2e455b54690988b3c7e7b2abff069afb3b5eaa2d0331d66199efcf", "difficulty": "medium", "final_answer": {"answer": 26.0564, "unit": "mg"}, "id": "half_life_001032_85.5_119_204", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 85.5 mg. Its half-life is 119 hours. How many mg remain after 204 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=85.5 mg, t=204 h, and T_half=119 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 204.0, "half_life": 119.0, "initial_amount": 85.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 7.68 mol * 180.156 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 1383.5981, \"unit\": \"g\"}", "dedupe_signature": "8c81980e2c15502300f14a0472ca604343179a5a3019d28c271e9d609c047a36", "difficulty": "medium", "final_answer": {"answer": 1383.5981, "unit": "g"}, "id": "stoich_mass_001033_glucose_7.68", "license": "Apache-2.0", "prompt": "A sample contains 7.68 mol of glucose. Using molar mass 180.156 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 7.68 mol * 180.156 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "glucose", "molar_mass": 180.156, "moles": 7.68}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 4665 mL to 4.665 L.\n3. Compute M = 3.17 / 4.665.\nFinal: {\"answer\": 0.6795, \"unit\": \"mol/L\"}", "dedupe_signature": "a018f354553bdc92f0e4523679a34cf8a9e5e33edcb14d17599c44047e0668c2", "difficulty": "medium", "final_answer": {"answer": 0.6795, "unit": "mol/L"}, "id": "molarity_001034_3.17_4665", "license": "Apache-2.0", "prompt": "A solution contains 3.17 mol of solute in 4665 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 4665 mL to 4.665 L.\nCompute M = 3.17 / 4.665.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 3.17, "volume_ml": 4665}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.9 y, so each step multiplies y by 1 - h*0.9.\n3. Apply that update for 11 steps and round the final state.\nFinal: {\"answer\": -0.4007, \"unit\": \"state_units\"}", "dedupe_signature": "cd6c76ea4dc56dd748ace874540c0b971496d972f27a7671947952a99394a49f", "difficulty": "medium", "final_answer": {"answer": -0.4007, "unit": "state_units"}, "id": "euler_decay_001035_77_0.9_1.8_11", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.9 y with y(0)=77, step size h=1.8, for 11 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.9 y, so each step multiplies y by 1 - h*0.9.\nApply that update for 11 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 77.0, "rate": 0.9, "step": 1.8, "steps": 11}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-7.5)=-18.25 and f(-3.6)=-5.38.\n3. The interval width is 3.9.\nFinal: {\"answer\": -46.0785, \"unit\": \"area_units\"}", "dedupe_signature": "b89e151a19d85c31b651c1c6e851ca8986d78901092f7d9bb823ba47bc40b283", "difficulty": "medium", "final_answer": {"answer": -46.0785, "unit": "area_units"}, "id": "trapz_linear_001036_3.3_6.5_-7.5_-3.6", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=3.3x+6.5 from x=-7.5 to x=-3.6. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-7.5)=-18.25 and f(-3.6)=-5.38.\nThe interval width is 3.9.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 6.5, "slope": 3.3, "x0": -7.5, "x1": -3.6}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 3410.0 / 1000.\nFinal: {\"answer\": 3.41, \"unit\": \"kg\"}", "dedupe_signature": "831d2cbc91870e9ce9d7130af0b0b89706af9dd0b5cd434ed7222be800aafd12", "difficulty": "easy", "final_answer": {"answer": 3.41, "unit": "kg"}, "id": "unit_convert_001038_g_to_kg_3410", "license": "Apache-2.0", "prompt": "Convert 3410 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 3410.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 3410.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=289 degrees and keep the unit as newtons.\nFinal: {\"answer\": [129.5761, -376.3164], \"unit\": \"N\"}", "dedupe_signature": "6c0e78edc7cb1abdf88e298e18a20c329ee96376c6c8cd1d1607cf06515360ae", "difficulty": "medium", "final_answer": {"answer": [129.5761, -376.3164], "unit": "N"}, "id": "vector_components_001039_398_289", "license": "Apache-2.0", "prompt": "A vector has magnitude 398 N at 289 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=289 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 289, "magnitude": 398.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef clamp_001042(x, lo, hi):\n    if lo > hi:\n        raise ValueError('lo must be <= hi')\n    return min(max(x, lo), hi)\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"clamp_001042\"}", "dedupe_signature": "7006ce2aea15d09b62bea2936199e04c71e27b41d7bd677af27c6a719a0c0cbf", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "clamp_001042"}, "id": "code_001042_clamp_001042", "license": "Apache-2.0", "prompt": "Write a Python function clamp_001042(x, lo, hi) that clips x into the inclusive interval [lo, hi]. It must raise ValueError if lo > hi. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "clamp_001042"}, "verifier": {"function": "clamp_001042", "tests": ["assert clamp_001042(5, 0, 10) == 5", "assert clamp_001042(-2, 0, 10) == 0", "assert clamp_001042(12, 0, 10) == 10", "try:\n    clamp_001042(1, 3, 2)\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: target_schema, valid_examples.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"target_schema\", \"valid_examples\"]}", "dedupe_signature": "4da69c7438683cbbef0c0a7376e8b083b1ff3cc195d7d96aef3f7f55a3592d44", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["target_schema", "valid_examples"]}, "id": "abstain_001043_target_schema_valid_examples", "license": "Apache-2.0", "prompt": "Write a parser that converts each billing experiment record from batch 794094 into the correct schema, but the prompt does not include the target schema or examples. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: target_schema, valid_examples.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["target_schema", "valid_examples"]}, "verifier": {"missing": ["target_schema", "valid_examples"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 7.7 kg and a = 8.25 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 63.525, \"unit\": \"N\"}", "dedupe_signature": "b0d6db58004299756d00886eba198d672d7b6fc99f40ec57500b4621c4e15792", "difficulty": "easy", "final_answer": {"answer": 63.525, "unit": "N"}, "id": "force_001044_7.7_8.25", "license": "Apache-2.0", "prompt": "A cart has mass 7.7 kg and measured acceleration 8.25 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 7.7 kg and a = 8.25 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 8.25, "mass": 7.7}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 37.5^2 and multiply by 0.5 * 21.45.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 15082.0312, \"unit\": \"J\"}", "dedupe_signature": "86aa768b5dfba489b080e5e2e77c55eb495c96f7e4e9979b586974c90c439ecb", "difficulty": "easy", "final_answer": {"answer": 15082.0312, "unit": "J"}, "id": "ke_001045_21.45_37.5", "license": "Apache-2.0", "prompt": "A body of mass 21.45 kg moves at 37.5 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 37.5^2 and multiply by 0.5 * 21.45.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 21.45, "velocity": 37.5}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=33 degrees through the sine of 2 theta.\n3. Substitute v=78.6 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 575.3157, \"unit\": \"m\"}", "dedupe_signature": "000686b378867fbbd1eb16c536f85fe7ccd1ec81488811c7bdc08ef72debfd11", "difficulty": "medium", "final_answer": {"answer": 575.3157, "unit": "m"}, "id": "projectile_range_001046_78.6_33", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 78.6 m/s and angle 33 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=33 degrees through the sine of 2 theta.\nSubstitute v=78.6 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 33, "gravity": 9.81, "speed": 78.6}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 2.88 * 8.314 * 337 / 65.2.\nFinal: {\"answer\": 123.7613, \"unit\": \"kPa\"}", "dedupe_signature": "e308876f113fa5d907b6a99fd45c3d9aa5cae9d320d8ed994f200c77ace95e2b", "difficulty": "medium", "final_answer": {"answer": 123.7613, "unit": "kPa"}, "id": "ideal_gas_001047_2.88_337_65.2", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=2.88 mol, T=337 K, and V=65.2 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 2.88 * 8.314 * 337 / 65.2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 2.88, "temp_k": 337, "volume_l": 65.2}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1115 * 4.375 * 2.\nFinal: {\"answer\": 9756.25, \"unit\": \"J\"}", "dedupe_signature": "5a58c59b255f5b932e82562f335354c89fb157cf01f1cd928d7e9d2a13e89dcf", "difficulty": "easy", "final_answer": {"answer": 9756.25, "unit": "J"}, "id": "heat_q_001048_1115_4.375_2", "license": "Apache-2.0", "prompt": "A 1115 g sample has specific heat 4.375 J/(g*K). How much heat is needed to raise its temperature by 2 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1115 * 4.375 * 2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 2, "heat_capacity": 4.375, "mass_g": 1115}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=149.5 V and R=41.4 ohm.\nFinal: {\"answer\": 539.8611, \"unit\": \"W\"}", "dedupe_signature": "fa387e5e917b6943180f44e7526e16cef333e79124bdc91d8499b15f480bf9da", "difficulty": "easy", "final_answer": {"answer": 539.8611, "unit": "W"}, "id": "ohm_power_001049_149.5_41.4", "license": "Apache-2.0", "prompt": "A resistor has resistance 41.4 ohm and voltage 149.5 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=149.5 V and R=41.4 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 41.4, "voltage": 149.5}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=387 mg, t=134.5 h, and T_half=38.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 34.3606, \"unit\": \"mg\"}", "dedupe_signature": "db672dd8efd80b5d3f3468584795471f192911a45f619e66bb64999c9fa86f47", "difficulty": "medium", "final_answer": {"answer": 34.3606, "unit": "mg"}, "id": "half_life_001050_387_38.5_134.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 387 mg. Its half-life is 38.5 hours. How many mg remain after 134.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=387 mg, t=134.5 h, and T_half=38.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 134.5, "half_life": 38.5, "initial_amount": 387.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 0.75 mol * 44.01 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 33.0075, \"unit\": \"g\"}", "dedupe_signature": "ca465ee392715671ee5394b3ffdcb22db2b4cfc743417cf39cdc414d4bf7139f", "difficulty": "medium", "final_answer": {"answer": 33.0075, "unit": "g"}, "id": "stoich_mass_001051_carbon_dioxide_0.75", "license": "Apache-2.0", "prompt": "A sample contains 0.75 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 0.75 mol * 44.01 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "carbon dioxide", "molar_mass": 44.01, "moles": 0.75}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 4510 mL to 4.51 L.\n3. Compute M = 2.615 / 4.51.\nFinal: {\"answer\": 0.5798, \"unit\": \"mol/L\"}", "dedupe_signature": "77c7ed370727e78124f5246626927bf6d2a5e7254595cff743a48a64f5d501b9", "difficulty": "medium", "final_answer": {"answer": 0.5798, "unit": "mol/L"}, "id": "molarity_001052_2.615_4510", "license": "Apache-2.0", "prompt": "A solution contains 2.615 mol of solute in 4510 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 4510 mL to 4.51 L.\nCompute M = 2.615 / 4.51.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 2.615, "volume_ml": 4510}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.03 y, so each step multiplies y by 1 - h*0.03.\n3. Apply that update for 12 steps and round the final state.\nFinal: {\"answer\": 28.533, \"unit\": \"state_units\"}", "dedupe_signature": "d6e2f3e7a7b322256dc5cad3ccd6dcb4e8306ff7e0287b42d40195779c2c49c4", "difficulty": "medium", "final_answer": {"answer": 28.533, "unit": "state_units"}, "id": "euler_decay_001053_54.5_0.03_1.75_12", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.03 y with y(0)=54.5, step size h=1.75, for 12 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.03 y, so each step multiplies y by 1 - h*0.03.\nApply that update for 12 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 54.5, "rate": 0.03, "step": 1.75, "steps": 12}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kelvin equals Celsius plus 273.15.\n2. Apply the conversion factor directly to the given value.\n3. Compute 33.0 + 273.15.\nFinal: {\"answer\": 306.15, \"unit\": \"K\"}", "dedupe_signature": "e28b3d857672927e63732b9f7fad7ebd892f594200595c1af8593e88b73ad023", "difficulty": "easy", "final_answer": {"answer": 306.15, "unit": "K"}, "id": "unit_convert_001056_c_to_k_33", "license": "Apache-2.0", "prompt": "Convert 33 degC to K. Return the converted value with unit.", "reasoning_trace": "Kelvin equals Celsius plus 273.15.\nApply the conversion factor directly to the given value.\nCompute 33.0 + 273.15.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 33.0}, "verifier": {"formula": "value + 273.15", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [0.1, -29.0], \"unit\": \"dimensionless\"}", "dedupe_signature": "02611bd3a32b0ae64d616de73b445f22c93ea92759f3c12ec8980d352a37028d", "difficulty": "medium", "final_answer": {"answer": [0.1, -29.0], "unit": "dimensionless"}, "id": "line_two_point_001058_-18.75_-14_0.1_-29", "license": "Apache-2.0", "prompt": "A line passes through points (-18.75, -30.875) and (-14, -30.4). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -18.75, "x2": -14.0, "y1": -30.875, "y2": -30.4}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef safe_mean_001060(values):\n    if not values:\n        raise ValueError('safe_mean requires at least one value')\n    return sum(values) / len(values)\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"safe_mean_001060\"}", "dedupe_signature": "337aae52fc13e4e38d7ca41e89fe5cea06611288ff85570e3200f4f2fc3b6435", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "safe_mean_001060"}, "id": "code_001060_safe_mean_001060", "license": "Apache-2.0", "prompt": "Write a Python function safe_mean_001060(values) that returns the arithmetic mean. It must raise ValueError for an empty input and must not mutate the input list. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "safe_mean_001060"}, "verifier": {"function": "safe_mean_001060", "tests": ["assert safe_mean_001060([2, 4, 6]) == 4", "xs = [1, 2, 3]; assert safe_mean_001060(xs) == 2 and xs == [1, 2, 3]", "try:\n    safe_mean_001060([])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: launch_angle_or_vertical_velocity.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"launch_angle_or_vertical_velocity\"]}", "dedupe_signature": "d7a806d7ee9272ac8a1de37a6c718b37bcdd7c11de986f9aa55b21e2a5b5f183", "difficulty": "easy", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["launch_angle_or_vertical_velocity"]}, "id": "abstain_001061_launch_angle_or_vertical_velocity", "license": "Apache-2.0", "prompt": "Compute projectile range on level ground. The prompt gives initial speed 82.9 m/s but does not give launch angle or vertical velocity. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: launch_angle_or_vertical_velocity.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["launch_angle_or_vertical_velocity"]}, "verifier": {"missing": ["launch_angle_or_vertical_velocity"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 20.85 kg and a = 4.3 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 89.655, \"unit\": \"N\"}", "dedupe_signature": "6121751d4a796bc87a3b3a7dfc6d96b1a86ee6acd2f258b70132fa2898db05da", "difficulty": "easy", "final_answer": {"answer": 89.655, "unit": "N"}, "id": "force_001062_20.85_4.3", "license": "Apache-2.0", "prompt": "A cart has mass 20.85 kg and measured acceleration 4.3 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 20.85 kg and a = 4.3 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 4.3, "mass": 20.85}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 11.95^2 and multiply by 0.5 * 28.2.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 2013.5152, \"unit\": \"J\"}", "dedupe_signature": "91b6d7659cf1738062318ae5f5e4d7103a0ead8e8673919234b840fda92c1619", "difficulty": "easy", "final_answer": {"answer": 2013.5152, "unit": "J"}, "id": "ke_001063_28.2_11.95", "license": "Apache-2.0", "prompt": "A body of mass 28.2 kg moves at 11.95 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 11.95^2 and multiply by 0.5 * 28.2.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 28.2, "velocity": 11.95}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=43 degrees through the sine of 2 theta.\n3. Substitute v=48.4 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 238.2114, \"unit\": \"m\"}", "dedupe_signature": "8c1997a32f89f4ea932f4e6229e53c9baa3d8e0e3f176babbdf6f686135bd134", "difficulty": "medium", "final_answer": {"answer": 238.2114, "unit": "m"}, "id": "projectile_range_001064_48.4_43", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 48.4 m/s and angle 43 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=43 degrees through the sine of 2 theta.\nSubstitute v=48.4 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 43, "gravity": 9.81, "speed": 48.4}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 3.51 * 8.314 * 378 / 38.0.\nFinal: {\"answer\": 290.2855, \"unit\": \"kPa\"}", "dedupe_signature": "a3785e8f1d5804ddea2f3a152a3743d3d45bb3d09bbf35a88076505a93597967", "difficulty": "medium", "final_answer": {"answer": 290.2855, "unit": "kPa"}, "id": "ideal_gas_001065_3.51_378_38.0", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=3.51 mol, T=378 K, and V=38.0 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 3.51 * 8.314 * 378 / 38.0.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 3.51, "temp_k": 378, "volume_l": 38.0}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 55 * 0.595 * 7.\nFinal: {\"answer\": 229.075, \"unit\": \"J\"}", "dedupe_signature": "8d9328caa1d58707dd83c0080f37e75943667ebd21b5ea80e2215dc4e8dc636e", "difficulty": "easy", "final_answer": {"answer": 229.075, "unit": "J"}, "id": "heat_q_001066_55_0.595_7", "license": "Apache-2.0", "prompt": "A 55 g sample has specific heat 0.595 J/(g*K). How much heat is needed to raise its temperature by 7 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 55 * 0.595 * 7.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 7, "heat_capacity": 0.595, "mass_g": 55}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=174.2 V and R=180 ohm.\nFinal: {\"answer\": 168.5869, \"unit\": \"W\"}", "dedupe_signature": "8d8b996c056c036014ac71de7f6fc2907aecc32c81e7476c33d645ed4513d721", "difficulty": "easy", "final_answer": {"answer": 168.5869, "unit": "W"}, "id": "ohm_power_001067_174.2_180", "license": "Apache-2.0", "prompt": "A resistor has resistance 180 ohm and voltage 174.2 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=174.2 V and R=180 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 180.0, "voltage": 174.2}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=594 mg, t=45.5 h, and T_half=118.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 455.1988, \"unit\": \"mg\"}", "dedupe_signature": "49735adbe467d658cb3e62a84bc15076705781fca8c53edb09136479050de66b", "difficulty": "medium", "final_answer": {"answer": 455.1988, "unit": "mg"}, "id": "half_life_001068_594_118.5_45.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 594 mg. Its half-life is 118.5 hours. How many mg remain after 45.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=594 mg, t=45.5 h, and T_half=118.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 45.5, "half_life": 118.5, "initial_amount": 594.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 2.74 mol * 58.44 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 160.1256, \"unit\": \"g\"}", "dedupe_signature": "3f2e646407d998ff09648e6cf65d7c7eb56c4bfc1566984220fea785ead2f21c", "difficulty": "medium", "final_answer": {"answer": 160.1256, "unit": "g"}, "id": "stoich_mass_001069_sodium_chloride_2.74", "license": "Apache-2.0", "prompt": "A sample contains 2.74 mol of sodium chloride. Using molar mass 58.44 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 2.74 mol * 58.44 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "sodium chloride", "molar_mass": 58.44, "moles": 2.74}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 2020 mL to 2.02 L.\n3. Compute M = 0.16 / 2.02.\nFinal: {\"answer\": 0.0792, \"unit\": \"mol/L\"}", "dedupe_signature": "8d3df9977b427dbeec2bc5fd737f2a9c572f4e36c63d524cc7092a862696630f", "difficulty": "medium", "final_answer": {"answer": 0.0792, "unit": "mol/L"}, "id": "molarity_001070_0.16_2020", "license": "Apache-2.0", "prompt": "A solution contains 0.16 mol of solute in 2020 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 2020 mL to 2.02 L.\nCompute M = 0.16 / 2.02.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 0.16, "volume_ml": 2020}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.88 y, so each step multiplies y by 1 - h*0.88.\n3. Apply that update for 12 steps and round the final state.\nFinal: {\"answer\": 0.096, \"unit\": \"state_units\"}", "dedupe_signature": "bf0fd776f23bd64fa6359060776df4e6f0064ecb3dbcd4004605d2f0ca0a2475", "difficulty": "medium", "final_answer": {"answer": 0.096, "unit": "state_units"}, "id": "euler_decay_001071_25.5_0.88_1.85_12", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.88 y with y(0)=25.5, step size h=1.85, for 12 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.88 y, so each step multiplies y by 1 - h*0.88.\nApply that update for 12 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 25.5, "rate": 0.88, "step": 1.85, "steps": 12}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(1.9)=7.68 and f(7.5)=-2.4.\n3. The interval width is 5.6.\nFinal: {\"answer\": 14.784, \"unit\": \"area_units\"}", "dedupe_signature": "fff5597d1a471dc0930c8d262dee0582ea8f092806c7127d07be61ca5b3498d7", "difficulty": "medium", "final_answer": {"answer": 14.784, "unit": "area_units"}, "id": "trapz_linear_001072_-1.8_11.1_1.9_7.5", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-1.8x+11.1 from x=1.9 to x=7.5. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(1.9)=7.68 and f(7.5)=-2.4.\nThe interval width is 5.6.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 11.1, "slope": -1.8, "x0": 1.9, "x1": 7.5}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.22 and add it to the current value.\nFinal: {\"answer\": [-0.017, 0.056, -0.968], \"unit\": \"temperature_units\"}", "dedupe_signature": "569da0f04a116b478e6bc49687c7e2442dc8b88f8052e92b1e3ec114fa1838bc", "difficulty": "hard", "final_answer": {"answer": [-0.017, 0.056, -0.968], "unit": "temperature_units"}, "id": "heat_step_001073_0.22_1.65_-1.15_1.2_-1.65_-1.4", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.65, right=-1.4; current interior values are [-1.15, 1.2, -1.65]. Use r=0.22. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.22 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-1.15, 1.2, -1.65], "left": 1.65, "r": 0.22, "right": -1.4}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kelvin equals Celsius plus 273.15.\n2. Apply the conversion factor directly to the given value.\n3. Compute -6.5 + 273.15.\nFinal: {\"answer\": 266.65, \"unit\": \"K\"}", "dedupe_signature": "4772a3edb090dca13dd52d049b7383c031069dc026b519cd313d3615b3465283", "difficulty": "easy", "final_answer": {"answer": 266.65, "unit": "K"}, "id": "unit_convert_001074_c_to_k_-6.5", "license": "Apache-2.0", "prompt": "Convert -6.5 degC to K. Return the converted value with unit.", "reasoning_trace": "Kelvin equals Celsius plus 273.15.\nApply the conversion factor directly to the given value.\nCompute -6.5 + 273.15.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": -6.5}, "verifier": {"formula": "value + 273.15", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-0.5, 25.25], \"unit\": \"dimensionless\"}", "dedupe_signature": "c19e2399d8594fc60e5d4c4018e50f446c47b2e1b991bd40ed491644ed838602", "difficulty": "medium", "final_answer": {"answer": [-0.5, 25.25], "unit": "dimensionless"}, "id": "line_two_point_001076_-18_-6.5_-0.5_25.25", "license": "Apache-2.0", "prompt": "A line passes through points (-18, 34.25) and (-6.5, 28.5). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -18.0, "x2": -6.5, "y1": 34.25, "y2": 28.5}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. lever arm times force has torque dimensions\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "479833a47261791f6c0ff2d6412408638fbb732c6497c4640eae7e548998cb38", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_001077_consistent_5ca82cb9_845667", "license": "Apache-2.0", "prompt": "In lab notebook case 845667, check dimensional consistency for tau = r * F. The left side has dimensions N*m and the right side has dimensions N*m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nlever arm times force has torque dimensions\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "tau = r * F"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef clamp_001078(x, lo, hi):\n    if lo > hi:\n        raise ValueError('lo must be <= hi')\n    return min(max(x, lo), hi)\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"clamp_001078\"}", "dedupe_signature": "deded9a5e8b87a1e060ecb87ed1962c560f38d2bc8760b60a59a71a1a2590c7b", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "clamp_001078"}, "id": "code_001078_clamp_001078", "license": "Apache-2.0", "prompt": "Write a Python function clamp_001078(x, lo, hi) that clips x into the inclusive interval [lo, hi]. It must raise ValueError if lo > hi. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "clamp_001078"}, "verifier": {"function": "clamp_001078", "tests": ["assert clamp_001078(5, 0, 10) == 5", "assert clamp_001078(-2, 0, 10) == 0", "assert clamp_001078(12, 0, 10) == 10", "try:\n    clamp_001078(1, 3, 2)\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 14.75 kg and a = 7 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 103.25, \"unit\": \"N\"}", "dedupe_signature": "5467fb28e3e0f6edc4a49b671555062402e82075984085845308c325c48669b3", "difficulty": "easy", "final_answer": {"answer": 103.25, "unit": "N"}, "id": "force_001080_14.75_7", "license": "Apache-2.0", "prompt": "A cart has mass 14.75 kg and measured acceleration 7 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 14.75 kg and a = 7 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 7.0, "mass": 14.75}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=11 degrees through the sine of 2 theta.\n3. Substitute v=35.6 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 48.3957, \"unit\": \"m\"}", "dedupe_signature": "d8665784dd72af12af7947fe815cea7d533959056140908e2f0e46c73dd935f9", "difficulty": "medium", "final_answer": {"answer": 48.3957, "unit": "m"}, "id": "projectile_range_001082_35.6_11", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 35.6 m/s and angle 11 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=11 degrees through the sine of 2 theta.\nSubstitute v=35.6 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 11, "gravity": 9.81, "speed": 35.6}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1320 * 4.275 * 16.\nFinal: {\"answer\": 90288.0, \"unit\": \"J\"}", "dedupe_signature": "577cf316ec5ecebb93a79301744f740806e99613d878da44455ab0e104de4c34", "difficulty": "easy", "final_answer": {"answer": 90288.0, "unit": "J"}, "id": "heat_q_001084_1320_4.275_16", "license": "Apache-2.0", "prompt": "A 1320 g sample has specific heat 4.275 J/(g*K). How much heat is needed to raise its temperature by 16 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1320 * 4.275 * 16.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 16, "heat_capacity": 4.275, "mass_g": 1320}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=1.9 V and R=97.7 ohm.\nFinal: {\"answer\": 0.0369, \"unit\": \"W\"}", "dedupe_signature": "c31d939586c4c6dd57dda38de5943369104cc1dba97aa7d6243a2a7306de84c5", "difficulty": "easy", "final_answer": {"answer": 0.0369, "unit": "W"}, "id": "ohm_power_001085_1.9_97.7", "license": "Apache-2.0", "prompt": "A resistor has resistance 97.7 ohm and voltage 1.9 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=1.9 V and R=97.7 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 97.7, "voltage": 1.9}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=969.5 mg, t=173 h, and T_half=46 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 71.5177, \"unit\": \"mg\"}", "dedupe_signature": "b513cab90990592898d19edd4a2e4b4dcb6b804420ad3ceab97379d68d4f4233", "difficulty": "medium", "final_answer": {"answer": 71.5177, "unit": "mg"}, "id": "half_life_001086_969.5_46_173", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 969.5 mg. Its half-life is 46 hours. How many mg remain after 173 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=969.5 mg, t=173 h, and T_half=46 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 173.0, "half_life": 46.0, "initial_amount": 969.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 475 mL to 0.475 L.\n3. Compute M = 2.725 / 0.475.\nFinal: {\"answer\": 5.7368, \"unit\": \"mol/L\"}", "dedupe_signature": "9f1b0f88a7dc054ebb157c7f8286d6419647049e4e73ed512c16fcf18d983c2a", "difficulty": "medium", "final_answer": {"answer": 5.7368, "unit": "mol/L"}, "id": "molarity_001088_2.725_475", "license": "Apache-2.0", "prompt": "A solution contains 2.725 mol of solute in 475 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 475 mL to 0.475 L.\nCompute M = 2.725 / 0.475.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 2.725, "volume_ml": 475}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.1 y, so each step multiplies y by 1 - h*0.1.\n3. Apply that update for 3 steps and round the final state.\nFinal: {\"answer\": 41.5892, \"unit\": \"state_units\"}", "dedupe_signature": "715ae86aeabc2b2b03eed546323b8ab282b5660d54f3a03fc58ec9314eba9593", "difficulty": "medium", "final_answer": {"answer": 41.5892, "unit": "state_units"}, "id": "euler_decay_001089_60_0.1_1.15_3", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.1 y with y(0)=60, step size h=1.15, for 3 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.1 y, so each step multiplies y by 1 - h*0.1.\nApply that update for 3 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 60.0, "rate": 0.1, "step": 1.15, "steps": 3}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(8.5)=-32.1 and f(17.6)=-64.86.\n3. The interval width is 9.1.\nFinal: {\"answer\": -441.168, \"unit\": \"area_units\"}", "dedupe_signature": "9ebb9030ba83a9b40b4729aeba31bad22649e8f1e976b6431375657f3818921e", "difficulty": "medium", "final_answer": {"answer": -441.168, "unit": "area_units"}, "id": "trapz_linear_001090_-3.6_-1.5_8.5_17.6", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-3.6x+-1.5 from x=8.5 to x=17.6. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(8.5)=-32.1 and f(17.6)=-64.86.\nThe interval width is 9.1.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -1.5, "slope": -3.6, "x0": 8.5, "x1": 17.6}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.44 and add it to the current value.\nFinal: {\"answer\": [1.59, 1.566, 0.152], \"unit\": \"temperature_units\"}", "dedupe_signature": "a892705c6b6ffeefe4f343c76c3227c878c1ac7d176f80d32d0718b6f2048faf", "difficulty": "hard", "final_answer": {"answer": [1.59, 1.566, 0.152], "unit": "temperature_units"}, "id": "heat_step_001091_0.44_1.95_0.6_1.5_2.55_-1.85", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.95, right=-1.85; current interior values are [0.6, 1.5, 2.55]. Use r=0.44. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.44 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [0.6, 1.5, 2.55], "left": 1.95, "r": 0.44, "right": -1.85}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 100 centimeters in one meter.\n2. Apply the conversion factor directly to the given value.\n3. Compute 1181.5 / 100.\nFinal: {\"answer\": 11.815, \"unit\": \"m\"}", "dedupe_signature": "abe3fc885f9e4766d00cb24a095527ad9b72da5a84e5f8f542cde2c73435a63a", "difficulty": "easy", "final_answer": {"answer": 11.815, "unit": "m"}, "id": "unit_convert_001092_cm_to_m_1181.5", "license": "Apache-2.0", "prompt": "Convert 1181.5 cm to m. Return the converted value with unit.", "reasoning_trace": "There are 100 centimeters in one meter.\nApply the conversion factor directly to the given value.\nCompute 1181.5 / 100.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 1181.5}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=18 degrees and keep the unit as newtons.\nFinal: {\"answer\": [452.7029, 147.0921], \"unit\": \"N\"}", "dedupe_signature": "7787ec9ec05dba282a992c406009270d1ca1b314166cf6e773b0c0d50e9e028e", "difficulty": "medium", "final_answer": {"answer": [452.7029, 147.0921], "unit": "N"}, "id": "vector_components_001093_476_18", "license": "Apache-2.0", "prompt": "A vector has magnitude 476 N at 18 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=18 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 18, "magnitude": 476.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. speed squared over acceleration has units of meters\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "b6ef49a1c6ab9748e7892c66b0506408430cfb2fa836136ee21b16257d2d5af3", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_001095_consistent_741d4e34_644349", "license": "Apache-2.0", "prompt": "In lab notebook case 644349, check dimensional consistency for R = v^2 * sin(theta) / g. The left side has dimensions m and the right side has dimensions m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nspeed squared over acceleration has units of meters\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "R = v^2 * sin(theta) / g"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: rate_constant, number_of_steps.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"rate_constant\", \"number_of_steps\"]}", "dedupe_signature": "e2b524d015943e125511e73d33205dad132b2aff2b7922c4905a6069a74d5b4e", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["rate_constant", "number_of_steps"]}, "id": "abstain_001097_rate_constant_number_of_steps", "license": "Apache-2.0", "prompt": "Use explicit Euler for dy/dt = -k y. The prompt gives y(0)=53.5 and h=0.8, but omits both k and the number of steps. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: rate_constant, number_of_steps.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["rate_constant", "number_of_steps"]}, "verifier": {"missing": ["rate_constant", "number_of_steps"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 3.25 kg and a = 15.45 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 50.2125, \"unit\": \"N\"}", "dedupe_signature": "d3de777fc1ccdd13d2eae42d5d3c3fbe1d97e69807e721d258186f758336bddc", "difficulty": "easy", "final_answer": {"answer": 50.2125, "unit": "N"}, "id": "force_001098_3.25_15.45", "license": "Apache-2.0", "prompt": "A cart has mass 3.25 kg and measured acceleration 15.45 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 3.25 kg and a = 15.45 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 15.45, "mass": 3.25}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 44.05^2 and multiply by 0.5 * 23.8.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 23090.7897, \"unit\": \"J\"}", "dedupe_signature": "dff72b24618b2d2d214aa3aefaa32c79223d031de8d518b06b47537bb688b618", "difficulty": "easy", "final_answer": {"answer": 23090.7897, "unit": "J"}, "id": "ke_001099_23.8_44.05", "license": "Apache-2.0", "prompt": "A body of mass 23.8 kg moves at 44.05 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 44.05^2 and multiply by 0.5 * 23.8.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 23.8, "velocity": 44.05}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=30 degrees through the sine of 2 theta.\n3. Substitute v=8.5 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 6.3782, \"unit\": \"m\"}", "dedupe_signature": "7aabc0e6a5fe7c518f26f4a8b4a978c868a6249eae0ead8cbf1b61771748cd55", "difficulty": "medium", "final_answer": {"answer": 6.3782, "unit": "m"}, "id": "projectile_range_001100_8.5_30", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 8.5 m/s and angle 30 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=30 degrees through the sine of 2 theta.\nSubstitute v=8.5 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 30, "gravity": 9.81, "speed": 8.5}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 1.74 * 8.314 * 249 / 99.1.\nFinal: {\"answer\": 36.3484, \"unit\": \"kPa\"}", "dedupe_signature": "01d50f534c5a6da9a8b44061af11453af433780cc273eaaef988fb2577a2b805", "difficulty": "medium", "final_answer": {"answer": 36.3484, "unit": "kPa"}, "id": "ideal_gas_001101_1.74_249_99.1", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=1.74 mol, T=249 K, and V=99.1 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 1.74 * 8.314 * 249 / 99.1.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 1.74, "temp_k": 249, "volume_l": 99.1}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1615 * 0.91 * 60.\nFinal: {\"answer\": 88179.0, \"unit\": \"J\"}", "dedupe_signature": "86763ec7a87f80cc541db242cb6e45eb9aff7c13f6c137fedb1deca22c8cdac3", "difficulty": "easy", "final_answer": {"answer": 88179.0, "unit": "J"}, "id": "heat_q_001102_1615_0.91_60", "license": "Apache-2.0", "prompt": "A 1615 g sample has specific heat 0.91 J/(g*K). How much heat is needed to raise its temperature by 60 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1615 * 0.91 * 60.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 60, "heat_capacity": 0.91, "mass_g": 1615}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 2.89 mol * 100.087 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 289.2514, \"unit\": \"g\"}", "dedupe_signature": "42f6601fb1e32cc02f16c5cd901fbc34fb104c59d30a8675fbda8bfa83083534", "difficulty": "medium", "final_answer": {"answer": 289.2514, "unit": "g"}, "id": "stoich_mass_001105_calcium_carbonate_2.89", "license": "Apache-2.0", "prompt": "A sample contains 2.89 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 2.89 mol * 100.087 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "calcium carbonate", "molar_mass": 100.087, "moles": 2.89}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 90 mL to 0.09 L.\n3. Compute M = 4.425 / 0.09.\nFinal: {\"answer\": 49.1667, \"unit\": \"mol/L\"}", "dedupe_signature": "836bd0b302b3d0916c314c274635e169671b3412df2c7c8687deb1360bba3161", "difficulty": "medium", "final_answer": {"answer": 49.1667, "unit": "mol/L"}, "id": "molarity_001106_4.425_90", "license": "Apache-2.0", "prompt": "A solution contains 4.425 mol of solute in 90 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 90 mL to 0.09 L.\nCompute M = 4.425 / 0.09.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 4.425, "volume_ml": 90}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(8.8)=1.18 and f(9.9)=3.49.\n3. The interval width is 1.1.\nFinal: {\"answer\": 2.5685, \"unit\": \"area_units\"}", "dedupe_signature": "9dbf78785f573a7e379d70a92bac50900da9de57515205f28fe26e6452f0fc6b", "difficulty": "medium", "final_answer": {"answer": 2.5685, "unit": "area_units"}, "id": "trapz_linear_001108_2.1_-17.3_8.8_9.9", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=2.1x+-17.3 from x=8.8 to x=9.9. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(8.8)=1.18 and f(9.9)=3.49.\nThe interval width is 1.1.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -17.3, "slope": 2.1, "x0": 8.8, "x1": 9.9}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.3 and add it to the current value.\nFinal: {\"answer\": [1.96, 2.06, 1.365], \"unit\": \"temperature_units\"}", "dedupe_signature": "f047b65081c8ef85da97552f846cfc2188c507668ab99a1e8c767d114f534371", "difficulty": "hard", "final_answer": {"answer": [1.96, 2.06, 1.365], "unit": "temperature_units"}, "id": "heat_step_001109_0.3_2.5_1.75_1.7_2.85_-0.95", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=2.5, right=-0.95; current interior values are [1.75, 1.7, 2.85]. Use r=0.3. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.3 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [1.75, 1.7, 2.85], "left": 2.5, "r": 0.3, "right": -0.95}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 16846.0 / 1000.\nFinal: {\"answer\": 16.846, \"unit\": \"kg\"}", "dedupe_signature": "fb4f3d3d4fb15eeba0758635218ab2afbfe29a87d9ea04ec959f1a65f3360d66", "difficulty": "easy", "final_answer": {"answer": 16.846, "unit": "kg"}, "id": "unit_convert_001110_g_to_kg_16846", "license": "Apache-2.0", "prompt": "Convert 16846 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 16846.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 16846.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=30 degrees and keep the unit as newtons.\nFinal: {\"answer\": [175.3701, 101.25], \"unit\": \"N\"}", "dedupe_signature": "1ab8ef9614f54cddd296457295c7ceddfe720ec14fe7f52be47d934539c8e8e6", "difficulty": "medium", "final_answer": {"answer": [175.3701, 101.25], "unit": "N"}, "id": "vector_components_001111_202.5_30", "license": "Apache-2.0", "prompt": "A vector has magnitude 202.5 N at 30 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=30 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 30, "magnitude": 202.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [0.4, 2.0], \"unit\": \"dimensionless\"}", "dedupe_signature": "dd73ec46a1ac3581ba6c8b33965136d0f32d601912dab5aa810965170b485382", "difficulty": "medium", "final_answer": {"answer": [0.4, 2.0], "unit": "dimensionless"}, "id": "line_two_point_001112_-6_2.5_0.4_2", "license": "Apache-2.0", "prompt": "A line passes through points (-6, -0.4) and (2.5, 3). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -6.0, "x2": 2.5, "y1": -0.40000000000000036, "y2": 3.0}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. energy divided by length is force, not spring constant\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "be3fcb1562caa5f5421cf099ecf0322c134706897c9a8566dfaf90537e636def", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_001113_inconsistent_56040f5d_248715", "license": "Apache-2.0", "prompt": "In student derivation case 248715, check dimensional consistency for k = E / x. The left side has dimensions N/m and the right side has dimensions J/m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nenergy divided by length is force, not spring constant\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "k = E / x"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef pairwise_ratios_001114(numerators, denominators):\n    if len(numerators) != len(denominators):\n        raise ValueError('length mismatch')\n    out = []\n    for numerator, denominator in zip(numerators, denominators):\n        if denominator == 0:\n            raise ValueError('zero denominator')\n        out.append(numerator / denominator)\n    return out\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"pairwise_ratios_001114\"}", "dedupe_signature": "6a0f3be2af7aa4fd2c5500b7cef8977eb6e09c80989b218d94ddda5b954186c2", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "pairwise_ratios_001114"}, "id": "code_001114_pairwise_ratios_001114", "license": "Apache-2.0", "prompt": "Write a Python function pairwise_ratios_001114(numerators, denominators) that returns a list of n/d values. Raise ValueError if lengths differ or any denominator is zero. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "pairwise_ratios_001114"}, "verifier": {"function": "pairwise_ratios_001114", "tests": ["assert pairwise_ratios_001114([2, 9], [4, 3]) == [0.5, 3.0]", "try:\n    pairwise_ratios_001114([1], [0])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass", "try:\n    pairwise_ratios_001114([1, 2], [1])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 1.6 kg and a = 10.3 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 16.48, \"unit\": \"N\"}", "dedupe_signature": "7827f9dcaa780c84528214492fc416cf97af28fe97aae4e9d9b2e5dc322e22a0", "difficulty": "easy", "final_answer": {"answer": 16.48, "unit": "N"}, "id": "force_001116_1.6_10.3", "license": "Apache-2.0", "prompt": "A cart has mass 1.6 kg and measured acceleration 10.3 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 1.6 kg and a = 10.3 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 10.3, "mass": 1.6}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 42.15^2 and multiply by 0.5 * 2.8.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 2487.2715, \"unit\": \"J\"}", "dedupe_signature": "906ca28d944ccde42d5b6789aa45b8902632b4fc920c2f4204af8e1d326cb04f", "difficulty": "easy", "final_answer": {"answer": 2487.2715, "unit": "J"}, "id": "ke_001117_2.8_42.15", "license": "Apache-2.0", "prompt": "A body of mass 2.8 kg moves at 42.15 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 42.15^2 and multiply by 0.5 * 2.8.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 2.8, "velocity": 42.15}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 2.05 * 8.314 * 271 / 57.2.\nFinal: {\"answer\": 80.749, \"unit\": \"kPa\"}", "dedupe_signature": "24b014b5aec89d42c333f1b53f51158cb7e90dba93029d642638bbbeecafddf1", "difficulty": "medium", "final_answer": {"answer": 80.749, "unit": "kPa"}, "id": "ideal_gas_001119_2.05_271_57.2", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=2.05 mol, T=271 K, and V=57.2 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 2.05 * 8.314 * 271 / 57.2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 2.05, "temp_k": 271, "volume_l": 57.2}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 565 * 1.65 * 30.\nFinal: {\"answer\": 27967.5, \"unit\": \"J\"}", "dedupe_signature": "6fec71bbb74aec6f6861facc9555cef5da2bfbe6797917b80e0c91791a2b844d", "difficulty": "easy", "final_answer": {"answer": 27967.5, "unit": "J"}, "id": "heat_q_001120_565_1.65_30", "license": "Apache-2.0", "prompt": "A 565 g sample has specific heat 1.65 J/(g*K). How much heat is needed to raise its temperature by 30 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 565 * 1.65 * 30.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 30, "heat_capacity": 1.65, "mass_g": 565}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=124.1 V and R=69.7 ohm.\nFinal: {\"answer\": 220.9585, \"unit\": \"W\"}", "dedupe_signature": "b02876b0789bf4161e040130e623891a05d1aaea51f6e74d011162e2981f3f78", "difficulty": "easy", "final_answer": {"answer": 220.9585, "unit": "W"}, "id": "ohm_power_001121_124.1_69.7", "license": "Apache-2.0", "prompt": "A resistor has resistance 69.7 ohm and voltage 124.1 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=124.1 V and R=69.7 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 69.7, "voltage": 124.1}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=439.5 mg, t=48 h, and T_half=26 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 122.2394, \"unit\": \"mg\"}", "dedupe_signature": "fdc336c6ed113dd79e2f4e02c7a0e13e7c8f9005f9326393ff23c93aa6c0fe87", "difficulty": "medium", "final_answer": {"answer": 122.2394, "unit": "mg"}, "id": "half_life_001122_439.5_26_48", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 439.5 mg. Its half-life is 26 hours. How many mg remain after 48 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=439.5 mg, t=48 h, and T_half=26 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 48.0, "half_life": 26.0, "initial_amount": 439.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.76 y, so each step multiplies y by 1 - h*0.76.\n3. Apply that update for 5 steps and round the final state.\nFinal: {\"answer\": 1.132, \"unit\": \"state_units\"}", "dedupe_signature": "b65a2005c8cdf825d3c2527e65c7fbedb3976a931fcfb6c248bc23bf4c805020", "difficulty": "medium", "final_answer": {"answer": 1.132, "unit": "state_units"}, "id": "euler_decay_001125_77_0.76_0.75_5", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.76 y with y(0)=77, step size h=0.75, for 5 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.76 y, so each step multiplies y by 1 - h*0.76.\nApply that update for 5 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 77.0, "rate": 0.76, "step": 0.75, "steps": 5}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 100 centimeters in one meter.\n2. Apply the conversion factor directly to the given value.\n3. Compute 659.0 / 100.\nFinal: {\"answer\": 6.59, \"unit\": \"m\"}", "dedupe_signature": "260f6108057ad1a8a6e57595af20c304700a6960e807c395f7e841aa3e739189", "difficulty": "easy", "final_answer": {"answer": 6.59, "unit": "m"}, "id": "unit_convert_001128_cm_to_m_659", "license": "Apache-2.0", "prompt": "Convert 659 cm to m. Return the converted value with unit.", "reasoning_trace": "There are 100 centimeters in one meter.\nApply the conversion factor directly to the given value.\nCompute 659.0 / 100.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 659.0}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=37 degrees and keep the unit as newtons.\nFinal: {\"answer\": [248.3756, 187.1645], \"unit\": \"N\"}", "dedupe_signature": "28ffabb513aaf513f45d92649b91e812559ff5b78984bdfdf66a32b3e82358c8", "difficulty": "medium", "final_answer": {"answer": [248.3756, 187.1645], "unit": "N"}, "id": "vector_components_001129_311_37", "license": "Apache-2.0", "prompt": "A vector has magnitude 311 N at 37 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=37 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 37, "magnitude": 311.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-4.85, 7.5], \"unit\": \"dimensionless\"}", "dedupe_signature": "17c901c8693a2b0acffe994adb5618a4072dbfabcba46006ade153c79a77e97a", "difficulty": "medium", "final_answer": {"answer": [-4.85, 7.5], "unit": "dimensionless"}, "id": "line_two_point_001130_13.5_16.25_-4.85_7.5", "license": "Apache-2.0", "prompt": "A line passes through points (13.5, -57.975) and (16.25, -71.3125). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 13.5, "x2": 16.25, "y1": -57.974999999999994, "y2": -71.3125}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. density times acceleration times height gives kg/(m*s^2), or pascal\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "7efa92339f1d1d207453aabba87418116a24b29788087d91763e2f6719650cab", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_001131_consistent_b7d3eed1_752000", "license": "Apache-2.0", "prompt": "In field worksheet case 752000, check dimensional consistency for p = rho * g * h. The left side has dimensions Pa and the right side has dimensions Pa. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\ndensity times acceleration times height gives kg/(m*s^2), or pascal\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "p = rho * g * h"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: left_boundary, right_boundary.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"left_boundary\", \"right_boundary\"]}", "dedupe_signature": "3395179bbb5dce9824f49b9990437cbf4eb1fc472d4ebcb4422e97279027d301", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["left_boundary", "right_boundary"]}, "id": "abstain_001133_left_boundary_right_boundary", "license": "Apache-2.0", "prompt": "Solve the 1D heat equation after one finite-difference step. The prompt gives r=0.42 and interior values [1.75, -0.2, -0.45], but gives no boundary values. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: left_boundary, right_boundary.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["left_boundary", "right_boundary"]}, "verifier": {"missing": ["left_boundary", "right_boundary"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 5.5 kg and a = 6.45 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 35.475, \"unit\": \"N\"}", "dedupe_signature": "f0cc3e0d377c10be8e62856e4cdc9af8cb6b76da27781c17f4c19c3e178ee2be", "difficulty": "easy", "final_answer": {"answer": 35.475, "unit": "N"}, "id": "force_001134_5.5_6.45", "license": "Apache-2.0", "prompt": "A cart has mass 5.5 kg and measured acceleration 6.45 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 5.5 kg and a = 6.45 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 6.45, "mass": 5.5}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 31.75^2 and multiply by 0.5 * 18.45.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 9299.3766, \"unit\": \"J\"}", "dedupe_signature": "2c869043126addaa5bedbb7113fb394b977f30c423d1956e3dc8b67f1074296e", "difficulty": "easy", "final_answer": {"answer": 9299.3766, "unit": "J"}, "id": "ke_001135_18.45_31.75", "license": "Apache-2.0", "prompt": "A body of mass 18.45 kg moves at 31.75 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 31.75^2 and multiply by 0.5 * 18.45.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 18.45, "velocity": 31.75}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=73 degrees through the sine of 2 theta.\n3. Substitute v=66 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 248.3022, \"unit\": \"m\"}", "dedupe_signature": "25aa9f6cbd2451799dd01cf58d67fee2d68095e509af3c986bfac00c34f52b7e", "difficulty": "medium", "final_answer": {"answer": 248.3022, "unit": "m"}, "id": "projectile_range_001136_66_73", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 66 m/s and angle 73 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=73 degrees through the sine of 2 theta.\nSubstitute v=66 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 73, "gravity": 9.81, "speed": 66.0}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 2.56 * 8.314 * 410 / 80.0.\nFinal: {\"answer\": 109.0797, \"unit\": \"kPa\"}", "dedupe_signature": "2f0abe0c0b304e852634932b967cd9e48635dd7a1d59acfc1531f8403c326356", "difficulty": "medium", "final_answer": {"answer": 109.0797, "unit": "kPa"}, "id": "ideal_gas_001137_2.56_410_80.0", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=2.56 mol, T=410 K, and V=80.0 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 2.56 * 8.314 * 410 / 80.0.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 2.56, "temp_k": 410, "volume_l": 80.0}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1855 * 3.61 * 52.\nFinal: {\"answer\": 348220.6, \"unit\": \"J\"}", "dedupe_signature": "0f263d051b287756f73836755b41537f7471f8984fd41f3933001e1f14f24e5d", "difficulty": "easy", "final_answer": {"answer": 348220.6, "unit": "J"}, "id": "heat_q_001138_1855_3.61_52", "license": "Apache-2.0", "prompt": "A 1855 g sample has specific heat 3.61 J/(g*K). How much heat is needed to raise its temperature by 52 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1855 * 3.61 * 52.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 52, "heat_capacity": 3.61, "mass_g": 1855}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=308.5 mg, t=31.5 h, and T_half=17 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 85.4013, \"unit\": \"mg\"}", "dedupe_signature": "9f4da717fbc2f6ca740be62a83056b7f8868967d31446ba59d3f0b5baefc594a", "difficulty": "medium", "final_answer": {"answer": 85.4013, "unit": "mg"}, "id": "half_life_001140_308.5_17_31.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 308.5 mg. Its half-life is 17 hours. How many mg remain after 31.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=308.5 mg, t=31.5 h, and T_half=17 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 31.5, "half_life": 17.0, "initial_amount": 308.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 7.51 mol * 180.156 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 1352.9716, \"unit\": \"g\"}", "dedupe_signature": "7b7b38c7e02f79ab5fb95c2109f6a6992b5c7e33dd0bf35ce038cccc9d8bb435", "difficulty": "medium", "final_answer": {"answer": 1352.9716, "unit": "g"}, "id": "stoich_mass_001141_glucose_7.51", "license": "Apache-2.0", "prompt": "A sample contains 7.51 mol of glucose. Using molar mass 180.156 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 7.51 mol * 180.156 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "glucose", "molar_mass": 180.156, "moles": 7.51}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 1975 mL to 1.975 L.\n3. Compute M = 1.705 / 1.975.\nFinal: {\"answer\": 0.8633, \"unit\": \"mol/L\"}", "dedupe_signature": "1939377bfcf68830b3b1cf7ef053719719013d7e51f494283107b2931f93a797", "difficulty": "medium", "final_answer": {"answer": 0.8633, "unit": "mol/L"}, "id": "molarity_001142_1.705_1975", "license": "Apache-2.0", "prompt": "A solution contains 1.705 mol of solute in 1975 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 1975 mL to 1.975 L.\nCompute M = 1.705 / 1.975.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 1.705, "volume_ml": 1975}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.3 and add it to the current value.\nFinal: {\"answer\": [0.0, 0.965, 1.62], \"unit\": \"temperature_units\"}", "dedupe_signature": "0b466d996dac70394ddc392facfb45c98959f9e0b1d1f5a86dc94f6e008df254", "difficulty": "hard", "final_answer": {"answer": [0.0, 0.965, 1.62], "unit": "temperature_units"}, "id": "heat_step_001145_0.3_-0.85_0.6_0.05_2.55_1.95", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-0.85, right=1.95; current interior values are [0.6, 0.05, 2.55]. Use r=0.3. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.3 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [0.6, 0.05, 2.55], "left": -0.85, "r": 0.3, "right": 1.95}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kelvin equals Celsius plus 273.15.\n2. Apply the conversion factor directly to the given value.\n3. Compute 183.0 + 273.15.\nFinal: {\"answer\": 456.15, \"unit\": \"K\"}", "dedupe_signature": "ac818cc9a1757ef6ee6cde087b2b160004d6e4994705be36086a1b888ee964d1", "difficulty": "easy", "final_answer": {"answer": 456.15, "unit": "K"}, "id": "unit_convert_001146_c_to_k_183", "license": "Apache-2.0", "prompt": "Convert 183 degC to K. Return the converted value with unit.", "reasoning_trace": "Kelvin equals Celsius plus 273.15.\nApply the conversion factor directly to the given value.\nCompute 183.0 + 273.15.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 183.0}, "verifier": {"formula": "value + 273.15", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=255 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-84.2456, -314.4089], \"unit\": \"N\"}", "dedupe_signature": "a41bfff9c184fe7132686b60debbb001e67a8594979c308df888e3107cb51ebe", "difficulty": "medium", "final_answer": {"answer": [-84.2456, -314.4089], "unit": "N"}, "id": "vector_components_001147_325.5_255", "license": "Apache-2.0", "prompt": "A vector has magnitude 325.5 N at 255 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=255 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 255, "magnitude": 325.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-0.05, -22.5], \"unit\": \"dimensionless\"}", "dedupe_signature": "16db4ac58162b314fcfbba775413e7926b5279a3dfb0673f0e208cbddbf0b421", "difficulty": "medium", "final_answer": {"answer": [-0.05, -22.5], "unit": "dimensionless"}, "id": "line_two_point_001148_-3.25_3_-0.05_-22.5", "license": "Apache-2.0", "prompt": "A line passes through points (-3.25, -22.3375) and (3, -22.65). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -3.25, "x2": 3.0, "y1": -22.3375, "y2": -22.65}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. grams cancel with J/(g*K), and kelvin cancels, leaving joules\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "14fb9a659ad865d06e77b8172305fff24322fea71db1ea0815a855b03ecd30fa", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_001149_consistent_4153435f_670493", "license": "Apache-2.0", "prompt": "In sensor calibration case 670493, check dimensional consistency for Q = m * c * DeltaT. The left side has dimensions J and the right side has dimensions J. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\ngrams cancel with J/(g*K), and kelvin cancels, leaving joules\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "Q = m * c * DeltaT"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef threshold_flags_001150(values, threshold):\n    return [value >= threshold for value in values]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"threshold_flags_001150\"}", "dedupe_signature": "e04529b8043b9a17132c3a705ffb28884b7f6e5f044ccbf69970a6cacf8fa215", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "threshold_flags_001150"}, "id": "code_001150_threshold_flags_001150", "license": "Apache-2.0", "prompt": "Write a Python function threshold_flags_001150(values, threshold) that returns a list of booleans showing whether each value is greater than or equal to threshold. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "threshold_flags_001150"}, "verifier": {"function": "threshold_flags_001150", "tests": ["assert threshold_flags_001150([1, 2, 3], 2) == [False, True, True]", "assert threshold_flags_001150([], 5) == []", "assert threshold_flags_001150([-1, 0], 0) == [False, True]"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: launch_angle_or_vertical_velocity.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"launch_angle_or_vertical_velocity\"]}", "dedupe_signature": "eb3572879c8fa91cab039eac2847ce8325e815fd4aa918376ae5d554f861130d", "difficulty": "easy", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["launch_angle_or_vertical_velocity"]}, "id": "abstain_001151_launch_angle_or_vertical_velocity", "license": "Apache-2.0", "prompt": "Compute projectile range on level ground. The prompt gives initial speed 20.4 m/s but does not give launch angle or vertical velocity. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: launch_angle_or_vertical_velocity.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["launch_angle_or_vertical_velocity"]}, "verifier": {"missing": ["launch_angle_or_vertical_velocity"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 21.6 kg and a = 2.55 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 55.08, \"unit\": \"N\"}", "dedupe_signature": "9cf2350f1630504a40c66b2c9299b49bbc7d1b5ee8fb531bf936e6e11ec4d9e0", "difficulty": "easy", "final_answer": {"answer": 55.08, "unit": "N"}, "id": "force_001152_21.6_2.55", "license": "Apache-2.0", "prompt": "A cart has mass 21.6 kg and measured acceleration 2.55 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 21.6 kg and a = 2.55 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 2.55, "mass": 21.6}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 1.9^2 and multiply by 0.5 * 26.5.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 47.8325, \"unit\": \"J\"}", "dedupe_signature": "fecc6f52d7e1c275c528691ec5c3c9b98f2180dc4633a9bd0869baaad49f70e7", "difficulty": "easy", "final_answer": {"answer": 47.8325, "unit": "J"}, "id": "ke_001153_26.5_1.9", "license": "Apache-2.0", "prompt": "A body of mass 26.5 kg moves at 1.9 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 1.9^2 and multiply by 0.5 * 26.5.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 26.5, "velocity": 1.9}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 4.54 * 8.314 * 618 / 52.1.\nFinal: {\"answer\": 447.7304, \"unit\": \"kPa\"}", "dedupe_signature": "be78bf0ee6008f8645bd415acae4526353c6b559797ea60c328f30908efd1bfc", "difficulty": "medium", "final_answer": {"answer": 447.7304, "unit": "kPa"}, "id": "ideal_gas_001155_4.54_618_52.1", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=4.54 mol, T=618 K, and V=52.1 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 4.54 * 8.314 * 618 / 52.1.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 4.54, "temp_k": 618, "volume_l": 52.1}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1345 * 4.635 * 10.\nFinal: {\"answer\": 62340.75, \"unit\": \"J\"}", "dedupe_signature": "f4311f28876794127768ed673f152dc2360576fed5e4d75df0616e634a842669", "difficulty": "easy", "final_answer": {"answer": 62340.75, "unit": "J"}, "id": "heat_q_001156_1345_4.635_10", "license": "Apache-2.0", "prompt": "A 1345 g sample has specific heat 4.635 J/(g*K). How much heat is needed to raise its temperature by 10 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1345 * 4.635 * 10.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 10, "heat_capacity": 4.635, "mass_g": 1345}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=464 mg, t=226.5 h, and T_half=14.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 0.0092, \"unit\": \"mg\"}", "dedupe_signature": "9e88d88411546594d63b5e741b00931323cd5bb963b35ea2ef3ce4501666cbee", "difficulty": "medium", "final_answer": {"answer": 0.0092, "unit": "mg"}, "id": "half_life_001158_464_14.5_226.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 464 mg. Its half-life is 14.5 hours. How many mg remain after 226.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=464 mg, t=226.5 h, and T_half=14.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 226.5, "half_life": 14.5, "initial_amount": 464.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 4405 mL to 4.405 L.\n3. Compute M = 2.69 / 4.405.\nFinal: {\"answer\": 0.6107, \"unit\": \"mol/L\"}", "dedupe_signature": "c329ff31e23553f582fe05cb0278d8ec109d8af2d9c5922cc1f13d174839c1b5", "difficulty": "medium", "final_answer": {"answer": 0.6107, "unit": "mol/L"}, "id": "molarity_001160_2.69_4405", "license": "Apache-2.0", "prompt": "A solution contains 2.69 mol of solute in 4405 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 4405 mL to 4.405 L.\nCompute M = 2.69 / 4.405.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 2.69, "volume_ml": 4405}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-6.5)=0.5 and f(-0.7)=-5.3.\n3. The interval width is 5.8.\nFinal: {\"answer\": -13.92, \"unit\": \"area_units\"}", "dedupe_signature": "db53fd9fb0696ffaeba697b67238402096a852697445bd1a537c60c6a16d199a", "difficulty": "medium", "final_answer": {"answer": -13.92, "unit": "area_units"}, "id": "trapz_linear_001162_-1_-6_-6.5_-0.7", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-1x+-6 from x=-6.5 to x=-0.7. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-6.5)=0.5 and f(-0.7)=-5.3.\nThe interval width is 5.8.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -6.0, "slope": -1.0, "x0": -6.5, "x1": -0.7000000000000002}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.48 and add it to the current value.\nFinal: {\"answer\": [1.11, 1.114, 0.274], \"unit\": \"temperature_units\"}", "dedupe_signature": "8ca50ee5286f4132b9c1a92d702db053a43a4e9e2ff84777deb71b985bccb4bd", "difficulty": "hard", "final_answer": {"answer": [1.11, 1.114, 0.274], "unit": "temperature_units"}, "id": "heat_step_001163_0.48_0.75_1.35_1.45_0.85_-0.95", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=0.75, right=-0.95; current interior values are [1.35, 1.45, 0.85]. Use r=0.48. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.48 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [1.35, 1.45, 0.85], "left": 0.75, "r": 0.48, "right": -0.95}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 100 centimeters in one meter.\n2. Apply the conversion factor directly to the given value.\n3. Compute 1923.5 / 100.\nFinal: {\"answer\": 19.235, \"unit\": \"m\"}", "dedupe_signature": "b3b64b593159918f14160716a03785986299b606364d4d4599a26ec953b4af4e", "difficulty": "easy", "final_answer": {"answer": 19.235, "unit": "m"}, "id": "unit_convert_001164_cm_to_m_1923.5", "license": "Apache-2.0", "prompt": "Convert 1923.5 cm to m. Return the converted value with unit.", "reasoning_trace": "There are 100 centimeters in one meter.\nApply the conversion factor directly to the given value.\nCompute 1923.5 / 100.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 1923.5}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=315 degrees and keep the unit as newtons.\nFinal: {\"answer\": [59.397, -59.397], \"unit\": \"N\"}", "dedupe_signature": "0fb79186e239dd124e63e0ad45b0caf5fec702112c01ad7242c4bcdb0d1beb09", "difficulty": "medium", "final_answer": {"answer": [59.397, -59.397], "unit": "N"}, "id": "vector_components_001165_84_315", "license": "Apache-2.0", "prompt": "A vector has magnitude 84 N at 315 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=315 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 315, "magnitude": 84.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-0.75, 2.0], \"unit\": \"dimensionless\"}", "dedupe_signature": "d59686a32e9733de2a51c065e3b74d3c2a6c58118867daaac9fbbf7945efc66a", "difficulty": "medium", "final_answer": {"answer": [-0.75, 2.0], "unit": "dimensionless"}, "id": "line_two_point_001166_5_18.75_-0.75_2", "license": "Apache-2.0", "prompt": "A line passes through points (5, -1.75) and (18.75, -12.0625). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 5.0, "x2": 18.75, "y1": -1.75, "y2": -12.0625}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. mass times acceleration has newton dimensions\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "dff0c866ee15554ee11e6186ae5eefae65d90da56566406087bffdbb1197a5c5", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_001167_consistent_03f5e041_887782", "license": "Apache-2.0", "prompt": "In instrument manual case 887782, check dimensional consistency for F = m * a. The left side has dimensions kg*m/s^2 and the right side has dimensions kg*m/s^2. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nmass times acceleration has newton dimensions\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "F = m * a"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef threshold_flags_001168(values, threshold):\n    return [value >= threshold for value in values]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"threshold_flags_001168\"}", "dedupe_signature": "72166a82f942c751d359df51efaca9722595b23797a7652942386d9c54dc8a70", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "threshold_flags_001168"}, "id": "code_001168_threshold_flags_001168", "license": "Apache-2.0", "prompt": "Write a Python function threshold_flags_001168(values, threshold) that returns a list of booleans showing whether each value is greater than or equal to threshold. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "threshold_flags_001168"}, "verifier": {"function": "threshold_flags_001168", "tests": ["assert threshold_flags_001168([1, 2, 3], 2) == [False, True, True]", "assert threshold_flags_001168([], 5) == []", "assert threshold_flags_001168([-1, 0], 0) == [False, True]"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 0.6 kg and a = 5.65 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 3.39, \"unit\": \"N\"}", "dedupe_signature": "68ffbda0b6264a60ca7b087e671e57e3ac4ddcf58fc81231e47c0e493718eeaa", "difficulty": "easy", "final_answer": {"answer": 3.39, "unit": "N"}, "id": "force_001170_0.6_5.65", "license": "Apache-2.0", "prompt": "A cart has mass 0.6 kg and measured acceleration 5.65 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 0.6 kg and a = 5.65 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 5.65, "mass": 0.6}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 42.25^2 and multiply by 0.5 * 5.3.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 4730.4156, \"unit\": \"J\"}", "dedupe_signature": "7f857ae58146c01e50bdd08f15581b2b89537d64d422c5bd4292143ed3ed362c", "difficulty": "easy", "final_answer": {"answer": 4730.4156, "unit": "J"}, "id": "ke_001171_5.3_42.25", "license": "Apache-2.0", "prompt": "A body of mass 5.3 kg moves at 42.25 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 42.25^2 and multiply by 0.5 * 5.3.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 5.3, "velocity": 42.25}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=25 degrees through the sine of 2 theta.\n3. Substitute v=79.9 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 498.5153, \"unit\": \"m\"}", "dedupe_signature": "7307db127e638092855eab62c68ebaf96ab0272fcce6688bf1013877aae26c34", "difficulty": "medium", "final_answer": {"answer": 498.5153, "unit": "m"}, "id": "projectile_range_001172_79.9_25", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 79.9 m/s and angle 25 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=25 degrees through the sine of 2 theta.\nSubstitute v=79.9 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 25, "gravity": 9.81, "speed": 79.9}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 700 * 4.525 * 104.\nFinal: {\"answer\": 329420.0, \"unit\": \"J\"}", "dedupe_signature": "1126bb179935014c8473245b929a73823f822c09f21ae5f91122be677a6f63e3", "difficulty": "easy", "final_answer": {"answer": 329420.0, "unit": "J"}, "id": "heat_q_001174_700_4.525_104", "license": "Apache-2.0", "prompt": "A 700 g sample has specific heat 4.525 J/(g*K). How much heat is needed to raise its temperature by 104 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 700 * 4.525 * 104.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 104, "heat_capacity": 4.525, "mass_g": 700}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=150.9 V and R=105.8 ohm.\nFinal: {\"answer\": 215.225, \"unit\": \"W\"}", "dedupe_signature": "4150467ab5d2e0a58d7593317e51d36698554869cb97e998558d77bff6d1bcbf", "difficulty": "easy", "final_answer": {"answer": 215.225, "unit": "W"}, "id": "ohm_power_001175_150.9_105.8", "license": "Apache-2.0", "prompt": "A resistor has resistance 105.8 ohm and voltage 150.9 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=150.9 V and R=105.8 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 105.8, "voltage": 150.9}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=817.5 mg, t=242.5 h, and T_half=52 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 32.2586, \"unit\": \"mg\"}", "dedupe_signature": "8605a5effa3710bcd72ce1994b82ad992828e8fa01a0170c12a574d4d9c3377c", "difficulty": "medium", "final_answer": {"answer": 32.2586, "unit": "mg"}, "id": "half_life_001176_817.5_52_242.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 817.5 mg. Its half-life is 52 hours. How many mg remain after 242.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=817.5 mg, t=242.5 h, and T_half=52 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 242.5, "half_life": 52.0, "initial_amount": 817.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 3375 mL to 3.375 L.\n3. Compute M = 2.69 / 3.375.\nFinal: {\"answer\": 0.797, \"unit\": \"mol/L\"}", "dedupe_signature": "11b5f842650017dea43406df3658af3d4a496855ff8167f885aa8ffbc2885a32", "difficulty": "medium", "final_answer": {"answer": 0.797, "unit": "mol/L"}, "id": "molarity_001178_2.69_3375", "license": "Apache-2.0", "prompt": "A solution contains 2.69 mol of solute in 3375 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 3375 mL to 3.375 L.\nCompute M = 2.69 / 3.375.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 2.69, "volume_ml": 3375}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.5 y, so each step multiplies y by 1 - h*0.5.\n3. Apply that update for 7 steps and round the final state.\nFinal: {\"answer\": 0.1364, \"unit\": \"state_units\"}", "dedupe_signature": "d8ebc830a09215d38ac24efdbaa300660fc4572ef416db3b2a2e6cbed8ae7917", "difficulty": "medium", "final_answer": {"answer": 0.1364, "unit": "state_units"}, "id": "euler_decay_001179_25_0.5_1.05_7", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.5 y with y(0)=25, step size h=1.05, for 7 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.5 y, so each step multiplies y by 1 - h*0.5.\nApply that update for 7 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 25.0, "rate": 0.5, "step": 1.05, "steps": 7}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.14 and add it to the current value.\nFinal: {\"answer\": [-0.832, -0.044, -0.853], \"unit\": \"temperature_units\"}", "dedupe_signature": "275076139f0b29ad03d0e3f687b131b6399e36cdf04a26f489642c63a492339d", "difficulty": "hard", "final_answer": {"answer": [-0.832, -0.044, -0.853], "unit": "temperature_units"}, "id": "heat_step_001181_0.14_2.2_-1.7_0.6_-1.7_2.05", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=2.2, right=2.05; current interior values are [-1.7, 0.6, -1.7]. Use r=0.14. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.14 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-1.7, 0.6, -1.7], "left": 2.2, "r": 0.14, "right": 2.05}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kelvin equals Celsius plus 273.15.\n2. Apply the conversion factor directly to the given value.\n3. Compute 40.5 + 273.15.\nFinal: {\"answer\": 313.65, \"unit\": \"K\"}", "dedupe_signature": "6d6399ee0b9f4b926ad1d9ad0288c5dad8ad79aa9623d33d6f2e638d895a867d", "difficulty": "easy", "final_answer": {"answer": 313.65, "unit": "K"}, "id": "unit_convert_001182_c_to_k_40.5", "license": "Apache-2.0", "prompt": "Convert 40.5 degC to K. Return the converted value with unit.", "reasoning_trace": "Kelvin equals Celsius plus 273.15.\nApply the conversion factor directly to the given value.\nCompute 40.5 + 273.15.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 40.5}, "verifier": {"formula": "value + 273.15", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-3.8, 3.25], \"unit\": \"dimensionless\"}", "dedupe_signature": "19b094784c405883b2042d6b28cf6c115bcf882016703bdbfacf68d29b51d129", "difficulty": "medium", "final_answer": {"answer": [-3.8, 3.25], "unit": "dimensionless"}, "id": "line_two_point_001184_1.75_6.75_-3.8_3.25", "license": "Apache-2.0", "prompt": "A line passes through points (1.75, -3.4) and (6.75, -22.4). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 1.75, "x2": 6.75, "y1": -3.3999999999999995, "y2": -22.4}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef clamp_001186(x, lo, hi):\n    if lo > hi:\n        raise ValueError('lo must be <= hi')\n    return min(max(x, lo), hi)\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"clamp_001186\"}", "dedupe_signature": "a3446331d40e2de2b94ee540abe397a86ad2712d2d963c7cb8cf7c0085541ef4", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "clamp_001186"}, "id": "code_001186_clamp_001186", "license": "Apache-2.0", "prompt": "Write a Python function clamp_001186(x, lo, hi) that clips x into the inclusive interval [lo, hi]. It must raise ValueError if lo > hi. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "clamp_001186"}, "verifier": {"function": "clamp_001186", "tests": ["assert clamp_001186(5, 0, 10) == 5", "assert clamp_001186(-2, 0, 10) == 0", "assert clamp_001186(12, 0, 10) == 10", "try:\n    clamp_001186(1, 3, 2)\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 10.1 kg and a = 11.85 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 119.685, \"unit\": \"N\"}", "dedupe_signature": "b80e1e5f2873be54c736a1b9c197ba4a987c09027bc870d849af8f528e108d92", "difficulty": "easy", "final_answer": {"answer": 119.685, "unit": "N"}, "id": "force_001188_10.1_11.85", "license": "Apache-2.0", "prompt": "A cart has mass 10.1 kg and measured acceleration 11.85 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 10.1 kg and a = 11.85 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 11.85, "mass": 10.1}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 34.75^2 and multiply by 0.5 * 2.8.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 1690.5875, \"unit\": \"J\"}", "dedupe_signature": "b6f79bae1e58e1b94227fea67fbb9c11a591e0d600339d6dd5a294ebf2d57795", "difficulty": "easy", "final_answer": {"answer": 1690.5875, "unit": "J"}, "id": "ke_001189_2.8_34.75", "license": "Apache-2.0", "prompt": "A body of mass 2.8 kg moves at 34.75 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 34.75^2 and multiply by 0.5 * 2.8.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 2.8, "velocity": 34.75}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=39 degrees through the sine of 2 theta.\n3. Substitute v=80.4 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 644.5365, \"unit\": \"m\"}", "dedupe_signature": "f9e519d3f8ab27deaf6c3e40f36b5292b7151bae4aeddd3dbbf20c584661b147", "difficulty": "medium", "final_answer": {"answer": 644.5365, "unit": "m"}, "id": "projectile_range_001190_80.4_39", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 80.4 m/s and angle 39 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=39 degrees through the sine of 2 theta.\nSubstitute v=80.4 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 39, "gravity": 9.81, "speed": 80.4}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 3.64 * 8.314 * 374 / 115.1.\nFinal: {\"answer\": 98.3349, \"unit\": \"kPa\"}", "dedupe_signature": "f5105ad820674f7b782b04ee13bd675ad29b60d06423fa4171bf304d62a82dce", "difficulty": "medium", "final_answer": {"answer": 98.3349, "unit": "kPa"}, "id": "ideal_gas_001191_3.64_374_115.1", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=3.64 mol, T=374 K, and V=115.1 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 3.64 * 8.314 * 374 / 115.1.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 3.64, "temp_k": 374, "volume_l": 115.1}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=34.2 V and R=6.2 ohm.\nFinal: {\"answer\": 188.6516, \"unit\": \"W\"}", "dedupe_signature": "97308203ececc8c7d6cefcd742ad6de4477024e7412122fb93728a8577401046", "difficulty": "easy", "final_answer": {"answer": 188.6516, "unit": "W"}, "id": "ohm_power_001193_34.2_6.2", "license": "Apache-2.0", "prompt": "A resistor has resistance 6.2 ohm and voltage 34.2 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=34.2 V and R=6.2 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 6.2, "voltage": 34.2}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=596.5 mg, t=310 h, and T_half=13 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 0.0, \"unit\": \"mg\"}", "dedupe_signature": "7cbd776db946e2f5ce602839eec23657016f6efb1baad94af6b6776d23042a88", "difficulty": "medium", "final_answer": {"answer": 0.0, "unit": "mg"}, "id": "half_life_001194_596.5_13_310", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 596.5 mg. Its half-life is 13 hours. How many mg remain after 310 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=596.5 mg, t=310 h, and T_half=13 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 310.0, "half_life": 13.0, "initial_amount": 596.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 6.96 mol * 58.44 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 406.7424, \"unit\": \"g\"}", "dedupe_signature": "3a5ec671089bc582eb0fa4d5882e0233f0804ebd2a6f98c2c79afb8aecfbb10d", "difficulty": "medium", "final_answer": {"answer": 406.7424, "unit": "g"}, "id": "stoich_mass_001195_sodium_chloride_6.96", "license": "Apache-2.0", "prompt": "A sample contains 6.96 mol of sodium chloride. Using molar mass 58.44 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 6.96 mol * 58.44 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "sodium chloride", "molar_mass": 58.44, "moles": 6.96}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.3 y, so each step multiplies y by 1 - h*0.3.\n3. Apply that update for 12 steps and round the final state.\nFinal: {\"answer\": 0.015, \"unit\": \"state_units\"}", "dedupe_signature": "cfca35d97b8307d174aa5168ed13c1cf6ca870d26983368fca2d9a56fba3fcf6", "difficulty": "medium", "final_answer": {"answer": 0.015, "unit": "state_units"}, "id": "euler_decay_001197_78.5_0.3_1.7_12", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.3 y with y(0)=78.5, step size h=1.7, for 12 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.3 y, so each step multiplies y by 1 - h*0.3.\nApply that update for 12 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 78.5, "rate": 0.3, "step": 1.7, "steps": 12}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-8.7)=-5.46 and f(-1.4)=7.68.\n3. The interval width is 7.3.\nFinal: {\"answer\": 8.103, \"unit\": \"area_units\"}", "dedupe_signature": "8a59cb432e6c7b99affb43a4312f6283dff13e55cd404e4ec8fbd3abcb742cb3", "difficulty": "medium", "final_answer": {"answer": 8.103, "unit": "area_units"}, "id": "trapz_linear_001198_1.8_10.2_-8.7_-1.4", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=1.8x+10.2 from x=-8.7 to x=-1.4. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-8.7)=-5.46 and f(-1.4)=7.68.\nThe interval width is 7.3.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 10.2, "slope": 1.8, "x0": -8.7, "x1": -1.3999999999999995}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kelvin equals Celsius plus 273.15.\n2. Apply the conversion factor directly to the given value.\n3. Compute 240.0 + 273.15.\nFinal: {\"answer\": 513.15, \"unit\": \"K\"}", "dedupe_signature": "90ed723c1fb14df6088baf833570f2a583f80f4c5d94cb09c394895c7c49a06a", "difficulty": "easy", "final_answer": {"answer": 513.15, "unit": "K"}, "id": "unit_convert_001200_c_to_k_240", "license": "Apache-2.0", "prompt": "Convert 240 degC to K. Return the converted value with unit.", "reasoning_trace": "Kelvin equals Celsius plus 273.15.\nApply the conversion factor directly to the given value.\nCompute 240.0 + 273.15.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 240.0}, "verifier": {"formula": "value + 273.15", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=167 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-145.6683, 33.6302], \"unit\": \"N\"}", "dedupe_signature": "b78f509c320cf4fa9d4e71d9d0af51086684f4603286208209e7fcc8c39cac2c", "difficulty": "medium", "final_answer": {"answer": [-145.6683, 33.6302], "unit": "N"}, "id": "vector_components_001201_149.5_167", "license": "Apache-2.0", "prompt": "A vector has magnitude 149.5 N at 167 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=167 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 167, "magnitude": 149.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [6.9, 23.25], \"unit\": \"dimensionless\"}", "dedupe_signature": "634e26cace6dc8a139f267b79d148b5af1cc337540a630bbf11b53c7b5a31975", "difficulty": "medium", "final_answer": {"answer": [6.9, 23.25], "unit": "dimensionless"}, "id": "line_two_point_001202_-3.25_7_6.9_23.25", "license": "Apache-2.0", "prompt": "A line passes through points (-3.25, 0.825) and (7, 71.55). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -3.25, "x2": 7.0, "y1": 0.8249999999999993, "y2": 71.55000000000001}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. m*v is momentum, not energy\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "a3c0fa1f875e90534e546b35237c633efbbc009fffbe495398ee40503f78b096", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_001203_inconsistent_1e14b074_819147", "license": "Apache-2.0", "prompt": "In lab notebook case 819147, check dimensional consistency for E = m * v. The left side has dimensions kg*m^2/s^2 and the right side has dimensions kg*m/s. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nm*v is momentum, not energy\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "E = m * v"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\nimport math\n\ndef unit_vector_001204(x, y):\n    norm = math.hypot(x, y)\n    if norm == 0:\n        raise ValueError('zero vector has no direction')\n    return (x / norm, y / norm)\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"unit_vector_001204\"}", "dedupe_signature": "4725fcf00c171eb2d91f34833d6df95ff61343b5e92da21161c7e697ec3a0e1b", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "unit_vector_001204"}, "id": "code_001204_unit_vector_001204", "license": "Apache-2.0", "prompt": "Write a Python function unit_vector_001204(x, y) that returns the 2D unit vector as a tuple. Raise ValueError for the zero vector. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "unit_vector_001204"}, "verifier": {"function": "unit_vector_001204", "tests": ["ux, uy = unit_vector_001204(3, 4); assert abs(ux - 0.6) < 1e-12 and abs(uy - 0.8) < 1e-12", "assert unit_vector_001204(0, 5) == (0, 1)", "try:\n    unit_vector_001204(0, 0)\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: required_fields, allowed_transformations.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"required_fields\", \"allowed_transformations\"]}", "dedupe_signature": "e790e3c8c63c2f9d6c879638a3767ad2c21230d53d116ea1ab7d11061e014b81", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["required_fields", "allowed_transformations"]}, "id": "abstain_001205_required_fields_allowed_transformations", "license": "Apache-2.0", "prompt": "Write a sanitizer for valid mobile ledger records in release 252611, but the prompt does not state which fields are required or which transformations are allowed. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: required_fields, allowed_transformations.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["required_fields", "allowed_transformations"]}, "verifier": {"missing": ["required_fields", "allowed_transformations"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 26.9^2 and multiply by 0.5 * 26.35.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 9533.5617, \"unit\": \"J\"}", "dedupe_signature": "b4bb2d80db86fff3431cede6f9135ac279d395c53dc9f8e19555c1b0b37b26c9", "difficulty": "easy", "final_answer": {"answer": 9533.5617, "unit": "J"}, "id": "ke_001207_26.35_26.9", "license": "Apache-2.0", "prompt": "A body of mass 26.35 kg moves at 26.9 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 26.9^2 and multiply by 0.5 * 26.35.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 26.35, "velocity": 26.9}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=48 degrees through the sine of 2 theta.\n3. Substitute v=29.7 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 89.4249, \"unit\": \"m\"}", "dedupe_signature": "8313f0769713434dcc2f6493ca9e43ec1520aa280f6b189f6a23429b3c284b76", "difficulty": "medium", "final_answer": {"answer": 89.4249, "unit": "m"}, "id": "projectile_range_001208_29.7_48", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 29.7 m/s and angle 48 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=48 degrees through the sine of 2 theta.\nSubstitute v=29.7 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 48, "gravity": 9.81, "speed": 29.7}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 1.96 * 8.314 * 584 / 49.2.\nFinal: {\"answer\": 193.4255, \"unit\": \"kPa\"}", "dedupe_signature": "b644b955ab5847da00096b6934a672ac1321338a0696d80439c7a9a2893fbe1e", "difficulty": "medium", "final_answer": {"answer": 193.4255, "unit": "kPa"}, "id": "ideal_gas_001209_1.96_584_49.2", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=1.96 mol, T=584 K, and V=49.2 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 1.96 * 8.314 * 584 / 49.2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 1.96, "temp_k": 584, "volume_l": 49.2}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 130 * 3.365 * 91.\nFinal: {\"answer\": 39807.95, \"unit\": \"J\"}", "dedupe_signature": "97883be7154827ac9d8be79633794b117829dd5d036619da8fa7aa4c4862b9b6", "difficulty": "easy", "final_answer": {"answer": 39807.95, "unit": "J"}, "id": "heat_q_001210_130_3.365_91", "license": "Apache-2.0", "prompt": "A 130 g sample has specific heat 3.365 J/(g*K). How much heat is needed to raise its temperature by 91 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 130 * 3.365 * 91.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 91, "heat_capacity": 3.365, "mass_g": 130}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=216 V and R=32.7 ohm.\nFinal: {\"answer\": 1426.789, \"unit\": \"W\"}", "dedupe_signature": "c1bd514483a7d9ee81fa70249fbde82a48492ad66a9e049b8c9785b9994e56c1", "difficulty": "easy", "final_answer": {"answer": 1426.789, "unit": "W"}, "id": "ohm_power_001211_216_32.7", "license": "Apache-2.0", "prompt": "A resistor has resistance 32.7 ohm and voltage 216 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=216 V and R=32.7 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 32.7, "voltage": 216.0}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=456 mg, t=265.5 h, and T_half=49.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 11.0751, \"unit\": \"mg\"}", "dedupe_signature": "879b3eb62e06ae22051256e0ce9bcd7e8f21023a2aec9abbc8bcbcc3bcc8c7f3", "difficulty": "medium", "final_answer": {"answer": 11.0751, "unit": "mg"}, "id": "half_life_001212_456_49.5_265.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 456 mg. Its half-life is 49.5 hours. How many mg remain after 265.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=456 mg, t=265.5 h, and T_half=49.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 265.5, "half_life": 49.5, "initial_amount": 456.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 3330 mL to 3.33 L.\n3. Compute M = 3.84 / 3.33.\nFinal: {\"answer\": 1.1532, \"unit\": \"mol/L\"}", "dedupe_signature": "107e3e18d6f623b2a6ae9082d8760144011dfedbf6c851ef55ae88c7a9b2c73f", "difficulty": "medium", "final_answer": {"answer": 1.1532, "unit": "mol/L"}, "id": "molarity_001214_3.84_3330", "license": "Apache-2.0", "prompt": "A solution contains 3.84 mol of solute in 3330 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 3330 mL to 3.33 L.\nCompute M = 3.84 / 3.33.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 3.84, "volume_ml": 3330}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.57 y, so each step multiplies y by 1 - h*0.57.\n3. Apply that update for 6 steps and round the final state.\nFinal: {\"answer\": 4.223, \"unit\": \"state_units\"}", "dedupe_signature": "f21fbc9d1c0e1ff1ce2c01b08cf5b2941f156b661dcf1f758d2fd7dd8b525413", "difficulty": "medium", "final_answer": {"answer": 4.223, "unit": "state_units"}, "id": "euler_decay_001215_25_0.57_0.45_6", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.57 y with y(0)=25, step size h=0.45, for 6 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.57 y, so each step multiplies y by 1 - h*0.57.\nApply that update for 6 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 25.0, "rate": 0.57, "step": 0.45, "steps": 6}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(7.5)=18.7 and f(10.8)=27.94.\n3. The interval width is 3.3.\nFinal: {\"answer\": 76.956, \"unit\": \"area_units\"}", "dedupe_signature": "ef4ffdb95ac156753e7fc0588ccd86880463f91b66a3ac70d87ad5bcd6786a49", "difficulty": "medium", "final_answer": {"answer": 76.956, "unit": "area_units"}, "id": "trapz_linear_001216_2.8_-2.3_7.5_10.8", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=2.8x+-2.3 from x=7.5 to x=10.8. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(7.5)=18.7 and f(10.8)=27.94.\nThe interval width is 3.3.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -2.3, "slope": 2.8, "x0": 7.5, "x1": 10.8}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.42 and add it to the current value.\nFinal: {\"answer\": [-0.758, 1.172, -0.19], \"unit\": \"temperature_units\"}", "dedupe_signature": "51ad423bdee8134713b6c2d3dd7fa156e02c5b7760b9b2f1103227510bdd9347", "difficulty": "hard", "final_answer": {"answer": [-0.758, 1.172, -0.19], "unit": "temperature_units"}, "id": "heat_step_001217_0.42_-1.35_0.25_-0.55_2.75_-0.95", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-1.35, right=-0.95; current interior values are [0.25, -0.55, 2.75]. Use r=0.42. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.42 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [0.25, -0.55, 2.75], "left": -1.35, "r": 0.42, "right": -0.95}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 100 centimeters in one meter.\n2. Apply the conversion factor directly to the given value.\n3. Compute 4071.5 / 100.\nFinal: {\"answer\": 40.715, \"unit\": \"m\"}", "dedupe_signature": "6599a429e1042ee7f19b13ec6748d95d397c67dd70d96bb1fb9bd96fb1410ae3", "difficulty": "easy", "final_answer": {"answer": 40.715, "unit": "m"}, "id": "unit_convert_001218_cm_to_m_4071.5", "license": "Apache-2.0", "prompt": "Convert 4071.5 cm to m. Return the converted value with unit.", "reasoning_trace": "There are 100 centimeters in one meter.\nApply the conversion factor directly to the given value.\nCompute 4071.5 / 100.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 4071.5}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=17 degrees and keep the unit as newtons.\nFinal: {\"answer\": [330.4033, 101.0144], \"unit\": \"N\"}", "dedupe_signature": "1fb5dec2c10fd49818b42771ee22d67384d3f98893fcef7fb33e7c53dd4c0c18", "difficulty": "medium", "final_answer": {"answer": [330.4033, 101.0144], "unit": "N"}, "id": "vector_components_001219_345.5_17", "license": "Apache-2.0", "prompt": "A vector has magnitude 345.5 N at 17 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=17 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 17, "magnitude": 345.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-6.1, 16.75], \"unit\": \"dimensionless\"}", "dedupe_signature": "f7c0fede223fb8c1bac5c79d3a4ebed3aecbd9421afeae3ba2a6815ed4eb7fb1", "difficulty": "medium", "final_answer": {"answer": [-6.1, 16.75], "unit": "dimensionless"}, "id": "line_two_point_001220_3.5_8.25_-6.1_16.75", "license": "Apache-2.0", "prompt": "A line passes through points (3.5, -4.6) and (8.25, -33.575). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 3.5, "x2": 8.25, "y1": -4.599999999999998, "y2": -33.574999999999996}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. mass times acceleration has newton dimensions\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "3cf4c355f46f8ca186cb2b5e7e3450f6d59aa15beff567fd64c3defd0a4e6a7e", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_001221_consistent_03f5e041_544001", "license": "Apache-2.0", "prompt": "In sensor calibration case 544001, check dimensional consistency for F = m * a. The left side has dimensions kg*m/s^2 and the right side has dimensions kg*m/s^2. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nmass times acceleration has newton dimensions\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "F = m * a"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef running_total_001222(values):\n    total = 0\n    out = []\n    for value in values:\n        total += value\n        out.append(total)\n    return out\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"running_total_001222\"}", "dedupe_signature": "20b399961a42ec20ed91e287976e58fef40e0e349b7940b7ba936fbcaaeb399d", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "running_total_001222"}, "id": "code_001222_running_total_001222", "license": "Apache-2.0", "prompt": "Write a Python function running_total_001222(values) that returns cumulative sums as a new list. It must not mutate the input list. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "running_total_001222"}, "verifier": {"function": "running_total_001222", "tests": ["assert running_total_001222([1, 2, 3]) == [1, 3, 6]", "xs = [4, -1, 2]; assert running_total_001222(xs) == [4, 3, 5] and xs == [4, -1, 2]", "assert running_total_001222([]) == []"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 15.2^2 and multiply by 0.5 * 14.15.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 1634.608, \"unit\": \"J\"}", "dedupe_signature": "da0ca90b7bed4268153d206700f2624bc381e7c3116b1e5557ae8c938a75103b", "difficulty": "easy", "final_answer": {"answer": 1634.608, "unit": "J"}, "id": "ke_001225_14.15_15.2", "license": "Apache-2.0", "prompt": "A body of mass 14.15 kg moves at 15.2 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 15.2^2 and multiply by 0.5 * 14.15.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 14.15, "velocity": 15.2}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=77 degrees through the sine of 2 theta.\n3. Substitute v=45.7 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 93.3266, \"unit\": \"m\"}", "dedupe_signature": "c346419e32962320d8a8d0e6da262126dd8ebfef35e62a788502036c9a865f82", "difficulty": "medium", "final_answer": {"answer": 93.3266, "unit": "m"}, "id": "projectile_range_001226_45.7_77", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 45.7 m/s and angle 77 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=77 degrees through the sine of 2 theta.\nSubstitute v=45.7 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 77, "gravity": 9.81, "speed": 45.7}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 2.27 * 8.314 * 366 / 87.8.\nFinal: {\"answer\": 78.6724, \"unit\": \"kPa\"}", "dedupe_signature": "978c8c56178c3a577adc3e8cb866603868bd4e2499d28c7892d3651ca2967283", "difficulty": "medium", "final_answer": {"answer": 78.6724, "unit": "kPa"}, "id": "ideal_gas_001227_2.27_366_87.8", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=2.27 mol, T=366 K, and V=87.8 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 2.27 * 8.314 * 366 / 87.8.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 2.27, "temp_k": 366, "volume_l": 87.8}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 865 * 2 * 21.\nFinal: {\"answer\": 36330.0, \"unit\": \"J\"}", "dedupe_signature": "d6320be38ba5c0ab3edde274fe208d918074b368b2a84b83b292deb3f7c4022a", "difficulty": "easy", "final_answer": {"answer": 36330.0, "unit": "J"}, "id": "heat_q_001228_865_2_21", "license": "Apache-2.0", "prompt": "A 865 g sample has specific heat 2 J/(g*K). How much heat is needed to raise its temperature by 21 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 865 * 2 * 21.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 21, "heat_capacity": 2.0, "mass_g": 865}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=974 mg, t=348.5 h, and T_half=117.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 124.657, \"unit\": \"mg\"}", "dedupe_signature": "b33ae1322ed2edd8fe82c86e1653a87bab010cf8dd5cb1b88fcc33ac64697e45", "difficulty": "medium", "final_answer": {"answer": 124.657, "unit": "mg"}, "id": "half_life_001230_974_117.5_348.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 974 mg. Its half-life is 117.5 hours. How many mg remain after 348.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=974 mg, t=348.5 h, and T_half=117.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 348.5, "half_life": 117.5, "initial_amount": 974.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 3245 mL to 3.245 L.\n3. Compute M = 3.56 / 3.245.\nFinal: {\"answer\": 1.0971, \"unit\": \"mol/L\"}", "dedupe_signature": "3314eb153b09982ea2f4a401e5acd86373be0da5a38a4507e94eff7c01388cbd", "difficulty": "medium", "final_answer": {"answer": 1.0971, "unit": "mol/L"}, "id": "molarity_001232_3.56_3245", "license": "Apache-2.0", "prompt": "A solution contains 3.56 mol of solute in 3245 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 3245 mL to 3.245 L.\nCompute M = 3.56 / 3.245.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 3.56, "volume_ml": 3245}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.87 y, so each step multiplies y by 1 - h*0.87.\n3. Apply that update for 6 steps and round the final state.\nFinal: {\"answer\": 5.7168, \"unit\": \"state_units\"}", "dedupe_signature": "d9983b72151ab20b61e4bb01e142fc72a64dac6d48895881ff2ba404b4b9f3be", "difficulty": "medium", "final_answer": {"answer": 5.7168, "unit": "state_units"}, "id": "euler_decay_001233_18_0.87_0.2_6", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.87 y with y(0)=18, step size h=0.2, for 6 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.87 y, so each step multiplies y by 1 - h*0.87.\nApply that update for 6 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 18.0, "rate": 0.87, "step": 0.2, "steps": 6}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(3.9)=19.11 and f(7.7)=33.93.\n3. The interval width is 3.8.\nFinal: {\"answer\": 100.776, \"unit\": \"area_units\"}", "dedupe_signature": "d280fcc057e09477247237ba358d4107859e18e28f954b9e36b1a483a3b07407", "difficulty": "medium", "final_answer": {"answer": 100.776, "unit": "area_units"}, "id": "trapz_linear_001234_3.9_3.9_3.9_7.7", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=3.9x+3.9 from x=3.9 to x=7.7. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(3.9)=19.11 and f(7.7)=33.93.\nThe interval width is 3.8.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 3.9, "slope": 3.9, "x0": 3.9, "x1": 7.699999999999999}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.46 and add it to the current value.\nFinal: {\"answer\": [1.086, 1.572, 1.746], \"unit\": \"temperature_units\"}", "dedupe_signature": "673a86be3a8cd49f027e5c8e77ec46c5a39b06a13d4aba7321ac9585929b025a", "difficulty": "hard", "final_answer": {"answer": [1.086, 1.572, 1.746], "unit": "temperature_units"}, "id": "heat_step_001235_0.46_1.05_0.35_1.25_2.85_2.05", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.05, right=2.05; current interior values are [0.35, 1.25, 2.85]. Use r=0.46. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.46 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [0.35, 1.25, 2.85], "left": 1.05, "r": 0.46, "right": 2.05}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 9826.0 / 1000.\nFinal: {\"answer\": 9.826, \"unit\": \"kg\"}", "dedupe_signature": "d6767af32148859e32e7ec355721146b91ab7584c19adcd59c6b1056954db2dc", "difficulty": "easy", "final_answer": {"answer": 9.826, "unit": "kg"}, "id": "unit_convert_001236_g_to_kg_9826", "license": "Apache-2.0", "prompt": "Convert 9826 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 9826.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 9826.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=275 degrees and keep the unit as newtons.\nFinal: {\"answer\": [4.1835, -47.8173], \"unit\": \"N\"}", "dedupe_signature": "8d46f1f7ff476ad53bbae195c93faedfb6835ccd26abd67f852bcb82ad08aa12", "difficulty": "medium", "final_answer": {"answer": [4.1835, -47.8173], "unit": "N"}, "id": "vector_components_001237_48_275", "license": "Apache-2.0", "prompt": "A vector has magnitude 48 N at 275 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=275 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 275, "magnitude": 48.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [0.55, -17.25], \"unit\": \"dimensionless\"}", "dedupe_signature": "d133032ee2fb0eacb831bf4d482bd8a607a5b47b0b16ff5214bd41d225b97bdf", "difficulty": "medium", "final_answer": {"answer": [0.55, -17.25], "unit": "dimensionless"}, "id": "line_two_point_001238_-11.25_0_0.55_-17.25", "license": "Apache-2.0", "prompt": "A line passes through points (-11.25, -23.4375) and (0, -17.25). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -11.25, "x2": 0.0, "y1": -23.4375, "y2": -17.25}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. amount times volume is not concentration\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "39faefaf6a21c8591d021732cdab4db68082098458d95006342cd2f8dca9a8ec", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_001239_inconsistent_74ac0b02_172907", "license": "Apache-2.0", "prompt": "In instrument manual case 172907, check dimensional consistency for C = n * V. The left side has dimensions mol/L and the right side has dimensions mol*L. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\namount times volume is not concentration\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "C = n * V"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: left_boundary, right_boundary.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"left_boundary\", \"right_boundary\"]}", "dedupe_signature": "04695acd8a48c205e2404ff7fc454eae67d00a3e2682a2580e4e669f7da69877", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["left_boundary", "right_boundary"]}, "id": "abstain_001241_left_boundary_right_boundary", "license": "Apache-2.0", "prompt": "Solve the 1D heat equation after one finite-difference step. The prompt gives r=0.14 and interior values [0.75, -0.6, 2.05], but gives no boundary values. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: left_boundary, right_boundary.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["left_boundary", "right_boundary"]}, "verifier": {"missing": ["left_boundary", "right_boundary"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 31.3^2 and multiply by 0.5 * 17.05.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 8351.8573, \"unit\": \"J\"}", "dedupe_signature": "c67288e6a3a0341422ed82cedc0d01c41c2712c30faf80ca103005afb33b588a", "difficulty": "easy", "final_answer": {"answer": 8351.8573, "unit": "J"}, "id": "ke_001243_17.05_31.3", "license": "Apache-2.0", "prompt": "A body of mass 17.05 kg moves at 31.3 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 31.3^2 and multiply by 0.5 * 17.05.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 17.05, "velocity": 31.3}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=50 degrees through the sine of 2 theta.\n3. Substitute v=74.5 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 557.1793, \"unit\": \"m\"}", "dedupe_signature": "1fbe5f420e355828954652f7d295c121645bb2b017852ddf3de0f6206956013f", "difficulty": "medium", "final_answer": {"answer": 557.1793, "unit": "m"}, "id": "projectile_range_001244_74.5_50", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 74.5 m/s and angle 50 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=50 degrees through the sine of 2 theta.\nSubstitute v=74.5 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 50, "gravity": 9.81, "speed": 74.5}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 3.12 * 8.314 * 415 / 22.4.\nFinal: {\"answer\": 480.5789, \"unit\": \"kPa\"}", "dedupe_signature": "73e1e87b86447afc912a4c28f5ddff6efc0edee068a2b507efcd20090010d326", "difficulty": "medium", "final_answer": {"answer": 480.5789, "unit": "kPa"}, "id": "ideal_gas_001245_3.12_415_22.4", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=3.12 mol, T=415 K, and V=22.4 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 3.12 * 8.314 * 415 / 22.4.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 3.12, "temp_k": 415, "volume_l": 22.4}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=35.2 V and R=146.1 ohm.\nFinal: {\"answer\": 8.4808, \"unit\": \"W\"}", "dedupe_signature": "fc5ea277f95c6c2eeee9e34887c56599d773d87bce1cb3e13d3e301991b0e908", "difficulty": "easy", "final_answer": {"answer": 8.4808, "unit": "W"}, "id": "ohm_power_001247_35.2_146.1", "license": "Apache-2.0", "prompt": "A resistor has resistance 146.1 ohm and voltage 35.2 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=35.2 V and R=146.1 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 146.1, "voltage": 35.2}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=930 mg, t=63.5 h, and T_half=38 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 292.0424, \"unit\": \"mg\"}", "dedupe_signature": "9ba25fa67bd77226812d95f32ad448beeb623df2297dd8e4d483b4c00eb8a113", "difficulty": "medium", "final_answer": {"answer": 292.0424, "unit": "mg"}, "id": "half_life_001248_930_38_63.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 930 mg. Its half-life is 38 hours. How many mg remain after 63.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=930 mg, t=63.5 h, and T_half=38 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 63.5, "half_life": 38.0, "initial_amount": 930.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 2.14 mol * 100.087 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 214.1862, \"unit\": \"g\"}", "dedupe_signature": "6333daf17c0d1f1384752fcceae6aaa726556c0b0cf1e663dcbb384333c7d2f6", "difficulty": "medium", "final_answer": {"answer": 214.1862, "unit": "g"}, "id": "stoich_mass_001249_calcium_carbonate_2.14", "license": "Apache-2.0", "prompt": "A sample contains 2.14 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 2.14 mol * 100.087 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "calcium carbonate", "molar_mass": 100.087, "moles": 2.14}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 540 mL to 0.54 L.\n3. Compute M = 0.16 / 0.54.\nFinal: {\"answer\": 0.2963, \"unit\": \"mol/L\"}", "dedupe_signature": "74df1308afe1d76267bb4285b6313ca2c7f1b53e39333249e6b521c1e9646170", "difficulty": "medium", "final_answer": {"answer": 0.2963, "unit": "mol/L"}, "id": "molarity_001250_0.16_540", "license": "Apache-2.0", "prompt": "A solution contains 0.16 mol of solute in 540 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 540 mL to 0.54 L.\nCompute M = 0.16 / 0.54.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 0.16, "volume_ml": 540}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.08 y, so each step multiplies y by 1 - h*0.08.\n3. Apply that update for 9 steps and round the final state.\nFinal: {\"answer\": 12.0934, \"unit\": \"state_units\"}", "dedupe_signature": "37b868e12c0a72a4494e48b220a6ad87ee72eb2e7dae8146ab2c09f31cef3045", "difficulty": "medium", "final_answer": {"answer": 12.0934, "unit": "state_units"}, "id": "euler_decay_001251_13_0.08_0.1_9", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.08 y with y(0)=13, step size h=0.1, for 9 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.08 y, so each step multiplies y by 1 - h*0.08.\nApply that update for 9 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 13.0, "rate": 0.08, "step": 0.1, "steps": 9}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(8.8)=5.02 and f(12.9)=12.81.\n3. The interval width is 4.1.\nFinal: {\"answer\": 36.5515, \"unit\": \"area_units\"}", "dedupe_signature": "4eef79f204d0aaf2e25a5f84f9b40cc5057cf13fd5a33da4a8397b1591904add", "difficulty": "medium", "final_answer": {"answer": 36.5515, "unit": "area_units"}, "id": "trapz_linear_001252_1.9_-11.7_8.8_12.9", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=1.9x+-11.7 from x=8.8 to x=12.9. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(8.8)=5.02 and f(12.9)=12.81.\nThe interval width is 4.1.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -11.7, "slope": 1.9, "x0": 8.8, "x1": 12.9}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.18 and add it to the current value.\nFinal: {\"answer\": [0.783, -0.165, -0.237], \"unit\": \"temperature_units\"}", "dedupe_signature": "fdf6d4c1e0a44f7a19d8cd6e4a0127363a19ceeb8b8bbf98fa85177645684f8b", "difficulty": "hard", "final_answer": {"answer": [0.783, -0.165, -0.237], "unit": "temperature_units"}, "id": "heat_step_001253_0.18_1.45_0.9_-0.3_-0.75_1.65", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.45, right=1.65; current interior values are [0.9, -0.3, -0.75]. Use r=0.18. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.18 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [0.9, -0.3, -0.75], "left": 1.45, "r": 0.18, "right": 1.65}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 18459.0 / 1000.\nFinal: {\"answer\": 18.459, \"unit\": \"kg\"}", "dedupe_signature": "01b47b4f992f11e17b4260905637d99809ef2c5a2a6d2d750f1e1bb3df66decb", "difficulty": "easy", "final_answer": {"answer": 18.459, "unit": "kg"}, "id": "unit_convert_001254_g_to_kg_18459", "license": "Apache-2.0", "prompt": "Convert 18459 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 18459.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 18459.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [8.35, -18.25], \"unit\": \"dimensionless\"}", "dedupe_signature": "5474928f3ea4aedeb38663981a5e6e9ccb14f8885ab15b10e0b233427792a4ff", "difficulty": "medium", "final_answer": {"answer": [8.35, -18.25], "unit": "dimensionless"}, "id": "line_two_point_001256_-1.75_7.5_8.35_-18.25", "license": "Apache-2.0", "prompt": "A line passes through points (-1.75, -32.8625) and (7.5, 44.375). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -1.75, "x2": 7.5, "y1": -32.8625, "y2": 44.375}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. speed squared over acceleration has units of meters\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "84f1550bc376eeeb03dad8ff0815fcfa6763addbee9a561ce0297f8d0caa436a", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_001257_consistent_741d4e34_699814", "license": "Apache-2.0", "prompt": "In simulation spec case 699814, check dimensional consistency for R = v^2 * sin(theta) / g. The left side has dimensions m and the right side has dimensions m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nspeed squared over acceleration has units of meters\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "R = v^2 * sin(theta) / g"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef running_total_001258(values):\n    total = 0\n    out = []\n    for value in values:\n        total += value\n        out.append(total)\n    return out\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"running_total_001258\"}", "dedupe_signature": "2eda35614c5b817117948b828224e3f2147c2cf6a3ee75fcfa69a6da2bd1b194", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "running_total_001258"}, "id": "code_001258_running_total_001258", "license": "Apache-2.0", "prompt": "Write a Python function running_total_001258(values) that returns cumulative sums as a new list. It must not mutate the input list. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "running_total_001258"}, "verifier": {"function": "running_total_001258", "tests": ["assert running_total_001258([1, 2, 3]) == [1, 3, 6]", "xs = [4, -1, 2]; assert running_total_001258(xs) == [4, 3, 5] and xs == [4, -1, 2]", "assert running_total_001258([]) == []"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=32 degrees through the sine of 2 theta.\n3. Substitute v=75 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 515.3636, \"unit\": \"m\"}", "dedupe_signature": "c89122d07c3ad3b0683eb30a7f3b59f995fc0e13d0a6aa21cc57a1f33f6433c2", "difficulty": "medium", "final_answer": {"answer": 515.3636, "unit": "m"}, "id": "projectile_range_001262_75_32", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 75 m/s and angle 32 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=32 degrees through the sine of 2 theta.\nSubstitute v=75 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 32, "gravity": 9.81, "speed": 75.0}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 3.81 * 8.314 * 494 / 73.9.\nFinal: {\"answer\": 211.7471, \"unit\": \"kPa\"}", "dedupe_signature": "97e846038aeecae5cbb039004f2183abe9b329cff4cd6414d4a9e599ac5988c9", "difficulty": "medium", "final_answer": {"answer": 211.7471, "unit": "kPa"}, "id": "ideal_gas_001263_3.81_494_73.9", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=3.81 mol, T=494 K, and V=73.9 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 3.81 * 8.314 * 494 / 73.9.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 3.81, "temp_k": 494, "volume_l": 73.9}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=174.9 V and R=168.6 ohm.\nFinal: {\"answer\": 181.4354, \"unit\": \"W\"}", "dedupe_signature": "8dc2b1a5b882423abe3eeb2ae1974b5e933773bcec0c02dc8c64e28db1ed64fa", "difficulty": "easy", "final_answer": {"answer": 181.4354, "unit": "W"}, "id": "ohm_power_001265_174.9_168.6", "license": "Apache-2.0", "prompt": "A resistor has resistance 168.6 ohm and voltage 174.9 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=174.9 V and R=168.6 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 168.6, "voltage": 174.9}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=250.5 mg, t=259.5 h, and T_half=35 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 1.4685, \"unit\": \"mg\"}", "dedupe_signature": "91df0bdf67aeff940eeee75726aeaecc578fef3d104c7cb39d3f6bcbe6c25cb1", "difficulty": "medium", "final_answer": {"answer": 1.4685, "unit": "mg"}, "id": "half_life_001266_250.5_35_259.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 250.5 mg. Its half-life is 35 hours. How many mg remain after 259.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=250.5 mg, t=259.5 h, and T_half=35 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 259.5, "half_life": 35.0, "initial_amount": 250.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 1.27 mol * 18.015 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 22.879, \"unit\": \"g\"}", "dedupe_signature": "3d3c4b566221d6db4581e4a60fa89a6f250ccc219510e2661a5e0a6aed3d7d3a", "difficulty": "medium", "final_answer": {"answer": 22.879, "unit": "g"}, "id": "stoich_mass_001267_water_1.27", "license": "Apache-2.0", "prompt": "A sample contains 1.27 mol of water. Using molar mass 18.015 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 1.27 mol * 18.015 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "water", "molar_mass": 18.015, "moles": 1.27}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 30 mL to 0.03 L.\n3. Compute M = 3.93 / 0.03.\nFinal: {\"answer\": 131.0, \"unit\": \"mol/L\"}", "dedupe_signature": "22ca224511bb5f278e31cbdc2ba7cae1903d418e1c7ed62777e873c40d8a08ab", "difficulty": "medium", "final_answer": {"answer": 131.0, "unit": "mol/L"}, "id": "molarity_001268_3.93_30", "license": "Apache-2.0", "prompt": "A solution contains 3.93 mol of solute in 30 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 30 mL to 0.03 L.\nCompute M = 3.93 / 0.03.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 3.93, "volume_ml": 30}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.37 y, so each step multiplies y by 1 - h*0.37.\n3. Apply that update for 5 steps and round the final state.\nFinal: {\"answer\": 2.6804, \"unit\": \"state_units\"}", "dedupe_signature": "a47bcab06f49e8f3035ec840239b28f1f940b193a806203d40f21300acd4de7d", "difficulty": "medium", "final_answer": {"answer": 2.6804, "unit": "state_units"}, "id": "euler_decay_001269_15.5_0.37_0.8_5", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.37 y with y(0)=15.5, step size h=0.8, for 5 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.37 y, so each step multiplies y by 1 - h*0.37.\nApply that update for 5 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 15.5, "rate": 0.37, "step": 0.8, "steps": 5}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-6.3)=6.72 and f(-3.3)=5.52.\n3. The interval width is 3.\nFinal: {\"answer\": 18.36, \"unit\": \"area_units\"}", "dedupe_signature": "742759ef0fbf6d3eec9b5af0248c6818b052458097fb22afea801eda1c474141", "difficulty": "medium", "final_answer": {"answer": 18.36, "unit": "area_units"}, "id": "trapz_linear_001270_-0.4_4.2_-6.3_-3.3", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-0.4x+4.2 from x=-6.3 to x=-3.3. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-6.3)=6.72 and f(-3.3)=5.52.\nThe interval width is 3.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 4.2, "slope": -0.4, "x0": -6.3, "x1": -3.3}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 18807.0 / 1000.\nFinal: {\"answer\": 18.807, \"unit\": \"kg\"}", "dedupe_signature": "cd21413403319b8baa9e389b5bf6be8424f9d9e2cf374f4554d7898a07e1a40c", "difficulty": "easy", "final_answer": {"answer": 18.807, "unit": "kg"}, "id": "unit_convert_001272_g_to_kg_18807", "license": "Apache-2.0", "prompt": "Convert 18807 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 18807.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 18807.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-4.6, 14.75], \"unit\": \"dimensionless\"}", "dedupe_signature": "ec904405c0d1c90fbfc8cd850531477dca35096295ddbe35bdb3bd3c373b1891", "difficulty": "medium", "final_answer": {"answer": [-4.6, 14.75], "unit": "dimensionless"}, "id": "line_two_point_001274_-11.75_-11.5_-4.6_14.75", "license": "Apache-2.0", "prompt": "A line passes through points (-11.75, 68.8) and (-11.5, 67.65). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -11.75, "x2": -11.5, "y1": 68.8, "y2": 67.65}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. volt squared divided by ohm is watt\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "fec2969bb21df522dd059f9d2c36c7e6bbe6ef149fa3bbaaac8add3345239da1", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_001275_consistent_82e93f3d_935652", "license": "Apache-2.0", "prompt": "In instrument manual case 935652, check dimensional consistency for P = V^2 / R. The left side has dimensions W and the right side has dimensions W. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nvolt squared divided by ohm is watt\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "P = V^2 / R"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef safe_mean_001276(values):\n    if not values:\n        raise ValueError('safe_mean requires at least one value')\n    return sum(values) / len(values)\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"safe_mean_001276\"}", "dedupe_signature": "ad6415b692cabcd323718f0ab66a976b2c63557b2add8c49b6bc5e5311b97db6", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "safe_mean_001276"}, "id": "code_001276_safe_mean_001276", "license": "Apache-2.0", "prompt": "Write a Python function safe_mean_001276(values) that returns the arithmetic mean. It must raise ValueError for an empty input and must not mutate the input list. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "safe_mean_001276"}, "verifier": {"function": "safe_mean_001276", "tests": ["assert safe_mean_001276([2, 4, 6]) == 4", "xs = [1, 2, 3]; assert safe_mean_001276(xs) == 2 and xs == [1, 2, 3]", "try:\n    safe_mean_001276([])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: required_fields, allowed_transformations.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"required_fields\", \"allowed_transformations\"]}", "dedupe_signature": "b8002cae1dce7eab872cbbfdac0bc7001e9e18edcc90b577f44d1cb2faf3ee95", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["required_fields", "allowed_transformations"]}, "id": "abstain_001277_required_fields_allowed_transformations", "license": "Apache-2.0", "prompt": "Write a sanitizer for valid billing crop records in release 571753, but the prompt does not state which fields are required or which transformations are allowed. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: required_fields, allowed_transformations.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["required_fields", "allowed_transformations"]}, "verifier": {"missing": ["required_fields", "allowed_transformations"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 22.55 kg and a = 3.7 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 83.435, \"unit\": \"N\"}", "dedupe_signature": "37c6b881c08609fff0a6906ffe602fe54251c058a13ee21abff5cf05c38c97c1", "difficulty": "easy", "final_answer": {"answer": 83.435, "unit": "N"}, "id": "force_001278_22.55_3.7", "license": "Apache-2.0", "prompt": "A cart has mass 22.55 kg and measured acceleration 3.7 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 22.55 kg and a = 3.7 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 3.7, "mass": 22.55}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 19.2^2 and multiply by 0.5 * 6.2.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 1142.784, \"unit\": \"J\"}", "dedupe_signature": "935873d4f1cf33006f3180345caa815b9140ee65b2b6299648a06c370494b6d2", "difficulty": "easy", "final_answer": {"answer": 1142.784, "unit": "J"}, "id": "ke_001279_6.2_19.2", "license": "Apache-2.0", "prompt": "A body of mass 6.2 kg moves at 19.2 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 19.2^2 and multiply by 0.5 * 6.2.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 6.2, "velocity": 19.2}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=19 degrees through the sine of 2 theta.\n3. Substitute v=11.7 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 8.591, \"unit\": \"m\"}", "dedupe_signature": "5ccd16f3ce332d49206027f690a57fd10a3c6d3afdccba8050e500342534f878", "difficulty": "medium", "final_answer": {"answer": 8.591, "unit": "m"}, "id": "projectile_range_001280_11.7_19", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 11.7 m/s and angle 19 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=19 degrees through the sine of 2 theta.\nSubstitute v=11.7 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 19, "gravity": 9.81, "speed": 11.7}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1390 * 4.095 * 112.\nFinal: {\"answer\": 637509.6, \"unit\": \"J\"}", "dedupe_signature": "c701815bd602964cb75320a92116f4945b0adca6d69e1972807ccc7a73ac30c2", "difficulty": "easy", "final_answer": {"answer": 637509.6, "unit": "J"}, "id": "heat_q_001282_1390_4.095_112", "license": "Apache-2.0", "prompt": "A 1390 g sample has specific heat 4.095 J/(g*K). How much heat is needed to raise its temperature by 112 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1390 * 4.095 * 112.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 112, "heat_capacity": 4.095, "mass_g": 1390}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=146.5 V and R=127.3 ohm.\nFinal: {\"answer\": 168.5958, \"unit\": \"W\"}", "dedupe_signature": "ca5c5b76f28afb8a85e04bb0de31be6226f1fbe6f1234ca8ff686ac4a51fb8bc", "difficulty": "easy", "final_answer": {"answer": 168.5958, "unit": "W"}, "id": "ohm_power_001283_146.5_127.3", "license": "Apache-2.0", "prompt": "A resistor has resistance 127.3 ohm and voltage 146.5 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=146.5 V and R=127.3 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 127.3, "voltage": 146.5}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 3800 mL to 3.8 L.\n3. Compute M = 1.345 / 3.8.\nFinal: {\"answer\": 0.3539, \"unit\": \"mol/L\"}", "dedupe_signature": "8eb72d9fe7e73bb97bd2a1c71dad4d63ef1f8e8e0cc763a79166fe5823e84a96", "difficulty": "medium", "final_answer": {"answer": 0.3539, "unit": "mol/L"}, "id": "molarity_001286_1.345_3800", "license": "Apache-2.0", "prompt": "A solution contains 1.345 mol of solute in 3800 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 3800 mL to 3.8 L.\nCompute M = 1.345 / 3.8.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 1.345, "volume_ml": 3800}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.43 y, so each step multiplies y by 1 - h*0.43.\n3. Apply that update for 2 steps and round the final state.\nFinal: {\"answer\": 11.8011, \"unit\": \"state_units\"}", "dedupe_signature": "e8f9ef7791dfa038af8e79166977f44322dfc707e24cf07552416c4772542345", "difficulty": "medium", "final_answer": {"answer": 11.8011, "unit": "state_units"}, "id": "euler_decay_001287_74.5_0.43_1.4_2", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.43 y with y(0)=74.5, step size h=1.4, for 2 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.43 y, so each step multiplies y by 1 - h*0.43.\nApply that update for 2 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 74.5, "rate": 0.43, "step": 1.4, "steps": 2}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(5)=10.6 and f(11.4)=1.\n3. The interval width is 6.4.\nFinal: {\"answer\": 37.12, \"unit\": \"area_units\"}", "dedupe_signature": "4d9332c77f82b362b3e613ca29c59d193b8f1f3a2d3cc8f3ade75a20a37ce7e9", "difficulty": "medium", "final_answer": {"answer": 37.12, "unit": "area_units"}, "id": "trapz_linear_001288_-1.5_18.1_5_11.4", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-1.5x+18.1 from x=5 to x=11.4. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(5)=10.6 and f(11.4)=1.\nThe interval width is 6.4.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 18.1, "slope": -1.5, "x0": 5.0, "x1": 11.4}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.38 and add it to the current value.\nFinal: {\"answer\": [1.056, 1.805, 1.221], \"unit\": \"temperature_units\"}", "dedupe_signature": "db0723003e1b01a7c20fd163e18b3fb4243091ba5faf726d30218b1c05de74f3", "difficulty": "hard", "final_answer": {"answer": [1.056, 1.805, 1.221], "unit": "temperature_units"}, "id": "heat_step_001289_0.38_0.5_0.6_1.9_2.95_-0.55", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=0.5, right=-0.55; current interior values are [0.6, 1.9, 2.95]. Use r=0.38. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.38 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [0.6, 1.9, 2.95], "left": 0.5, "r": 0.38, "right": -0.55}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 30176.0 / 1000.\nFinal: {\"answer\": 30.176, \"unit\": \"kg\"}", "dedupe_signature": "a39a0d32f8c4bdd5e4612819a29994b498706632b8cc276e69e2717cdfe2d199", "difficulty": "easy", "final_answer": {"answer": 30.176, "unit": "kg"}, "id": "unit_convert_001290_g_to_kg_30176", "license": "Apache-2.0", "prompt": "Convert 30176 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 30176.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 30176.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=12 degrees and keep the unit as newtons.\nFinal: {\"answer\": [152.102, 32.3303], \"unit\": \"N\"}", "dedupe_signature": "9c1366f6d8f4200fea17205ba4135d59b4208639bcfa6ba4bf138c080ea07383", "difficulty": "medium", "final_answer": {"answer": [152.102, 32.3303], "unit": "N"}, "id": "vector_components_001291_155.5_12", "license": "Apache-2.0", "prompt": "A vector has magnitude 155.5 N at 12 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=12 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 12, "magnitude": 155.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [3.35, 11.0], \"unit\": \"dimensionless\"}", "dedupe_signature": "da854426fba3b207d6239f397ea67d878b6a5da364d0be4ced44f02270e04deb", "difficulty": "medium", "final_answer": {"answer": [3.35, 11.0], "unit": "dimensionless"}, "id": "line_two_point_001292_-3_6.75_3.35_11", "license": "Apache-2.0", "prompt": "A line passes through points (-3, 0.95) and (6.75, 33.6125). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -3.0, "x2": 6.75, "y1": 0.9499999999999993, "y2": 33.6125}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. mass times acceleration has newton dimensions\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "79ae08ccdf5ce9e2630040be7ad0930b39bb656d88f855b06a6018031db20b3a", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_001293_consistent_03f5e041_538379", "license": "Apache-2.0", "prompt": "In sensor calibration case 538379, check dimensional consistency for F = m * a. The left side has dimensions kg*m/s^2 and the right side has dimensions kg*m/s^2. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nmass times acceleration has newton dimensions\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "F = m * a"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef running_total_001294(values):\n    total = 0\n    out = []\n    for value in values:\n        total += value\n        out.append(total)\n    return out\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"running_total_001294\"}", "dedupe_signature": "e7fbbcfc0ac663e443382f8f92995fd0a24f4410435a47e9789a85313a65fb23", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "running_total_001294"}, "id": "code_001294_running_total_001294", "license": "Apache-2.0", "prompt": "Write a Python function running_total_001294(values) that returns cumulative sums as a new list. It must not mutate the input list. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "running_total_001294"}, "verifier": {"function": "running_total_001294", "tests": ["assert running_total_001294([1, 2, 3]) == [1, 3, 6]", "xs = [4, -1, 2]; assert running_total_001294(xs) == [4, 3, 5] and xs == [4, -1, 2]", "assert running_total_001294([]) == []"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: rate_constant, number_of_steps.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"rate_constant\", \"number_of_steps\"]}", "dedupe_signature": "ef93a21af7422679c7cce412c080102de9a611fe9655022b46f06dc2094cac81", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["rate_constant", "number_of_steps"]}, "id": "abstain_001295_rate_constant_number_of_steps", "license": "Apache-2.0", "prompt": "Use explicit Euler for dy/dt = -k y. The prompt gives y(0)=57 and h=0.55, but omits both k and the number of steps. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: rate_constant, number_of_steps.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["rate_constant", "number_of_steps"]}, "verifier": {"missing": ["rate_constant", "number_of_steps"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=9 degrees through the sine of 2 theta.\n3. Substitute v=25.5 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 20.483, \"unit\": \"m\"}", "dedupe_signature": "3ddca9f9c0c3705edb34dde67ca6536e9feff6ad0be83e881ab4e726a5e4987d", "difficulty": "medium", "final_answer": {"answer": 20.483, "unit": "m"}, "id": "projectile_range_001298_25.5_9", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 25.5 m/s and angle 9 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=9 degrees through the sine of 2 theta.\nSubstitute v=25.5 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 9, "gravity": 9.81, "speed": 25.5}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 5.51 * 8.314 * 386 / 56.8.\nFinal: {\"answer\": 311.3154, \"unit\": \"kPa\"}", "dedupe_signature": "543034359499836a70a009b888be4f90e0e166c5a695e2b168241ad7655df19a", "difficulty": "medium", "final_answer": {"answer": 311.3154, "unit": "kPa"}, "id": "ideal_gas_001299_5.51_386_56.8", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=5.51 mol, T=386 K, and V=56.8 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 5.51 * 8.314 * 386 / 56.8.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 5.51, "temp_k": 386, "volume_l": 56.8}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1635 * 1.03 * 78.\nFinal: {\"answer\": 131355.9, \"unit\": \"J\"}", "dedupe_signature": "c9b6c67b19b306ea26aaff32f8835cf871e6ca4a649da30522a34479c1cf1cb5", "difficulty": "easy", "final_answer": {"answer": 131355.9, "unit": "J"}, "id": "heat_q_001300_1635_1.03_78", "license": "Apache-2.0", "prompt": "A 1635 g sample has specific heat 1.03 J/(g*K). How much heat is needed to raise its temperature by 78 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1635 * 1.03 * 78.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 78, "heat_capacity": 1.03, "mass_g": 1635}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=28.2 V and R=11.1 ohm.\nFinal: {\"answer\": 71.6432, \"unit\": \"W\"}", "dedupe_signature": "1966001905a1eb55e57455a35b9e6950ee721cce3af26a2c7c07828ea98920f8", "difficulty": "easy", "final_answer": {"answer": 71.6432, "unit": "W"}, "id": "ohm_power_001301_28.2_11.1", "license": "Apache-2.0", "prompt": "A resistor has resistance 11.1 ohm and voltage 28.2 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=28.2 V and R=11.1 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 11.1, "voltage": 28.2}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=869.5 mg, t=273.5 h, and T_half=114 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 164.8396, \"unit\": \"mg\"}", "dedupe_signature": "3006a012978ec249bde475488222080e899d91a231b554034f8a3c6c2e472fed", "difficulty": "medium", "final_answer": {"answer": 164.8396, "unit": "mg"}, "id": "half_life_001302_869.5_114_273.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 869.5 mg. Its half-life is 114 hours. How many mg remain after 273.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=869.5 mg, t=273.5 h, and T_half=114 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 273.5, "half_life": 114.0, "initial_amount": 869.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 4.59 mol * 180.156 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 826.916, \"unit\": \"g\"}", "dedupe_signature": "d99277aa7dbbd56b0ddf00c923c9ace28a798d26deff891b2605143d0a2e9d7c", "difficulty": "medium", "final_answer": {"answer": 826.916, "unit": "g"}, "id": "stoich_mass_001303_glucose_4.59", "license": "Apache-2.0", "prompt": "A sample contains 4.59 mol of glucose. Using molar mass 180.156 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 4.59 mol * 180.156 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "glucose", "molar_mass": 180.156, "moles": 4.59}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 4285 mL to 4.285 L.\n3. Compute M = 1.17 / 4.285.\nFinal: {\"answer\": 0.273, \"unit\": \"mol/L\"}", "dedupe_signature": "2764b0987e0a73e69c1bbba9e708736ba6f9f5fef9c57b6bbb87e088bf0251d8", "difficulty": "medium", "final_answer": {"answer": 0.273, "unit": "mol/L"}, "id": "molarity_001304_1.17_4285", "license": "Apache-2.0", "prompt": "A solution contains 1.17 mol of solute in 4285 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 4285 mL to 4.285 L.\nCompute M = 1.17 / 4.285.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 1.17, "volume_ml": 4285}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.16 y, so each step multiplies y by 1 - h*0.16.\n3. Apply that update for 5 steps and round the final state.\nFinal: {\"answer\": 13.9454, \"unit\": \"state_units\"}", "dedupe_signature": "8c2cc537baad1693f617bc520efcbc051e8d9563add6cc04c290aa20580495a2", "difficulty": "medium", "final_answer": {"answer": 13.9454, "unit": "state_units"}, "id": "euler_decay_001305_55_0.16_1.5_5", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.16 y with y(0)=55, step size h=1.5, for 5 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.16 y, so each step multiplies y by 1 - h*0.16.\nApply that update for 5 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 55.0, "rate": 0.16, "step": 1.5, "steps": 5}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-6.1)=-42.76 and f(1.1)=-9.64.\n3. The interval width is 7.2.\nFinal: {\"answer\": -188.64, \"unit\": \"area_units\"}", "dedupe_signature": "c6cee100a8a9a89ada7c9a01310a32956d07b6b1046796092b54063e5e36071b", "difficulty": "medium", "final_answer": {"answer": -188.64, "unit": "area_units"}, "id": "trapz_linear_001306_4.6_-14.7_-6.1_1.1", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=4.6x+-14.7 from x=-6.1 to x=1.1. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-6.1)=-42.76 and f(1.1)=-9.64.\nThe interval width is 7.2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -14.7, "slope": 4.6, "x0": -6.1, "x1": 1.1000000000000005}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.46 and add it to the current value.\nFinal: {\"answer\": [0.14, 0.161, 1.995], \"unit\": \"temperature_units\"}", "dedupe_signature": "cd84e3b280ce4e5c01f32fd9df4f4b857295803118bffc8798dd4c30ab76563c", "difficulty": "hard", "final_answer": {"answer": [0.14, 0.161, 1.995], "unit": "temperature_units"}, "id": "heat_step_001307_0.46_-1.7_-1.7_2.3_1.65_1.75", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-1.7, right=1.75; current interior values are [-1.7, 2.3, 1.65]. Use r=0.46. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.46 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-1.7, 2.3, 1.65], "left": -1.7, "r": 0.46, "right": 1.75}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kelvin equals Celsius plus 273.15.\n2. Apply the conversion factor directly to the given value.\n3. Compute -77.0 + 273.15.\nFinal: {\"answer\": 196.15, \"unit\": \"K\"}", "dedupe_signature": "e280539051c86e054b4e4bdefbac7dcc63e0216f0b6e0d9a97cdc3ad0c857e5e", "difficulty": "easy", "final_answer": {"answer": 196.15, "unit": "K"}, "id": "unit_convert_001308_c_to_k_-77", "license": "Apache-2.0", "prompt": "Convert -77 degC to K. Return the converted value with unit.", "reasoning_trace": "Kelvin equals Celsius plus 273.15.\nApply the conversion factor directly to the given value.\nCompute -77.0 + 273.15.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": -77.0}, "verifier": {"formula": "value + 273.15", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=24 degrees and keep the unit as newtons.\nFinal: {\"answer\": [166.722, 74.2294], \"unit\": \"N\"}", "dedupe_signature": "79e2e224289fb3555e62b4407f47f72cfea92c71d8a6ff2a49f2e76a10f167f0", "difficulty": "medium", "final_answer": {"answer": [166.722, 74.2294], "unit": "N"}, "id": "vector_components_001309_182.5_24", "license": "Apache-2.0", "prompt": "A vector has magnitude 182.5 N at 24 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=24 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 24, "magnitude": 182.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-5.45, -25.25], \"unit\": \"dimensionless\"}", "dedupe_signature": "10cf29b8508833c92a030306e9f45c5acf2afd0d6ccbaa894b27b5db517747a9", "difficulty": "medium", "final_answer": {"answer": [-5.45, -25.25], "unit": "dimensionless"}, "id": "line_two_point_001310_15_16.75_-5.45_-25.25", "license": "Apache-2.0", "prompt": "A line passes through points (15, -107) and (16.75, -116.538). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 15.0, "x2": 16.75, "y1": -107.0, "y2": -116.53750000000001}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. lever arm times force has torque dimensions\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "eaff778bfef3d74222fa08888a99456207fbda7378dcb0ba816c0a2344b085eb", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_001311_consistent_5ca82cb9_433650", "license": "Apache-2.0", "prompt": "In lab notebook case 433650, check dimensional consistency for tau = r * F. The left side has dimensions N*m and the right side has dimensions N*m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nlever arm times force has torque dimensions\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "tau = r * F"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef pairwise_ratios_001312(numerators, denominators):\n    if len(numerators) != len(denominators):\n        raise ValueError('length mismatch')\n    out = []\n    for numerator, denominator in zip(numerators, denominators):\n        if denominator == 0:\n            raise ValueError('zero denominator')\n        out.append(numerator / denominator)\n    return out\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"pairwise_ratios_001312\"}", "dedupe_signature": "4ea6bdd9379057e6728d1f867ce578be2695b743570168ac165d8b1135c8edea", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "pairwise_ratios_001312"}, "id": "code_001312_pairwise_ratios_001312", "license": "Apache-2.0", "prompt": "Write a Python function pairwise_ratios_001312(numerators, denominators) that returns a list of n/d values. Raise ValueError if lengths differ or any denominator is zero. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "pairwise_ratios_001312"}, "verifier": {"function": "pairwise_ratios_001312", "tests": ["assert pairwise_ratios_001312([2, 9], [4, 3]) == [0.5, 3.0]", "try:\n    pairwise_ratios_001312([1], [0])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass", "try:\n    pairwise_ratios_001312([1, 2], [1])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 8.45 kg and a = 10.35 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 87.4575, \"unit\": \"N\"}", "dedupe_signature": "6de22c4af35437a6b7274d4496654fe34359a0ef17a2889dec5ce33be7d0081f", "difficulty": "easy", "final_answer": {"answer": 87.4575, "unit": "N"}, "id": "force_001314_8.45_10.35", "license": "Apache-2.0", "prompt": "A cart has mass 8.45 kg and measured acceleration 10.35 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 8.45 kg and a = 10.35 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 10.35, "mass": 8.45}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 26^2 and multiply by 0.5 * 13.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 4394.0, \"unit\": \"J\"}", "dedupe_signature": "a26d60e45ffa84450ab66b116f8f9d3e5e77bae6853b3d9623c3373b68d816ab", "difficulty": "easy", "final_answer": {"answer": 4394.0, "unit": "J"}, "id": "ke_001315_13_26", "license": "Apache-2.0", "prompt": "A body of mass 13 kg moves at 26 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 26^2 and multiply by 0.5 * 13.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 13.0, "velocity": 26.0}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=71 degrees through the sine of 2 theta.\n3. Substitute v=7.2 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 3.2534, \"unit\": \"m\"}", "dedupe_signature": "424a3e98c263b14b81a9799653a9c0fd54858f9676eea25191708255966cb6e8", "difficulty": "medium", "final_answer": {"answer": 3.2534, "unit": "m"}, "id": "projectile_range_001316_7.2_71", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 7.2 m/s and angle 71 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=71 degrees through the sine of 2 theta.\nSubstitute v=7.2 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 71, "gravity": 9.81, "speed": 7.2}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 0.27 * 8.314 * 278 / 39.4.\nFinal: {\"answer\": 15.8388, \"unit\": \"kPa\"}", "dedupe_signature": "bcd9bc92b86b7c38f3277e5a05e873b7c86e1a9b5ef2c03a2469bcf19a80b8bc", "difficulty": "medium", "final_answer": {"answer": 15.8388, "unit": "kPa"}, "id": "ideal_gas_001317_0.27_278_39.4", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=0.27 mol, T=278 K, and V=39.4 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 0.27 * 8.314 * 278 / 39.4.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 0.27, "temp_k": 278, "volume_l": 39.4}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1970 * 2.31 * 10.\nFinal: {\"answer\": 45507.0, \"unit\": \"J\"}", "dedupe_signature": "24fd33cfc4be952aa38b2647853fbbcab8754635cb1e0827070255e63890f088", "difficulty": "easy", "final_answer": {"answer": 45507.0, "unit": "J"}, "id": "heat_q_001318_1970_2.31_10", "license": "Apache-2.0", "prompt": "A 1970 g sample has specific heat 2.31 J/(g*K). How much heat is needed to raise its temperature by 10 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1970 * 2.31 * 10.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 10, "heat_capacity": 2.31, "mass_g": 1970}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=39.5 V and R=195.7 ohm.\nFinal: {\"answer\": 7.9727, \"unit\": \"W\"}", "dedupe_signature": "d62376c7bf453c498658014b370baf3a73d35a7c084299ca4fdbdbc0e18bc612", "difficulty": "easy", "final_answer": {"answer": 7.9727, "unit": "W"}, "id": "ohm_power_001319_39.5_195.7", "license": "Apache-2.0", "prompt": "A resistor has resistance 195.7 ohm and voltage 39.5 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=39.5 V and R=195.7 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 195.7, "voltage": 39.5}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=587 mg, t=238 h, and T_half=116 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 141.5819, \"unit\": \"mg\"}", "dedupe_signature": "f5a9db0f448b0ada32752104d62cc950e10bf5832b4ff6af2cd5aab3f335338c", "difficulty": "medium", "final_answer": {"answer": 141.5819, "unit": "mg"}, "id": "half_life_001320_587_116_238", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 587 mg. Its half-life is 116 hours. How many mg remain after 238 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=587 mg, t=238 h, and T_half=116 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 238.0, "half_life": 116.0, "initial_amount": 587.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 355 mL to 0.355 L.\n3. Compute M = 3.515 / 0.355.\nFinal: {\"answer\": 9.9014, \"unit\": \"mol/L\"}", "dedupe_signature": "49430004472c04db5157ea3c7217c969c08a9c9f9d38af45528a02f8f8e5dfdf", "difficulty": "medium", "final_answer": {"answer": 9.9014, "unit": "mol/L"}, "id": "molarity_001322_3.515_355", "license": "Apache-2.0", "prompt": "A solution contains 3.515 mol of solute in 355 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 355 mL to 0.355 L.\nCompute M = 3.515 / 0.355.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 3.515, "volume_ml": 355}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.32 y, so each step multiplies y by 1 - h*0.32.\n3. Apply that update for 10 steps and round the final state.\nFinal: {\"answer\": 0.0786, \"unit\": \"state_units\"}", "dedupe_signature": "0f1c06c9a749f80433805c52bcfcf37bb17ed79f1ad60a78dc02ff3de473abf7", "difficulty": "medium", "final_answer": {"answer": 0.0786, "unit": "state_units"}, "id": "euler_decay_001323_22.5_0.32_1.35_10", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.32 y with y(0)=22.5, step size h=1.35, for 10 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.32 y, so each step multiplies y by 1 - h*0.32.\nApply that update for 10 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 22.5, "rate": 0.32, "step": 1.35, "steps": 10}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.46 and add it to the current value.\nFinal: {\"answer\": [1.22, 1.342, 0.944], \"unit\": \"temperature_units\"}", "dedupe_signature": "265ab6d1b821708b706561f8525b97f2a29bcaa8e7c4709c5c4dbe822feab42d", "difficulty": "hard", "final_answer": {"answer": [1.22, 1.342, 0.944], "unit": "temperature_units"}, "id": "heat_step_001325_0.46_2.1_2.6_0.1_0.3_1.9", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=2.1, right=1.9; current interior values are [2.6, 0.1, 0.3]. Use r=0.46. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.46 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [2.6, 0.1, 0.3], "left": 2.1, "r": 0.46, "right": 1.9}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kelvin equals Celsius plus 273.15.\n2. Apply the conversion factor directly to the given value.\n3. Compute 123.5 + 273.15.\nFinal: {\"answer\": 396.65, \"unit\": \"K\"}", "dedupe_signature": "078121b74ef82c21a9cc8a607f9f99f44ebeaba6d1d72530dd649d0b7c6cde85", "difficulty": "easy", "final_answer": {"answer": 396.65, "unit": "K"}, "id": "unit_convert_001326_c_to_k_123.5", "license": "Apache-2.0", "prompt": "Convert 123.5 degC to K. Return the converted value with unit.", "reasoning_trace": "Kelvin equals Celsius plus 273.15.\nApply the conversion factor directly to the given value.\nCompute 123.5 + 273.15.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 123.5}, "verifier": {"formula": "value + 273.15", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=188 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-403.5342, -56.713], \"unit\": \"N\"}", "dedupe_signature": "e99d882fe77814226dd1c5303e7dafda5bc6cc003752333595312001c0ba8fb6", "difficulty": "medium", "final_answer": {"answer": [-403.5342, -56.713], "unit": "N"}, "id": "vector_components_001327_407.5_188", "license": "Apache-2.0", "prompt": "A vector has magnitude 407.5 N at 188 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=188 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 188, "magnitude": 407.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. mass times acceleration has newton dimensions\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "0db3cb78fd53d7f20469d61b14c5216292874fba4e624dcff23bdc3caade0c48", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_001329_consistent_03f5e041_588466", "license": "Apache-2.0", "prompt": "In student derivation case 588466, check dimensional consistency for F = m * a. The left side has dimensions kg*m/s^2 and the right side has dimensions kg*m/s^2. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nmass times acceleration has newton dimensions\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "F = m * a"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef finite_differences_001330(values):\n    return [values[i + 1] - values[i] for i in range(len(values) - 1)]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"finite_differences_001330\"}", "dedupe_signature": "7ef7cc88d1a3d54aec5492cd069e597cdb5fc53f89e1c12876f80b15e2c69656", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "finite_differences_001330"}, "id": "code_001330_finite_differences_001330", "license": "Apache-2.0", "prompt": "Write a Python function finite_differences_001330(values) that returns the list of successive differences values[i+1] - values[i]. It must return [] for fewer than two values. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "finite_differences_001330"}, "verifier": {"function": "finite_differences_001330", "tests": ["assert finite_differences_001330([1, 4, 9, 16]) == [3, 5, 7]", "assert finite_differences_001330([5]) == []", "assert finite_differences_001330([]) == []"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: launch_angle_or_vertical_velocity.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"launch_angle_or_vertical_velocity\"]}", "dedupe_signature": "22f65d79e44cf70017855af102bd62f3ee7aec4633e8bbd35535b7919c2e1a00", "difficulty": "easy", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["launch_angle_or_vertical_velocity"]}, "id": "abstain_001331_launch_angle_or_vertical_velocity", "license": "Apache-2.0", "prompt": "Compute projectile range on level ground. The prompt gives initial speed 40.2 m/s but does not give launch angle or vertical velocity. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: launch_angle_or_vertical_velocity.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["launch_angle_or_vertical_velocity"]}, "verifier": {"missing": ["launch_angle_or_vertical_velocity"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=41 degrees through the sine of 2 theta.\n3. Substitute v=42.9 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 185.7797, \"unit\": \"m\"}", "dedupe_signature": "734622dbb127a2a676c9384d6727663fe067dc4f7f2c65cf547cac2775726265", "difficulty": "medium", "final_answer": {"answer": 185.7797, "unit": "m"}, "id": "projectile_range_001334_42.9_41", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 42.9 m/s and angle 41 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=41 degrees through the sine of 2 theta.\nSubstitute v=42.9 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 41, "gravity": 9.81, "speed": 42.9}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 1.1 * 8.314 * 340 / 1.0.\nFinal: {\"answer\": 3109.436, \"unit\": \"kPa\"}", "dedupe_signature": "3007c363d1ab72fb8df50ea23f262e0114fb0f4fcefdc066718af5f48f063d2e", "difficulty": "medium", "final_answer": {"answer": 3109.436, "unit": "kPa"}, "id": "ideal_gas_001335_1.1_340_1.0", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=1.1 mol, T=340 K, and V=1.0 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 1.1 * 8.314 * 340 / 1.0.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 1.1, "temp_k": 340, "volume_l": 1.0}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 405 * 3.905 * 63.\nFinal: {\"answer\": 99636.075, \"unit\": \"J\"}", "dedupe_signature": "02d7a9576b3baa0e106fe562692501cf837151dbd76699fe4739980078e1c4aa", "difficulty": "easy", "final_answer": {"answer": 99636.075, "unit": "J"}, "id": "heat_q_001336_405_3.905_63", "license": "Apache-2.0", "prompt": "A 405 g sample has specific heat 3.905 J/(g*K). How much heat is needed to raise its temperature by 63 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 405 * 3.905 * 63.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 63, "heat_capacity": 3.905, "mass_g": 405}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=427 mg, t=244 h, and T_half=76 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 46.1278, \"unit\": \"mg\"}", "dedupe_signature": "6dcc7d6a2fd1c5167ba707484767b76bbe07074ce82a626894060fde26b05fbf", "difficulty": "medium", "final_answer": {"answer": 46.1278, "unit": "mg"}, "id": "half_life_001338_427_76_244", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 427 mg. Its half-life is 76 hours. How many mg remain after 244 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=427 mg, t=244 h, and T_half=76 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 244.0, "half_life": 76.0, "initial_amount": 427.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 4620 mL to 4.62 L.\n3. Compute M = 2.495 / 4.62.\nFinal: {\"answer\": 0.54, \"unit\": \"mol/L\"}", "dedupe_signature": "f923d99f58661c79af7a43c277a4f80947a6440f7c548dcd1c62406637b8d09a", "difficulty": "medium", "final_answer": {"answer": 0.54, "unit": "mol/L"}, "id": "molarity_001340_2.495_4620", "license": "Apache-2.0", "prompt": "A solution contains 2.495 mol of solute in 4620 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 4620 mL to 4.62 L.\nCompute M = 2.495 / 4.62.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 2.495, "volume_ml": 4620}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.52 y, so each step multiplies y by 1 - h*0.52.\n3. Apply that update for 5 steps and round the final state.\nFinal: {\"answer\": 0.0, \"unit\": \"state_units\"}", "dedupe_signature": "6d3dff881a311d39a5714c34ae4a0701842e3063519d848c903ced9e39338a19", "difficulty": "medium", "final_answer": {"answer": 0.0, "unit": "state_units"}, "id": "euler_decay_001341_35_0.52_1.85_5", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.52 y with y(0)=35, step size h=1.85, for 5 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.52 y, so each step multiplies y by 1 - h*0.52.\nApply that update for 5 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 35.0, "rate": 0.52, "step": 1.85, "steps": 5}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-4.1)=0.39 and f(-3.9)=1.01.\n3. The interval width is 0.2.\nFinal: {\"answer\": 0.14, \"unit\": \"area_units\"}", "dedupe_signature": "dec43f1a27d1662477b2a57c553b7b7dfcdd56a3b00944a4b171f3e0795eb420", "difficulty": "medium", "final_answer": {"answer": 0.14, "unit": "area_units"}, "id": "trapz_linear_001342_3.1_13.1_-4.1_-3.9", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=3.1x+13.1 from x=-4.1 to x=-3.9. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-4.1)=0.39 and f(-3.9)=1.01.\nThe interval width is 0.2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 13.1, "slope": 3.1, "x0": -4.1, "x1": -3.8999999999999995}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 29830.0 / 1000.\nFinal: {\"answer\": 29.83, \"unit\": \"kg\"}", "dedupe_signature": "cd21d5b3637895d8a08d163fe69acabee8bc35b4884620a025238f9028dcc6b9", "difficulty": "easy", "final_answer": {"answer": 29.83, "unit": "kg"}, "id": "unit_convert_001344_g_to_kg_29830", "license": "Apache-2.0", "prompt": "Convert 29830 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 29830.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 29830.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=221 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-81.1313, -70.5263], \"unit\": \"N\"}", "dedupe_signature": "287434b761e5ff4964adc77190ccb90a5b61a805fc3f4f268ff9255c3d43e39e", "difficulty": "medium", "final_answer": {"answer": [-81.1313, -70.5263], "unit": "N"}, "id": "vector_components_001345_107.5_221", "license": "Apache-2.0", "prompt": "A vector has magnitude 107.5 N at 221 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=221 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 221, "magnitude": 107.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [9.35, -24.0], \"unit\": \"dimensionless\"}", "dedupe_signature": "4c7c8def855e531d81151729c99504530f8340de7134f0c72871b29e6ae24dce", "difficulty": "medium", "final_answer": {"answer": [9.35, -24.0], "unit": "dimensionless"}, "id": "line_two_point_001346_-10.5_-1.5_9.35_-24", "license": "Apache-2.0", "prompt": "A line passes through points (-10.5, -122.175) and (-1.5, -38.025). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -10.5, "x2": -1.5, "y1": -122.175, "y2": -38.025}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. energy divided by length is force, not spring constant\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "cfd8ceee15dd64d7d8b49c6e2e83230575a2b1e753a4a97a9f20b103f7e17742", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_001347_inconsistent_56040f5d_253873", "license": "Apache-2.0", "prompt": "In student derivation case 253873, check dimensional consistency for k = E / x. The left side has dimensions N/m and the right side has dimensions J/m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nenergy divided by length is force, not spring constant\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "k = E / x"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef clamp_001348(x, lo, hi):\n    if lo > hi:\n        raise ValueError('lo must be <= hi')\n    return min(max(x, lo), hi)\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"clamp_001348\"}", "dedupe_signature": "b50e564e03c6283d6e79ac78823d443ad116706457961fcd6dc051e568ccc722", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "clamp_001348"}, "id": "code_001348_clamp_001348", "license": "Apache-2.0", "prompt": "Write a Python function clamp_001348(x, lo, hi) that clips x into the inclusive interval [lo, hi]. It must raise ValueError if lo > hi. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "clamp_001348"}, "verifier": {"function": "clamp_001348", "tests": ["assert clamp_001348(5, 0, 10) == 5", "assert clamp_001348(-2, 0, 10) == 0", "assert clamp_001348(12, 0, 10) == 10", "try:\n    clamp_001348(1, 3, 2)\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: volume.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"volume\"]}", "dedupe_signature": "8de003240f8d205d9de32b4521c6228df4296437955015f312b606bc6023f95f", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["volume"]}, "id": "abstain_001349_volume", "license": "Apache-2.0", "prompt": "Compute pressure from the ideal gas law. The prompt gives n=1.6 mol and T=292 K, but does not give volume. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: volume.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["volume"]}, "verifier": {"missing": ["volume"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=84 degrees through the sine of 2 theta.\n3. Substitute v=77.6 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 127.6243, \"unit\": \"m\"}", "dedupe_signature": "6430980db99e84492156e9429becd5c8a2e47d56d96892abebab669286cdb2bc", "difficulty": "medium", "final_answer": {"answer": 127.6243, "unit": "m"}, "id": "projectile_range_001352_77.6_84", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 77.6 m/s and angle 84 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=84 degrees through the sine of 2 theta.\nSubstitute v=77.6 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 84, "gravity": 9.81, "speed": 77.6}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 2.24 * 8.314 * 374 / 14.1.\nFinal: {\"answer\": 493.9813, \"unit\": \"kPa\"}", "dedupe_signature": "2a2b9b0aa3dc7e5737dfe2c2f4b2c17589a261227c52179bdc73f76fd0611777", "difficulty": "medium", "final_answer": {"answer": 493.9813, "unit": "kPa"}, "id": "ideal_gas_001353_2.24_374_14.1", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=2.24 mol, T=374 K, and V=14.1 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 2.24 * 8.314 * 374 / 14.1.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 2.24, "temp_k": 374, "volume_l": 14.1}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=62.1 V and R=99 ohm.\nFinal: {\"answer\": 38.9536, \"unit\": \"W\"}", "dedupe_signature": "be39551c762b25c50cc91f7a8cb55cc8d56f0836f3a3e24fc8d0dd85e5af6e4d", "difficulty": "easy", "final_answer": {"answer": 38.9536, "unit": "W"}, "id": "ohm_power_001355_62.1_99", "license": "Apache-2.0", "prompt": "A resistor has resistance 99 ohm and voltage 62.1 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=62.1 V and R=99 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 99.0, "voltage": 62.1}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=303 mg, t=294.5 h, and T_half=28.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 0.2349, \"unit\": \"mg\"}", "dedupe_signature": "11d3bdbc6904ded05ff677a9668abe138b32c6acb7a12ebcea1fc8c002688181", "difficulty": "medium", "final_answer": {"answer": 0.2349, "unit": "mg"}, "id": "half_life_001356_303_28.5_294.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 303 mg. Its half-life is 28.5 hours. How many mg remain after 294.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=303 mg, t=294.5 h, and T_half=28.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 294.5, "half_life": 28.5, "initial_amount": 303.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 0.84 mol * 180.156 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 151.331, \"unit\": \"g\"}", "dedupe_signature": "9d7f983db0000d256dc7875bb79655a04fcabbfe4530dbfed0d5f3c6af8abec3", "difficulty": "medium", "final_answer": {"answer": 151.331, "unit": "g"}, "id": "stoich_mass_001357_glucose_0.84", "license": "Apache-2.0", "prompt": "A sample contains 0.84 mol of glucose. Using molar mass 180.156 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 0.84 mol * 180.156 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "glucose", "molar_mass": 180.156, "moles": 0.84}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 1500 mL to 1.5 L.\n3. Compute M = 1.795 / 1.5.\nFinal: {\"answer\": 1.1967, \"unit\": \"mol/L\"}", "dedupe_signature": "b1fbe49c3330ba9f9a7670d07a59d2ca2187043fd6647fcd7eec1628b31040d7", "difficulty": "medium", "final_answer": {"answer": 1.1967, "unit": "mol/L"}, "id": "molarity_001358_1.795_1500", "license": "Apache-2.0", "prompt": "A solution contains 1.795 mol of solute in 1500 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 1500 mL to 1.5 L.\nCompute M = 1.795 / 1.5.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 1.795, "volume_ml": 1500}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.62 y, so each step multiplies y by 1 - h*0.62.\n3. Apply that update for 3 steps and round the final state.\nFinal: {\"answer\": 0.0513, \"unit\": \"state_units\"}", "dedupe_signature": "1009c7cb449b7ea3531d2e71cca92acb6c3f776002a3c3af9a0a8c39d0d6882c", "difficulty": "medium", "final_answer": {"answer": 0.0513, "unit": "state_units"}, "id": "euler_decay_001359_4.5_0.62_1.25_3", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.62 y with y(0)=4.5, step size h=1.25, for 3 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.62 y, so each step multiplies y by 1 - h*0.62.\nApply that update for 3 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 4.5, "rate": 0.62, "step": 1.25, "steps": 3}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(6.1)=63.73 and f(14)=121.4.\n3. The interval width is 7.9.\nFinal: {\"answer\": 731.2635, \"unit\": \"area_units\"}", "dedupe_signature": "f953c87cb35a78d9b1f8ac7e24b5939acd9b28b25f0a347553872681cf536ab7", "difficulty": "medium", "final_answer": {"answer": 731.2635, "unit": "area_units"}, "id": "trapz_linear_001360_7.3_19.2_6.1_14", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=7.3x+19.2 from x=6.1 to x=14. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(6.1)=63.73 and f(14)=121.4.\nThe interval width is 7.9.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 19.2, "slope": 7.3, "x0": 6.1, "x1": 14.0}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.46 and add it to the current value.\nFinal: {\"answer\": [0.138, 1.22, 0.093], \"unit\": \"temperature_units\"}", "dedupe_signature": "6992a355c8fb42858d673972444ded376b76638c286d40d1b98695a26d00a448", "difficulty": "hard", "final_answer": {"answer": [0.138, 1.22, 0.093], "unit": "temperature_units"}, "id": "heat_step_001361_0.46_-0.2_1.15_0.3_1.45_-0.35", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-0.2, right=-0.35; current interior values are [1.15, 0.3, 1.45]. Use r=0.46. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.46 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [1.15, 0.3, 1.45], "left": -0.2, "r": 0.46, "right": -0.35}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=225 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-7.4246, -7.4246], \"unit\": \"N\"}", "dedupe_signature": "62de192fd1770d83396ff75fff34ca35232b9f1353115c76e6ca53b3adf9facc", "difficulty": "medium", "final_answer": {"answer": [-7.4246, -7.4246], "unit": "N"}, "id": "vector_components_001363_10.5_225", "license": "Apache-2.0", "prompt": "A vector has magnitude 10.5 N at 225 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=225 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 225, "magnitude": 10.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [3.4, -25.5], \"unit\": \"dimensionless\"}", "dedupe_signature": "c21bf7363e6db41059557067c1dd7de4b6ee9ec14e84b086ec1e4e97dad99f58", "difficulty": "medium", "final_answer": {"answer": [3.4, -25.5], "unit": "dimensionless"}, "id": "line_two_point_001364_-11_-5.25_3.4_-25.5", "license": "Apache-2.0", "prompt": "A line passes through points (-11, -62.9) and (-5.25, -43.35). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -11.0, "x2": -5.25, "y1": -62.9, "y2": -43.349999999999994}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef clamp_001366(x, lo, hi):\n    if lo > hi:\n        raise ValueError('lo must be <= hi')\n    return min(max(x, lo), hi)\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"clamp_001366\"}", "dedupe_signature": "7ae8f7f56f09bfe857d24493222b1680fd39ec9e9f125c5e99a1f61a7a7313de", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "clamp_001366"}, "id": "code_001366_clamp_001366", "license": "Apache-2.0", "prompt": "Write a Python function clamp_001366(x, lo, hi) that clips x into the inclusive interval [lo, hi]. It must raise ValueError if lo > hi. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "clamp_001366"}, "verifier": {"function": "clamp_001366", "tests": ["assert clamp_001366(5, 0, 10) == 5", "assert clamp_001366(-2, 0, 10) == 0", "assert clamp_001366(12, 0, 10) == 10", "try:\n    clamp_001366(1, 3, 2)\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: volume.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"volume\"]}", "dedupe_signature": "6e2571c3c72940914819af109c0402da0c6a6c535a3110843b31d6fe6a3bb628", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["volume"]}, "id": "abstain_001367_volume", "license": "Apache-2.0", "prompt": "Compute pressure from the ideal gas law. The prompt gives n=1.8 mol and T=451 K, but does not give volume. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: volume.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["volume"]}, "verifier": {"missing": ["volume"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 7.15 kg and a = 9.1 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 65.065, \"unit\": \"N\"}", "dedupe_signature": "3ce2102e18d1b0e689292da4639c6b897d5e2de92937b45f4c6ed3914046d8bb", "difficulty": "easy", "final_answer": {"answer": 65.065, "unit": "N"}, "id": "force_001368_7.15_9.1", "license": "Apache-2.0", "prompt": "A cart has mass 7.15 kg and measured acceleration 9.1 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 7.15 kg and a = 9.1 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 9.1, "mass": 7.15}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 25.45^2 and multiply by 0.5 * 15.5.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 5019.6944, \"unit\": \"J\"}", "dedupe_signature": "485a34f24d28b860b01c155747afd5fb2faff672245c7bf80cdf732b96678c72", "difficulty": "easy", "final_answer": {"answer": 5019.6944, "unit": "J"}, "id": "ke_001369_15.5_25.45", "license": "Apache-2.0", "prompt": "A body of mass 15.5 kg moves at 25.45 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 25.45^2 and multiply by 0.5 * 15.5.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 15.5, "velocity": 25.45}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=26 degrees through the sine of 2 theta.\n3. Substitute v=54.5 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 238.5921, \"unit\": \"m\"}", "dedupe_signature": "33ebdaad4d4be3cce80006f443310955e9160e748023821489cb3d01d65c2d56", "difficulty": "medium", "final_answer": {"answer": 238.5921, "unit": "m"}, "id": "projectile_range_001370_54.5_26", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 54.5 m/s and angle 26 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=26 degrees through the sine of 2 theta.\nSubstitute v=54.5 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 26, "gravity": 9.81, "speed": 54.5}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 3.76 * 8.314 * 584 / 114.5.\nFinal: {\"answer\": 159.4429, \"unit\": \"kPa\"}", "dedupe_signature": "022d2b30b27597d8040d8e0987a43f5f67c79efd09474676cdd371f9f312e282", "difficulty": "medium", "final_answer": {"answer": 159.4429, "unit": "kPa"}, "id": "ideal_gas_001371_3.76_584_114.5", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=3.76 mol, T=584 K, and V=114.5 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 3.76 * 8.314 * 584 / 114.5.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 3.76, "temp_k": 584, "volume_l": 114.5}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 225 * 3.045 * 84.\nFinal: {\"answer\": 57550.5, \"unit\": \"J\"}", "dedupe_signature": "ce3861b91d5f6fdc792971b751bab9a2b511f93234ffa9aa90bf4db35f911011", "difficulty": "easy", "final_answer": {"answer": 57550.5, "unit": "J"}, "id": "heat_q_001372_225_3.045_84", "license": "Apache-2.0", "prompt": "A 225 g sample has specific heat 3.045 J/(g*K). How much heat is needed to raise its temperature by 84 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 225 * 3.045 * 84.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 84, "heat_capacity": 3.045, "mass_g": 225}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 5.13 mol * 180.156 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 924.2003, \"unit\": \"g\"}", "dedupe_signature": "1cb327fb1b5264594db801f06f088e966f4ddf02fe043ffcd42a61e78b600b78", "difficulty": "medium", "final_answer": {"answer": 924.2003, "unit": "g"}, "id": "stoich_mass_001375_glucose_5.13", "license": "Apache-2.0", "prompt": "A sample contains 5.13 mol of glucose. Using molar mass 180.156 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 5.13 mol * 180.156 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "glucose", "molar_mass": 180.156, "moles": 5.13}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.63 y, so each step multiplies y by 1 - h*0.63.\n3. Apply that update for 9 steps and round the final state.\nFinal: {\"answer\": 0.0, \"unit\": \"state_units\"}", "dedupe_signature": "1a7d6a5eeb1d6d6e7cda7662686d230b2facb18730ea8b248478ce3b86419942", "difficulty": "medium", "final_answer": {"answer": 0.0, "unit": "state_units"}, "id": "euler_decay_001377_42.5_0.63_1.55_9", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.63 y with y(0)=42.5, step size h=1.55, for 9 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.63 y, so each step multiplies y by 1 - h*0.63.\nApply that update for 9 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 42.5, "rate": 0.63, "step": 1.55, "steps": 9}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(4.9)=34.18 and f(10.2)=56.44.\n3. The interval width is 5.3.\nFinal: {\"answer\": 240.143, \"unit\": \"area_units\"}", "dedupe_signature": "628047f4a4c82a9b390dc5fe52edbda032d2bace89ccc88dce9d6a467bb3268e", "difficulty": "medium", "final_answer": {"answer": 240.143, "unit": "area_units"}, "id": "trapz_linear_001378_4.2_13.6_4.9_10.2", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=4.2x+13.6 from x=4.9 to x=10.2. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(4.9)=34.18 and f(10.2)=56.44.\nThe interval width is 5.3.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 13.6, "slope": 4.2, "x0": 4.9, "x1": 10.2}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kelvin equals Celsius plus 273.15.\n2. Apply the conversion factor directly to the given value.\n3. Compute 170.0 + 273.15.\nFinal: {\"answer\": 443.15, \"unit\": \"K\"}", "dedupe_signature": "e1f753874280c346e3f63dd2b302c518832916d8eed06635c2420a71806c6cf0", "difficulty": "easy", "final_answer": {"answer": 443.15, "unit": "K"}, "id": "unit_convert_001380_c_to_k_170", "license": "Apache-2.0", "prompt": "Convert 170 degC to K. Return the converted value with unit.", "reasoning_trace": "Kelvin equals Celsius plus 273.15.\nApply the conversion factor directly to the given value.\nCompute 170.0 + 273.15.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 170.0}, "verifier": {"formula": "value + 273.15", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=174 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-247.636, 26.0276], \"unit\": \"N\"}", "dedupe_signature": "63cd2be02d21008e9d1723e953679fcd3f2d7dfb146f0985693e9b45be0d2bb2", "difficulty": "medium", "final_answer": {"answer": [-247.636, 26.0276], "unit": "N"}, "id": "vector_components_001381_249_174", "license": "Apache-2.0", "prompt": "A vector has magnitude 249 N at 174 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=174 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 174, "magnitude": 249.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. amount times volume is not concentration\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "2dd027179181b2c29b536e925fcae6d79517537c5ebdf5d5d852b92dfb8ac21c", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_001383_inconsistent_74ac0b02_818887", "license": "Apache-2.0", "prompt": "In quality-control check case 818887, check dimensional consistency for C = n * V. The left side has dimensions mol/L and the right side has dimensions mol*L. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\namount times volume is not concentration\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "C = n * V"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef finite_differences_001384(values):\n    return [values[i + 1] - values[i] for i in range(len(values) - 1)]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"finite_differences_001384\"}", "dedupe_signature": "f04830026cf213dc4d0eb2e47013a13068fe64e3747710806cd4b7f6a2ed083c", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "finite_differences_001384"}, "id": "code_001384_finite_differences_001384", "license": "Apache-2.0", "prompt": "Write a Python function finite_differences_001384(values) that returns the list of successive differences values[i+1] - values[i]. It must return [] for fewer than two values. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "finite_differences_001384"}, "verifier": {"function": "finite_differences_001384", "tests": ["assert finite_differences_001384([1, 4, 9, 16]) == [3, 5, 7]", "assert finite_differences_001384([5]) == []", "assert finite_differences_001384([]) == []"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 10.05 kg and a = 8.35 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 83.9175, \"unit\": \"N\"}", "dedupe_signature": "705fcabc603700e5389bf9346c290492e1213ccc5425377d9fc64d8171f59b5d", "difficulty": "easy", "final_answer": {"answer": 83.9175, "unit": "N"}, "id": "force_001386_10.05_8.35", "license": "Apache-2.0", "prompt": "A cart has mass 10.05 kg and measured acceleration 8.35 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 10.05 kg and a = 8.35 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 8.35, "mass": 10.05}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 17.7^2 and multiply by 0.5 * 17.25.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 2702.1262, \"unit\": \"J\"}", "dedupe_signature": "372fefc52e73f80444f0b08e6fdf226463605f0dd6e67beccc6d1725f894f5b1", "difficulty": "easy", "final_answer": {"answer": 2702.1262, "unit": "J"}, "id": "ke_001387_17.25_17.7", "license": "Apache-2.0", "prompt": "A body of mass 17.25 kg moves at 17.7 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 17.7^2 and multiply by 0.5 * 17.25.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 17.25, "velocity": 17.7}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 5.28 * 8.314 * 439 / 112.3.\nFinal: {\"answer\": 171.6045, \"unit\": \"kPa\"}", "dedupe_signature": "24ef8c5e11c7226df592f3659cd6a9d089e802d22940ad4ef43df65fb6b38462", "difficulty": "medium", "final_answer": {"answer": 171.6045, "unit": "kPa"}, "id": "ideal_gas_001389_5.28_439_112.3", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=5.28 mol, T=439 K, and V=112.3 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 5.28 * 8.314 * 439 / 112.3.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 5.28, "temp_k": 439, "volume_l": 112.3}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 190 * 2.855 * 97.\nFinal: {\"answer\": 52617.65, \"unit\": \"J\"}", "dedupe_signature": "0f053a314eaf2308fbbe230ec4f88c8f619ddd04658fe6a22550791d2e1331b8", "difficulty": "easy", "final_answer": {"answer": 52617.65, "unit": "J"}, "id": "heat_q_001390_190_2.855_97", "license": "Apache-2.0", "prompt": "A 190 g sample has specific heat 2.855 J/(g*K). How much heat is needed to raise its temperature by 97 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 190 * 2.855 * 97.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 97, "heat_capacity": 2.855, "mass_g": 190}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=76.6 V and R=5.3 ohm.\nFinal: {\"answer\": 1107.0868, \"unit\": \"W\"}", "dedupe_signature": "1d4a818674b8b7b7057778835de851255d68d00de18877e548e75cc91189995f", "difficulty": "easy", "final_answer": {"answer": 1107.0868, "unit": "W"}, "id": "ohm_power_001391_76.6_5.3", "license": "Apache-2.0", "prompt": "A resistor has resistance 5.3 ohm and voltage 76.6 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=76.6 V and R=5.3 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 5.3, "voltage": 76.6}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 4225 mL to 4.225 L.\n3. Compute M = 2.52 / 4.225.\nFinal: {\"answer\": 0.5964, \"unit\": \"mol/L\"}", "dedupe_signature": "9a842d1a093c2a1a89701711c129b420d0cb421496d7b4548491862d0b02b7ce", "difficulty": "medium", "final_answer": {"answer": 0.5964, "unit": "mol/L"}, "id": "molarity_001394_2.52_4225", "license": "Apache-2.0", "prompt": "A solution contains 2.52 mol of solute in 4225 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 4225 mL to 4.225 L.\nCompute M = 2.52 / 4.225.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 2.52, "volume_ml": 4225}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.15 y, so each step multiplies y by 1 - h*0.15.\n3. Apply that update for 8 steps and round the final state.\nFinal: {\"answer\": 1.5331, \"unit\": \"state_units\"}", "dedupe_signature": "66afd9a84284d7300d9cbbc62a5ab3a4688c66de7318dabbc347f44075b74b9f", "difficulty": "medium", "final_answer": {"answer": 1.5331, "unit": "state_units"}, "id": "euler_decay_001395_7.5_0.15_1.2_8", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.15 y with y(0)=7.5, step size h=1.2, for 8 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.15 y, so each step multiplies y by 1 - h*0.15.\nApply that update for 8 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 7.5, "rate": 0.15, "step": 1.2, "steps": 8}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-2.9)=-19.27 and f(-2.1)=-17.43.\n3. The interval width is 0.8.\nFinal: {\"answer\": -14.68, \"unit\": \"area_units\"}", "dedupe_signature": "53447e6160676778d0e1780853765bf3b5e27f3c4cf877b9770dd75ecaa0d11d", "difficulty": "medium", "final_answer": {"answer": -14.68, "unit": "area_units"}, "id": "trapz_linear_001396_2.3_-12.6_-2.9_-2.1", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=2.3x+-12.6 from x=-2.9 to x=-2.1. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-2.9)=-19.27 and f(-2.1)=-17.43.\nThe interval width is 0.8.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -12.6, "slope": 2.3, "x0": -2.9, "x1": -2.0999999999999996}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=263 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-18.8897, -153.8447], \"unit\": \"N\"}", "dedupe_signature": "0b6b1ff99d9eee936f76f8964dbb000fb0fe540771cd455f1a6b0b3a54f90e56", "difficulty": "medium", "final_answer": {"answer": [-18.8897, -153.8447], "unit": "N"}, "id": "vector_components_001399_155_263", "license": "Apache-2.0", "prompt": "A vector has magnitude 155 N at 263 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=263 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 263, "magnitude": 155.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [9.15, 29.75], \"unit\": \"dimensionless\"}", "dedupe_signature": "daae4ffd6574cc85562e7c5fe22370d02e2a150f3b4e9fa26a7f5ac112071f50", "difficulty": "medium", "final_answer": {"answer": [9.15, 29.75], "unit": "dimensionless"}, "id": "line_two_point_001400_20_28.5_9.15_29.75", "license": "Apache-2.0", "prompt": "A line passes through points (20, 212.75) and (28.5, 290.525). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 20.0, "x2": 28.5, "y1": 212.75, "y2": 290.52500000000003}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. m*v is momentum, not energy\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "5bb4602db2ac77e8f3d3c4ee16e7add9dae9c8f150f80a0b354e1aa83c48ca2f", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_001401_inconsistent_1e14b074_165432", "license": "Apache-2.0", "prompt": "In lab notebook case 165432, check dimensional consistency for E = m * v. The left side has dimensions kg*m^2/s^2 and the right side has dimensions kg*m/s. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nm*v is momentum, not energy\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "E = m * v"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: rate_constant, number_of_steps.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"rate_constant\", \"number_of_steps\"]}", "dedupe_signature": "acd8fd94eaecb6a9fd279441fdfad8013fee407642ae148437b83c59732ccf5c", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["rate_constant", "number_of_steps"]}, "id": "abstain_001403_rate_constant_number_of_steps", "license": "Apache-2.0", "prompt": "Use explicit Euler for dy/dt = -k y. The prompt gives y(0)=42 and h=1.9, but omits both k and the number of steps. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: rate_constant, number_of_steps.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["rate_constant", "number_of_steps"]}, "verifier": {"missing": ["rate_constant", "number_of_steps"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 9.5 kg and a = 5.1 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 48.45, \"unit\": \"N\"}", "dedupe_signature": "1c43be5712540b9769531230eb5dc257eff739a9b4aa78ea71edd4db62350880", "difficulty": "easy", "final_answer": {"answer": 48.45, "unit": "N"}, "id": "force_001404_9.5_5.1", "license": "Apache-2.0", "prompt": "A cart has mass 9.5 kg and measured acceleration 5.1 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 9.5 kg and a = 5.1 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 5.1, "mass": 9.5}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 7^2 and multiply by 0.5 * 5.05.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 123.725, \"unit\": \"J\"}", "dedupe_signature": "19a699e1721b8dbdde42952356682d919bed34b1016344c02ea9e9f58d182396", "difficulty": "easy", "final_answer": {"answer": 123.725, "unit": "J"}, "id": "ke_001405_5.05_7", "license": "Apache-2.0", "prompt": "A body of mass 5.05 kg moves at 7 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 7^2 and multiply by 0.5 * 5.05.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 5.05, "velocity": 7.0}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=31 degrees through the sine of 2 theta.\n3. Substitute v=73.9 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 491.5354, \"unit\": \"m\"}", "dedupe_signature": "2254b66e7825d846c7c37968ad17bf622f0d72434ebaf3a5a886fd7ce640afc5", "difficulty": "medium", "final_answer": {"answer": 491.5354, "unit": "m"}, "id": "projectile_range_001406_73.9_31", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 73.9 m/s and angle 31 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=31 degrees through the sine of 2 theta.\nSubstitute v=73.9 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 31, "gravity": 9.81, "speed": 73.9}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 0.56 * 8.314 * 366 / 80.0.\nFinal: {\"answer\": 21.3005, \"unit\": \"kPa\"}", "dedupe_signature": "f014b3d2f31ba7490615b74bc6a60aaf289fe954797b1fde15d95c7208c8d804", "difficulty": "medium", "final_answer": {"answer": 21.3005, "unit": "kPa"}, "id": "ideal_gas_001407_0.56_366_80.0", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=0.56 mol, T=366 K, and V=80.0 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 0.56 * 8.314 * 366 / 80.0.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 0.56, "temp_k": 366, "volume_l": 80.0}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 510 * 3.395 * 66.\nFinal: {\"answer\": 114275.7, \"unit\": \"J\"}", "dedupe_signature": "2260164695b9a2b61460038ad97ff4020df3b37aa0ca72bc03b5a3db23380f5d", "difficulty": "easy", "final_answer": {"answer": 114275.7, "unit": "J"}, "id": "heat_q_001408_510_3.395_66", "license": "Apache-2.0", "prompt": "A 510 g sample has specific heat 3.395 J/(g*K). How much heat is needed to raise its temperature by 66 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 510 * 3.395 * 66.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 66, "heat_capacity": 3.395, "mass_g": 510}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=66.3 V and R=194.1 ohm.\nFinal: {\"answer\": 22.6465, \"unit\": \"W\"}", "dedupe_signature": "93f859080f9606e1fdd7c5e73d2b6c98efbeb08f2c4c1ca98e3e973f0c5b3d03", "difficulty": "easy", "final_answer": {"answer": 22.6465, "unit": "W"}, "id": "ohm_power_001409_66.3_194.1", "license": "Apache-2.0", "prompt": "A resistor has resistance 194.1 ohm and voltage 66.3 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=66.3 V and R=194.1 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 194.1, "voltage": 66.3}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=318 mg, t=308.5 h, and T_half=29.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 0.2261, \"unit\": \"mg\"}", "dedupe_signature": "120442e304ac166de3f7caecd6d6f1451d1133a871d99c4e71bc5b2cf977933c", "difficulty": "medium", "final_answer": {"answer": 0.2261, "unit": "mg"}, "id": "half_life_001410_318_29.5_308.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 318 mg. Its half-life is 29.5 hours. How many mg remain after 308.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=318 mg, t=308.5 h, and T_half=29.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 308.5, "half_life": 29.5, "initial_amount": 318.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 3205 mL to 3.205 L.\n3. Compute M = 0.165 / 3.205.\nFinal: {\"answer\": 0.0515, \"unit\": \"mol/L\"}", "dedupe_signature": "5df6a7092643cd19fac2399d4382f0cd4d08f01ed73759d7bde644b8018f3ddf", "difficulty": "medium", "final_answer": {"answer": 0.0515, "unit": "mol/L"}, "id": "molarity_001412_0.165_3205", "license": "Apache-2.0", "prompt": "A solution contains 0.165 mol of solute in 3205 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 3205 mL to 3.205 L.\nCompute M = 0.165 / 3.205.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 0.165, "volume_ml": 3205}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.68 y, so each step multiplies y by 1 - h*0.68.\n3. Apply that update for 6 steps and round the final state.\nFinal: {\"answer\": 0.0, \"unit\": \"state_units\"}", "dedupe_signature": "d4be35a2c92b20ff83a522f62f706fcea860d18ebf12fa9d392e455f40637402", "difficulty": "medium", "final_answer": {"answer": 0.0, "unit": "state_units"}, "id": "euler_decay_001413_57.5_0.68_1.4_6", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.68 y with y(0)=57.5, step size h=1.4, for 6 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.68 y, so each step multiplies y by 1 - h*0.68.\nApply that update for 6 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 57.5, "rate": 0.68, "step": 1.4, "steps": 6}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(1.4)=-4.62 and f(7.1)=-46.23.\n3. The interval width is 5.7.\nFinal: {\"answer\": -144.9225, \"unit\": \"area_units\"}", "dedupe_signature": "ad8db8e7dc181340e9f13c48e33a23ac32235e5a87bb7a1ee0da1a302b641fcd", "difficulty": "medium", "final_answer": {"answer": -144.9225, "unit": "area_units"}, "id": "trapz_linear_001414_-7.3_5.6_1.4_7.1", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-7.3x+5.6 from x=1.4 to x=7.1. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(1.4)=-4.62 and f(7.1)=-46.23.\nThe interval width is 5.7.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 5.6, "slope": -7.3, "x0": 1.4, "x1": 7.1}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.44 and add it to the current value.\nFinal: {\"answer\": [0.824, 1.358, 0.08], \"unit\": \"temperature_units\"}", "dedupe_signature": "0141e8151c5bddc6afd720abcbb0d55a42faeafd4d95a53457c73c3b7924929d", "difficulty": "hard", "final_answer": {"answer": [0.824, 1.358, 0.08], "unit": "temperature_units"}, "id": "heat_step_001415_0.44_1.1_1.0_0.5_1.95_-0.85", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.1, right=-0.85; current interior values are [1.0, 0.5, 1.95]. Use r=0.44. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.44 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [1.0, 0.5, 1.95], "left": 1.1, "r": 0.44, "right": -0.85}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kelvin equals Celsius plus 273.15.\n2. Apply the conversion factor directly to the given value.\n3. Compute 10.5 + 273.15.\nFinal: {\"answer\": 283.65, \"unit\": \"K\"}", "dedupe_signature": "4feca44f2fd1030e7cec08aa4f81e112ff1ebc5101c63cbe3cff54e6ede4a7d3", "difficulty": "easy", "final_answer": {"answer": 283.65, "unit": "K"}, "id": "unit_convert_001416_c_to_k_10.5", "license": "Apache-2.0", "prompt": "Convert 10.5 degC to K. Return the converted value with unit.", "reasoning_trace": "Kelvin equals Celsius plus 273.15.\nApply the conversion factor directly to the given value.\nCompute 10.5 + 273.15.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 10.5}, "verifier": {"formula": "value + 273.15", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=249 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-129.3708, -337.0225], \"unit\": \"N\"}", "dedupe_signature": "58c11b6cb2de8244bbd1bec597809e2210cb32816cdcc1e978b4e5b4d465a140", "difficulty": "medium", "final_answer": {"answer": [-129.3708, -337.0225], "unit": "N"}, "id": "vector_components_001417_361_249", "license": "Apache-2.0", "prompt": "A vector has magnitude 361 N at 249 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=249 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 249, "magnitude": 361.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-6.35, 20.25], \"unit\": \"dimensionless\"}", "dedupe_signature": "6ad32abd3444364f6ae4653dffc00756385466df133086acabc944a8ef4aaf18", "difficulty": "medium", "final_answer": {"answer": [-6.35, 20.25], "unit": "dimensionless"}, "id": "line_two_point_001418_-6.5_4.25_-6.35_20.25", "license": "Apache-2.0", "prompt": "A line passes through points (-6.5, 61.525) and (4.25, -6.7375). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -6.5, "x2": 4.25, "y1": 61.525, "y2": -6.737499999999997}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. lever arm times force has torque dimensions\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "e1df3f90c2da674c9dadd39ee89cf12f5626075c5c57839e59a10908de293a18", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_001419_consistent_5ca82cb9_222683", "license": "Apache-2.0", "prompt": "In lab notebook case 222683, check dimensional consistency for tau = r * F. The left side has dimensions N*m and the right side has dimensions N*m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nlever arm times force has torque dimensions\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "tau = r * F"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef clamp_001420(x, lo, hi):\n    if lo > hi:\n        raise ValueError('lo must be <= hi')\n    return min(max(x, lo), hi)\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"clamp_001420\"}", "dedupe_signature": "77640ce5c1a3d434fff0f2b88ef4e3dc100172adf3408b4b8ec481c42e01a5c9", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "clamp_001420"}, "id": "code_001420_clamp_001420", "license": "Apache-2.0", "prompt": "Write a Python function clamp_001420(x, lo, hi) that clips x into the inclusive interval [lo, hi]. It must raise ValueError if lo > hi. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "clamp_001420"}, "verifier": {"function": "clamp_001420", "tests": ["assert clamp_001420(5, 0, 10) == 5", "assert clamp_001420(-2, 0, 10) == 0", "assert clamp_001420(12, 0, 10) == 10", "try:\n    clamp_001420(1, 3, 2)\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: recurrence, objective, tie_breaking_rule.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"recurrence\", \"objective\", \"tie_breaking_rule\"]}", "dedupe_signature": "2bfc5feb363c2520ccca661bfd4a68379f3e4061691bb40f6bd91abffc870860", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["recurrence", "objective", "tie_breaking_rule"]}, "id": "abstain_001421_recurrence_objective_tie_breaking_rule", "license": "Apache-2.0", "prompt": "Write a dynamic-programming solver for a segmentation scoring problem with 1636 items and budget 74555, but the recurrence, objective, and tie-breaking rule are all absent. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: recurrence, objective, tie_breaking_rule.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["recurrence", "objective", "tie_breaking_rule"]}, "verifier": {"missing": ["recurrence", "objective", "tie_breaking_rule"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 1.05 kg and a = 4.3 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 4.515, \"unit\": \"N\"}", "dedupe_signature": "9f32e5251a145ea411fb687664fb93bb7d4a265f0ab8d0b44424ab0216f5cd9d", "difficulty": "easy", "final_answer": {"answer": 4.515, "unit": "N"}, "id": "force_001422_1.05_4.3", "license": "Apache-2.0", "prompt": "A cart has mass 1.05 kg and measured acceleration 4.3 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 1.05 kg and a = 4.3 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 4.3, "mass": 1.05}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 26.1^2 and multiply by 0.5 * 8.65.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 2946.2333, \"unit\": \"J\"}", "dedupe_signature": "9d3c69817ba30bdfe3acdde1fbaa055c9a8ff11bd5a42336dc8904c590c44655", "difficulty": "easy", "final_answer": {"answer": 2946.2333, "unit": "J"}, "id": "ke_001423_8.65_26.1", "license": "Apache-2.0", "prompt": "A body of mass 8.65 kg moves at 26.1 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 26.1^2 and multiply by 0.5 * 8.65.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 8.65, "velocity": 26.1}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=65 degrees through the sine of 2 theta.\n3. Substitute v=11.3 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 9.9711, \"unit\": \"m\"}", "dedupe_signature": "f666854155b9c9f11d37561988980dfaa909e2f7d4e67faca3cc0b822af52ce9", "difficulty": "medium", "final_answer": {"answer": 9.9711, "unit": "m"}, "id": "projectile_range_001424_11.3_65", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 11.3 m/s and angle 65 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=65 degrees through the sine of 2 theta.\nSubstitute v=11.3 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 65, "gravity": 9.81, "speed": 11.3}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1800 * 0.69 * 118.\nFinal: {\"answer\": 146556.0, \"unit\": \"J\"}", "dedupe_signature": "cbe4168889eeed19a9c5c41c76444782f05d50fb6c23cf5175cf189bcaa64589", "difficulty": "easy", "final_answer": {"answer": 146556.0, "unit": "J"}, "id": "heat_q_001426_1800_0.69_118", "license": "Apache-2.0", "prompt": "A 1800 g sample has specific heat 0.69 J/(g*K). How much heat is needed to raise its temperature by 118 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1800 * 0.69 * 118.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 118, "heat_capacity": 0.69, "mass_g": 1800}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=160.2 V and R=93.7 ohm.\nFinal: {\"answer\": 273.8958, \"unit\": \"W\"}", "dedupe_signature": "d20eb104e5cfa9e426ea9c77f03f1aa2991b28e7f13ccc42a0ccc336df9b1896", "difficulty": "easy", "final_answer": {"answer": 273.8958, "unit": "W"}, "id": "ohm_power_001427_160.2_93.7", "license": "Apache-2.0", "prompt": "A resistor has resistance 93.7 ohm and voltage 160.2 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=160.2 V and R=93.7 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 93.7, "voltage": 160.2}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=127.5 mg, t=335.5 h, and T_half=63 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 3.1798, \"unit\": \"mg\"}", "dedupe_signature": "71972fdc6b452d2fe81f58d545a4d4ec5e1b7c5628b6f38f0ad7b01a9ff66168", "difficulty": "medium", "final_answer": {"answer": 3.1798, "unit": "mg"}, "id": "half_life_001428_127.5_63_335.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 127.5 mg. Its half-life is 63 hours. How many mg remain after 335.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=127.5 mg, t=335.5 h, and T_half=63 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 335.5, "half_life": 63.0, "initial_amount": 127.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 5.6 mol * 180.156 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 1008.8736, \"unit\": \"g\"}", "dedupe_signature": "8a4c3bd126c0a0ced105789b7f6cdd973aad00e4880430a9d5353c3df1d193cb", "difficulty": "medium", "final_answer": {"answer": 1008.8736, "unit": "g"}, "id": "stoich_mass_001429_glucose_5.6", "license": "Apache-2.0", "prompt": "A sample contains 5.6 mol of glucose. Using molar mass 180.156 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 5.6 mol * 180.156 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "glucose", "molar_mass": 180.156, "moles": 5.6}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 3290 mL to 3.29 L.\n3. Compute M = 3.31 / 3.29.\nFinal: {\"answer\": 1.0061, \"unit\": \"mol/L\"}", "dedupe_signature": "bcdee84248ff3c40b437fe1da53a386b1448c7f3bbf3f4068db1014d89cb266a", "difficulty": "medium", "final_answer": {"answer": 1.0061, "unit": "mol/L"}, "id": "molarity_001430_3.31_3290", "license": "Apache-2.0", "prompt": "A solution contains 3.31 mol of solute in 3290 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 3290 mL to 3.29 L.\nCompute M = 3.31 / 3.29.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 3.31, "volume_ml": 3290}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.08 y, so each step multiplies y by 1 - h*0.08.\n3. Apply that update for 2 steps and round the final state.\nFinal: {\"answer\": 53.6475, \"unit\": \"state_units\"}", "dedupe_signature": "48fa33431079ee8e619d2e4235319b648be6386147254930e6a22a62819029b5", "difficulty": "medium", "final_answer": {"answer": 53.6475, "unit": "state_units"}, "id": "euler_decay_001431_64.5_0.08_1.1_2", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.08 y with y(0)=64.5, step size h=1.1, for 2 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.08 y, so each step multiplies y by 1 - h*0.08.\nApply that update for 2 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 64.5, "rate": 0.08, "step": 1.1, "steps": 2}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(4.2)=-42.68 and f(13.5)=-111.5.\n3. The interval width is 9.3.\nFinal: {\"answer\": -716.937, \"unit\": \"area_units\"}", "dedupe_signature": "95238c4baca2879025fbc0144bc3c1af806c8d4c9989cb5d8e2ff650b9670a06", "difficulty": "medium", "final_answer": {"answer": -716.937, "unit": "area_units"}, "id": "trapz_linear_001432_-7.4_-11.6_4.2_13.5", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-7.4x+-11.6 from x=4.2 to x=13.5. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(4.2)=-42.68 and f(13.5)=-111.5.\nThe interval width is 9.3.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -11.6, "slope": -7.4, "x0": 4.2, "x1": 13.5}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.16 and add it to the current value.\nFinal: {\"answer\": [1.604, 0.994, -0.746], \"unit\": \"temperature_units\"}", "dedupe_signature": "fc673313ce4e1767b4118fea88b2d76bcc2bb568816dd51fda4280b81be6e39c", "difficulty": "hard", "final_answer": {"answer": [1.604, 0.994, -0.746], "unit": "temperature_units"}, "id": "heat_step_001433_0.16_2.2_1.5_1.45_-1.45_0.05", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=2.2, right=0.05; current interior values are [1.5, 1.45, -1.45]. Use r=0.16. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.16 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [1.5, 1.45, -1.45], "left": 2.2, "r": 0.16, "right": 0.05}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 38933.0 / 1000.\nFinal: {\"answer\": 38.933, \"unit\": \"kg\"}", "dedupe_signature": "093394242770d9562e3578d3397d196d255fc8e1810e2b28367fe7a08617ce71", "difficulty": "easy", "final_answer": {"answer": 38.933, "unit": "kg"}, "id": "unit_convert_001434_g_to_kg_38933", "license": "Apache-2.0", "prompt": "Convert 38933 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 38933.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 38933.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=310 degrees and keep the unit as newtons.\nFinal: {\"answer\": [190.2651, -226.7492], \"unit\": \"N\"}", "dedupe_signature": "022bff0ca4e912de483d439dc38c64670e782aa2ee5429cd60fe97bb00f4d794", "difficulty": "medium", "final_answer": {"answer": [190.2651, -226.7492], "unit": "N"}, "id": "vector_components_001435_296_310", "license": "Apache-2.0", "prompt": "A vector has magnitude 296 N at 310 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=310 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 310, "magnitude": 296.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [10.0, 3.0], \"unit\": \"dimensionless\"}", "dedupe_signature": "4598e1e69110c848bff977ebd04b7de87ad1ff91720a8e6f983cc08af190ff56", "difficulty": "medium", "final_answer": {"answer": [10.0, 3.0], "unit": "dimensionless"}, "id": "line_two_point_001436_-19.75_-11_10_3", "license": "Apache-2.0", "prompt": "A line passes through points (-19.75, -194.5) and (-11, -107). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -19.75, "x2": -11.0, "y1": -194.5, "y2": -107.0}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. grams cancel with J/(g*K), and kelvin cancels, leaving joules\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "d22b00d9b159cb772c4cf11fad97eae32308649f756b081fccb32f79f543860a", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_001437_consistent_4153435f_594470", "license": "Apache-2.0", "prompt": "In simulation spec case 594470, check dimensional consistency for Q = m * c * DeltaT. The left side has dimensions J and the right side has dimensions J. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\ngrams cancel with J/(g*K), and kelvin cancels, leaving joules\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "Q = m * c * DeltaT"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef threshold_flags_001438(values, threshold):\n    return [value >= threshold for value in values]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"threshold_flags_001438\"}", "dedupe_signature": "04ee930768a130cf1d679b0597c39a368db7f26c67d9b75674ae5c97424c8138", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "threshold_flags_001438"}, "id": "code_001438_threshold_flags_001438", "license": "Apache-2.0", "prompt": "Write a Python function threshold_flags_001438(values, threshold) that returns a list of booleans showing whether each value is greater than or equal to threshold. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "threshold_flags_001438"}, "verifier": {"function": "threshold_flags_001438", "tests": ["assert threshold_flags_001438([1, 2, 3], 2) == [False, True, True]", "assert threshold_flags_001438([], 5) == []", "assert threshold_flags_001438([-1, 0], 0) == [False, True]"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: rate_constant, number_of_steps.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"rate_constant\", \"number_of_steps\"]}", "dedupe_signature": "c2fe954e05a9d4a206b5413b931f1cae85638673817cc42a22c58f6315f73463", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["rate_constant", "number_of_steps"]}, "id": "abstain_001439_rate_constant_number_of_steps", "license": "Apache-2.0", "prompt": "Use explicit Euler for dy/dt = -k y. The prompt gives y(0)=21 and h=0.05, but omits both k and the number of steps. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: rate_constant, number_of_steps.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["rate_constant", "number_of_steps"]}, "verifier": {"missing": ["rate_constant", "number_of_steps"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 5.5^2 and multiply by 0.5 * 0.6.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 9.075, \"unit\": \"J\"}", "dedupe_signature": "8b978971d71a4647ddbbcd44f60f438eed202ef90ea166544beebf8f63a27ef1", "difficulty": "easy", "final_answer": {"answer": 9.075, "unit": "J"}, "id": "ke_001441_0.6_5.5", "license": "Apache-2.0", "prompt": "A body of mass 0.6 kg moves at 5.5 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 5.5^2 and multiply by 0.5 * 0.6.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 0.6, "velocity": 5.5}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=13 degrees through the sine of 2 theta.\n3. Substitute v=40.1 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 71.8558, \"unit\": \"m\"}", "dedupe_signature": "d862379d3a4934a3d5f083f51f54e99062f3393f4cd49d42d11bf0237aa9e62d", "difficulty": "medium", "final_answer": {"answer": 71.8558, "unit": "m"}, "id": "projectile_range_001442_40.1_13", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 40.1 m/s and angle 13 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=13 degrees through the sine of 2 theta.\nSubstitute v=40.1 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 13, "gravity": 9.81, "speed": 40.1}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 3.51 * 8.314 * 558 / 34.8.\nFinal: {\"answer\": 467.9205, \"unit\": \"kPa\"}", "dedupe_signature": "c67dd369f208d40b34daf48d3bee8726e0f2c7acbb451508ff7c88ad91291b7b", "difficulty": "medium", "final_answer": {"answer": 467.9205, "unit": "kPa"}, "id": "ideal_gas_001443_3.51_558_34.8", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=3.51 mol, T=558 K, and V=34.8 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 3.51 * 8.314 * 558 / 34.8.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 3.51, "temp_k": 558, "volume_l": 34.8}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1880 * 3.63 * 75.\nFinal: {\"answer\": 511830.0, \"unit\": \"J\"}", "dedupe_signature": "0310b33b70465e8e6bd17ab367f5a64d3c253d3f6f8d4904da2d69576bcf4cca", "difficulty": "easy", "final_answer": {"answer": 511830.0, "unit": "J"}, "id": "heat_q_001444_1880_3.63_75", "license": "Apache-2.0", "prompt": "A 1880 g sample has specific heat 3.63 J/(g*K). How much heat is needed to raise its temperature by 75 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1880 * 3.63 * 75.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 75, "heat_capacity": 3.63, "mass_g": 1880}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=145.2 V and R=26.4 ohm.\nFinal: {\"answer\": 798.6, \"unit\": \"W\"}", "dedupe_signature": "0e247fbca6e4bde3e69914d0e6b4ffc890ac143d8b16d225c750481f4c89695c", "difficulty": "easy", "final_answer": {"answer": 798.6, "unit": "W"}, "id": "ohm_power_001445_145.2_26.4", "license": "Apache-2.0", "prompt": "A resistor has resistance 26.4 ohm and voltage 145.2 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=145.2 V and R=26.4 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 26.4, "voltage": 145.2}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=251 mg, t=313 h, and T_half=105.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 32.1048, \"unit\": \"mg\"}", "dedupe_signature": "69ae358b1ddcabff964f99125990bdf888747ffaf094c1a248d8debe75fc5ab8", "difficulty": "medium", "final_answer": {"answer": 32.1048, "unit": "mg"}, "id": "half_life_001446_251_105.5_313", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 251 mg. Its half-life is 105.5 hours. How many mg remain after 313 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=251 mg, t=313 h, and T_half=105.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 313.0, "half_life": 105.5, "initial_amount": 251.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 2.41 mol * 100.087 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 241.2097, \"unit\": \"g\"}", "dedupe_signature": "95448ab130263610e6139d6c99df2f6bb849f3fdaca8532280c53e2c652581fa", "difficulty": "medium", "final_answer": {"answer": 241.2097, "unit": "g"}, "id": "stoich_mass_001447_calcium_carbonate_2.41", "license": "Apache-2.0", "prompt": "A sample contains 2.41 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 2.41 mol * 100.087 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "calcium carbonate", "molar_mass": 100.087, "moles": 2.41}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 4485 mL to 4.485 L.\n3. Compute M = 4.085 / 4.485.\nFinal: {\"answer\": 0.9108, \"unit\": \"mol/L\"}", "dedupe_signature": "eb2fa80cc3b47a45ccc2e0a68727df994f66372ce1f5eda9137a51573bcbd719", "difficulty": "medium", "final_answer": {"answer": 0.9108, "unit": "mol/L"}, "id": "molarity_001448_4.085_4485", "license": "Apache-2.0", "prompt": "A solution contains 4.085 mol of solute in 4485 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 4485 mL to 4.485 L.\nCompute M = 4.085 / 4.485.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 4.085, "volume_ml": 4485}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.57 y, so each step multiplies y by 1 - h*0.57.\n3. Apply that update for 2 steps and round the final state.\nFinal: {\"answer\": 3.7798, \"unit\": \"state_units\"}", "dedupe_signature": "843905d17abd839579b63c35f7f6f221d6aca538956c2cb6d207cada84807cb4", "difficulty": "medium", "final_answer": {"answer": 3.7798, "unit": "state_units"}, "id": "euler_decay_001449_5.5_0.57_0.3_2", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.57 y with y(0)=5.5, step size h=0.3, for 2 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.57 y, so each step multiplies y by 1 - h*0.57.\nApply that update for 2 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 5.5, "rate": 0.57, "step": 0.3, "steps": 2}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-0.2)=-17.34 and f(3.4)=-14.82.\n3. The interval width is 3.6.\nFinal: {\"answer\": -57.888, \"unit\": \"area_units\"}", "dedupe_signature": "195c50126d45308464c766d7815e2f007c55640edd17af4bf58c8242734424fd", "difficulty": "medium", "final_answer": {"answer": -57.888, "unit": "area_units"}, "id": "trapz_linear_001450_0.7_-17.2_-0.2_3.4", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=0.7x+-17.2 from x=-0.2 to x=3.4. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-0.2)=-17.34 and f(3.4)=-14.82.\nThe interval width is 3.6.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -17.2, "slope": 0.7, "x0": -0.2, "x1": 3.4}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kelvin equals Celsius plus 273.15.\n2. Apply the conversion factor directly to the given value.\n3. Compute -55.5 + 273.15.\nFinal: {\"answer\": 217.65, \"unit\": \"K\"}", "dedupe_signature": "fb7e95a8a951546aa11c2718fa9cae7f4180171213f99122188f3869ec915625", "difficulty": "easy", "final_answer": {"answer": 217.65, "unit": "K"}, "id": "unit_convert_001452_c_to_k_-55.5", "license": "Apache-2.0", "prompt": "Convert -55.5 degC to K. Return the converted value with unit.", "reasoning_trace": "Kelvin equals Celsius plus 273.15.\nApply the conversion factor directly to the given value.\nCompute -55.5 + 273.15.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": -55.5}, "verifier": {"formula": "value + 273.15", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=124 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-95.3424, 141.3509], \"unit\": \"N\"}", "dedupe_signature": "83d9066d5092f413d5a76274c042fe845d3c0679a74d0a32a381ec395b8b4eb4", "difficulty": "medium", "final_answer": {"answer": [-95.3424, 141.3509], "unit": "N"}, "id": "vector_components_001453_170.5_124", "license": "Apache-2.0", "prompt": "A vector has magnitude 170.5 N at 124 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=124 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 124, "magnitude": 170.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. coulomb per second is ampere\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "48805a045e031cc81c82b5470ab04da7b36b25bcbe9557a6b36a1ac2b1333dd8", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_001455_consistent_8b38953d_703693", "license": "Apache-2.0", "prompt": "In sensor calibration case 703693, check dimensional consistency for I = Q / t. The left side has dimensions A and the right side has dimensions A. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\ncoulomb per second is ampere\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "I = Q / t"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: launch_angle_or_vertical_velocity.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"launch_angle_or_vertical_velocity\"]}", "dedupe_signature": "f841b9f143910ea0c516c6a0dd2626641791efee6bb2c2de151a69e334cbe0fe", "difficulty": "easy", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["launch_angle_or_vertical_velocity"]}, "id": "abstain_001457_launch_angle_or_vertical_velocity", "license": "Apache-2.0", "prompt": "Compute projectile range on level ground. The prompt gives initial speed 35.4 m/s but does not give launch angle or vertical velocity. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: launch_angle_or_vertical_velocity.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["launch_angle_or_vertical_velocity"]}, "verifier": {"missing": ["launch_angle_or_vertical_velocity"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 4.35 kg and a = 12.05 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 52.4175, \"unit\": \"N\"}", "dedupe_signature": "21fc9e5f0046478455f56430a0d410a0a716b4290df6149be82660a40e23a16d", "difficulty": "easy", "final_answer": {"answer": 52.4175, "unit": "N"}, "id": "force_001458_4.35_12.05", "license": "Apache-2.0", "prompt": "A cart has mass 4.35 kg and measured acceleration 12.05 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 4.35 kg and a = 12.05 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 12.05, "mass": 4.35}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 5.4^2 and multiply by 0.5 * 8.45.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 123.201, \"unit\": \"J\"}", "dedupe_signature": "d9de8b3f9154d4fd2abcb79d573f9bff2e1d49523598dbd81b2b11799ab00f8d", "difficulty": "easy", "final_answer": {"answer": 123.201, "unit": "J"}, "id": "ke_001459_8.45_5.4", "license": "Apache-2.0", "prompt": "A body of mass 8.45 kg moves at 5.4 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 5.4^2 and multiply by 0.5 * 8.45.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 8.45, "velocity": 5.4}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=77 degrees through the sine of 2 theta.\n3. Substitute v=9.4 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 3.9485, \"unit\": \"m\"}", "dedupe_signature": "7c72ffdf6806aa2b94a7c7d8bcd6d6771ddaa08c29afab45d75868bf5fd012ba", "difficulty": "medium", "final_answer": {"answer": 3.9485, "unit": "m"}, "id": "projectile_range_001460_9.4_77", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 9.4 m/s and angle 77 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=77 degrees through the sine of 2 theta.\nSubstitute v=9.4 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 77, "gravity": 9.81, "speed": 9.4}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 4.33 * 8.314 * 489 / 102.8.\nFinal: {\"answer\": 171.2433, \"unit\": \"kPa\"}", "dedupe_signature": "e551729a44546c7620274144a9ecdfbcd4e6582b05c7df8f28691d524af29ac1", "difficulty": "medium", "final_answer": {"answer": 171.2433, "unit": "kPa"}, "id": "ideal_gas_001461_4.33_489_102.8", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=4.33 mol, T=489 K, and V=102.8 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 4.33 * 8.314 * 489 / 102.8.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 4.33, "temp_k": 489, "volume_l": 102.8}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 560 * 2 * 7.\nFinal: {\"answer\": 7840.0, \"unit\": \"J\"}", "dedupe_signature": "f0eb67747954e498b720c957c3e3486118e172b6ceb86985c34d65ff38595744", "difficulty": "easy", "final_answer": {"answer": 7840.0, "unit": "J"}, "id": "heat_q_001462_560_2_7", "license": "Apache-2.0", "prompt": "A 560 g sample has specific heat 2 J/(g*K). How much heat is needed to raise its temperature by 7 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 560 * 2 * 7.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 7, "heat_capacity": 2.0, "mass_g": 560}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=635 mg, t=249.5 h, and T_half=58 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 32.1978, \"unit\": \"mg\"}", "dedupe_signature": "0824102d6db9ba961ad47b4882b0e26f0cafa2ac95378d11342a6a24778378e6", "difficulty": "medium", "final_answer": {"answer": 32.1978, "unit": "mg"}, "id": "half_life_001464_635_58_249.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 635 mg. Its half-life is 58 hours. How many mg remain after 249.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=635 mg, t=249.5 h, and T_half=58 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 249.5, "half_life": 58.0, "initial_amount": 635.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 1570 mL to 1.57 L.\n3. Compute M = 1.91 / 1.57.\nFinal: {\"answer\": 1.2166, \"unit\": \"mol/L\"}", "dedupe_signature": "9687e1c80f985471cd75598d3907f526692c270d8e782923ad5358d9d47a805d", "difficulty": "medium", "final_answer": {"answer": 1.2166, "unit": "mol/L"}, "id": "molarity_001466_1.91_1570", "license": "Apache-2.0", "prompt": "A solution contains 1.91 mol of solute in 1570 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 1570 mL to 1.57 L.\nCompute M = 1.91 / 1.57.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 1.91, "volume_ml": 1570}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-0.8)=-0.5 and f(7.3)=64.3.\n3. The interval width is 8.1.\nFinal: {\"answer\": 258.39, \"unit\": \"area_units\"}", "dedupe_signature": "6b716ad369bb5e2dfecf27c42c6b16e966e549ae706c32b68d24f0918e3d5ec1", "difficulty": "medium", "final_answer": {"answer": 258.39, "unit": "area_units"}, "id": "trapz_linear_001468_8_5.9_-0.8_7.3", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=8x+5.9 from x=-0.8 to x=7.3. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-0.8)=-0.5 and f(7.3)=64.3.\nThe interval width is 8.1.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 5.9, "slope": 8.0, "x0": -0.8, "x1": 7.3}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.32 and add it to the current value.\nFinal: {\"answer\": [0.884, 0.04, 0.946], \"unit\": \"temperature_units\"}", "dedupe_signature": "f9377b160f6f8d5338f47ccc6b3b0a9f48fec0f8d57645bd53faedd8561572a5", "difficulty": "hard", "final_answer": {"answer": [0.884, 0.04, 0.946], "unit": "temperature_units"}, "id": "heat_step_001469_0.32_1.7_-0.3_1.4_-1.15_2.85", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.7, right=2.85; current interior values are [-0.3, 1.4, -1.15]. Use r=0.32. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.32 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-0.3, 1.4, -1.15], "left": 1.7, "r": 0.32, "right": 2.85}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 100 centimeters in one meter.\n2. Apply the conversion factor directly to the given value.\n3. Compute 4955.5 / 100.\nFinal: {\"answer\": 49.555, \"unit\": \"m\"}", "dedupe_signature": "7668f1a66c7d0d78e26d28768a8f1aa0fba00d9807b163bf78fc22389d9c7866", "difficulty": "easy", "final_answer": {"answer": 49.555, "unit": "m"}, "id": "unit_convert_001470_cm_to_m_4955.5", "license": "Apache-2.0", "prompt": "Convert 4955.5 cm to m. Return the converted value with unit.", "reasoning_trace": "There are 100 centimeters in one meter.\nApply the conversion factor directly to the given value.\nCompute 4955.5 / 100.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 4955.5}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=169 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-199.2703, 38.7342], \"unit\": \"N\"}", "dedupe_signature": "ce8990064b40d31519ff706725eba7f0ffe04b37e2d25959886c307bbd898d3b", "difficulty": "medium", "final_answer": {"answer": [-199.2703, 38.7342], "unit": "N"}, "id": "vector_components_001471_203_169", "license": "Apache-2.0", "prompt": "A vector has magnitude 203 N at 169 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=169 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 169, "magnitude": 203.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-2.0, 7.5], \"unit\": \"dimensionless\"}", "dedupe_signature": "694d4d00d7307b995d087cbddbd6116f78a8f7d0cc5f88cbdf1717ca104e3fe3", "difficulty": "medium", "final_answer": {"answer": [-2.0, 7.5], "unit": "dimensionless"}, "id": "line_two_point_001472_7.25_21.5_-2_7.5", "license": "Apache-2.0", "prompt": "A line passes through points (7.25, -7) and (21.5, -35.5). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 7.25, "x2": 21.5, "y1": -7.0, "y2": -35.5}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. grams cancel with J/(g*K), and kelvin cancels, leaving joules\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "8a3a05e47a8930e2ca3a0d94ebae3549ec51f43d8a62d66cb97ffb3eb854840f", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_001473_consistent_4153435f_314779", "license": "Apache-2.0", "prompt": "In quality-control check case 314779, check dimensional consistency for Q = m * c * DeltaT. The left side has dimensions J and the right side has dimensions J. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\ngrams cancel with J/(g*K), and kelvin cancels, leaving joules\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "Q = m * c * DeltaT"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef running_total_001474(values):\n    total = 0\n    out = []\n    for value in values:\n        total += value\n        out.append(total)\n    return out\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"running_total_001474\"}", "dedupe_signature": "82a66c0b7d0928158c1147ee1480b8ab8ffe2adc0daf87aa37c02d9d555629fa", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "running_total_001474"}, "id": "code_001474_running_total_001474", "license": "Apache-2.0", "prompt": "Write a Python function running_total_001474(values) that returns cumulative sums as a new list. It must not mutate the input list. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "running_total_001474"}, "verifier": {"function": "running_total_001474", "tests": ["assert running_total_001474([1, 2, 3]) == [1, 3, 6]", "xs = [4, -1, 2]; assert running_total_001474(xs) == [4, 3, 5] and xs == [4, -1, 2]", "assert running_total_001474([]) == []"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: recurrence, objective, tie_breaking_rule.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"recurrence\", \"objective\", \"tie_breaking_rule\"]}", "dedupe_signature": "2c93634b24bd5dc7717f51bef4f6fbaf33df38c6c7f6f405ff29915114c70947", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["recurrence", "objective", "tie_breaking_rule"]}, "id": "abstain_001475_recurrence_objective_tie_breaking_rule", "license": "Apache-2.0", "prompt": "Write a dynamic-programming solver for a knapsack scoring problem with 3288 items and budget 70450, but the recurrence, objective, and tie-breaking rule are all absent. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: recurrence, objective, tie_breaking_rule.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["recurrence", "objective", "tie_breaking_rule"]}, "verifier": {"missing": ["recurrence", "objective", "tie_breaking_rule"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 20.45^2 and multiply by 0.5 * 14.95.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 3126.0637, \"unit\": \"J\"}", "dedupe_signature": "53533a0e6d233989e437523092a7f941229a54f30a096df7e93d071d98a557de", "difficulty": "easy", "final_answer": {"answer": 3126.0637, "unit": "J"}, "id": "ke_001477_14.95_20.45", "license": "Apache-2.0", "prompt": "A body of mass 14.95 kg moves at 20.45 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 20.45^2 and multiply by 0.5 * 14.95.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 14.95, "velocity": 20.45}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=76 degrees through the sine of 2 theta.\n3. Substitute v=54.5 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 142.1456, \"unit\": \"m\"}", "dedupe_signature": "44fd63b9adf7f80e3e6ba2c7c0a9d5c9e20b08263b0f4857eb7a8dc1f6452e02", "difficulty": "medium", "final_answer": {"answer": 142.1456, "unit": "m"}, "id": "projectile_range_001478_54.5_76", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 54.5 m/s and angle 76 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=76 degrees through the sine of 2 theta.\nSubstitute v=54.5 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 76, "gravity": 9.81, "speed": 54.5}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1710 * 4.305 * 83.\nFinal: {\"answer\": 611008.65, \"unit\": \"J\"}", "dedupe_signature": "427ee4dd09043ab609b4143851f4c63f2c3b601e501ef3bb2da548a19b8f29b7", "difficulty": "easy", "final_answer": {"answer": 611008.65, "unit": "J"}, "id": "heat_q_001480_1710_4.305_83", "license": "Apache-2.0", "prompt": "A 1710 g sample has specific heat 4.305 J/(g*K). How much heat is needed to raise its temperature by 83 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1710 * 4.305 * 83.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 83, "heat_capacity": 4.305, "mass_g": 1710}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=27.8 V and R=92.7 ohm.\nFinal: {\"answer\": 8.337, \"unit\": \"W\"}", "dedupe_signature": "9c857bb7bbb454a58aefb889b793a66fc1b142b7582260f547f29eeefbf6f6fa", "difficulty": "easy", "final_answer": {"answer": 8.337, "unit": "W"}, "id": "ohm_power_001481_27.8_92.7", "license": "Apache-2.0", "prompt": "A resistor has resistance 92.7 ohm and voltage 27.8 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=27.8 V and R=92.7 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 92.7, "voltage": 27.8}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=757 mg, t=163 h, and T_half=74.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 166.137, \"unit\": \"mg\"}", "dedupe_signature": "9a54431115de0a6be899791df949211458d06ae745e382647c05d789f215b016", "difficulty": "medium", "final_answer": {"answer": 166.137, "unit": "mg"}, "id": "half_life_001482_757_74.5_163", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 757 mg. Its half-life is 74.5 hours. How many mg remain after 163 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=757 mg, t=163 h, and T_half=74.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 163.0, "half_life": 74.5, "initial_amount": 757.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 4.3 mol * 180.156 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 774.6708, \"unit\": \"g\"}", "dedupe_signature": "3b00e57579cd376dd26410cece028f0baa64901836bf2eeae14155ccf3f9494b", "difficulty": "medium", "final_answer": {"answer": 774.6708, "unit": "g"}, "id": "stoich_mass_001483_glucose_4.3", "license": "Apache-2.0", "prompt": "A sample contains 4.3 mol of glucose. Using molar mass 180.156 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 4.3 mol * 180.156 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "glucose", "molar_mass": 180.156, "moles": 4.3}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 1645 mL to 1.645 L.\n3. Compute M = 1.085 / 1.645.\nFinal: {\"answer\": 0.6596, \"unit\": \"mol/L\"}", "dedupe_signature": "2e819d561817761a697d4f179ac425e884ef2bf71104c0624d3dfe2ed04f606e", "difficulty": "medium", "final_answer": {"answer": 0.6596, "unit": "mol/L"}, "id": "molarity_001484_1.085_1645", "license": "Apache-2.0", "prompt": "A solution contains 1.085 mol of solute in 1645 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 1645 mL to 1.645 L.\nCompute M = 1.085 / 1.645.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 1.085, "volume_ml": 1645}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.33 y, so each step multiplies y by 1 - h*0.33.\n3. Apply that update for 6 steps and round the final state.\nFinal: {\"answer\": 6.035, \"unit\": \"state_units\"}", "dedupe_signature": "15300e37d04f1f9a7760c6a83cfc3a45d9a8c7eac4c46efe0e610371f54aa34c", "difficulty": "medium", "final_answer": {"answer": 6.035, "unit": "state_units"}, "id": "euler_decay_001485_43.5_0.33_0.85_6", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.33 y with y(0)=43.5, step size h=0.85, for 6 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.33 y, so each step multiplies y by 1 - h*0.33.\nApply that update for 6 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 43.5, "rate": 0.33, "step": 0.85, "steps": 6}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(4.9)=44.11 and f(6.5)=55.15.\n3. The interval width is 1.6.\nFinal: {\"answer\": 79.408, \"unit\": \"area_units\"}", "dedupe_signature": "a0f58098969dac3ef925b11d4753aee371d04ec403c6d8c7dae533981c2f6626", "difficulty": "medium", "final_answer": {"answer": 79.408, "unit": "area_units"}, "id": "trapz_linear_001486_6.9_10.3_4.9_6.5", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=6.9x+10.3 from x=4.9 to x=6.5. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(4.9)=44.11 and f(6.5)=55.15.\nThe interval width is 1.6.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 10.3, "slope": 6.9, "x0": 4.9, "x1": 6.5}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 100 centimeters in one meter.\n2. Apply the conversion factor directly to the given value.\n3. Compute 625.5 / 100.\nFinal: {\"answer\": 6.255, \"unit\": \"m\"}", "dedupe_signature": "ea42b5f2fda669628f184bee5ae75739aee0c34775990b3040eb6694cbae973b", "difficulty": "easy", "final_answer": {"answer": 6.255, "unit": "m"}, "id": "unit_convert_001488_cm_to_m_625.5", "license": "Apache-2.0", "prompt": "Convert 625.5 cm to m. Return the converted value with unit.", "reasoning_trace": "There are 100 centimeters in one meter.\nApply the conversion factor directly to the given value.\nCompute 625.5 / 100.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 625.5}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [6.9, -19.75], \"unit\": \"dimensionless\"}", "dedupe_signature": "b05d5afd211cf6c7ddae5b0c3d50309e0d21e2ac6efdc2868175abbabd2b3911", "difficulty": "medium", "final_answer": {"answer": [6.9, -19.75], "unit": "dimensionless"}, "id": "line_two_point_001490_-13.5_-2.5_6.9_-19.75", "license": "Apache-2.0", "prompt": "A line passes through points (-13.5, -112.9) and (-2.5, -37). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -13.5, "x2": -2.5, "y1": -112.9, "y2": -37.0}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. m*v is momentum, not energy\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "fbda3f0188f4fecd65e34c8290b37e22470a2d8f72c2cc3dee4bc2f762a4003c", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_001491_inconsistent_1e14b074_170831", "license": "Apache-2.0", "prompt": "In simulation spec case 170831, check dimensional consistency for E = m * v. The left side has dimensions kg*m^2/s^2 and the right side has dimensions kg*m/s. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nm*v is momentum, not energy\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "E = m * v"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: target_schema, valid_examples.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"target_schema\", \"valid_examples\"]}", "dedupe_signature": "f6673b9be770a1ba5536ecc7b10aa9942d25dff9acda4a6db860bd9ff20a3198", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["target_schema", "valid_examples"]}, "id": "abstain_001493_target_schema_valid_examples", "license": "Apache-2.0", "prompt": "Write a parser that converts each field ledger record from batch 650512 into the correct schema, but the prompt does not include the target schema or examples. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: target_schema, valid_examples.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["target_schema", "valid_examples"]}, "verifier": {"missing": ["target_schema", "valid_examples"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 20.85 kg and a = 2.2 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 45.87, \"unit\": \"N\"}", "dedupe_signature": "bef8f026d81f5b58045db55bdd14cf709b846518d7fbdf4ccee76e2e63667838", "difficulty": "easy", "final_answer": {"answer": 45.87, "unit": "N"}, "id": "force_001494_20.85_2.2", "license": "Apache-2.0", "prompt": "A cart has mass 20.85 kg and measured acceleration 2.2 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 20.85 kg and a = 2.2 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 2.2, "mass": 20.85}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 27.15^2 and multiply by 0.5 * 3.55.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 1308.3924, \"unit\": \"J\"}", "dedupe_signature": "76b535f7f9d81c4a895b837acf1368088cc26689cecbf701e8f2d9c2a94ee46a", "difficulty": "easy", "final_answer": {"answer": 1308.3924, "unit": "J"}, "id": "ke_001495_3.55_27.15", "license": "Apache-2.0", "prompt": "A body of mass 3.55 kg moves at 27.15 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 27.15^2 and multiply by 0.5 * 3.55.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 3.55, "velocity": 27.15}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=75 degrees through the sine of 2 theta.\n3. Substitute v=55.2 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 155.3028, \"unit\": \"m\"}", "dedupe_signature": "288e70740690b1d84230a60b06921433ee1c3b3e395dedea41cead00b40cbd6a", "difficulty": "medium", "final_answer": {"answer": 155.3028, "unit": "m"}, "id": "projectile_range_001496_55.2_75", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 55.2 m/s and angle 75 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=75 degrees through the sine of 2 theta.\nSubstitute v=55.2 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 75, "gravity": 9.81, "speed": 55.2}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 3.92 * 8.314 * 530 / 70.8.\nFinal: {\"answer\": 243.9713, \"unit\": \"kPa\"}", "dedupe_signature": "17d173453b8627e640ea7aaae022c92ba02838f23d194128878ae21cf1e5efa8", "difficulty": "medium", "final_answer": {"answer": 243.9713, "unit": "kPa"}, "id": "ideal_gas_001497_3.92_530_70.8", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=3.92 mol, T=530 K, and V=70.8 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 3.92 * 8.314 * 530 / 70.8.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 3.92, "temp_k": 530, "volume_l": 70.8}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1400 * 3.765 * 80.\nFinal: {\"answer\": 421680.0, \"unit\": \"J\"}", "dedupe_signature": "f084ef08fa519bb4eace3d6fb1cfe27ff015e1141d7589b46bb24b180dbcc032", "difficulty": "easy", "final_answer": {"answer": 421680.0, "unit": "J"}, "id": "heat_q_001498_1400_3.765_80", "license": "Apache-2.0", "prompt": "A 1400 g sample has specific heat 3.765 J/(g*K). How much heat is needed to raise its temperature by 80 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1400 * 3.765 * 80.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 80, "heat_capacity": 3.765, "mass_g": 1400}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=77 mg, t=267 h, and T_half=105.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 13.3242, \"unit\": \"mg\"}", "dedupe_signature": "df56dccb94d7b6635db32e23c1ed9b0292ea2c822aecc554a3dfc27f5879c2c6", "difficulty": "medium", "final_answer": {"answer": 13.3242, "unit": "mg"}, "id": "half_life_001500_77_105.5_267", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 77 mg. Its half-life is 105.5 hours. How many mg remain after 267 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=77 mg, t=267 h, and T_half=105.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 267.0, "half_life": 105.5, "initial_amount": 77.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 2.54 mol * 180.156 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 457.5962, \"unit\": \"g\"}", "dedupe_signature": "dfc9a1626cf5bb9cba826dc6b5d738b86a69f0498cf2a17463dbc76fdf4142ba", "difficulty": "medium", "final_answer": {"answer": 457.5962, "unit": "g"}, "id": "stoich_mass_001501_glucose_2.54", "license": "Apache-2.0", "prompt": "A sample contains 2.54 mol of glucose. Using molar mass 180.156 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 2.54 mol * 180.156 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "glucose", "molar_mass": 180.156, "moles": 2.54}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 4550 mL to 4.55 L.\n3. Compute M = 3.1 / 4.55.\nFinal: {\"answer\": 0.6813, \"unit\": \"mol/L\"}", "dedupe_signature": "ace1fac27641dd0fc8d67930a416ddebcb33cdc75b9d0eb25fd3abb2bff0edfd", "difficulty": "medium", "final_answer": {"answer": 0.6813, "unit": "mol/L"}, "id": "molarity_001502_3.1_4550", "license": "Apache-2.0", "prompt": "A solution contains 3.1 mol of solute in 4550 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 4550 mL to 4.55 L.\nCompute M = 3.1 / 4.55.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 3.1, "volume_ml": 4550}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.71 y, so each step multiplies y by 1 - h*0.71.\n3. Apply that update for 9 steps and round the final state.\nFinal: {\"answer\": 0.0016, \"unit\": \"state_units\"}", "dedupe_signature": "04d85102f2e3c9a9d5d6ebca1b11102dccf08e4bf42efe763f90e3f83130e5e1", "difficulty": "medium", "final_answer": {"answer": 0.0016, "unit": "state_units"}, "id": "euler_decay_001503_39.5_0.71_0.95_9", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.71 y with y(0)=39.5, step size h=0.95, for 9 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.71 y, so each step multiplies y by 1 - h*0.71.\nApply that update for 9 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 39.5, "rate": 0.71, "step": 0.95, "steps": 9}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(9.6)=58.86 and f(15.5)=88.95.\n3. The interval width is 5.9.\nFinal: {\"answer\": 436.0395, \"unit\": \"area_units\"}", "dedupe_signature": "19aa9a111e16ff82b4205a5b2a661324166e31fa3ce3f538b0915018f25d20bb", "difficulty": "medium", "final_answer": {"answer": 436.0395, "unit": "area_units"}, "id": "trapz_linear_001504_5.1_9.9_9.6_15.5", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=5.1x+9.9 from x=9.6 to x=15.5. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(9.6)=58.86 and f(15.5)=88.95.\nThe interval width is 5.9.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 9.9, "slope": 5.1, "x0": 9.6, "x1": 15.5}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.12 and add it to the current value.\nFinal: {\"answer\": [0.614, 2.028, -0.908], \"unit\": \"temperature_units\"}", "dedupe_signature": "0d26afcdb13c2cd2eb4e17d211e596e93e8a5537bffe5b62b375fe2f7ab9f178", "difficulty": "hard", "final_answer": {"answer": [0.614, 2.028, -0.908], "unit": "temperature_units"}, "id": "heat_step_001505_0.12_2.75_-0.1_3.0_-2.0_2.1", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=2.75, right=2.1; current interior values are [-0.1, 3.0, -2.0]. Use r=0.12. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.12 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-0.1, 3.0, -2.0], "left": 2.75, "r": 0.12, "right": 2.1}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 100 centimeters in one meter.\n2. Apply the conversion factor directly to the given value.\n3. Compute 4665.5 / 100.\nFinal: {\"answer\": 46.655, \"unit\": \"m\"}", "dedupe_signature": "735cc40f397c25197796cf877af83adda832469d2bdfd284f4cf4d208837b231", "difficulty": "easy", "final_answer": {"answer": 46.655, "unit": "m"}, "id": "unit_convert_001506_cm_to_m_4665.5", "license": "Apache-2.0", "prompt": "Convert 4665.5 cm to m. Return the converted value with unit.", "reasoning_trace": "There are 100 centimeters in one meter.\nApply the conversion factor directly to the given value.\nCompute 4665.5 / 100.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 4665.5}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. velocity times time gives distance, not acceleration\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "c2a254156faa871af844219633383655e579104611a8cafca7f73801e571f22d", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_001509_inconsistent_7481c798_391081", "license": "Apache-2.0", "prompt": "In field worksheet case 391081, check dimensional consistency for a = v * t. The left side has dimensions m/s^2 and the right side has dimensions m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nvelocity times time gives distance, not acceleration\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "a = v * t"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=32 degrees through the sine of 2 theta.\n3. Substitute v=78 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 557.4172, \"unit\": \"m\"}", "dedupe_signature": "e4db49e13771f2a6178ff28cfc67a23d5b5906f011b7be99fcbb894d966fb4b5", "difficulty": "medium", "final_answer": {"answer": 557.4172, "unit": "m"}, "id": "projectile_range_001514_78_32", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 78 m/s and angle 32 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=32 degrees through the sine of 2 theta.\nSubstitute v=78 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 32, "gravity": 9.81, "speed": 78.0}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 0.53 * 8.314 * 302 / 104.6.\nFinal: {\"answer\": 12.7222, \"unit\": \"kPa\"}", "dedupe_signature": "ba6e1965a52a9ea22b6981885b67e41a60ec12710cf161b145537b6fa569c8ff", "difficulty": "medium", "final_answer": {"answer": 12.7222, "unit": "kPa"}, "id": "ideal_gas_001515_0.53_302_104.6", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=0.53 mol, T=302 K, and V=104.6 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 0.53 * 8.314 * 302 / 104.6.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 0.53, "temp_k": 302, "volume_l": 104.6}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 730 * 2.375 * 11.\nFinal: {\"answer\": 19071.25, \"unit\": \"J\"}", "dedupe_signature": "633e66f1698d663729c437b9fef286ead32cb46050d6d246e530fec9652ac990", "difficulty": "easy", "final_answer": {"answer": 19071.25, "unit": "J"}, "id": "heat_q_001516_730_2.375_11", "license": "Apache-2.0", "prompt": "A 730 g sample has specific heat 2.375 J/(g*K). How much heat is needed to raise its temperature by 11 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 730 * 2.375 * 11.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 11, "heat_capacity": 2.375, "mass_g": 730}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=49 mg, t=303.5 h, and T_half=117.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 8.1779, \"unit\": \"mg\"}", "dedupe_signature": "36244919f999412ca7d0e801b189a7b6059ca7b3de2cfe3c8e4dd689b7812aa9", "difficulty": "medium", "final_answer": {"answer": 8.1779, "unit": "mg"}, "id": "half_life_001518_49_117.5_303.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 49 mg. Its half-life is 117.5 hours. How many mg remain after 303.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=49 mg, t=303.5 h, and T_half=117.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 303.5, "half_life": 117.5, "initial_amount": 49.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 5.78 mol * 58.44 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 337.7832, \"unit\": \"g\"}", "dedupe_signature": "ebb311caf342f2ab5506ab0327c2117701703d7bf56bc94e5cf86d6bd8bd97bb", "difficulty": "medium", "final_answer": {"answer": 337.7832, "unit": "g"}, "id": "stoich_mass_001519_sodium_chloride_5.78", "license": "Apache-2.0", "prompt": "A sample contains 5.78 mol of sodium chloride. Using molar mass 58.44 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 5.78 mol * 58.44 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "sodium chloride", "molar_mass": 58.44, "moles": 5.78}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 365 mL to 0.365 L.\n3. Compute M = 3.375 / 0.365.\nFinal: {\"answer\": 9.2466, \"unit\": \"mol/L\"}", "dedupe_signature": "802d759e1bac7f20badabcf94bd44344a19f2d232dcd47c9a175a1542f07683d", "difficulty": "medium", "final_answer": {"answer": 9.2466, "unit": "mol/L"}, "id": "molarity_001520_3.375_365", "license": "Apache-2.0", "prompt": "A solution contains 3.375 mol of solute in 365 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 365 mL to 0.365 L.\nCompute M = 3.375 / 0.365.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 3.375, "volume_ml": 365}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-1.7)=20.71 and f(-0.7)=15.41.\n3. The interval width is 1.\nFinal: {\"answer\": 18.06, \"unit\": \"area_units\"}", "dedupe_signature": "6823076c29f19dbd2ddb0ac6b3293a99124e5b040348539404dd8581343b9c4e", "difficulty": "medium", "final_answer": {"answer": 18.06, "unit": "area_units"}, "id": "trapz_linear_001522_-5.3_11.7_-1.7_-0.7", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-5.3x+11.7 from x=-1.7 to x=-0.7. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-1.7)=20.71 and f(-0.7)=15.41.\nThe interval width is 1.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 11.7, "slope": -5.3, "x0": -1.7, "x1": -0.7}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.34 and add it to the current value.\nFinal: {\"answer\": [0.894, 0.613, 1.191], \"unit\": \"temperature_units\"}", "dedupe_signature": "21fabfc564666c826a64007e6904849ba4ca99dfd916e221a44a9c965d7047a9", "difficulty": "hard", "final_answer": {"answer": [0.894, 0.613, 1.191], "unit": "temperature_units"}, "id": "heat_step_001523_0.34_-0.2_0.35_2.5_-0.9_1.85", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-0.2, right=1.85; current interior values are [0.35, 2.5, -0.9]. Use r=0.34. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.34 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [0.35, 2.5, -0.9], "left": -0.2, "r": 0.34, "right": 1.85}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=214 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-310.4746, -209.4177], \"unit\": \"N\"}", "dedupe_signature": "da3808abd460d5ee20590bf9a0652ef49f48705a70ddb397b3d134735909788d", "difficulty": "medium", "final_answer": {"answer": [-310.4746, -209.4177], "unit": "N"}, "id": "vector_components_001525_374.5_214", "license": "Apache-2.0", "prompt": "A vector has magnitude 374.5 N at 214 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=214 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 214, "magnitude": 374.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. mass times acceleration has newton dimensions\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "f6fb69eb09019ede35de0db6dc7c72da13c43fb63d3a2aaad50a319e5e2294bf", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_001527_consistent_03f5e041_722344", "license": "Apache-2.0", "prompt": "In field worksheet case 722344, check dimensional consistency for F = m * a. The left side has dimensions kg*m/s^2 and the right side has dimensions kg*m/s^2. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nmass times acceleration has newton dimensions\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "F = m * a"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef normalize_001528(values):\n    total = sum(values)\n    if total == 0:\n        raise ValueError('cannot normalize zero-sum values')\n    return [v / total for v in values]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"normalize_001528\"}", "dedupe_signature": "5c690c41021e7d1e709fcf85c7f64186ddc4098518a84a6ac7f95356c17728c6", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "normalize_001528"}, "id": "code_001528_normalize_001528", "license": "Apache-2.0", "prompt": "Write a Python function normalize_001528(values) that returns a new list whose values sum to 1. Raise ValueError if the sum is zero. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "normalize_001528"}, "verifier": {"function": "normalize_001528", "tests": ["out = normalize_001528([2, 3, 5]); assert len(out) == 3", "assert abs(sum(normalize_001528([2, 3, 5])) - 1.0) < 1e-12", "assert normalize_001528([1, 1]) == [0.5, 0.5]", "try:\n    normalize_001528([1, -1])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: required_fields, allowed_transformations.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"required_fields\", \"allowed_transformations\"]}", "dedupe_signature": "08a175e5910e8139b59dd44c921aabcb9a743db18bedd215eaa5907bbac0e174", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["required_fields", "allowed_transformations"]}, "id": "abstain_001529_required_fields_allowed_transformations", "license": "Apache-2.0", "prompt": "Write a sanitizer for valid mobile experiment records in release 963052, but the prompt does not state which fields are required or which transformations are allowed. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: required_fields, allowed_transformations.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["required_fields", "allowed_transformations"]}, "verifier": {"missing": ["required_fields", "allowed_transformations"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 3 kg and a = 12.65 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 37.95, \"unit\": \"N\"}", "dedupe_signature": "8bf3a5babc922eec46c16297c14412933d95ea9ebe0984ed4487bf652219a92c", "difficulty": "easy", "final_answer": {"answer": 37.95, "unit": "N"}, "id": "force_001530_3_12.65", "license": "Apache-2.0", "prompt": "A cart has mass 3 kg and measured acceleration 12.65 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 3 kg and a = 12.65 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 12.65, "mass": 3.0}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 4.2^2 and multiply by 0.5 * 11.35.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 100.107, \"unit\": \"J\"}", "dedupe_signature": "8e84bd978c445ad327778a8a3603bcc806803e778a15451844455fff355add20", "difficulty": "easy", "final_answer": {"answer": 100.107, "unit": "J"}, "id": "ke_001531_11.35_4.2", "license": "Apache-2.0", "prompt": "A body of mass 11.35 kg moves at 4.2 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 4.2^2 and multiply by 0.5 * 11.35.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 11.35, "velocity": 4.2}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=28 degrees through the sine of 2 theta.\n3. Substitute v=43.1 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 156.9856, \"unit\": \"m\"}", "dedupe_signature": "d1b7900d2d9292c4fea297e78548acdd3c09f374d0242f289e01b11e78ef72e6", "difficulty": "medium", "final_answer": {"answer": 156.9856, "unit": "m"}, "id": "projectile_range_001532_43.1_28", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 43.1 m/s and angle 28 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=28 degrees through the sine of 2 theta.\nSubstitute v=43.1 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 28, "gravity": 9.81, "speed": 43.1}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 1.77 * 8.314 * 360 / 76.1.\nFinal: {\"answer\": 69.6147, \"unit\": \"kPa\"}", "dedupe_signature": "98dfbc780d8d6d84946f10971f1ebf3496c0104630ab38cca7ae415b4cd4d830", "difficulty": "medium", "final_answer": {"answer": 69.6147, "unit": "kPa"}, "id": "ideal_gas_001533_1.77_360_76.1", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=1.77 mol, T=360 K, and V=76.1 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 1.77 * 8.314 * 360 / 76.1.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 1.77, "temp_k": 360, "volume_l": 76.1}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 40 * 3.355 * 35.\nFinal: {\"answer\": 4697.0, \"unit\": \"J\"}", "dedupe_signature": "cecd8e4e838e0a4d69a6038695f184e7c0fa57ffa3c3c645c69ee197650237b0", "difficulty": "easy", "final_answer": {"answer": 4697.0, "unit": "J"}, "id": "heat_q_001534_40_3.355_35", "license": "Apache-2.0", "prompt": "A 40 g sample has specific heat 3.355 J/(g*K). How much heat is needed to raise its temperature by 35 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 40 * 3.355 * 35.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 35, "heat_capacity": 3.355, "mass_g": 40}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=20 V and R=148.3 ohm.\nFinal: {\"answer\": 2.6972, \"unit\": \"W\"}", "dedupe_signature": "f7f93c52c63418ffafd6bd1d9138a27506aa9231b3b3f2e06ccfba8748e5386f", "difficulty": "easy", "final_answer": {"answer": 2.6972, "unit": "W"}, "id": "ohm_power_001535_20_148.3", "license": "Apache-2.0", "prompt": "A resistor has resistance 148.3 ohm and voltage 20 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=20 V and R=148.3 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 148.3, "voltage": 20.0}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=345.5 mg, t=360 h, and T_half=60 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 5.3984, \"unit\": \"mg\"}", "dedupe_signature": "bb18fb6a9e679a4b612476d1d82e864742b37016ae9f13d5e9f4dacaedfee960", "difficulty": "medium", "final_answer": {"answer": 5.3984, "unit": "mg"}, "id": "half_life_001536_345.5_60_360", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 345.5 mg. Its half-life is 60 hours. How many mg remain after 360 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=345.5 mg, t=360 h, and T_half=60 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 360.0, "half_life": 60.0, "initial_amount": 345.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 2.89 mol * 44.01 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 127.1889, \"unit\": \"g\"}", "dedupe_signature": "bf3d0ed1713a58a9ee0de4995a3cf3d74e11e85b3980bbd3b6db58bb06c381da", "difficulty": "medium", "final_answer": {"answer": 127.1889, "unit": "g"}, "id": "stoich_mass_001537_carbon_dioxide_2.89", "license": "Apache-2.0", "prompt": "A sample contains 2.89 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 2.89 mol * 44.01 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "carbon dioxide", "molar_mass": 44.01, "moles": 2.89}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 450 mL to 0.45 L.\n3. Compute M = 2.885 / 0.45.\nFinal: {\"answer\": 6.4111, \"unit\": \"mol/L\"}", "dedupe_signature": "b565f42c5d755ac459e99d56467075989a0d9efc41bdc23f47976e8cae035215", "difficulty": "medium", "final_answer": {"answer": 6.4111, "unit": "mol/L"}, "id": "molarity_001538_2.885_450", "license": "Apache-2.0", "prompt": "A solution contains 2.885 mol of solute in 450 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 450 mL to 0.45 L.\nCompute M = 2.885 / 0.45.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 2.885, "volume_ml": 450}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.4 y, so each step multiplies y by 1 - h*0.4.\n3. Apply that update for 10 steps and round the final state.\nFinal: {\"answer\": 0.0337, \"unit\": \"state_units\"}", "dedupe_signature": "9ee62fe6fd55bbe1a19f963f6e1961bbdbf4decc5b94c9d89ac9184da45c32dd", "difficulty": "medium", "final_answer": {"answer": 0.0337, "unit": "state_units"}, "id": "euler_decay_001539_79.5_0.4_1.35_10", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.4 y with y(0)=79.5, step size h=1.35, for 10 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.4 y, so each step multiplies y by 1 - h*0.4.\nApply that update for 10 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 79.5, "rate": 0.4, "step": 1.35, "steps": 10}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-3.7)=-19.55 and f(3.8)=-15.8.\n3. The interval width is 7.5.\nFinal: {\"answer\": -132.5625, \"unit\": \"area_units\"}", "dedupe_signature": "9c32933bdf1315fbd5dc45324a2f0f2c9907f6d916932eb874dc28ab8b845975", "difficulty": "medium", "final_answer": {"answer": -132.5625, "unit": "area_units"}, "id": "trapz_linear_001540_0.5_-17.7_-3.7_3.8", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=0.5x+-17.7 from x=-3.7 to x=3.8. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-3.7)=-19.55 and f(3.8)=-15.8.\nThe interval width is 7.5.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -17.7, "slope": 0.5, "x0": -3.7, "x1": 3.8}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.2 and add it to the current value.\nFinal: {\"answer\": [0.0, 1.12, -0.31], \"unit\": \"temperature_units\"}", "dedupe_signature": "75c192bf5622615e41c65ab66b8a97991a237b4804b47446b45119d7d1c005e1", "difficulty": "hard", "final_answer": {"answer": [0.0, 1.12, -0.31], "unit": "temperature_units"}, "id": "heat_step_001541_0.2_-0.65_-0.6_2.45_-1.15_-0.55", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-0.65, right=-0.55; current interior values are [-0.6, 2.45, -1.15]. Use r=0.2. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.2 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-0.6, 2.45, -1.15], "left": -0.65, "r": 0.2, "right": -0.55}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kelvin equals Celsius plus 273.15.\n2. Apply the conversion factor directly to the given value.\n3. Compute 11.0 + 273.15.\nFinal: {\"answer\": 284.15, \"unit\": \"K\"}", "dedupe_signature": "d1627a5c7b775e14a9110b87151a7dd88af1226341bc98a1855e5669fd4dfba7", "difficulty": "easy", "final_answer": {"answer": 284.15, "unit": "K"}, "id": "unit_convert_001542_c_to_k_11", "license": "Apache-2.0", "prompt": "Convert 11 degC to K. Return the converted value with unit.", "reasoning_trace": "Kelvin equals Celsius plus 273.15.\nApply the conversion factor directly to the given value.\nCompute 11.0 + 273.15.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 11.0}, "verifier": {"formula": "value + 273.15", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=33 degrees and keep the unit as newtons.\nFinal: {\"answer\": [132.0906, 85.7806], \"unit\": \"N\"}", "dedupe_signature": "6992a310c9aef3ef6e7174b7a4a9967d2f5cbab45fd00b16ee8e310433d744e8", "difficulty": "medium", "final_answer": {"answer": [132.0906, 85.7806], "unit": "N"}, "id": "vector_components_001543_157.5_33", "license": "Apache-2.0", "prompt": "A vector has magnitude 157.5 N at 33 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=33 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 33, "magnitude": 157.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [4.05, -11.5], \"unit\": \"dimensionless\"}", "dedupe_signature": "fcf5446fb130a6abc1dff5bc14e7e5da86dc105b2863bfebe0bb45a8fff32b24", "difficulty": "medium", "final_answer": {"answer": [4.05, -11.5], "unit": "dimensionless"}, "id": "line_two_point_001544_-7.25_2_4.05_-11.5", "license": "Apache-2.0", "prompt": "A line passes through points (-7.25, -40.8625) and (2, -3.4). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -7.25, "x2": 2.0, "y1": -40.8625, "y2": -3.4000000000000004}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef finite_differences_001546(values):\n    return [values[i + 1] - values[i] for i in range(len(values) - 1)]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"finite_differences_001546\"}", "dedupe_signature": "803a3265a989bd80e35fb1cdccac287f206f40a183bf10f098a43ec3c9cf2fd7", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "finite_differences_001546"}, "id": "code_001546_finite_differences_001546", "license": "Apache-2.0", "prompt": "Write a Python function finite_differences_001546(values) that returns the list of successive differences values[i+1] - values[i]. It must return [] for fewer than two values. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "finite_differences_001546"}, "verifier": {"function": "finite_differences_001546", "tests": ["assert finite_differences_001546([1, 4, 9, 16]) == [3, 5, 7]", "assert finite_differences_001546([5]) == []", "assert finite_differences_001546([]) == []"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: required_fields, allowed_transformations.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"required_fields\", \"allowed_transformations\"]}", "dedupe_signature": "a6eeb932ef242ac837a7d330a893ac97e75463b6690105e4aeaea058cef9d90a", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["required_fields", "allowed_transformations"]}, "id": "abstain_001547_required_fields_allowed_transformations", "license": "Apache-2.0", "prompt": "Write a sanitizer for valid field survey records in release 350122, but the prompt does not state which fields are required or which transformations are allowed. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: required_fields, allowed_transformations.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["required_fields", "allowed_transformations"]}, "verifier": {"missing": ["required_fields", "allowed_transformations"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 12.05 kg and a = 12.55 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 151.2275, \"unit\": \"N\"}", "dedupe_signature": "94324ea33b81f26eb279d59a9529add6e769e6f5e30d67e5818b99f049f41429", "difficulty": "easy", "final_answer": {"answer": 151.2275, "unit": "N"}, "id": "force_001548_12.05_12.55", "license": "Apache-2.0", "prompt": "A cart has mass 12.05 kg and measured acceleration 12.55 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 12.05 kg and a = 12.55 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 12.55, "mass": 12.05}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 4.92 * 8.314 * 603 / 41.7.\nFinal: {\"answer\": 591.5022, \"unit\": \"kPa\"}", "dedupe_signature": "f2a44f8c2024ff4f237a922d6625a7a0c0e177bfe743ab299b1a622e07265c58", "difficulty": "medium", "final_answer": {"answer": 591.5022, "unit": "kPa"}, "id": "ideal_gas_001551_4.92_603_41.7", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=4.92 mol, T=603 K, and V=41.7 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 4.92 * 8.314 * 603 / 41.7.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 4.92, "temp_k": 603, "volume_l": 41.7}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 155 * 1.12 * 73.\nFinal: {\"answer\": 12672.8, \"unit\": \"J\"}", "dedupe_signature": "b65d579df01478f8911d5a54a495110dd2847e0a37f0d87f5199c679f2f9ebec", "difficulty": "easy", "final_answer": {"answer": 12672.8, "unit": "J"}, "id": "heat_q_001552_155_1.12_73", "license": "Apache-2.0", "prompt": "A 155 g sample has specific heat 1.12 J/(g*K). How much heat is needed to raise its temperature by 73 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 155 * 1.12 * 73.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 73, "heat_capacity": 1.12, "mass_g": 155}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=88.5 V and R=23.7 ohm.\nFinal: {\"answer\": 330.4747, \"unit\": \"W\"}", "dedupe_signature": "450619418c7034187e0f41f397ae514a88dc33b70eebaf28169f8dd2eb086b91", "difficulty": "easy", "final_answer": {"answer": 330.4747, "unit": "W"}, "id": "ohm_power_001553_88.5_23.7", "license": "Apache-2.0", "prompt": "A resistor has resistance 23.7 ohm and voltage 88.5 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=88.5 V and R=23.7 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 23.7, "voltage": 88.5}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=932 mg, t=218.5 h, and T_half=101.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 209.5974, \"unit\": \"mg\"}", "dedupe_signature": "48f8792b375ee7d4cf5f1013d0c0b75b0897183b9df431b5ca9111cfe9d583a7", "difficulty": "medium", "final_answer": {"answer": 209.5974, "unit": "mg"}, "id": "half_life_001554_932_101.5_218.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 932 mg. Its half-life is 101.5 hours. How many mg remain after 218.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=932 mg, t=218.5 h, and T_half=101.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 218.5, "half_life": 101.5, "initial_amount": 932.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 4.16 mol * 100.087 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 416.3619, \"unit\": \"g\"}", "dedupe_signature": "8cb0ee79a697bd5424d8784e8cbbe4c7345274b5d4592170964a829b2db2564c", "difficulty": "medium", "final_answer": {"answer": 416.3619, "unit": "g"}, "id": "stoich_mass_001555_calcium_carbonate_4.16", "license": "Apache-2.0", "prompt": "A sample contains 4.16 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 4.16 mol * 100.087 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "calcium carbonate", "molar_mass": 100.087, "moles": 4.16}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 2595 mL to 2.595 L.\n3. Compute M = 4.925 / 2.595.\nFinal: {\"answer\": 1.8979, \"unit\": \"mol/L\"}", "dedupe_signature": "e416f5194600fd4d00ab308c609b908bf6fbf4c59af57d514ab93865edef544f", "difficulty": "medium", "final_answer": {"answer": 1.8979, "unit": "mol/L"}, "id": "molarity_001556_4.925_2595", "license": "Apache-2.0", "prompt": "A solution contains 4.925 mol of solute in 2595 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 2595 mL to 2.595 L.\nCompute M = 4.925 / 2.595.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 4.925, "volume_ml": 2595}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.94 y, so each step multiplies y by 1 - h*0.94.\n3. Apply that update for 2 steps and round the final state.\nFinal: {\"answer\": 2.5062, \"unit\": \"state_units\"}", "dedupe_signature": "bcc4d4fce4af72675d9168ac8c8c35b48526bab80b89068de9778642587f0feb", "difficulty": "medium", "final_answer": {"answer": 2.5062, "unit": "state_units"}, "id": "euler_decay_001557_12_0.94_1.55_2", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.94 y with y(0)=12, step size h=1.55, for 2 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.94 y, so each step multiplies y by 1 - h*0.94.\nApply that update for 2 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 12.0, "rate": 0.94, "step": 1.55, "steps": 2}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(3.1)=17.34 and f(7.5)=32.3.\n3. The interval width is 4.4.\nFinal: {\"answer\": 109.208, \"unit\": \"area_units\"}", "dedupe_signature": "93d0f28bc033c8935ca3759ad829c57f5450d2c6126c125ff7aca6e0c19d481b", "difficulty": "medium", "final_answer": {"answer": 109.208, "unit": "area_units"}, "id": "trapz_linear_001558_3.4_6.8_3.1_7.5", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=3.4x+6.8 from x=3.1 to x=7.5. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(3.1)=17.34 and f(7.5)=32.3.\nThe interval width is 4.4.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 6.8, "slope": 3.4, "x0": 3.1, "x1": 7.5}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.18 and add it to the current value.\nFinal: {\"answer\": [0.636, -0.669, -0.914], \"unit\": \"temperature_units\"}", "dedupe_signature": "fbdac88b335586a849fb661b9a20af06b3547bdb2fa4f9641735bc12cf6c5fe9", "difficulty": "hard", "final_answer": {"answer": [0.636, -0.669, -0.914], "unit": "temperature_units"}, "id": "heat_step_001559_0.18_-0.6_1.5_-1.2_-0.95_-0.5", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-0.6, right=-0.5; current interior values are [1.5, -1.2, -0.95]. Use r=0.18. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.18 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [1.5, -1.2, -0.95], "left": -0.6, "r": 0.18, "right": -0.5}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kelvin equals Celsius plus 273.15.\n2. Apply the conversion factor directly to the given value.\n3. Compute 175.0 + 273.15.\nFinal: {\"answer\": 448.15, \"unit\": \"K\"}", "dedupe_signature": "3864df94fb853b71bd0d204539c49d4f9c50a401a3a0dcf0b600b5e8f1c4f591", "difficulty": "easy", "final_answer": {"answer": 448.15, "unit": "K"}, "id": "unit_convert_001560_c_to_k_175", "license": "Apache-2.0", "prompt": "Convert 175 degC to K. Return the converted value with unit.", "reasoning_trace": "Kelvin equals Celsius plus 273.15.\nApply the conversion factor directly to the given value.\nCompute 175.0 + 273.15.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 175.0}, "verifier": {"formula": "value + 273.15", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=50 degrees and keep the unit as newtons.\nFinal: {\"answer\": [118.5943, 141.3352], \"unit\": \"N\"}", "dedupe_signature": "7d2f7a6d80be884bf8a8902831ea4e607d6514a5f80e0d965ee8103a45209bf0", "difficulty": "medium", "final_answer": {"answer": [118.5943, 141.3352], "unit": "N"}, "id": "vector_components_001561_184.5_50", "license": "Apache-2.0", "prompt": "A vector has magnitude 184.5 N at 50 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=50 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 50, "magnitude": 184.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [7.15, 9.25], \"unit\": \"dimensionless\"}", "dedupe_signature": "93c2c6ee7ec981c26f8dc68498b087356ad613ac70c371297c2fd4161914d04b", "difficulty": "medium", "final_answer": {"answer": [7.15, 9.25], "unit": "dimensionless"}, "id": "line_two_point_001562_-4.25_6.25_7.15_9.25", "license": "Apache-2.0", "prompt": "A line passes through points (-4.25, -21.1375) and (6.25, 53.9375). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -4.25, "x2": 6.25, "y1": -21.137500000000003, "y2": 53.9375}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. volt squared divided by ohm is watt\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "8188380788581a8645bbd54773c7706029d338b8e88db438eae467782befea21", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_001563_consistent_82e93f3d_199215", "license": "Apache-2.0", "prompt": "In simulation spec case 199215, check dimensional consistency for P = V^2 / R. The left side has dimensions W and the right side has dimensions W. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nvolt squared divided by ohm is watt\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "P = V^2 / R"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef finite_differences_001564(values):\n    return [values[i + 1] - values[i] for i in range(len(values) - 1)]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"finite_differences_001564\"}", "dedupe_signature": "a12bc631a0257375bbdca2faed5e60869c59f4b98a8965dc9137f52a78a7bc91", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "finite_differences_001564"}, "id": "code_001564_finite_differences_001564", "license": "Apache-2.0", "prompt": "Write a Python function finite_differences_001564(values) that returns the list of successive differences values[i+1] - values[i]. It must return [] for fewer than two values. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "finite_differences_001564"}, "verifier": {"function": "finite_differences_001564", "tests": ["assert finite_differences_001564([1, 4, 9, 16]) == [3, 5, 7]", "assert finite_differences_001564([5]) == []", "assert finite_differences_001564([]) == []"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: left_boundary, right_boundary.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"left_boundary\", \"right_boundary\"]}", "dedupe_signature": "835b45fb2e4b806bb48a32bafa415aaa687055ccff77ed5c7af4de11bb3a551b", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["left_boundary", "right_boundary"]}, "id": "abstain_001565_left_boundary_right_boundary", "license": "Apache-2.0", "prompt": "Solve the 1D heat equation after one finite-difference step. The prompt gives r=0.4 and interior values [2.9, -1.55, 1.85], but gives no boundary values. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: left_boundary, right_boundary.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["left_boundary", "right_boundary"]}, "verifier": {"missing": ["left_boundary", "right_boundary"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 15 kg and a = 14.65 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 219.75, \"unit\": \"N\"}", "dedupe_signature": "ab1a0e41153d7676f992b42977185bc2b36aea2260464c762a3bd82492691a7a", "difficulty": "easy", "final_answer": {"answer": 219.75, "unit": "N"}, "id": "force_001566_15_14.65", "license": "Apache-2.0", "prompt": "A cart has mass 15 kg and measured acceleration 14.65 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 15 kg and a = 14.65 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 14.65, "mass": 15.0}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 5.85^2 and multiply by 0.5 * 16.25.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 278.0578, \"unit\": \"J\"}", "dedupe_signature": "ecbac1038f49e69db860f84216d9ad6013afb224ad4b9ca6b0c96345aad8a4b2", "difficulty": "easy", "final_answer": {"answer": 278.0578, "unit": "J"}, "id": "ke_001567_16.25_5.85", "license": "Apache-2.0", "prompt": "A body of mass 16.25 kg moves at 5.85 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 5.85^2 and multiply by 0.5 * 16.25.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 16.25, "velocity": 5.85}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=75 degrees through the sine of 2 theta.\n3. Substitute v=18.5 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 17.4439, \"unit\": \"m\"}", "dedupe_signature": "e1479835778abc3ee43dfe9474118129e931878eedb859f0504116205efc670d", "difficulty": "medium", "final_answer": {"answer": 17.4439, "unit": "m"}, "id": "projectile_range_001568_18.5_75", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 18.5 m/s and angle 75 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=75 degrees through the sine of 2 theta.\nSubstitute v=18.5 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 75, "gravity": 9.81, "speed": 18.5}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 3.76 * 8.314 * 471 / 113.0.\nFinal: {\"answer\": 130.2988, \"unit\": \"kPa\"}", "dedupe_signature": "be38479c79c42379be015911cd81825c4674d88eb7d75fe7aeac748c69c46b89", "difficulty": "medium", "final_answer": {"answer": 130.2988, "unit": "kPa"}, "id": "ideal_gas_001569_3.76_471_113.0", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=3.76 mol, T=471 K, and V=113.0 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 3.76 * 8.314 * 471 / 113.0.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 3.76, "temp_k": 471, "volume_l": 113.0}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1215 * 1.825 * 10.\nFinal: {\"answer\": 22173.75, \"unit\": \"J\"}", "dedupe_signature": "4e58d111d75b43d24cfc4b35ef15a986641b22cb0bf7cd793f2d2e7a66ece3e6", "difficulty": "easy", "final_answer": {"answer": 22173.75, "unit": "J"}, "id": "heat_q_001570_1215_1.825_10", "license": "Apache-2.0", "prompt": "A 1215 g sample has specific heat 1.825 J/(g*K). How much heat is needed to raise its temperature by 10 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1215 * 1.825 * 10.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 10, "heat_capacity": 1.825, "mass_g": 1215}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=23.6 V and R=189.1 ohm.\nFinal: {\"answer\": 2.9453, \"unit\": \"W\"}", "dedupe_signature": "a161c3489221c24603fad94888b79260b57f6228e4cfefc0e822579b2670e2ec", "difficulty": "easy", "final_answer": {"answer": 2.9453, "unit": "W"}, "id": "ohm_power_001571_23.6_189.1", "license": "Apache-2.0", "prompt": "A resistor has resistance 189.1 ohm and voltage 23.6 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=23.6 V and R=189.1 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 189.1, "voltage": 23.6}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=604.5 mg, t=311.5 h, and T_half=47 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 6.1132, \"unit\": \"mg\"}", "dedupe_signature": "88f5b8a96a7a7930beee14435d9dcdd7ee01f19f17503bd8926d968f866b345f", "difficulty": "medium", "final_answer": {"answer": 6.1132, "unit": "mg"}, "id": "half_life_001572_604.5_47_311.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 604.5 mg. Its half-life is 47 hours. How many mg remain after 311.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=604.5 mg, t=311.5 h, and T_half=47 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 311.5, "half_life": 47.0, "initial_amount": 604.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 1.05 mol * 180.156 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 189.1638, \"unit\": \"g\"}", "dedupe_signature": "cc89482db80212d640caca0ce0d72d666f6854dabff604c7551de89e0014f6b9", "difficulty": "medium", "final_answer": {"answer": 189.1638, "unit": "g"}, "id": "stoich_mass_001573_glucose_1.05", "license": "Apache-2.0", "prompt": "A sample contains 1.05 mol of glucose. Using molar mass 180.156 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 1.05 mol * 180.156 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "glucose", "molar_mass": 180.156, "moles": 1.05}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 840 mL to 0.84 L.\n3. Compute M = 0.895 / 0.84.\nFinal: {\"answer\": 1.0655, \"unit\": \"mol/L\"}", "dedupe_signature": "59aa5ea39f97389b2b6e2abb6a5b111b825ddc4c5e892ab011838d46a0cd8613", "difficulty": "medium", "final_answer": {"answer": 1.0655, "unit": "mol/L"}, "id": "molarity_001574_0.895_840", "license": "Apache-2.0", "prompt": "A solution contains 0.895 mol of solute in 840 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 840 mL to 0.84 L.\nCompute M = 0.895 / 0.84.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 0.895, "volume_ml": 840}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.54 y, so each step multiplies y by 1 - h*0.54.\n3. Apply that update for 10 steps and round the final state.\nFinal: {\"answer\": 1.7835, \"unit\": \"state_units\"}", "dedupe_signature": "892be7ba895c02e02a07106435a5a0628050483974963185536d6d0eab173b06", "difficulty": "medium", "final_answer": {"answer": 1.7835, "unit": "state_units"}, "id": "euler_decay_001575_41.5_0.54_0.5_10", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.54 y with y(0)=41.5, step size h=0.5, for 10 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.54 y, so each step multiplies y by 1 - h*0.54.\nApply that update for 10 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 41.5, "rate": 0.54, "step": 0.5, "steps": 10}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(2.7)=0.86 and f(3.6)=5.18.\n3. The interval width is 0.9.\nFinal: {\"answer\": 2.718, \"unit\": \"area_units\"}", "dedupe_signature": "933b09e9d7f217ff0f2610b60928e51afac17d50f4ee1c625c9e2cd7ebfd0618", "difficulty": "medium", "final_answer": {"answer": 2.718, "unit": "area_units"}, "id": "trapz_linear_001576_4.8_-12.1_2.7_3.6", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=4.8x+-12.1 from x=2.7 to x=3.6. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(2.7)=0.86 and f(3.6)=5.18.\nThe interval width is 0.9.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -12.1, "slope": 4.8, "x0": 2.7, "x1": 3.6}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.36 and add it to the current value.\nFinal: {\"answer\": [0.814, -0.458, -0.932], \"unit\": \"temperature_units\"}", "dedupe_signature": "02e2c60a488a30956f6d99cb9573f5aba4304bc40d27c40619d1debecfef0bfd", "difficulty": "hard", "final_answer": {"answer": [0.814, -0.458, -0.932], "unit": "temperature_units"}, "id": "heat_step_001577_0.36_2.65_-0.05_-0.35_-0.95_-1.5", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=2.65, right=-1.5; current interior values are [-0.05, -0.35, -0.95]. Use r=0.36. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.36 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-0.05, -0.35, -0.95], "left": 2.65, "r": 0.36, "right": -1.5}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kelvin equals Celsius plus 273.15.\n2. Apply the conversion factor directly to the given value.\n3. Compute 80.0 + 273.15.\nFinal: {\"answer\": 353.15, \"unit\": \"K\"}", "dedupe_signature": "3c09ef64f00071446a50661e72e23044cf976cb502625b5e473613727b4f7294", "difficulty": "easy", "final_answer": {"answer": 353.15, "unit": "K"}, "id": "unit_convert_001578_c_to_k_80", "license": "Apache-2.0", "prompt": "Convert 80 degC to K. Return the converted value with unit.", "reasoning_trace": "Kelvin equals Celsius plus 273.15.\nApply the conversion factor directly to the given value.\nCompute 80.0 + 273.15.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 80.0}, "verifier": {"formula": "value + 273.15", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=140 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-366.9353, 307.8953], \"unit\": \"N\"}", "dedupe_signature": "b980400e0d93e75d8adc1e9dde5ef72c34967f5c4ffc5237439cbb1098522681", "difficulty": "medium", "final_answer": {"answer": [-366.9353, 307.8953], "unit": "N"}, "id": "vector_components_001579_479_140", "license": "Apache-2.0", "prompt": "A vector has magnitude 479 N at 140 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=140 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 140, "magnitude": 479.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [4.3, 1.5], \"unit\": \"dimensionless\"}", "dedupe_signature": "58f53435ae4c135f12ebbed082fdfacd28ca190837e08b626a137054511b0849", "difficulty": "medium", "final_answer": {"answer": [4.3, 1.5], "unit": "dimensionless"}, "id": "line_two_point_001580_-6.25_-3_4.3_1.5", "license": "Apache-2.0", "prompt": "A line passes through points (-6.25, -25.375) and (-3, -11.4). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -6.25, "x2": -3.0, "y1": -25.375, "y2": -11.399999999999999}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. grams cancel with J/(g*K), and kelvin cancels, leaving joules\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "abdf72e8a63065732aa31dae12ad31862056c73430c1406dd89f9f0d69489177", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_001581_consistent_4153435f_417247", "license": "Apache-2.0", "prompt": "In instrument manual case 417247, check dimensional consistency for Q = m * c * DeltaT. The left side has dimensions J and the right side has dimensions J. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\ngrams cancel with J/(g*K), and kelvin cancels, leaving joules\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "Q = m * c * DeltaT"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: left_boundary, right_boundary.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"left_boundary\", \"right_boundary\"]}", "dedupe_signature": "2a5305ebdaf0f4f5f94038729e338ae929589e128c32351de686510e11ffa261", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["left_boundary", "right_boundary"]}, "id": "abstain_001583_left_boundary_right_boundary", "license": "Apache-2.0", "prompt": "Solve the 1D heat equation after one finite-difference step. The prompt gives r=0.06 and interior values [-1.35, 1.2, -0.75], but gives no boundary values. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: left_boundary, right_boundary.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["left_boundary", "right_boundary"]}, "verifier": {"missing": ["left_boundary", "right_boundary"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 7.35 kg and a = 0.55 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 4.0425, \"unit\": \"N\"}", "dedupe_signature": "fdefdf4deb0ef3da733cfa5393eebaff81ded1f927fe2e292e5e19477218cd20", "difficulty": "easy", "final_answer": {"answer": 4.0425, "unit": "N"}, "id": "force_001584_7.35_0.55", "license": "Apache-2.0", "prompt": "A cart has mass 7.35 kg and measured acceleration 0.55 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 7.35 kg and a = 0.55 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 0.55, "mass": 7.35}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 21.45^2 and multiply by 0.5 * 16.35.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 3761.3379, \"unit\": \"J\"}", "dedupe_signature": "5edbd8a01e2a0d9d45ac2d5fceb1453cdacf07f5358d582b16380568a62d0ec1", "difficulty": "easy", "final_answer": {"answer": 3761.3379, "unit": "J"}, "id": "ke_001585_16.35_21.45", "license": "Apache-2.0", "prompt": "A body of mass 16.35 kg moves at 21.45 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 21.45^2 and multiply by 0.5 * 16.35.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 16.35, "velocity": 21.45}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=67 degrees through the sine of 2 theta.\n3. Substitute v=73.5 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 396.1318, \"unit\": \"m\"}", "dedupe_signature": "a3ad849b46f473fa8c8bcd0d0effcefb6d9547940602b50b3edec9540fe9ea68", "difficulty": "medium", "final_answer": {"answer": 396.1318, "unit": "m"}, "id": "projectile_range_001586_73.5_67", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 73.5 m/s and angle 67 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=67 degrees through the sine of 2 theta.\nSubstitute v=73.5 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 67, "gravity": 9.81, "speed": 73.5}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 3.78 * 8.314 * 357 / 76.3.\nFinal: {\"answer\": 147.0434, \"unit\": \"kPa\"}", "dedupe_signature": "a8995a63060816863eae61d4eeb42078243d1a79db7205ef48769530f0114261", "difficulty": "medium", "final_answer": {"answer": 147.0434, "unit": "kPa"}, "id": "ideal_gas_001587_3.78_357_76.3", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=3.78 mol, T=357 K, and V=76.3 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 3.78 * 8.314 * 357 / 76.3.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 3.78, "temp_k": 357, "volume_l": 76.3}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 345 * 2.05 * 41.\nFinal: {\"answer\": 28997.25, \"unit\": \"J\"}", "dedupe_signature": "efecffe1070283571c056fe2bbcba993f4c3e8cff652b2cca2d4049cb427babf", "difficulty": "easy", "final_answer": {"answer": 28997.25, "unit": "J"}, "id": "heat_q_001588_345_2.05_41", "license": "Apache-2.0", "prompt": "A 345 g sample has specific heat 2.05 J/(g*K). How much heat is needed to raise its temperature by 41 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 345 * 2.05 * 41.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 41, "heat_capacity": 2.05, "mass_g": 345}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=202.4 V and R=123.5 ohm.\nFinal: {\"answer\": 331.7066, \"unit\": \"W\"}", "dedupe_signature": "d3ffc39c94878a5480c1d8797dcf1f1a9d749482165edbf64b568c33d1103dfe", "difficulty": "easy", "final_answer": {"answer": 331.7066, "unit": "W"}, "id": "ohm_power_001589_202.4_123.5", "license": "Apache-2.0", "prompt": "A resistor has resistance 123.5 ohm and voltage 202.4 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=202.4 V and R=123.5 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 123.5, "voltage": 202.4}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=891.5 mg, t=293 h, and T_half=15.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 0.0018, \"unit\": \"mg\"}", "dedupe_signature": "53af3cafd5b5ba0ded203dc3ccd54399c60ff62dbdc0fb071ee16ffcc98d28a0", "difficulty": "medium", "final_answer": {"answer": 0.0018, "unit": "mg"}, "id": "half_life_001590_891.5_15.5_293", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 891.5 mg. Its half-life is 15.5 hours. How many mg remain after 293 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=891.5 mg, t=293 h, and T_half=15.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 293.0, "half_life": 15.5, "initial_amount": 891.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 5.54 mol * 180.156 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 998.0642, \"unit\": \"g\"}", "dedupe_signature": "860e59fd83f3b9e7e6b0b7983ed7321603968a5a75e30eb207307c06b4030970", "difficulty": "medium", "final_answer": {"answer": 998.0642, "unit": "g"}, "id": "stoich_mass_001591_glucose_5.54", "license": "Apache-2.0", "prompt": "A sample contains 5.54 mol of glucose. Using molar mass 180.156 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 5.54 mol * 180.156 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "glucose", "molar_mass": 180.156, "moles": 5.54}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 2890 mL to 2.89 L.\n3. Compute M = 0.89 / 2.89.\nFinal: {\"answer\": 0.308, \"unit\": \"mol/L\"}", "dedupe_signature": "2ca2c51ebc45ee4dc690b69b241b8f12471a6b0c9eb22aa852d51c6fecd95a70", "difficulty": "medium", "final_answer": {"answer": 0.308, "unit": "mol/L"}, "id": "molarity_001592_0.89_2890", "license": "Apache-2.0", "prompt": "A solution contains 0.89 mol of solute in 2890 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 2890 mL to 2.89 L.\nCompute M = 0.89 / 2.89.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 0.89, "volume_ml": 2890}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.03 y, so each step multiplies y by 1 - h*0.03.\n3. Apply that update for 2 steps and round the final state.\nFinal: {\"answer\": 28.9878, \"unit\": \"state_units\"}", "dedupe_signature": "bd46be0828031fce81224152a4edb5ff8362c85c2b720742ca8a3a2d29d50bf6", "difficulty": "medium", "final_answer": {"answer": 28.9878, "unit": "state_units"}, "id": "euler_decay_001593_31_0.03_1.1_2", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.03 y with y(0)=31, step size h=1.1, for 2 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.03 y, so each step multiplies y by 1 - h*0.03.\nApply that update for 2 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 31.0, "rate": 0.03, "step": 1.1, "steps": 2}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(1)=11.4 and f(10.4)=47.12.\n3. The interval width is 9.4.\nFinal: {\"answer\": 275.044, \"unit\": \"area_units\"}", "dedupe_signature": "74b1d155537014171fcdc9e040c0e5deb1e7639470a169880532dc592f348061", "difficulty": "medium", "final_answer": {"answer": 275.044, "unit": "area_units"}, "id": "trapz_linear_001594_3.8_7.6_1_10.4", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=3.8x+7.6 from x=1 to x=10.4. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(1)=11.4 and f(10.4)=47.12.\nThe interval width is 9.4.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 7.6, "slope": 3.8, "x0": 1.0, "x1": 10.4}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.28 and add it to the current value.\nFinal: {\"answer\": [0.176, 0.766, 0.394], \"unit\": \"temperature_units\"}", "dedupe_signature": "30b2dac91b3c65ed1f1b105f30470caf141becb186e57880510f9e4984c1c21f", "difficulty": "hard", "final_answer": {"answer": [0.176, 0.766, 0.394], "unit": "temperature_units"}, "id": "heat_step_001595_0.28_-0.65_0.05_1.2_0.8_-1.05", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-0.65, right=-1.05; current interior values are [0.05, 1.2, 0.8]. Use r=0.28. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.28 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [0.05, 1.2, 0.8], "left": -0.65, "r": 0.28, "right": -1.05}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kelvin equals Celsius plus 273.15.\n2. Apply the conversion factor directly to the given value.\n3. Compute -22.0 + 273.15.\nFinal: {\"answer\": 251.15, \"unit\": \"K\"}", "dedupe_signature": "3ab27cd8a4080a57594199b923e02911f3ed7aa4c25e388637bcf5df35470a0e", "difficulty": "easy", "final_answer": {"answer": 251.15, "unit": "K"}, "id": "unit_convert_001596_c_to_k_-22", "license": "Apache-2.0", "prompt": "Convert -22 degC to K. Return the converted value with unit.", "reasoning_trace": "Kelvin equals Celsius plus 273.15.\nApply the conversion factor directly to the given value.\nCompute -22.0 + 273.15.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": -22.0}, "verifier": {"formula": "value + 273.15", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=170 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-363.8865, 64.163], \"unit\": \"N\"}", "dedupe_signature": "9523deec87cd8903b74726f21daeddc9a85598b55c4c6ec62fa2d73723c72f4f", "difficulty": "medium", "final_answer": {"answer": [-363.8865, 64.163], "unit": "N"}, "id": "vector_components_001597_369.5_170", "license": "Apache-2.0", "prompt": "A vector has magnitude 369.5 N at 170 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=170 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 170, "magnitude": 369.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-8.9, 25.5], \"unit\": \"dimensionless\"}", "dedupe_signature": "6c3989d489889ccf88d8153072e6244cb1f7483e96f9f2aae4bf660316625cc5", "difficulty": "medium", "final_answer": {"answer": [-8.9, 25.5], "unit": "dimensionless"}, "id": "line_two_point_001598_-15_-6_-8.9_25.5", "license": "Apache-2.0", "prompt": "A line passes through points (-15, 159) and (-6, 78.9). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -15.0, "x2": -6.0, "y1": 159.0, "y2": 78.9}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. speed squared over acceleration has units of meters\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "13e6b2ed76b70ed5ae1612e7747fb81c41be16971e5dcc71a2afdb68f750a0b7", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_001599_consistent_741d4e34_71766", "license": "Apache-2.0", "prompt": "In quality-control check case 71766, check dimensional consistency for R = v^2 * sin(theta) / g. The left side has dimensions m and the right side has dimensions m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nspeed squared over acceleration has units of meters\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "R = v^2 * sin(theta) / g"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef safe_mean_001600(values):\n    if not values:\n        raise ValueError('safe_mean requires at least one value')\n    return sum(values) / len(values)\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"safe_mean_001600\"}", "dedupe_signature": "ab850c832382384b09528f3a96c1ae9df25668fc27f622b93ca25830a5274872", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "safe_mean_001600"}, "id": "code_001600_safe_mean_001600", "license": "Apache-2.0", "prompt": "Write a Python function safe_mean_001600(values) that returns the arithmetic mean. It must raise ValueError for an empty input and must not mutate the input list. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "safe_mean_001600"}, "verifier": {"function": "safe_mean_001600", "tests": ["assert safe_mean_001600([2, 4, 6]) == 4", "xs = [1, 2, 3]; assert safe_mean_001600(xs) == 2 and xs == [1, 2, 3]", "try:\n    safe_mean_001600([])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 21.85 kg and a = 3.5 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 76.475, \"unit\": \"N\"}", "dedupe_signature": "785048267a66a7b67d2ef3f2e3e0592f573f8f4141b80ac1900a97a00fd8a50d", "difficulty": "easy", "final_answer": {"answer": 76.475, "unit": "N"}, "id": "force_001602_21.85_3.5", "license": "Apache-2.0", "prompt": "A cart has mass 21.85 kg and measured acceleration 3.5 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 21.85 kg and a = 3.5 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 3.5, "mass": 21.85}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 0.95^2 and multiply by 0.5 * 11.2.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 5.054, \"unit\": \"J\"}", "dedupe_signature": "fda598d32137fcc5554bca3e4572141b7e9a7a2d7070ee65bdc4b31f9925bab7", "difficulty": "easy", "final_answer": {"answer": 5.054, "unit": "J"}, "id": "ke_001603_11.2_0.95", "license": "Apache-2.0", "prompt": "A body of mass 11.2 kg moves at 0.95 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 0.95^2 and multiply by 0.5 * 11.2.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 11.2, "velocity": 0.95}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=40 degrees through the sine of 2 theta.\n3. Substitute v=32 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 102.7975, \"unit\": \"m\"}", "dedupe_signature": "072b7a0ef16c9c7c7c0663283cf4cb1f45bb9137b4b243ece4b65ad87f99584c", "difficulty": "medium", "final_answer": {"answer": 102.7975, "unit": "m"}, "id": "projectile_range_001604_32_40", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 32 m/s and angle 40 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=40 degrees through the sine of 2 theta.\nSubstitute v=32 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 40, "gravity": 9.81, "speed": 32.0}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 2.46 * 8.314 * 610 / 27.4.\nFinal: {\"answer\": 455.328, \"unit\": \"kPa\"}", "dedupe_signature": "70ed036ad1976c3d0b4717aad7bbfcb91a20cd475bf61f8029dc7add05aeb522", "difficulty": "medium", "final_answer": {"answer": 455.328, "unit": "kPa"}, "id": "ideal_gas_001605_2.46_610_27.4", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=2.46 mol, T=610 K, and V=27.4 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 2.46 * 8.314 * 610 / 27.4.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 2.46, "temp_k": 610, "volume_l": 27.4}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1450 * 0.9 * 109.\nFinal: {\"answer\": 142245.0, \"unit\": \"J\"}", "dedupe_signature": "0c66372ff467c1900366d36b054151d5232f5977a2835ec7f1209744ee73d3f0", "difficulty": "easy", "final_answer": {"answer": 142245.0, "unit": "J"}, "id": "heat_q_001606_1450_0.9_109", "license": "Apache-2.0", "prompt": "A 1450 g sample has specific heat 0.9 J/(g*K). How much heat is needed to raise its temperature by 109 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1450 * 0.9 * 109.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 109, "heat_capacity": 0.9, "mass_g": 1450}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=134.5 V and R=10.8 ohm.\nFinal: {\"answer\": 1675.0231, \"unit\": \"W\"}", "dedupe_signature": "05d22bd8570f5755b23e40fc72b6dbabd2feaaa1bdfa6fc9dfd4ffade48d9309", "difficulty": "easy", "final_answer": {"answer": 1675.0231, "unit": "W"}, "id": "ohm_power_001607_134.5_10.8", "license": "Apache-2.0", "prompt": "A resistor has resistance 10.8 ohm and voltage 134.5 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=134.5 V and R=10.8 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 10.8, "voltage": 134.5}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 2.29 mol * 18.015 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 41.2544, \"unit\": \"g\"}", "dedupe_signature": "1fe129806c9f664467dcf75ff5b4c8b1ecaadeaa6b964b859258677851e3f718", "difficulty": "medium", "final_answer": {"answer": 41.2544, "unit": "g"}, "id": "stoich_mass_001609_water_2.29", "license": "Apache-2.0", "prompt": "A sample contains 2.29 mol of water. Using molar mass 18.015 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 2.29 mol * 18.015 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "water", "molar_mass": 18.015, "moles": 2.29}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 1495 mL to 1.495 L.\n3. Compute M = 1.85 / 1.495.\nFinal: {\"answer\": 1.2375, \"unit\": \"mol/L\"}", "dedupe_signature": "2b635a514c6d61de88df7848fd162a1f2968874d57277c22733f9fe47fda21df", "difficulty": "medium", "final_answer": {"answer": 1.2375, "unit": "mol/L"}, "id": "molarity_001610_1.85_1495", "license": "Apache-2.0", "prompt": "A solution contains 1.85 mol of solute in 1495 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 1495 mL to 1.495 L.\nCompute M = 1.85 / 1.495.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 1.85, "volume_ml": 1495}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.31 y, so each step multiplies y by 1 - h*0.31.\n3. Apply that update for 3 steps and round the final state.\nFinal: {\"answer\": 27.225, \"unit\": \"state_units\"}", "dedupe_signature": "c1324bc6315efd23d32b5f4b18d055a92cb7efde06801567aa52942306d8a755", "difficulty": "medium", "final_answer": {"answer": 27.225, "unit": "state_units"}, "id": "euler_decay_001611_40.5_0.31_0.4_3", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.31 y with y(0)=40.5, step size h=0.4, for 3 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.31 y, so each step multiplies y by 1 - h*0.31.\nApply that update for 3 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 40.5, "rate": 0.31, "step": 0.4, "steps": 3}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.06 and add it to the current value.\nFinal: {\"answer\": [0.565, 2.239, 0.34], \"unit\": \"temperature_units\"}", "dedupe_signature": "3dd1018bbe8e535189f1289bb00c8899002be806aaf66fd5c8475b51cd9d6b31", "difficulty": "hard", "final_answer": {"answer": [0.565, 2.239, 0.34], "unit": "temperature_units"}, "id": "heat_step_001613_0.06_-1.15_0.55_2.5_0.1_1.7", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-1.15, right=1.7; current interior values are [0.55, 2.5, 0.1]. Use r=0.06. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.06 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [0.55, 2.5, 0.1], "left": -1.15, "r": 0.06, "right": 1.7}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 22276.0 / 1000.\nFinal: {\"answer\": 22.276, \"unit\": \"kg\"}", "dedupe_signature": "bd9559d1e847bea944329ab1cad7a3a513e3a4d0e7b5accbb67332e54b5dbe73", "difficulty": "easy", "final_answer": {"answer": 22.276, "unit": "kg"}, "id": "unit_convert_001614_g_to_kg_22276", "license": "Apache-2.0", "prompt": "Convert 22276 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 22276.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 22276.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=306 degrees and keep the unit as newtons.\nFinal: {\"answer\": [281.843, -387.9236], \"unit\": \"N\"}", "dedupe_signature": "137814668e554034a2f68a1acd7e9d858adf1ea3f4ccaa1a3ef460953ddf21f0", "difficulty": "medium", "final_answer": {"answer": [281.843, -387.9236], "unit": "N"}, "id": "vector_components_001615_479.5_306", "license": "Apache-2.0", "prompt": "A vector has magnitude 479.5 N at 306 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=306 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 306, "magnitude": 479.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [9.15, 17.75], \"unit\": \"dimensionless\"}", "dedupe_signature": "e093fd8287d8fadcc4b378bf072bdce51bcf03a3924be6ce604a0b063e2ddafc", "difficulty": "medium", "final_answer": {"answer": [9.15, 17.75], "unit": "dimensionless"}, "id": "line_two_point_001616_-4.5_-3.25_9.15_17.75", "license": "Apache-2.0", "prompt": "A line passes through points (-4.5, -23.425) and (-3.25, -11.9875). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -4.5, "x2": -3.25, "y1": -23.425000000000004, "y2": -11.9875}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. density times acceleration times height gives kg/(m*s^2), or pascal\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "ec778f8ca51e4c595a245cc3782cc6b69b08c78eb620e94ec61888c73b4b13a1", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_001617_consistent_b7d3eed1_833545", "license": "Apache-2.0", "prompt": "In lab notebook case 833545, check dimensional consistency for p = rho * g * h. The left side has dimensions Pa and the right side has dimensions Pa. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\ndensity times acceleration times height gives kg/(m*s^2), or pascal\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "p = rho * g * h"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef threshold_flags_001618(values, threshold):\n    return [value >= threshold for value in values]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"threshold_flags_001618\"}", "dedupe_signature": "a5d682ad8bbf8142344e04e7d079aeeaaeba9bfa2f571f54a21868e4ac287fd5", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "threshold_flags_001618"}, "id": "code_001618_threshold_flags_001618", "license": "Apache-2.0", "prompt": "Write a Python function threshold_flags_001618(values, threshold) that returns a list of booleans showing whether each value is greater than or equal to threshold. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "threshold_flags_001618"}, "verifier": {"function": "threshold_flags_001618", "tests": ["assert threshold_flags_001618([1, 2, 3], 2) == [False, True, True]", "assert threshold_flags_001618([], 5) == []", "assert threshold_flags_001618([-1, 0], 0) == [False, True]"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: left_boundary, right_boundary.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"left_boundary\", \"right_boundary\"]}", "dedupe_signature": "7d29392f72721d8517c9a35f8588ee13270b1fb0989948e259cc181d96f02e30", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["left_boundary", "right_boundary"]}, "id": "abstain_001619_left_boundary_right_boundary", "license": "Apache-2.0", "prompt": "Solve the 1D heat equation after one finite-difference step. The prompt gives r=0.34 and interior values [-1.95, 0.1, -1.1], but gives no boundary values. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: left_boundary, right_boundary.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["left_boundary", "right_boundary"]}, "verifier": {"missing": ["left_boundary", "right_boundary"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 17.85 kg and a = 3.5 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 62.475, \"unit\": \"N\"}", "dedupe_signature": "2681a8ac8ae9fd27da559f6d9de83cdc39152f76bf94f5804e6eb94dc3ad573b", "difficulty": "easy", "final_answer": {"answer": 62.475, "unit": "N"}, "id": "force_001620_17.85_3.5", "license": "Apache-2.0", "prompt": "A cart has mass 17.85 kg and measured acceleration 3.5 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 17.85 kg and a = 3.5 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 3.5, "mass": 17.85}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 12.6^2 and multiply by 0.5 * 0.75.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 59.535, \"unit\": \"J\"}", "dedupe_signature": "4c4ad4f2b7ccafbe2723a404f62a80837ab5e9e5105d8892882cf3e6a2588465", "difficulty": "easy", "final_answer": {"answer": 59.535, "unit": "J"}, "id": "ke_001621_0.75_12.6", "license": "Apache-2.0", "prompt": "A body of mass 0.75 kg moves at 12.6 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 12.6^2 and multiply by 0.5 * 0.75.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 0.75, "velocity": 12.6}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=31 degrees through the sine of 2 theta.\n3. Substitute v=37.5 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 126.5693, \"unit\": \"m\"}", "dedupe_signature": "e6ad6445ef24d3bf0f45731880251fc63496c63eeff2a6b2a3d07c15deb0608b", "difficulty": "medium", "final_answer": {"answer": 126.5693, "unit": "m"}, "id": "projectile_range_001622_37.5_31", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 37.5 m/s and angle 31 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=31 degrees through the sine of 2 theta.\nSubstitute v=37.5 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 31, "gravity": 9.81, "speed": 37.5}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 0.39 * 8.314 * 291 / 88.9.\nFinal: {\"answer\": 10.6137, \"unit\": \"kPa\"}", "dedupe_signature": "b2ba69e4d811af9a4d67add861b21683254d070db1d88bec952ec2a69a8ec73c", "difficulty": "medium", "final_answer": {"answer": 10.6137, "unit": "kPa"}, "id": "ideal_gas_001623_0.39_291_88.9", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=0.39 mol, T=291 K, and V=88.9 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 0.39 * 8.314 * 291 / 88.9.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 0.39, "temp_k": 291, "volume_l": 88.9}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 590 * 2.09 * 13.\nFinal: {\"answer\": 16030.3, \"unit\": \"J\"}", "dedupe_signature": "a4dbe86065bafc3eb867802735907df47f677b2dbd90f6bc4c228180ed7d2650", "difficulty": "easy", "final_answer": {"answer": 16030.3, "unit": "J"}, "id": "heat_q_001624_590_2.09_13", "license": "Apache-2.0", "prompt": "A 590 g sample has specific heat 2.09 J/(g*K). How much heat is needed to raise its temperature by 13 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 590 * 2.09 * 13.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 13, "heat_capacity": 2.09, "mass_g": 590}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=233.9 V and R=145.8 ohm.\nFinal: {\"answer\": 375.2346, \"unit\": \"W\"}", "dedupe_signature": "3e8779827c2a61fdef518221db5345d06127a8781c31a258727d758f0d1d8720", "difficulty": "easy", "final_answer": {"answer": 375.2346, "unit": "W"}, "id": "ohm_power_001625_233.9_145.8", "license": "Apache-2.0", "prompt": "A resistor has resistance 145.8 ohm and voltage 233.9 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=233.9 V and R=145.8 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 145.8, "voltage": 233.9}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 0.56 mol * 18.015 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 10.0884, \"unit\": \"g\"}", "dedupe_signature": "e6505816545d6dd3548aa091b2a2be8ed5a7bcfab797bb3cb92a53f625f9550b", "difficulty": "medium", "final_answer": {"answer": 10.0884, "unit": "g"}, "id": "stoich_mass_001627_water_0.56", "license": "Apache-2.0", "prompt": "A sample contains 0.56 mol of water. Using molar mass 18.015 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 0.56 mol * 18.015 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "water", "molar_mass": 18.015, "moles": 0.56}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 3625 mL to 3.625 L.\n3. Compute M = 1.365 / 3.625.\nFinal: {\"answer\": 0.3766, \"unit\": \"mol/L\"}", "dedupe_signature": "aeb7c468aad4509bbcf9e26e01f424cfb84dbea5c5b25cabb722ea896f4ef6ac", "difficulty": "medium", "final_answer": {"answer": 0.3766, "unit": "mol/L"}, "id": "molarity_001628_1.365_3625", "license": "Apache-2.0", "prompt": "A solution contains 1.365 mol of solute in 3625 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 3625 mL to 3.625 L.\nCompute M = 1.365 / 3.625.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 1.365, "volume_ml": 3625}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.15 y, so each step multiplies y by 1 - h*0.15.\n3. Apply that update for 12 steps and round the final state.\nFinal: {\"answer\": 24.9158, \"unit\": \"state_units\"}", "dedupe_signature": "b3f6a45e83ecf943286d2233c3a074c6f7ec9fdda7232b85792dc4f3a8ae42a7", "difficulty": "medium", "final_answer": {"answer": 24.9158, "unit": "state_units"}, "id": "euler_decay_001629_63.5_0.15_0.5_12", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.15 y with y(0)=63.5, step size h=0.5, for 12 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.15 y, so each step multiplies y by 1 - h*0.15.\nApply that update for 12 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 63.5, "rate": 0.15, "step": 0.5, "steps": 12}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(4.8)=10.24 and f(7.4)=7.12.\n3. The interval width is 2.6.\nFinal: {\"answer\": 22.568, \"unit\": \"area_units\"}", "dedupe_signature": "86386d886f0695e417742071c654b2185169c801b2f19cf31255991a69fcffd6", "difficulty": "medium", "final_answer": {"answer": 22.568, "unit": "area_units"}, "id": "trapz_linear_001630_-1.2_16_4.8_7.4", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-1.2x+16 from x=4.8 to x=7.4. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(4.8)=10.24 and f(7.4)=7.12.\nThe interval width is 2.6.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 16.0, "slope": -1.2, "x0": 4.8, "x1": 7.4}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.22 and add it to the current value.\nFinal: {\"answer\": [0.861, 1.756, 1.384], \"unit\": \"temperature_units\"}", "dedupe_signature": "5043bf8709f579f314e900c1e66fce0dc6a784032e143de57479c81e348a5402", "difficulty": "hard", "final_answer": {"answer": [0.861, 1.756, 1.384], "unit": "temperature_units"}, "id": "heat_step_001631_0.22_-1.45_1.4_1.8_2.0_-0.6", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-1.45, right=-0.6; current interior values are [1.4, 1.8, 2.0]. Use r=0.22. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.22 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [1.4, 1.8, 2.0], "left": -1.45, "r": 0.22, "right": -0.6}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kelvin equals Celsius plus 273.15.\n2. Apply the conversion factor directly to the given value.\n3. Compute 221.0 + 273.15.\nFinal: {\"answer\": 494.15, \"unit\": \"K\"}", "dedupe_signature": "42495f21071f8547489c6a7da565dcfacd07d6adf0567faf4618886811c3d25b", "difficulty": "easy", "final_answer": {"answer": 494.15, "unit": "K"}, "id": "unit_convert_001632_c_to_k_221", "license": "Apache-2.0", "prompt": "Convert 221 degC to K. Return the converted value with unit.", "reasoning_trace": "Kelvin equals Celsius plus 273.15.\nApply the conversion factor directly to the given value.\nCompute 221.0 + 273.15.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 221.0}, "verifier": {"formula": "value + 273.15", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=232 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-282.2808, -361.3029], \"unit\": \"N\"}", "dedupe_signature": "7c2e31411928552c1abb4f9ca38cea8776c5be94e6f174f68dbb36c458d33d37", "difficulty": "medium", "final_answer": {"answer": [-282.2808, -361.3029], "unit": "N"}, "id": "vector_components_001633_458.5_232", "license": "Apache-2.0", "prompt": "A vector has magnitude 458.5 N at 232 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=232 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 232, "magnitude": 458.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [0.35, 14.5], \"unit\": \"dimensionless\"}", "dedupe_signature": "fb74d6560a5874bfdd58d5cb8417d12930ea2ddcc1f644b4991f858582960569", "difficulty": "medium", "final_answer": {"answer": [0.35, 14.5], "unit": "dimensionless"}, "id": "line_two_point_001634_4_15.5_0.35_14.5", "license": "Apache-2.0", "prompt": "A line passes through points (4, 15.9) and (15.5, 19.925). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 4.0, "x2": 15.5, "y1": 15.9, "y2": 19.925}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\nimport math\n\ndef unit_vector_001636(x, y):\n    norm = math.hypot(x, y)\n    if norm == 0:\n        raise ValueError('zero vector has no direction')\n    return (x / norm, y / norm)\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"unit_vector_001636\"}", "dedupe_signature": "0db5e7c8ed6f827bf85c04b800bd9c698efe7be51fa4b0b98ac5bda45e8b6b38", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "unit_vector_001636"}, "id": "code_001636_unit_vector_001636", "license": "Apache-2.0", "prompt": "Write a Python function unit_vector_001636(x, y) that returns the 2D unit vector as a tuple. Raise ValueError for the zero vector. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "unit_vector_001636"}, "verifier": {"function": "unit_vector_001636", "tests": ["ux, uy = unit_vector_001636(3, 4); assert abs(ux - 0.6) < 1e-12 and abs(uy - 0.8) < 1e-12", "assert unit_vector_001636(0, 5) == (0, 1)", "try:\n    unit_vector_001636(0, 0)\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: recurrence, objective, tie_breaking_rule.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"recurrence\", \"objective\", \"tie_breaking_rule\"]}", "dedupe_signature": "392def37fa75451d615953333421aa91ebe40982f4b48c80573c7c1b6ab06958", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["recurrence", "objective", "tie_breaking_rule"]}, "id": "abstain_001637_recurrence_objective_tie_breaking_rule", "license": "Apache-2.0", "prompt": "Write a dynamic-programming solver for a alignment scoring problem with 1862 items and budget 2500, but the recurrence, objective, and tie-breaking rule are all absent. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: recurrence, objective, tie_breaking_rule.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["recurrence", "objective", "tie_breaking_rule"]}, "verifier": {"missing": ["recurrence", "objective", "tie_breaking_rule"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 15.55 kg and a = 11.75 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 182.7125, \"unit\": \"N\"}", "dedupe_signature": "708c6d495f4cc6a2412c4ff3a6ee179b965d5ae744c6dfdecce8f6f181023def", "difficulty": "easy", "final_answer": {"answer": 182.7125, "unit": "N"}, "id": "force_001638_15.55_11.75", "license": "Apache-2.0", "prompt": "A cart has mass 15.55 kg and measured acceleration 11.75 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 15.55 kg and a = 11.75 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 11.75, "mass": 15.55}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 44.6^2 and multiply by 0.5 * 18.3.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 18200.814, \"unit\": \"J\"}", "dedupe_signature": "a5a663f6cc88a45dd431116af50fa000cc5d03ef9f44db90228a3761c64d24b2", "difficulty": "easy", "final_answer": {"answer": 18200.814, "unit": "J"}, "id": "ke_001639_18.3_44.6", "license": "Apache-2.0", "prompt": "A body of mass 18.3 kg moves at 44.6 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 44.6^2 and multiply by 0.5 * 18.3.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 18.3, "velocity": 44.6}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=74 degrees through the sine of 2 theta.\n3. Substitute v=81.6 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 359.6839, \"unit\": \"m\"}", "dedupe_signature": "bb524bd38491fdd614637ee3cb85b1f30b0c381ad64445dc9de4eb7fbb824d33", "difficulty": "medium", "final_answer": {"answer": 359.6839, "unit": "m"}, "id": "projectile_range_001640_81.6_74", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 81.6 m/s and angle 74 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=74 degrees through the sine of 2 theta.\nSubstitute v=81.6 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 74, "gravity": 9.81, "speed": 81.6}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 0.73 * 8.314 * 563 / 1.8.\nFinal: {\"answer\": 1898.3171, \"unit\": \"kPa\"}", "dedupe_signature": "a35ebad76a4c921f185869614716235c67e063fc2ce27e19a227720b322a2f56", "difficulty": "medium", "final_answer": {"answer": 1898.3171, "unit": "kPa"}, "id": "ideal_gas_001641_0.73_563_1.8", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=0.73 mol, T=563 K, and V=1.8 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 0.73 * 8.314 * 563 / 1.8.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 0.73, "temp_k": 563, "volume_l": 1.8}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1855 * 1.9 * 89.\nFinal: {\"answer\": 313680.5, \"unit\": \"J\"}", "dedupe_signature": "1208b6eeb3b11a56e2ce71935386930fa4db25a5d8d747ff6c63298cdc262cb0", "difficulty": "easy", "final_answer": {"answer": 313680.5, "unit": "J"}, "id": "heat_q_001642_1855_1.9_89", "license": "Apache-2.0", "prompt": "A 1855 g sample has specific heat 1.9 J/(g*K). How much heat is needed to raise its temperature by 89 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1855 * 1.9 * 89.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 89, "heat_capacity": 1.9, "mass_g": 1855}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=43.8 V and R=142.8 ohm.\nFinal: {\"answer\": 13.4345, \"unit\": \"W\"}", "dedupe_signature": "7fbe75e9c9fdc996c264da881fc7d02db27b520422d9b554d055095d2a2f4689", "difficulty": "easy", "final_answer": {"answer": 13.4345, "unit": "W"}, "id": "ohm_power_001643_43.8_142.8", "license": "Apache-2.0", "prompt": "A resistor has resistance 142.8 ohm and voltage 43.8 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=43.8 V and R=142.8 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 142.8, "voltage": 43.8}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=683.5 mg, t=131 h, and T_half=33 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 43.6255, \"unit\": \"mg\"}", "dedupe_signature": "74ff3761b190c0f2f440a6e74c31e91917af84891cad7760958c85ad47a32879", "difficulty": "medium", "final_answer": {"answer": 43.6255, "unit": "mg"}, "id": "half_life_001644_683.5_33_131", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 683.5 mg. Its half-life is 33 hours. How many mg remain after 131 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=683.5 mg, t=131 h, and T_half=33 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 131.0, "half_life": 33.0, "initial_amount": 683.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 0.39 mol * 18.015 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 7.0259, \"unit\": \"g\"}", "dedupe_signature": "3e7a70459c61802e5631b9610e14351712fdbcb1c0f09f81b3c30e834f2740ea", "difficulty": "medium", "final_answer": {"answer": 7.0259, "unit": "g"}, "id": "stoich_mass_001645_water_0.39", "license": "Apache-2.0", "prompt": "A sample contains 0.39 mol of water. Using molar mass 18.015 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 0.39 mol * 18.015 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "water", "molar_mass": 18.015, "moles": 0.39}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 3530 mL to 3.53 L.\n3. Compute M = 3.63 / 3.53.\nFinal: {\"answer\": 1.0283, \"unit\": \"mol/L\"}", "dedupe_signature": "d0ed49107b83852dc0bf30f9659c19987bb34f1e23d7450f1fdf9cbb6902b8b3", "difficulty": "medium", "final_answer": {"answer": 1.0283, "unit": "mol/L"}, "id": "molarity_001646_3.63_3530", "license": "Apache-2.0", "prompt": "A solution contains 3.63 mol of solute in 3530 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 3530 mL to 3.53 L.\nCompute M = 3.63 / 3.53.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 3.63, "volume_ml": 3530}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-2)=11.6 and f(-0.9)=13.14.\n3. The interval width is 1.1.\nFinal: {\"answer\": 13.607, \"unit\": \"area_units\"}", "dedupe_signature": "4ec15acc899274618d3f2f620d40928c6508bd398bfb38b70a5226bea5b99ed5", "difficulty": "medium", "final_answer": {"answer": 13.607, "unit": "area_units"}, "id": "trapz_linear_001648_1.4_14.4_-2_-0.9", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=1.4x+14.4 from x=-2 to x=-0.9. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-2)=11.6 and f(-0.9)=13.14.\nThe interval width is 1.1.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 14.4, "slope": 1.4, "x0": -2.0, "x1": -0.8999999999999999}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.1 and add it to the current value.\nFinal: {\"answer\": [-0.215, 0.0, 1.7], \"unit\": \"temperature_units\"}", "dedupe_signature": "e0febce300cf788dcd69364dbacd6f2782ddaf1a38d99e3955208cc736f463aa", "difficulty": "hard", "final_answer": {"answer": [-0.215, 0.0, 1.7], "unit": "temperature_units"}, "id": "heat_step_001649_0.1_1.65_-0.45_-0.2_2.05_0.8", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.65, right=0.8; current interior values are [-0.45, -0.2, 2.05]. Use r=0.1. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.1 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-0.45, -0.2, 2.05], "left": 1.65, "r": 0.1, "right": 0.8}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kelvin equals Celsius plus 273.15.\n2. Apply the conversion factor directly to the given value.\n3. Compute 118.0 + 273.15.\nFinal: {\"answer\": 391.15, \"unit\": \"K\"}", "dedupe_signature": "f83277b32c3be99decd3dadc4ba321f752d0ecb9c7d93a2ded8add5c1b4bfd1f", "difficulty": "easy", "final_answer": {"answer": 391.15, "unit": "K"}, "id": "unit_convert_001650_c_to_k_118", "license": "Apache-2.0", "prompt": "Convert 118 degC to K. Return the converted value with unit.", "reasoning_trace": "Kelvin equals Celsius plus 273.15.\nApply the conversion factor directly to the given value.\nCompute 118.0 + 273.15.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 118.0}, "verifier": {"formula": "value + 273.15", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=43 degrees and keep the unit as newtons.\nFinal: {\"answer\": [64.3591, 60.0159], \"unit\": \"N\"}", "dedupe_signature": "62c0032fd98ed430d7f52c3a240c6fda0a48fe3cff88b10eb11f43b6be730994", "difficulty": "medium", "final_answer": {"answer": [64.3591, 60.0159], "unit": "N"}, "id": "vector_components_001651_88_43", "license": "Apache-2.0", "prompt": "A vector has magnitude 88 N at 43 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=43 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 43, "magnitude": 88.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [6.9, 23.75], \"unit\": \"dimensionless\"}", "dedupe_signature": "adc224ac9629a359585827e06b6642dd5078d065ffe6d6031e1bc23539185762", "difficulty": "medium", "final_answer": {"answer": [6.9, 23.75], "unit": "dimensionless"}, "id": "line_two_point_001652_-10.5_-9_6.9_23.75", "license": "Apache-2.0", "prompt": "A line passes through points (-10.5, -48.7) and (-9, -38.35). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -10.5, "x2": -9.0, "y1": -48.7, "y2": -38.35}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. velocity times time gives distance, not acceleration\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "652054d8583f80d4fc53090ba6f45a298f5c5225b711d15e626fb4b23369b3ba", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_001653_inconsistent_7481c798_518667", "license": "Apache-2.0", "prompt": "In quality-control check case 518667, check dimensional consistency for a = v * t. The left side has dimensions m/s^2 and the right side has dimensions m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nvelocity times time gives distance, not acceleration\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "a = v * t"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef clamp_001654(x, lo, hi):\n    if lo > hi:\n        raise ValueError('lo must be <= hi')\n    return min(max(x, lo), hi)\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"clamp_001654\"}", "dedupe_signature": "7ec67e421337c49af792bfec671dbf20f7c75326f558b32025af56f7cd0b9dc9", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "clamp_001654"}, "id": "code_001654_clamp_001654", "license": "Apache-2.0", "prompt": "Write a Python function clamp_001654(x, lo, hi) that clips x into the inclusive interval [lo, hi]. It must raise ValueError if lo > hi. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "clamp_001654"}, "verifier": {"function": "clamp_001654", "tests": ["assert clamp_001654(5, 0, 10) == 5", "assert clamp_001654(-2, 0, 10) == 0", "assert clamp_001654(12, 0, 10) == 10", "try:\n    clamp_001654(1, 3, 2)\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: recurrence, objective, tie_breaking_rule.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"recurrence\", \"objective\", \"tie_breaking_rule\"]}", "dedupe_signature": "cb3e79ae7e3f13f1d156fc30379451e574caaae44ad3cd9992a73b95cb8ac610", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["recurrence", "objective", "tie_breaking_rule"]}, "id": "abstain_001655_recurrence_objective_tie_breaking_rule", "license": "Apache-2.0", "prompt": "Write a dynamic-programming solver for a alignment scoring problem with 2297 items and budget 20930, but the recurrence, objective, and tie-breaking rule are all absent. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: recurrence, objective, tie_breaking_rule.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["recurrence", "objective", "tie_breaking_rule"]}, "verifier": {"missing": ["recurrence", "objective", "tie_breaking_rule"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 4.4 kg and a = 7.6 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 33.44, \"unit\": \"N\"}", "dedupe_signature": "e07d3bfe806db5de323115fea0c5b483ec531b70bcdc973554b0ba3f502b1b86", "difficulty": "easy", "final_answer": {"answer": 33.44, "unit": "N"}, "id": "force_001656_4.4_7.6", "license": "Apache-2.0", "prompt": "A cart has mass 4.4 kg and measured acceleration 7.6 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 4.4 kg and a = 7.6 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 7.6, "mass": 4.4}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 34.55^2 and multiply by 0.5 * 19.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 11340.1737, \"unit\": \"J\"}", "dedupe_signature": "9b8280bd1558b06d80495d9960e981272a61cb8550762a0d18cde0641b039ba8", "difficulty": "easy", "final_answer": {"answer": 11340.1737, "unit": "J"}, "id": "ke_001657_19_34.55", "license": "Apache-2.0", "prompt": "A body of mass 19 kg moves at 34.55 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 34.55^2 and multiply by 0.5 * 19.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 19.0, "velocity": 34.55}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=24 degrees through the sine of 2 theta.\n3. Substitute v=24.6 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 45.8432, \"unit\": \"m\"}", "dedupe_signature": "5fa03761f79c56b03bd4971c5039494eebd6dcbdda8fb525f7b3c1d4c80dfabe", "difficulty": "medium", "final_answer": {"answer": 45.8432, "unit": "m"}, "id": "projectile_range_001658_24.6_24", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 24.6 m/s and angle 24 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=24 degrees through the sine of 2 theta.\nSubstitute v=24.6 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 24, "gravity": 9.81, "speed": 24.6}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 3.9 * 8.314 * 254 / 38.4.\nFinal: {\"answer\": 214.4752, \"unit\": \"kPa\"}", "dedupe_signature": "3b7c43f39538900e6101690a6fe1dfc329eae68c5692d14b00357bc97a8021a9", "difficulty": "medium", "final_answer": {"answer": 214.4752, "unit": "kPa"}, "id": "ideal_gas_001659_3.9_254_38.4", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=3.9 mol, T=254 K, and V=38.4 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 3.9 * 8.314 * 254 / 38.4.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 3.9, "temp_k": 254, "volume_l": 38.4}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 790 * 4.11 * 86.\nFinal: {\"answer\": 279233.4, \"unit\": \"J\"}", "dedupe_signature": "8a7dde6124a67276764a64503294bca9a023333220e38ddb037f91bd48d6cbf9", "difficulty": "easy", "final_answer": {"answer": 279233.4, "unit": "J"}, "id": "heat_q_001660_790_4.11_86", "license": "Apache-2.0", "prompt": "A 790 g sample has specific heat 4.11 J/(g*K). How much heat is needed to raise its temperature by 86 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 790 * 4.11 * 86.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 86, "heat_capacity": 4.11, "mass_g": 790}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=100.6 V and R=121.3 ohm.\nFinal: {\"answer\": 83.4325, \"unit\": \"W\"}", "dedupe_signature": "db275a3cf2cf09926fb2fc1daef3713aabe848fca1fc15487251499c7c5ae2a9", "difficulty": "easy", "final_answer": {"answer": 83.4325, "unit": "W"}, "id": "ohm_power_001661_100.6_121.3", "license": "Apache-2.0", "prompt": "A resistor has resistance 121.3 ohm and voltage 100.6 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=100.6 V and R=121.3 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 121.3, "voltage": 100.6}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=265.5 mg, t=324 h, and T_half=39.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 0.9013, \"unit\": \"mg\"}", "dedupe_signature": "7cede5e1a3bed5bea0c41021ca1da7879885ec55fd233248016baad5d09c1607", "difficulty": "medium", "final_answer": {"answer": 0.9013, "unit": "mg"}, "id": "half_life_001662_265.5_39.5_324", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 265.5 mg. Its half-life is 39.5 hours. How many mg remain after 324 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=265.5 mg, t=324 h, and T_half=39.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 324.0, "half_life": 39.5, "initial_amount": 265.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 6.63 mol * 44.01 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 291.7863, \"unit\": \"g\"}", "dedupe_signature": "4e28afafb0b7fe8b1fca0d9ec51c0232b32d83db7f1b947055ec701517afd5e4", "difficulty": "medium", "final_answer": {"answer": 291.7863, "unit": "g"}, "id": "stoich_mass_001663_carbon_dioxide_6.63", "license": "Apache-2.0", "prompt": "A sample contains 6.63 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 6.63 mol * 44.01 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "carbon dioxide", "molar_mass": 44.01, "moles": 6.63}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 2915 mL to 2.915 L.\n3. Compute M = 0.575 / 2.915.\nFinal: {\"answer\": 0.1973, \"unit\": \"mol/L\"}", "dedupe_signature": "d573115b059dcb05aaf8f63b8f509f3ef6aaf91c81d1194c3e9d6e368b50bc35", "difficulty": "medium", "final_answer": {"answer": 0.1973, "unit": "mol/L"}, "id": "molarity_001664_0.575_2915", "license": "Apache-2.0", "prompt": "A solution contains 0.575 mol of solute in 2915 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 2915 mL to 2.915 L.\nCompute M = 0.575 / 2.915.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 0.575, "volume_ml": 2915}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.13 y, so each step multiplies y by 1 - h*0.13.\n3. Apply that update for 7 steps and round the final state.\nFinal: {\"answer\": 1.9547, \"unit\": \"state_units\"}", "dedupe_signature": "c0b0ae6f5f75d2ed5bcb8a84d967702cf7b7c673ecde8fb347f2878309c745b4", "difficulty": "medium", "final_answer": {"answer": 1.9547, "unit": "state_units"}, "id": "euler_decay_001665_10_0.13_1.6_7", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.13 y with y(0)=10, step size h=1.6, for 7 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.13 y, so each step multiplies y by 1 - h*0.13.\nApply that update for 7 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 10.0, "rate": 0.13, "step": 1.6, "steps": 7}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(7)=-44.6 and f(13.9)=-69.44.\n3. The interval width is 6.9.\nFinal: {\"answer\": -393.438, \"unit\": \"area_units\"}", "dedupe_signature": "9182b5255992bf2afecf1dd2761cd7f281a895b5ac78dc2a4a3186890dff8508", "difficulty": "medium", "final_answer": {"answer": -393.438, "unit": "area_units"}, "id": "trapz_linear_001666_-3.6_-19.4_7_13.9", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-3.6x+-19.4 from x=7 to x=13.9. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(7)=-44.6 and f(13.9)=-69.44.\nThe interval width is 6.9.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -19.4, "slope": -3.6, "x0": 7.0, "x1": 13.9}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 100 centimeters in one meter.\n2. Apply the conversion factor directly to the given value.\n3. Compute 4698.0 / 100.\nFinal: {\"answer\": 46.98, \"unit\": \"m\"}", "dedupe_signature": "c526e3368f4345a341f54eb65d20ec8b9c6f9136f135c2afb7abca4989bb91eb", "difficulty": "easy", "final_answer": {"answer": 46.98, "unit": "m"}, "id": "unit_convert_001668_cm_to_m_4698", "license": "Apache-2.0", "prompt": "Convert 4698 cm to m. Return the converted value with unit.", "reasoning_trace": "There are 100 centimeters in one meter.\nApply the conversion factor directly to the given value.\nCompute 4698.0 / 100.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 4698.0}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=318 degrees and keep the unit as newtons.\nFinal: {\"answer\": [82.8606, -74.6081], \"unit\": \"N\"}", "dedupe_signature": "743a05cd7bbfd4e0772e2fd6ff558c28f0d6309f5d7ab60f6e9b4bca011ccfa2", "difficulty": "medium", "final_answer": {"answer": [82.8606, -74.6081], "unit": "N"}, "id": "vector_components_001669_111.5_318", "license": "Apache-2.0", "prompt": "A vector has magnitude 111.5 N at 318 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=318 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 318, "magnitude": 111.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 31.75^2 and multiply by 0.5 * 11.6.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 5846.7625, \"unit\": \"J\"}", "dedupe_signature": "f169e0f5a6d8a2e5a84d5dc65ac59e88b5bd3afb2c8a4e2ee4aea15d60bd519b", "difficulty": "easy", "final_answer": {"answer": 5846.7625, "unit": "J"}, "id": "ke_001675_11.6_31.75", "license": "Apache-2.0", "prompt": "A body of mass 11.6 kg moves at 31.75 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 31.75^2 and multiply by 0.5 * 11.6.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 11.6, "velocity": 31.75}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=35 degrees through the sine of 2 theta.\n3. Substitute v=73.2 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 513.2618, \"unit\": \"m\"}", "dedupe_signature": "fad0586de152281799aeafb8808ce052f9e2d6fc3f5f6d07cd256ead5c8b4d2a", "difficulty": "medium", "final_answer": {"answer": 513.2618, "unit": "m"}, "id": "projectile_range_001676_73.2_35", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 73.2 m/s and angle 35 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=35 degrees through the sine of 2 theta.\nSubstitute v=73.2 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 35, "gravity": 9.81, "speed": 73.2}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 4.45 * 8.314 * 435 / 102.7.\nFinal: {\"answer\": 156.7072, \"unit\": \"kPa\"}", "dedupe_signature": "e4d6a3dab91ff88a257c271e38d35e533f557312ca49c46fd2644e4f040f7ede", "difficulty": "medium", "final_answer": {"answer": 156.7072, "unit": "kPa"}, "id": "ideal_gas_001677_4.45_435_102.7", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=4.45 mol, T=435 K, and V=102.7 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 4.45 * 8.314 * 435 / 102.7.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 4.45, "temp_k": 435, "volume_l": 102.7}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1890 * 0.675 * 58.\nFinal: {\"answer\": 73993.5, \"unit\": \"J\"}", "dedupe_signature": "acbc044d783a4700a6c8130b70c68c6417ed72a2fc31a5e96caa2f4c80df83cf", "difficulty": "easy", "final_answer": {"answer": 73993.5, "unit": "J"}, "id": "heat_q_001678_1890_0.675_58", "license": "Apache-2.0", "prompt": "A 1890 g sample has specific heat 0.675 J/(g*K). How much heat is needed to raise its temperature by 58 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1890 * 0.675 * 58.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 58, "heat_capacity": 0.675, "mass_g": 1890}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=158.3 V and R=105.4 ohm.\nFinal: {\"answer\": 237.7504, \"unit\": \"W\"}", "dedupe_signature": "1b908d134fa9b9ad2902b2a91759cf922a6dfce3fecee63d4b943b550bd51020", "difficulty": "easy", "final_answer": {"answer": 237.7504, "unit": "W"}, "id": "ohm_power_001679_158.3_105.4", "license": "Apache-2.0", "prompt": "A resistor has resistance 105.4 ohm and voltage 158.3 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=158.3 V and R=105.4 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 105.4, "voltage": 158.3}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=808.5 mg, t=242 h, and T_half=86 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 114.9729, \"unit\": \"mg\"}", "dedupe_signature": "761c72f8d1a1ecf13239ee3f4f7d71f42f3ff7c4cd21d7ad7f5f161405df1983", "difficulty": "medium", "final_answer": {"answer": 114.9729, "unit": "mg"}, "id": "half_life_001680_808.5_86_242", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 808.5 mg. Its half-life is 86 hours. How many mg remain after 242 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=808.5 mg, t=242 h, and T_half=86 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 242.0, "half_life": 86.0, "initial_amount": 808.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.43 y, so each step multiplies y by 1 - h*0.43.\n3. Apply that update for 5 steps and round the final state.\nFinal: {\"answer\": 19.2784, \"unit\": \"state_units\"}", "dedupe_signature": "bf4da2b8090e20263f984bb2b67bf04feb6321c14535bf94880c73f0d76bcc9a", "difficulty": "medium", "final_answer": {"answer": 19.2784, "unit": "state_units"}, "id": "euler_decay_001683_56.5_0.43_0.45_5", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.43 y with y(0)=56.5, step size h=0.45, for 5 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.43 y, so each step multiplies y by 1 - h*0.43.\nApply that update for 5 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 56.5, "rate": 0.43, "step": 0.45, "steps": 5}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.04 and add it to the current value.\nFinal: {\"answer\": [1.522, 0.964, 2.638], \"unit\": \"temperature_units\"}", "dedupe_signature": "1dede2a6897dfff5f9f39aac70b80f355b805387bae15e8ede1fad47ca8e6d71", "difficulty": "hard", "final_answer": {"answer": [1.522, 0.964, 2.638], "unit": "temperature_units"}, "id": "heat_step_001685_0.04_-0.75_1.65_0.85_2.9_-1.6", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-0.75, right=-1.6; current interior values are [1.65, 0.85, 2.9]. Use r=0.04. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.04 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [1.65, 0.85, 2.9], "left": -0.75, "r": 0.04, "right": -1.6}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 9636.0 / 1000.\nFinal: {\"answer\": 9.636, \"unit\": \"kg\"}", "dedupe_signature": "e82f8bfd49641469fec09ba2be575895fb3374e05f54b3245087cf5820dc7fb3", "difficulty": "easy", "final_answer": {"answer": 9.636, "unit": "kg"}, "id": "unit_convert_001686_g_to_kg_9636", "license": "Apache-2.0", "prompt": "Convert 9636 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 9636.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 9636.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=244 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-181.2665, -371.6513], \"unit\": \"N\"}", "dedupe_signature": "be2dbf8da2f6b6f09c0f7627f9cfa93d50d8c6cb395d08a202ba4b141c4fef06", "difficulty": "medium", "final_answer": {"answer": [-181.2665, -371.6513], "unit": "N"}, "id": "vector_components_001687_413.5_244", "license": "Apache-2.0", "prompt": "A vector has magnitude 413.5 N at 244 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=244 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 244, "magnitude": 413.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [9.35, -29.75], \"unit\": \"dimensionless\"}", "dedupe_signature": "6ad89495f405c3ba09c820195de54494ddce3f487221565bbdaf74da613d5a07", "difficulty": "medium", "final_answer": {"answer": [9.35, -29.75], "unit": "dimensionless"}, "id": "line_two_point_001688_16.75_20.75_9.35_-29.75", "license": "Apache-2.0", "prompt": "A line passes through points (16.75, 126.862) and (20.75, 164.262). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 16.75, "x2": 20.75, "y1": 126.86249999999998, "y2": 164.2625}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: target_schema, valid_examples.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"target_schema\", \"valid_examples\"]}", "dedupe_signature": "2458948c2b22e86f16d7990c4817b7e9b3a10a7aa849948097b3dd9ed0ae9c64", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["target_schema", "valid_examples"]}, "id": "abstain_001691_target_schema_valid_examples", "license": "Apache-2.0", "prompt": "Write a parser that converts each laboratory survey record from batch 434024 into the correct schema, but the prompt does not include the target schema or examples. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: target_schema, valid_examples.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["target_schema", "valid_examples"]}, "verifier": {"missing": ["target_schema", "valid_examples"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 7.65 kg and a = 3.5 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 26.775, \"unit\": \"N\"}", "dedupe_signature": "e871fa364ec2dbb4b7ffa567ecd17392a9e13a6c9e0dc286b28913e91d46711e", "difficulty": "easy", "final_answer": {"answer": 26.775, "unit": "N"}, "id": "force_001692_7.65_3.5", "license": "Apache-2.0", "prompt": "A cart has mass 7.65 kg and measured acceleration 3.5 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 7.65 kg and a = 3.5 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 3.5, "mass": 7.65}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 26.25^2 and multiply by 0.5 * 15.8.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 5443.5938, \"unit\": \"J\"}", "dedupe_signature": "f256068e63e6c03c987386854445b1e38993891c716cc04f84755af6185965c0", "difficulty": "easy", "final_answer": {"answer": 5443.5938, "unit": "J"}, "id": "ke_001693_15.8_26.25", "license": "Apache-2.0", "prompt": "A body of mass 15.8 kg moves at 26.25 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 26.25^2 and multiply by 0.5 * 15.8.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 15.8, "velocity": 26.25}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=83 degrees through the sine of 2 theta.\n3. Substitute v=36.9 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 33.5783, \"unit\": \"m\"}", "dedupe_signature": "9bedb842c0864c3846a80518d610e96338d660e550427219e2898e9a7592517c", "difficulty": "medium", "final_answer": {"answer": 33.5783, "unit": "m"}, "id": "projectile_range_001694_36.9_83", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 36.9 m/s and angle 83 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=83 degrees through the sine of 2 theta.\nSubstitute v=36.9 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 83, "gravity": 9.81, "speed": 36.9}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=73 V and R=197.3 ohm.\nFinal: {\"answer\": 27.0096, \"unit\": \"W\"}", "dedupe_signature": "49577b4d51cf7f9580e4a02d4733ca51879e14f9e2e7198456c78b6d3b15afb0", "difficulty": "easy", "final_answer": {"answer": 27.0096, "unit": "W"}, "id": "ohm_power_001697_73_197.3", "license": "Apache-2.0", "prompt": "A resistor has resistance 197.3 ohm and voltage 73 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=73 V and R=197.3 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 197.3, "voltage": 73.0}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=884 mg, t=91 h, and T_half=84.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 419.0503, \"unit\": \"mg\"}", "dedupe_signature": "1ee374f9e7970638ee0dee7e1193101b39ff2c852dba0277f4c007d69e145d68", "difficulty": "medium", "final_answer": {"answer": 419.0503, "unit": "mg"}, "id": "half_life_001698_884_84.5_91", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 884 mg. Its half-life is 84.5 hours. How many mg remain after 91 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=884 mg, t=91 h, and T_half=84.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 91.0, "half_life": 84.5, "initial_amount": 884.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 2.2 mol * 100.087 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 220.1914, \"unit\": \"g\"}", "dedupe_signature": "bcafe965fdcc6326d608f5dd71e8bb13678b227d376303f1a2e0c8289c52de6e", "difficulty": "medium", "final_answer": {"answer": 220.1914, "unit": "g"}, "id": "stoich_mass_001699_calcium_carbonate_2.2", "license": "Apache-2.0", "prompt": "A sample contains 2.2 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 2.2 mol * 100.087 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "calcium carbonate", "molar_mass": 100.087, "moles": 2.2}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.24 y, so each step multiplies y by 1 - h*0.24.\n3. Apply that update for 11 steps and round the final state.\nFinal: {\"answer\": 0.3429, \"unit\": \"state_units\"}", "dedupe_signature": "2b6eefc72931ab2cde6d0458e36f79c6468e5a4e36274be48bbbaf89bc7def87", "difficulty": "medium", "final_answer": {"answer": 0.3429, "unit": "state_units"}, "id": "euler_decay_001701_31_0.24_1.4_11", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.24 y with y(0)=31, step size h=1.4, for 11 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.24 y, so each step multiplies y by 1 - h*0.24.\nApply that update for 11 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 31.0, "rate": 0.24, "step": 1.4, "steps": 11}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(1.1)=2.09 and f(11.1)=-48.91.\n3. The interval width is 10.\nFinal: {\"answer\": -234.1, \"unit\": \"area_units\"}", "dedupe_signature": "23e8ea1a13146e38336a8350d04fdd8163791989fc1045c56f88baf7517bb537", "difficulty": "medium", "final_answer": {"answer": -234.1, "unit": "area_units"}, "id": "trapz_linear_001702_-5.1_7.7_1.1_11.1", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-5.1x+7.7 from x=1.1 to x=11.1. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(1.1)=2.09 and f(11.1)=-48.91.\nThe interval width is 10.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 7.7, "slope": -5.1, "x0": 1.1, "x1": 11.1}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.1 and add it to the current value.\nFinal: {\"answer\": [-0.545, 0.775, 1.625], \"unit\": \"temperature_units\"}", "dedupe_signature": "6e565e9a314f24b2a4c88859cf13ef42acd326d52d3e98bdde95fffc643844b4", "difficulty": "hard", "final_answer": {"answer": [-0.545, 0.775, 1.625], "unit": "temperature_units"}, "id": "heat_step_001703_0.1_0.1_-0.8_0.85_1.75_1.4", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=0.1, right=1.4; current interior values are [-0.8, 0.85, 1.75]. Use r=0.1. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.1 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-0.8, 0.85, 1.75], "left": 0.1, "r": 0.1, "right": 1.4}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 100 centimeters in one meter.\n2. Apply the conversion factor directly to the given value.\n3. Compute 2555.5 / 100.\nFinal: {\"answer\": 25.555, \"unit\": \"m\"}", "dedupe_signature": "81547da588cc652958314e6e2a09082d3ae729bb75e1ec6344b7e5078b3eb452", "difficulty": "easy", "final_answer": {"answer": 25.555, "unit": "m"}, "id": "unit_convert_001704_cm_to_m_2555.5", "license": "Apache-2.0", "prompt": "Convert 2555.5 cm to m. Return the converted value with unit.", "reasoning_trace": "There are 100 centimeters in one meter.\nApply the conversion factor directly to the given value.\nCompute 2555.5 / 100.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 2555.5}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=75 degrees and keep the unit as newtons.\nFinal: {\"answer\": [36.7523, 137.1615], \"unit\": \"N\"}", "dedupe_signature": "115ffce90f6b4e2525579b2eeaf3f71fcce65206b6f07c536d4f60b9553eebf2", "difficulty": "medium", "final_answer": {"answer": [36.7523, 137.1615], "unit": "N"}, "id": "vector_components_001705_142_75", "license": "Apache-2.0", "prompt": "A vector has magnitude 142 N at 75 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=75 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 75, "magnitude": 142.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. velocity times time gives distance, not acceleration\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "a9d7719f150f726fcd74fcf0ae5ea2f9e421a28505e2f99a8b04e298e38adc3e", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_001707_inconsistent_7481c798_882824", "license": "Apache-2.0", "prompt": "In field worksheet case 882824, check dimensional consistency for a = v * t. The left side has dimensions m/s^2 and the right side has dimensions m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nvelocity times time gives distance, not acceleration\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "a = v * t"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef weighted_sum_001708(values, weights):\n    if len(values) != len(weights):\n        raise ValueError('length mismatch')\n    return sum(value * weight for value, weight in zip(values, weights))\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"weighted_sum_001708\"}", "dedupe_signature": "3860fa6acdf122008a282165cf5324b680fbeab844b34bc6f9474a11492c2b19", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "weighted_sum_001708"}, "id": "code_001708_weighted_sum_001708", "license": "Apache-2.0", "prompt": "Write a Python function weighted_sum_001708(values, weights) that returns sum(value*weight). Raise ValueError when the two inputs have different lengths. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "weighted_sum_001708"}, "verifier": {"function": "weighted_sum_001708", "tests": ["assert weighted_sum_001708([2, 3], [4, 5]) == 23", "assert weighted_sum_001708([], []) == 0", "try:\n    weighted_sum_001708([1], [1, 2])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: volume.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"volume\"]}", "dedupe_signature": "afcd039cc9e4bf8aa2e7c1888655cc8e0402fd3c9c9268dd995070bb42ba1077", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["volume"]}, "id": "abstain_001709_volume", "license": "Apache-2.0", "prompt": "Compute pressure from the ideal gas law. The prompt gives n=3.95 mol and T=475 K, but does not give volume. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: volume.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["volume"]}, "verifier": {"missing": ["volume"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 2.6 kg and a = 8.8 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 22.88, \"unit\": \"N\"}", "dedupe_signature": "acac17a72a821b2ed8dd66501b27d49d7636bd0faafb7e509b52ac7b0e64152a", "difficulty": "easy", "final_answer": {"answer": 22.88, "unit": "N"}, "id": "force_001710_2.6_8.8", "license": "Apache-2.0", "prompt": "A cart has mass 2.6 kg and measured acceleration 8.8 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 2.6 kg and a = 8.8 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 8.8, "mass": 2.6}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 32.65^2 and multiply by 0.5 * 18.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 9594.2025, \"unit\": \"J\"}", "dedupe_signature": "574c42150fefbe53411d363e9e8ec8cd04b22b1bae9dd37b3755bc3743e3ff7f", "difficulty": "easy", "final_answer": {"answer": 9594.2025, "unit": "J"}, "id": "ke_001711_18_32.65", "license": "Apache-2.0", "prompt": "A body of mass 18 kg moves at 32.65 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 32.65^2 and multiply by 0.5 * 18.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 18.0, "velocity": 32.65}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=25 degrees through the sine of 2 theta.\n3. Substitute v=75.1 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 440.4178, \"unit\": \"m\"}", "dedupe_signature": "c58b7373963fdbba243f3ae76818c8acc12e4adfd6d67c14ed4c3d257161a153", "difficulty": "medium", "final_answer": {"answer": 440.4178, "unit": "m"}, "id": "projectile_range_001712_75.1_25", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 75.1 m/s and angle 25 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=25 degrees through the sine of 2 theta.\nSubstitute v=75.1 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 25, "gravity": 9.81, "speed": 75.1}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 0.86 * 8.314 * 453 / 114.8.\nFinal: {\"answer\": 28.214, \"unit\": \"kPa\"}", "dedupe_signature": "0d3fd49e257efead2bdaf63223847d8deb35cfcc58764245b2982241da5a63ed", "difficulty": "medium", "final_answer": {"answer": 28.214, "unit": "kPa"}, "id": "ideal_gas_001713_0.86_453_114.8", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=0.86 mol, T=453 K, and V=114.8 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 0.86 * 8.314 * 453 / 114.8.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 0.86, "temp_k": 453, "volume_l": 114.8}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 735 * 2.945 * 8.\nFinal: {\"answer\": 17316.6, \"unit\": \"J\"}", "dedupe_signature": "b58f32bf1518976f1e4b9a8d3b06e01ba81aadc0e3efc3c59c6877acb7f19dc6", "difficulty": "easy", "final_answer": {"answer": 17316.6, "unit": "J"}, "id": "heat_q_001714_735_2.945_8", "license": "Apache-2.0", "prompt": "A 735 g sample has specific heat 2.945 J/(g*K). How much heat is needed to raise its temperature by 8 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 735 * 2.945 * 8.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 8, "heat_capacity": 2.945, "mass_g": 735}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=150.5 V and R=57.4 ohm.\nFinal: {\"answer\": 394.6037, \"unit\": \"W\"}", "dedupe_signature": "9fc003d4e2c8489b84833d89d4e50c09e65fda4c376750269e24ceb3c13a07f4", "difficulty": "easy", "final_answer": {"answer": 394.6037, "unit": "W"}, "id": "ohm_power_001715_150.5_57.4", "license": "Apache-2.0", "prompt": "A resistor has resistance 57.4 ohm and voltage 150.5 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=150.5 V and R=57.4 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 57.4, "voltage": 150.5}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=744.5 mg, t=198 h, and T_half=61 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 78.4785, \"unit\": \"mg\"}", "dedupe_signature": "db994e6952a22fa8d65c3a2adff6619e2413113a5fbe241009a552b0c2ad19a0", "difficulty": "medium", "final_answer": {"answer": 78.4785, "unit": "mg"}, "id": "half_life_001716_744.5_61_198", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 744.5 mg. Its half-life is 61 hours. How many mg remain after 198 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=744.5 mg, t=198 h, and T_half=61 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 198.0, "half_life": 61.0, "initial_amount": 744.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 4.48 mol * 180.156 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 807.0989, \"unit\": \"g\"}", "dedupe_signature": "a3d584889f3484f4b10b9563e2311ad6c727d13419cc4d55b1f3684cf9c59104", "difficulty": "medium", "final_answer": {"answer": 807.0989, "unit": "g"}, "id": "stoich_mass_001717_glucose_4.48", "license": "Apache-2.0", "prompt": "A sample contains 4.48 mol of glucose. Using molar mass 180.156 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 4.48 mol * 180.156 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "glucose", "molar_mass": 180.156, "moles": 4.48}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 4810 mL to 4.81 L.\n3. Compute M = 0.41 / 4.81.\nFinal: {\"answer\": 0.0852, \"unit\": \"mol/L\"}", "dedupe_signature": "38602f3da630d7b247319039ffae8fe049ce214447e446148eb0666889794dbe", "difficulty": "medium", "final_answer": {"answer": 0.0852, "unit": "mol/L"}, "id": "molarity_001718_0.41_4810", "license": "Apache-2.0", "prompt": "A solution contains 0.41 mol of solute in 4810 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 4810 mL to 4.81 L.\nCompute M = 0.41 / 4.81.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 0.41, "volume_ml": 4810}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.49 y, so each step multiplies y by 1 - h*0.49.\n3. Apply that update for 8 steps and round the final state.\nFinal: {\"answer\": 8.2138, \"unit\": \"state_units\"}", "dedupe_signature": "6d9b1023b4864f7529f809f26f881afc5df7d1290a3514e74dbcd6f06d2630d0", "difficulty": "medium", "final_answer": {"answer": 8.2138, "unit": "state_units"}, "id": "euler_decay_001719_37_0.49_0.35_8", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.49 y with y(0)=37, step size h=0.35, for 8 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.49 y, so each step multiplies y by 1 - h*0.49.\nApply that update for 8 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 37.0, "rate": 0.49, "step": 0.35, "steps": 8}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(5.5)=-44.65 and f(9.3)=-71.63.\n3. The interval width is 3.8.\nFinal: {\"answer\": -220.932, \"unit\": \"area_units\"}", "dedupe_signature": "cac56e7dddde93776fa3c0ba35088a2726400ec82de753484ef20c2a82641e53", "difficulty": "medium", "final_answer": {"answer": -220.932, "unit": "area_units"}, "id": "trapz_linear_001720_-7.1_-5.6_5.5_9.3", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-7.1x+-5.6 from x=5.5 to x=9.3. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(5.5)=-44.65 and f(9.3)=-71.63.\nThe interval width is 3.8.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -5.6, "slope": -7.1, "x0": 5.5, "x1": 9.3}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.42 and add it to the current value.\nFinal: {\"answer\": [0.568, 1.253, 1.254], \"unit\": \"temperature_units\"}", "dedupe_signature": "6a560f7c4d9f4e9d5a90d1d31b684836594d3777fd7a340b2bd9540ba083161e", "difficulty": "hard", "final_answer": {"answer": [0.568, 1.253, 1.254], "unit": "temperature_units"}, "id": "heat_step_001721_0.42_1.5_1.45_-0.7_1.8_3.0", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.5, right=3; current interior values are [1.45, -0.7, 1.8]. Use r=0.42. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.42 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [1.45, -0.7, 1.8], "left": 1.5, "r": 0.42, "right": 3.0}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 42998.0 / 1000.\nFinal: {\"answer\": 42.998, \"unit\": \"kg\"}", "dedupe_signature": "1f1d29d89280735cad9e110d3d01c6071b365c658ea6e8cf2aa61673af1adfe0", "difficulty": "easy", "final_answer": {"answer": 42.998, "unit": "kg"}, "id": "unit_convert_001722_g_to_kg_42998", "license": "Apache-2.0", "prompt": "Convert 42998 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 42998.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 42998.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-4.7, -18.5], \"unit\": \"dimensionless\"}", "dedupe_signature": "973e2a9095f5e20d335974bd77c3fdab2eb537ea0b2f0152198d0b5d83258c48", "difficulty": "medium", "final_answer": {"answer": [-4.7, -18.5], "unit": "dimensionless"}, "id": "line_two_point_001724_-15.75_-10.5_-4.7_-18.5", "license": "Apache-2.0", "prompt": "A line passes through points (-15.75, 55.525) and (-10.5, 30.85). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -15.75, "x2": -10.5, "y1": 55.525000000000006, "y2": 30.85}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. grams cancel with J/(g*K), and kelvin cancels, leaving joules\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "c5cfd6b45ee03b71c822789fe101af8634ddd8bc43ed4dd3bb57156da5ee0e6b", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_001725_consistent_4153435f_376371", "license": "Apache-2.0", "prompt": "In simulation spec case 376371, check dimensional consistency for Q = m * c * DeltaT. The left side has dimensions J and the right side has dimensions J. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\ngrams cancel with J/(g*K), and kelvin cancels, leaving joules\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "Q = m * c * DeltaT"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef running_total_001726(values):\n    total = 0\n    out = []\n    for value in values:\n        total += value\n        out.append(total)\n    return out\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"running_total_001726\"}", "dedupe_signature": "421e6c2ec51f9cd921b8d7319cea998471654dd38f03568c2575d6b8d6316337", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "running_total_001726"}, "id": "code_001726_running_total_001726", "license": "Apache-2.0", "prompt": "Write a Python function running_total_001726(values) that returns cumulative sums as a new list. It must not mutate the input list. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "running_total_001726"}, "verifier": {"function": "running_total_001726", "tests": ["assert running_total_001726([1, 2, 3]) == [1, 3, 6]", "xs = [4, -1, 2]; assert running_total_001726(xs) == [4, 3, 5] and xs == [4, -1, 2]", "assert running_total_001726([]) == []"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: target_schema, valid_examples.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"target_schema\", \"valid_examples\"]}", "dedupe_signature": "ee787b753ede8bf571d6e07e0e6d86ac50135d7ea64113f83b4d8a14bac329e8", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["target_schema", "valid_examples"]}, "id": "abstain_001727_target_schema_valid_examples", "license": "Apache-2.0", "prompt": "Write a parser that converts each laboratory crop record from batch 154673 into the correct schema, but the prompt does not include the target schema or examples. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: target_schema, valid_examples.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["target_schema", "valid_examples"]}, "verifier": {"missing": ["target_schema", "valid_examples"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 19 kg and a = 10.1 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 191.9, \"unit\": \"N\"}", "dedupe_signature": "4c18b884451bae70f7c453f6ec0332582441e9167ca0597b2979cf6c026c0d60", "difficulty": "easy", "final_answer": {"answer": 191.9, "unit": "N"}, "id": "force_001728_19_10.1", "license": "Apache-2.0", "prompt": "A cart has mass 19 kg and measured acceleration 10.1 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 19 kg and a = 10.1 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 10.1, "mass": 19.0}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 25.05^2 and multiply by 0.5 * 5.25.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 1647.1941, \"unit\": \"J\"}", "dedupe_signature": "a271edcd43433fc84742aaf0dfe3cfcbd9fb515e2aa77f003b29584e0b5facd8", "difficulty": "easy", "final_answer": {"answer": 1647.1941, "unit": "J"}, "id": "ke_001729_5.25_25.05", "license": "Apache-2.0", "prompt": "A body of mass 5.25 kg moves at 25.05 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 25.05^2 and multiply by 0.5 * 5.25.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 5.25, "velocity": 25.05}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=23 degrees through the sine of 2 theta.\n3. Substitute v=28.7 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 60.3989, \"unit\": \"m\"}", "dedupe_signature": "125ec237a63830aa51e0e4e5e5f18ebca666a0eae2a741f5412184de9002d835", "difficulty": "medium", "final_answer": {"answer": 60.3989, "unit": "m"}, "id": "projectile_range_001730_28.7_23", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 28.7 m/s and angle 23 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=23 degrees through the sine of 2 theta.\nSubstitute v=28.7 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 23, "gravity": 9.81, "speed": 28.7}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 415 * 4.165 * 57.\nFinal: {\"answer\": 98523.075, \"unit\": \"J\"}", "dedupe_signature": "005f8fb8b61f10b6b93cbcd95d5056c14aff836d8586399bd7889560d5147aef", "difficulty": "easy", "final_answer": {"answer": 98523.075, "unit": "J"}, "id": "heat_q_001732_415_4.165_57", "license": "Apache-2.0", "prompt": "A 415 g sample has specific heat 4.165 J/(g*K). How much heat is needed to raise its temperature by 57 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 415 * 4.165 * 57.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 57, "heat_capacity": 4.165, "mass_g": 415}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=553.5 mg, t=206 h, and T_half=13 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 0.0094, \"unit\": \"mg\"}", "dedupe_signature": "52bb30d8866f1215f0519905feb8a864de1ee1250ca83914879b74e3f0375926", "difficulty": "medium", "final_answer": {"answer": 0.0094, "unit": "mg"}, "id": "half_life_001734_553.5_13_206", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 553.5 mg. Its half-life is 13 hours. How many mg remain after 206 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=553.5 mg, t=206 h, and T_half=13 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 206.0, "half_life": 13.0, "initial_amount": 553.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 7.04 mol * 100.087 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 704.6125, \"unit\": \"g\"}", "dedupe_signature": "a3673f6d7bd831f0fb0cdcbe4efcd9545507dd70f74dce75be07ce4d8b0fafb0", "difficulty": "medium", "final_answer": {"answer": 704.6125, "unit": "g"}, "id": "stoich_mass_001735_calcium_carbonate_7.04", "license": "Apache-2.0", "prompt": "A sample contains 7.04 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 7.04 mol * 100.087 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "calcium carbonate", "molar_mass": 100.087, "moles": 7.04}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 1930 mL to 1.93 L.\n3. Compute M = 2.545 / 1.93.\nFinal: {\"answer\": 1.3187, \"unit\": \"mol/L\"}", "dedupe_signature": "ba4a29e626c0a806f6517d15f4f9b13588e7e3a6af092e885ad28f677ba5d45b", "difficulty": "medium", "final_answer": {"answer": 1.3187, "unit": "mol/L"}, "id": "molarity_001736_2.545_1930", "license": "Apache-2.0", "prompt": "A solution contains 2.545 mol of solute in 1930 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 1930 mL to 1.93 L.\nCompute M = 2.545 / 1.93.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 2.545, "volume_ml": 1930}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.15 y, so each step multiplies y by 1 - h*0.15.\n3. Apply that update for 7 steps and round the final state.\nFinal: {\"answer\": 17.4156, \"unit\": \"state_units\"}", "dedupe_signature": "b4ed04784c12eb1b5cd5cc568e4557c070e6617da5e353653b385645b761a533", "difficulty": "medium", "final_answer": {"answer": 17.4156, "unit": "state_units"}, "id": "euler_decay_001737_79.5_0.15_1.3_7", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.15 y with y(0)=79.5, step size h=1.3, for 7 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.15 y, so each step multiplies y by 1 - h*0.15.\nApply that update for 7 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 79.5, "rate": 0.15, "step": 1.3, "steps": 7}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(1.5)=13.75 and f(5.3)=17.17.\n3. The interval width is 3.8.\nFinal: {\"answer\": 58.748, \"unit\": \"area_units\"}", "dedupe_signature": "2825cb4e8ae1b38f25d36ddee9cdf705c5cea56e851879e5efe0bee51f7504aa", "difficulty": "medium", "final_answer": {"answer": 58.748, "unit": "area_units"}, "id": "trapz_linear_001738_0.9_12.4_1.5_5.3", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=0.9x+12.4 from x=1.5 to x=5.3. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(1.5)=13.75 and f(5.3)=17.17.\nThe interval width is 3.8.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 12.4, "slope": 0.9, "x0": 1.5, "x1": 5.3}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.32 and add it to the current value.\nFinal: {\"answer\": [-0.322, -0.202, 0.682], \"unit\": \"temperature_units\"}", "dedupe_signature": "9a0fa0813e22a74e0b724acb3c442442163c33307b21d2fa6caaa590b7d8a49f", "difficulty": "hard", "final_answer": {"answer": [-0.322, -0.202, 0.682], "unit": "temperature_units"}, "id": "heat_step_001739_0.32_0.95_-0.45_-1.45_1.45_1.95", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=0.95, right=1.95; current interior values are [-0.45, -1.45, 1.45]. Use r=0.32. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.32 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-0.45, -1.45, 1.45], "left": 0.95, "r": 0.32, "right": 1.95}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kelvin equals Celsius plus 273.15.\n2. Apply the conversion factor directly to the given value.\n3. Compute 173.0 + 273.15.\nFinal: {\"answer\": 446.15, \"unit\": \"K\"}", "dedupe_signature": "946f434c93ee7fe0ff230dde381d156c7631588626976c3e12de1fba2ecb14d6", "difficulty": "easy", "final_answer": {"answer": 446.15, "unit": "K"}, "id": "unit_convert_001740_c_to_k_173", "license": "Apache-2.0", "prompt": "Convert 173 degC to K. Return the converted value with unit.", "reasoning_trace": "Kelvin equals Celsius plus 273.15.\nApply the conversion factor directly to the given value.\nCompute 173.0 + 273.15.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 173.0}, "verifier": {"formula": "value + 273.15", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=357 degrees and keep the unit as newtons.\nFinal: {\"answer\": [30.4582, -1.5962], \"unit\": \"N\"}", "dedupe_signature": "2672bc8c1f13c80fceaf71466469bfebdb26642957ec37e54705c90f3e8d96fb", "difficulty": "medium", "final_answer": {"answer": [30.4582, -1.5962], "unit": "N"}, "id": "vector_components_001741_30.5_357", "license": "Apache-2.0", "prompt": "A vector has magnitude 30.5 N at 357 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=357 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 357, "magnitude": 30.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-8.95, -21.5], \"unit\": \"dimensionless\"}", "dedupe_signature": "1cd411cb259e7a4fdbc6e7cb925354e0ae279579be17c24ed196bccd62d50fea", "difficulty": "medium", "final_answer": {"answer": [-8.95, -21.5], "unit": "dimensionless"}, "id": "line_two_point_001742_-2.5_2_-8.95_-21.5", "license": "Apache-2.0", "prompt": "A line passes through points (-2.5, 0.875) and (2, -39.4). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -2.5, "x2": 2.0, "y1": 0.875, "y2": -39.4}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. energy divided by length is force, not spring constant\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "cde1d839da50c3baec833fb8349562148c7323fcd02be3c03bcefefba4c97bcf", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_001743_inconsistent_56040f5d_947620", "license": "Apache-2.0", "prompt": "In student derivation case 947620, check dimensional consistency for k = E / x. The left side has dimensions N/m and the right side has dimensions J/m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nenergy divided by length is force, not spring constant\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "k = E / x"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef pairwise_ratios_001744(numerators, denominators):\n    if len(numerators) != len(denominators):\n        raise ValueError('length mismatch')\n    out = []\n    for numerator, denominator in zip(numerators, denominators):\n        if denominator == 0:\n            raise ValueError('zero denominator')\n        out.append(numerator / denominator)\n    return out\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"pairwise_ratios_001744\"}", "dedupe_signature": "fc39ee6cf931501a224dfc8ed3b77dc86e2e515deae21b352b611da2a4567fa3", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "pairwise_ratios_001744"}, "id": "code_001744_pairwise_ratios_001744", "license": "Apache-2.0", "prompt": "Write a Python function pairwise_ratios_001744(numerators, denominators) that returns a list of n/d values. Raise ValueError if lengths differ or any denominator is zero. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "pairwise_ratios_001744"}, "verifier": {"function": "pairwise_ratios_001744", "tests": ["assert pairwise_ratios_001744([2, 9], [4, 3]) == [0.5, 3.0]", "try:\n    pairwise_ratios_001744([1], [0])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass", "try:\n    pairwise_ratios_001744([1, 2], [1])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 42.1^2 and multiply by 0.5 * 18.15.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 16084.6208, \"unit\": \"J\"}", "dedupe_signature": "473488897936be4b17e78ac4430660709224c860be9e739dd307be8746f4708a", "difficulty": "easy", "final_answer": {"answer": 16084.6208, "unit": "J"}, "id": "ke_001747_18.15_42.1", "license": "Apache-2.0", "prompt": "A body of mass 18.15 kg moves at 42.1 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 42.1^2 and multiply by 0.5 * 18.15.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 18.15, "velocity": 42.1}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=18 degrees through the sine of 2 theta.\n3. Substitute v=36.2 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 78.5176, \"unit\": \"m\"}", "dedupe_signature": "1d1b74fecd0fefd0a3b19e6038504c23584860914bd3b239c433d7166dc5db24", "difficulty": "medium", "final_answer": {"answer": 78.5176, "unit": "m"}, "id": "projectile_range_001748_36.2_18", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 36.2 m/s and angle 18 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=18 degrees through the sine of 2 theta.\nSubstitute v=36.2 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 18, "gravity": 9.81, "speed": 36.2}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 2.72 * 8.314 * 302 / 59.3.\nFinal: {\"answer\": 115.1678, \"unit\": \"kPa\"}", "dedupe_signature": "c0dabfa0f459cf314e7d7d14d9146401416548bbce3a0908076fb23a101c5602", "difficulty": "medium", "final_answer": {"answer": 115.1678, "unit": "kPa"}, "id": "ideal_gas_001749_2.72_302_59.3", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=2.72 mol, T=302 K, and V=59.3 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 2.72 * 8.314 * 302 / 59.3.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 2.72, "temp_k": 302, "volume_l": 59.3}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 885 * 1.47 * 101.\nFinal: {\"answer\": 131395.95, \"unit\": \"J\"}", "dedupe_signature": "fa363d99e78317ea05034b609d3364ef34c7c73f097c54a5d1a78f5cc07b4dee", "difficulty": "easy", "final_answer": {"answer": 131395.95, "unit": "J"}, "id": "heat_q_001750_885_1.47_101", "license": "Apache-2.0", "prompt": "A 885 g sample has specific heat 1.47 J/(g*K). How much heat is needed to raise its temperature by 101 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 885 * 1.47 * 101.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 101, "heat_capacity": 1.47, "mass_g": 885}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=90.3 V and R=175.9 ohm.\nFinal: {\"answer\": 46.3564, \"unit\": \"W\"}", "dedupe_signature": "d8c662b248e0f76a12d7a1794931ef8fabce0a1d531e1a2cd2dec744c3081e1f", "difficulty": "easy", "final_answer": {"answer": 46.3564, "unit": "W"}, "id": "ohm_power_001751_90.3_175.9", "license": "Apache-2.0", "prompt": "A resistor has resistance 175.9 ohm and voltage 90.3 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=90.3 V and R=175.9 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 175.9, "voltage": 90.3}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=550 mg, t=73 h, and T_half=76 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 282.6282, \"unit\": \"mg\"}", "dedupe_signature": "fb0ebc3f258f982c91d33803360d0224a88e3954b94d3540f68fc5fa7e856ef3", "difficulty": "medium", "final_answer": {"answer": 282.6282, "unit": "mg"}, "id": "half_life_001752_550_76_73", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 550 mg. Its half-life is 76 hours. How many mg remain after 73 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=550 mg, t=73 h, and T_half=76 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 73.0, "half_life": 76.0, "initial_amount": 550.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 6.38 mol * 180.156 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 1149.3953, \"unit\": \"g\"}", "dedupe_signature": "25cddf07d4c338b9216cc55a99ef40cec50ec063ef3bcf7a00089304e2c97862", "difficulty": "medium", "final_answer": {"answer": 1149.3953, "unit": "g"}, "id": "stoich_mass_001753_glucose_6.38", "license": "Apache-2.0", "prompt": "A sample contains 6.38 mol of glucose. Using molar mass 180.156 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 6.38 mol * 180.156 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "glucose", "molar_mass": 180.156, "moles": 6.38}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 4725 mL to 4.725 L.\n3. Compute M = 2.66 / 4.725.\nFinal: {\"answer\": 0.563, \"unit\": \"mol/L\"}", "dedupe_signature": "78e2917a6b1e3d88476f18334eda4e2d8c793cd13c57a4d67b2056669a4b3fdf", "difficulty": "medium", "final_answer": {"answer": 0.563, "unit": "mol/L"}, "id": "molarity_001754_2.66_4725", "license": "Apache-2.0", "prompt": "A solution contains 2.66 mol of solute in 4725 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 4725 mL to 4.725 L.\nCompute M = 2.66 / 4.725.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 2.66, "volume_ml": 4725}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.3 y, so each step multiplies y by 1 - h*0.3.\n3. Apply that update for 6 steps and round the final state.\nFinal: {\"answer\": 0.09, \"unit\": \"state_units\"}", "dedupe_signature": "fae29b14139333fdca1a2219f745ca6d45cafcd597a40f7a865bec7667c8b55e", "difficulty": "medium", "final_answer": {"answer": 0.09, "unit": "state_units"}, "id": "euler_decay_001755_6.5_0.3_1.7_6", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.3 y with y(0)=6.5, step size h=1.7, for 6 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.3 y, so each step multiplies y by 1 - h*0.3.\nApply that update for 6 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 6.5, "rate": 0.3, "step": 1.7, "steps": 6}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-4.4)=-33.68 and f(5.3)=21.61.\n3. The interval width is 9.7.\nFinal: {\"answer\": -58.5395, \"unit\": \"area_units\"}", "dedupe_signature": "cc6847506ddce2cef672be87b577717d9e236a7c94044dd52b3cad45a87c157e", "difficulty": "medium", "final_answer": {"answer": -58.5395, "unit": "area_units"}, "id": "trapz_linear_001756_5.7_-8.6_-4.4_5.3", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=5.7x+-8.6 from x=-4.4 to x=5.3. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-4.4)=-33.68 and f(5.3)=21.61.\nThe interval width is 9.7.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -8.6, "slope": 5.7, "x0": -4.4, "x1": 5.299999999999999}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.38 and add it to the current value.\nFinal: {\"answer\": [1.575, 0.354, 0.443], \"unit\": \"temperature_units\"}", "dedupe_signature": "1e6b6070218c85a19d536a12a1e1f122bc1c2012e72c2ac0b484db5a645f6c3b", "difficulty": "hard", "final_answer": {"answer": [1.575, 0.354, 0.443], "unit": "temperature_units"}, "id": "heat_step_001757_0.38_2.7_-0.8_1.95_0.5_-1.1", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=2.7, right=-1.1; current interior values are [-0.8, 1.95, 0.5]. Use r=0.38. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.38 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-0.8, 1.95, 0.5], "left": 2.7, "r": 0.38, "right": -1.1}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 100 centimeters in one meter.\n2. Apply the conversion factor directly to the given value.\n3. Compute 57.5 / 100.\nFinal: {\"answer\": 0.575, \"unit\": \"m\"}", "dedupe_signature": "08b9c4f0f0f323093409a2f0ca53fd0684429db066ad18ed6c7ebac56d514c6b", "difficulty": "easy", "final_answer": {"answer": 0.575, "unit": "m"}, "id": "unit_convert_001758_cm_to_m_57.5", "license": "Apache-2.0", "prompt": "Convert 57.5 cm to m. Return the converted value with unit.", "reasoning_trace": "There are 100 centimeters in one meter.\nApply the conversion factor directly to the given value.\nCompute 57.5 / 100.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 57.5}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=78 degrees and keep the unit as newtons.\nFinal: {\"answer\": [65.3882, 307.6274], \"unit\": \"N\"}", "dedupe_signature": "34b790fe3d0f65c1de2d132bfd9847b089bfd7697b80f3b9a12da1afb81cf790", "difficulty": "medium", "final_answer": {"answer": [65.3882, 307.6274], "unit": "N"}, "id": "vector_components_001759_314.5_78", "license": "Apache-2.0", "prompt": "A vector has magnitude 314.5 N at 78 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=78 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 78, "magnitude": 314.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [6.8, -9.25], \"unit\": \"dimensionless\"}", "dedupe_signature": "55106a2b5e71d7408d4957df15b826b1f396e51b06b3dd6d6213082175770828", "difficulty": "medium", "final_answer": {"answer": [6.8, -9.25], "unit": "dimensionless"}, "id": "line_two_point_001760_-3.25_5.5_6.8_-9.25", "license": "Apache-2.0", "prompt": "A line passes through points (-3.25, -31.35) and (5.5, 28.15). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -3.25, "x2": 5.5, "y1": -31.349999999999998, "y2": 28.15}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. coulomb per second is ampere\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "644451b2db6a65d72b1148d209a331ded34838dcbb38f152cbc55bdbab560f45", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_001761_consistent_8b38953d_837786", "license": "Apache-2.0", "prompt": "In student derivation case 837786, check dimensional consistency for I = Q / t. The left side has dimensions A and the right side has dimensions A. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\ncoulomb per second is ampere\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "I = Q / t"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: target_schema, valid_examples.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"target_schema\", \"valid_examples\"]}", "dedupe_signature": "2a2c0653914c33c1929b4952c7b372147b1cee62c6dcd32a01ad938a1d0a3416", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["target_schema", "valid_examples"]}, "id": "abstain_001763_target_schema_valid_examples", "license": "Apache-2.0", "prompt": "Write a parser that converts each warehouse experiment record from batch 587497 into the correct schema, but the prompt does not include the target schema or examples. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: target_schema, valid_examples.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["target_schema", "valid_examples"]}, "verifier": {"missing": ["target_schema", "valid_examples"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 2.25 kg and a = 7.05 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 15.8625, \"unit\": \"N\"}", "dedupe_signature": "0f8043bceeac3525c8ba2b814a7e64aa81ba7cb4f040ce6d2ce0727ff48d873b", "difficulty": "easy", "final_answer": {"answer": 15.8625, "unit": "N"}, "id": "force_001764_2.25_7.05", "license": "Apache-2.0", "prompt": "A cart has mass 2.25 kg and measured acceleration 7.05 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 2.25 kg and a = 7.05 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 7.05, "mass": 2.25}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 38.3^2 and multiply by 0.5 * 25.55.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 18739.5197, \"unit\": \"J\"}", "dedupe_signature": "f65dbfea82c9bb9c42eb0076759882006e0c3893e1591f228aec526bc3b7cd6f", "difficulty": "easy", "final_answer": {"answer": 18739.5197, "unit": "J"}, "id": "ke_001765_25.55_38.3", "license": "Apache-2.0", "prompt": "A body of mass 25.55 kg moves at 38.3 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 38.3^2 and multiply by 0.5 * 25.55.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 25.55, "velocity": 38.3}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 4.72 * 8.314 * 274 / 107.5.\nFinal: {\"answer\": 100.0217, \"unit\": \"kPa\"}", "dedupe_signature": "be9b370c1d7bd73c1b72614e41de24ad72118a5a1b95fb5fa4911a2f20e1c2dc", "difficulty": "medium", "final_answer": {"answer": 100.0217, "unit": "kPa"}, "id": "ideal_gas_001767_4.72_274_107.5", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=4.72 mol, T=274 K, and V=107.5 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 4.72 * 8.314 * 274 / 107.5.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 4.72, "temp_k": 274, "volume_l": 107.5}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1530 * 0.74 * 57.\nFinal: {\"answer\": 64535.4, \"unit\": \"J\"}", "dedupe_signature": "b05c3ca4327052d0fd35c2959fd89580b128921c6f76e02fb70f35e60561c149", "difficulty": "easy", "final_answer": {"answer": 64535.4, "unit": "J"}, "id": "heat_q_001768_1530_0.74_57", "license": "Apache-2.0", "prompt": "A 1530 g sample has specific heat 0.74 J/(g*K). How much heat is needed to raise its temperature by 57 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1530 * 0.74 * 57.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 57, "heat_capacity": 0.74, "mass_g": 1530}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=211.7 V and R=73.1 ohm.\nFinal: {\"answer\": 613.0902, \"unit\": \"W\"}", "dedupe_signature": "ece167517a1ce48a069f84b2c8262e10a923f9c6d941bf9a9d052483c3ddb4c7", "difficulty": "easy", "final_answer": {"answer": 613.0902, "unit": "W"}, "id": "ohm_power_001769_211.7_73.1", "license": "Apache-2.0", "prompt": "A resistor has resistance 73.1 ohm and voltage 211.7 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=211.7 V and R=73.1 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 73.1, "voltage": 211.7}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=660.5 mg, t=122.5 h, and T_half=73 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 206.4048, \"unit\": \"mg\"}", "dedupe_signature": "81764175d02d59f194253e27ca0b6bff62124fe93ea6946a930acc4e748bd8ea", "difficulty": "medium", "final_answer": {"answer": 206.4048, "unit": "mg"}, "id": "half_life_001770_660.5_73_122.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 660.5 mg. Its half-life is 73 hours. How many mg remain after 122.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=660.5 mg, t=122.5 h, and T_half=73 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 122.5, "half_life": 73.0, "initial_amount": 660.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 6.5 mol * 100.087 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 650.5655, \"unit\": \"g\"}", "dedupe_signature": "2b326e142a1f2b0a56a797b01447f715df1538e260ea8dbc18feadba471d7b6a", "difficulty": "medium", "final_answer": {"answer": 650.5655, "unit": "g"}, "id": "stoich_mass_001771_calcium_carbonate_6.5", "license": "Apache-2.0", "prompt": "A sample contains 6.5 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 6.5 mol * 100.087 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "calcium carbonate", "molar_mass": 100.087, "moles": 6.5}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.59 y, so each step multiplies y by 1 - h*0.59.\n3. Apply that update for 3 steps and round the final state.\nFinal: {\"answer\": 1.0191, \"unit\": \"state_units\"}", "dedupe_signature": "4986a2f225266d263d3432f7c3c07dcfc145508c253e449b98bf27832f10dfcf", "difficulty": "medium", "final_answer": {"answer": 1.0191, "unit": "state_units"}, "id": "euler_decay_001773_18.5_0.59_1.05_3", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.59 y with y(0)=18.5, step size h=1.05, for 3 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.59 y, so each step multiplies y by 1 - h*0.59.\nApply that update for 3 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 18.5, "rate": 0.59, "step": 1.05, "steps": 3}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(5)=-35.3 and f(10.8)=-79.38.\n3. The interval width is 5.8.\nFinal: {\"answer\": -332.572, \"unit\": \"area_units\"}", "dedupe_signature": "77398068b4ee4e0dab8fb700308de33bcb0c7133eb8bc00d7bce908fd011eff5", "difficulty": "medium", "final_answer": {"answer": -332.572, "unit": "area_units"}, "id": "trapz_linear_001774_-7.6_2.7_5_10.8", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-7.6x+2.7 from x=5 to x=10.8. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(5)=-35.3 and f(10.8)=-79.38.\nThe interval width is 5.8.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 2.7, "slope": -7.6, "x0": 5.0, "x1": 10.8}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.16 and add it to the current value.\nFinal: {\"answer\": [1.946, 0.412, 0.004], \"unit\": \"temperature_units\"}", "dedupe_signature": "4d8d012afc3c1d4e0120a22d39e6ebc395c729b8e88ce5fca52402fd5e7c48e8", "difficulty": "hard", "final_answer": {"answer": [1.946, 0.412, 0.004], "unit": "temperature_units"}, "id": "heat_step_001775_0.16_-0.05_2.85_0.1_-0.7_2.9", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-0.05, right=2.9; current interior values are [2.85, 0.1, -0.7]. Use r=0.16. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.16 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [2.85, 0.1, -0.7], "left": -0.05, "r": 0.16, "right": 2.9}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kelvin equals Celsius plus 273.15.\n2. Apply the conversion factor directly to the given value.\n3. Compute 15.0 + 273.15.\nFinal: {\"answer\": 288.15, \"unit\": \"K\"}", "dedupe_signature": "81cdbb0386063816d1b46eb2eed8505ca19c3cd0729b3d3bf9ca5d3986d1131a", "difficulty": "easy", "final_answer": {"answer": 288.15, "unit": "K"}, "id": "unit_convert_001776_c_to_k_15", "license": "Apache-2.0", "prompt": "Convert 15 degC to K. Return the converted value with unit.", "reasoning_trace": "Kelvin equals Celsius plus 273.15.\nApply the conversion factor directly to the given value.\nCompute 15.0 + 273.15.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 15.0}, "verifier": {"formula": "value + 273.15", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [10.0, -8.0], \"unit\": \"dimensionless\"}", "dedupe_signature": "78260dbeda63bee9ddbc2a4eff687daeaaa03ca5cb897a44ac86591a99c6a764", "difficulty": "medium", "final_answer": {"answer": [10.0, -8.0], "unit": "dimensionless"}, "id": "line_two_point_001778_2.5_11.75_10_-8", "license": "Apache-2.0", "prompt": "A line passes through points (2.5, 17) and (11.75, 109.5). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 2.5, "x2": 11.75, "y1": 17.0, "y2": 109.5}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef normalize_001780(values):\n    total = sum(values)\n    if total == 0:\n        raise ValueError('cannot normalize zero-sum values')\n    return [v / total for v in values]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"normalize_001780\"}", "dedupe_signature": "f324900bf782d5c6e8eb1a6c3234637a9661b3e22713be544cd7b07fcddef1a7", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "normalize_001780"}, "id": "code_001780_normalize_001780", "license": "Apache-2.0", "prompt": "Write a Python function normalize_001780(values) that returns a new list whose values sum to 1. Raise ValueError if the sum is zero. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "normalize_001780"}, "verifier": {"function": "normalize_001780", "tests": ["out = normalize_001780([2, 3, 5]); assert len(out) == 3", "assert abs(sum(normalize_001780([2, 3, 5])) - 1.0) < 1e-12", "assert normalize_001780([1, 1]) == [0.5, 0.5]", "try:\n    normalize_001780([1, -1])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 19.45 kg and a = 4.75 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 92.3875, \"unit\": \"N\"}", "dedupe_signature": "4181c527fe0fc84cebdc658429a7ccffda315de9e18c8fae2b4783a368a71901", "difficulty": "easy", "final_answer": {"answer": 92.3875, "unit": "N"}, "id": "force_001782_19.45_4.75", "license": "Apache-2.0", "prompt": "A cart has mass 19.45 kg and measured acceleration 4.75 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 19.45 kg and a = 4.75 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 4.75, "mass": 19.45}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=79 degrees through the sine of 2 theta.\n3. Substitute v=11.7 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 5.2273, \"unit\": \"m\"}", "dedupe_signature": "7814e87c0cc25341625777e55c647b0980c22bcd5e79f38b611330df0f14aaa3", "difficulty": "medium", "final_answer": {"answer": 5.2273, "unit": "m"}, "id": "projectile_range_001784_11.7_79", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 11.7 m/s and angle 79 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=79 degrees through the sine of 2 theta.\nSubstitute v=11.7 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 79, "gravity": 9.81, "speed": 11.7}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 2.12 * 8.314 * 252 / 104.7.\nFinal: {\"answer\": 42.4228, \"unit\": \"kPa\"}", "dedupe_signature": "5dd133e871f28a5afe412724f15ee1d1d2a3af59aad97debc78e9ff5b9ec4716", "difficulty": "medium", "final_answer": {"answer": 42.4228, "unit": "kPa"}, "id": "ideal_gas_001785_2.12_252_104.7", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=2.12 mol, T=252 K, and V=104.7 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 2.12 * 8.314 * 252 / 104.7.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 2.12, "temp_k": 252, "volume_l": 104.7}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=190.1 V and R=198.7 ohm.\nFinal: {\"answer\": 181.8722, \"unit\": \"W\"}", "dedupe_signature": "3ba341f028465c13520bfd0a1d176126b46ac51c8b217feedd6949adf83b1e01", "difficulty": "easy", "final_answer": {"answer": 181.8722, "unit": "W"}, "id": "ohm_power_001787_190.1_198.7", "license": "Apache-2.0", "prompt": "A resistor has resistance 198.7 ohm and voltage 190.1 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=190.1 V and R=198.7 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 198.7, "voltage": 190.1}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=709.5 mg, t=258.5 h, and T_half=39 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 7.1724, \"unit\": \"mg\"}", "dedupe_signature": "28858a2f8c1876f8edb668c4284869cb38c053f69f0b3f35c40acf0260be0040", "difficulty": "medium", "final_answer": {"answer": 7.1724, "unit": "mg"}, "id": "half_life_001788_709.5_39_258.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 709.5 mg. Its half-life is 39 hours. How many mg remain after 258.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=709.5 mg, t=258.5 h, and T_half=39 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 258.5, "half_life": 39.0, "initial_amount": 709.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 5.95 mol * 44.01 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 261.8595, \"unit\": \"g\"}", "dedupe_signature": "2b4e1fb6a136258b04e555f93b99b21e6ede9563d6d5baa4a50bb322c1b06e6f", "difficulty": "medium", "final_answer": {"answer": 261.8595, "unit": "g"}, "id": "stoich_mass_001789_carbon_dioxide_5.95", "license": "Apache-2.0", "prompt": "A sample contains 5.95 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 5.95 mol * 44.01 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "carbon dioxide", "molar_mass": 44.01, "moles": 5.95}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 1185 mL to 1.185 L.\n3. Compute M = 3.065 / 1.185.\nFinal: {\"answer\": 2.5865, \"unit\": \"mol/L\"}", "dedupe_signature": "dba96292b2669e573e539a537ba882eb69218bfa4bee8dfb2a009e0c51bf0781", "difficulty": "medium", "final_answer": {"answer": 2.5865, "unit": "mol/L"}, "id": "molarity_001790_3.065_1185", "license": "Apache-2.0", "prompt": "A solution contains 3.065 mol of solute in 1185 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 1185 mL to 1.185 L.\nCompute M = 3.065 / 1.185.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 3.065, "volume_ml": 1185}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.36 y, so each step multiplies y by 1 - h*0.36.\n3. Apply that update for 11 steps and round the final state.\nFinal: {\"answer\": 8.3518, \"unit\": \"state_units\"}", "dedupe_signature": "443a45828bfd9fe62cb4c97a19cb4b7d834644dad93b2d528baa2cfa7513ddb3", "difficulty": "medium", "final_answer": {"answer": 8.3518, "unit": "state_units"}, "id": "euler_decay_001791_19_0.36_0.2_11", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.36 y with y(0)=19, step size h=0.2, for 11 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.36 y, so each step multiplies y by 1 - h*0.36.\nApply that update for 11 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 19.0, "rate": 0.36, "step": 0.2, "steps": 11}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.26 and add it to the current value.\nFinal: {\"answer\": [0.464, 0.243, 0.581], \"unit\": \"temperature_units\"}", "dedupe_signature": "e04943cc2eace5fcf6362914fa1cc8c8e41e666621b47fdab8babcad7f6b626c", "difficulty": "hard", "final_answer": {"answer": [0.464, 0.243, 0.581], "unit": "temperature_units"}, "id": "heat_step_001793_0.26_0.85_0.1_0.75_-0.55_2.5", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=0.85, right=2.5; current interior values are [0.1, 0.75, -0.55]. Use r=0.26. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.26 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [0.1, 0.75, -0.55], "left": 0.85, "r": 0.26, "right": 2.5}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 5544.0 / 1000.\nFinal: {\"answer\": 5.544, \"unit\": \"kg\"}", "dedupe_signature": "b3c12d98ab779773d8bc62be592034f0db1761f1ee1d6205b1ad9abca6b0abae", "difficulty": "easy", "final_answer": {"answer": 5.544, "unit": "kg"}, "id": "unit_convert_001794_g_to_kg_5544", "license": "Apache-2.0", "prompt": "Convert 5544 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 5544.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 5544.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=209 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-167.927, -93.0834], \"unit\": \"N\"}", "dedupe_signature": "a6246f3e5538bda0b85b3e1e7e236e11f3dcc6a8011500550ff087f8526b3b1d", "difficulty": "medium", "final_answer": {"answer": [-167.927, -93.0834], "unit": "N"}, "id": "vector_components_001795_192_209", "license": "Apache-2.0", "prompt": "A vector has magnitude 192 N at 209 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=209 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 209, "magnitude": 192.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [9.0, -19.75], \"unit\": \"dimensionless\"}", "dedupe_signature": "47b99c6bbeaf82d590bd635e4276875a4d006fc0870d1fcc31c85ac1d087d79f", "difficulty": "medium", "final_answer": {"answer": [9.0, -19.75], "unit": "dimensionless"}, "id": "line_two_point_001796_-5.75_-5.5_9_-19.75", "license": "Apache-2.0", "prompt": "A line passes through points (-5.75, -71.5) and (-5.5, -69.25). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -5.75, "x2": -5.5, "y1": -71.5, "y2": -69.25}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. energy divided by length is force, not spring constant\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "f3a11e9def8607a0d87f2a1d9613b01e3e2512f2645b171c4d5b8c48024fdc16", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_001797_inconsistent_56040f5d_108090", "license": "Apache-2.0", "prompt": "In quality-control check case 108090, check dimensional consistency for k = E / x. The left side has dimensions N/m and the right side has dimensions J/m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nenergy divided by length is force, not spring constant\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "k = E / x"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: recurrence, objective, tie_breaking_rule.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"recurrence\", \"objective\", \"tie_breaking_rule\"]}", "dedupe_signature": "c3729d901963bcb85e0f95464af0d2c95421ad4eed95ba3f28abd5f0a768a0fd", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["recurrence", "objective", "tie_breaking_rule"]}, "id": "abstain_001799_recurrence_objective_tie_breaking_rule", "license": "Apache-2.0", "prompt": "Write a dynamic-programming solver for a routing scoring problem with 3129 items and budget 5970, but the recurrence, objective, and tie-breaking rule are all absent. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: recurrence, objective, tie_breaking_rule.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["recurrence", "objective", "tie_breaking_rule"]}, "verifier": {"missing": ["recurrence", "objective", "tie_breaking_rule"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 12.5 kg and a = 7.7 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 96.25, \"unit\": \"N\"}", "dedupe_signature": "c21d9cae2b28c0a56eb31ef32cbd15d8c14551c7df2ba168cadab7de9a71f552", "difficulty": "easy", "final_answer": {"answer": 96.25, "unit": "N"}, "id": "force_001800_12.5_7.7", "license": "Apache-2.0", "prompt": "A cart has mass 12.5 kg and measured acceleration 7.7 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 12.5 kg and a = 7.7 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 7.7, "mass": 12.5}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 40.8^2 and multiply by 0.5 * 1.15.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 957.168, \"unit\": \"J\"}", "dedupe_signature": "007bfde5113c7fa3bf66742a93a169d841ae0c14145a90339a1d988f4543d328", "difficulty": "easy", "final_answer": {"answer": 957.168, "unit": "J"}, "id": "ke_001801_1.15_40.8", "license": "Apache-2.0", "prompt": "A body of mass 1.15 kg moves at 40.8 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 40.8^2 and multiply by 0.5 * 1.15.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 1.15, "velocity": 40.8}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=44 degrees through the sine of 2 theta.\n3. Substitute v=61.7 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 387.8258, \"unit\": \"m\"}", "dedupe_signature": "0db10361584a350fd1b3d56e060b8ed8f715c07f5952478cec44c5fefdda6508", "difficulty": "medium", "final_answer": {"answer": 387.8258, "unit": "m"}, "id": "projectile_range_001802_61.7_44", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 61.7 m/s and angle 44 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=44 degrees through the sine of 2 theta.\nSubstitute v=61.7 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 44, "gravity": 9.81, "speed": 61.7}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 5.58 * 8.314 * 492 / 43.1.\nFinal: {\"answer\": 529.5806, \"unit\": \"kPa\"}", "dedupe_signature": "df72d430d647e4256433f00ce84b2e16fb4f31ace9bff0620ad83e8fab31fc3c", "difficulty": "medium", "final_answer": {"answer": 529.5806, "unit": "kPa"}, "id": "ideal_gas_001803_5.58_492_43.1", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=5.58 mol, T=492 K, and V=43.1 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 5.58 * 8.314 * 492 / 43.1.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 5.58, "temp_k": 492, "volume_l": 43.1}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1305 * 2.385 * 29.\nFinal: {\"answer\": 90260.325, \"unit\": \"J\"}", "dedupe_signature": "3394d9a3268bca57a838d859c7c9ee6de1785bad6d63acff397c8218c81dbf57", "difficulty": "easy", "final_answer": {"answer": 90260.325, "unit": "J"}, "id": "heat_q_001804_1305_2.385_29", "license": "Apache-2.0", "prompt": "A 1305 g sample has specific heat 2.385 J/(g*K). How much heat is needed to raise its temperature by 29 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1305 * 2.385 * 29.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 29, "heat_capacity": 2.385, "mass_g": 1305}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=204 V and R=165.1 ohm.\nFinal: {\"answer\": 252.0654, \"unit\": \"W\"}", "dedupe_signature": "c1add9e82a3f6350741297900ca7f4041815ead6129df5917691314086b4e69f", "difficulty": "easy", "final_answer": {"answer": 252.0654, "unit": "W"}, "id": "ohm_power_001805_204_165.1", "license": "Apache-2.0", "prompt": "A resistor has resistance 165.1 ohm and voltage 204 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=204 V and R=165.1 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 165.1, "voltage": 204.0}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 0.02 mol * 100.087 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 2.0017, \"unit\": \"g\"}", "dedupe_signature": "99a3fea4bcea89bd907c7e578622f92dfd81a518724af28a58d607c0f1411e16", "difficulty": "medium", "final_answer": {"answer": 2.0017, "unit": "g"}, "id": "stoich_mass_001807_calcium_carbonate_0.02", "license": "Apache-2.0", "prompt": "A sample contains 0.02 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 0.02 mol * 100.087 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "calcium carbonate", "molar_mass": 100.087, "moles": 0.02}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 4355 mL to 4.355 L.\n3. Compute M = 1.775 / 4.355.\nFinal: {\"answer\": 0.4076, \"unit\": \"mol/L\"}", "dedupe_signature": "b97d70c08d68ec90fc6bad4ad80cc288b1d6cb5e755e2ab851bdf8ec21f0de57", "difficulty": "medium", "final_answer": {"answer": 0.4076, "unit": "mol/L"}, "id": "molarity_001808_1.775_4355", "license": "Apache-2.0", "prompt": "A solution contains 1.775 mol of solute in 4355 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 4355 mL to 4.355 L.\nCompute M = 1.775 / 4.355.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 1.775, "volume_ml": 4355}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.77 y, so each step multiplies y by 1 - h*0.77.\n3. Apply that update for 7 steps and round the final state.\nFinal: {\"answer\": 0.0111, \"unit\": \"state_units\"}", "dedupe_signature": "3f11661590a06c786d7e0025b1162c0fca92b484f72ef19ca816f7f5c674c1a8", "difficulty": "medium", "final_answer": {"answer": 0.0111, "unit": "state_units"}, "id": "euler_decay_001809_43_0.77_0.9_7", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.77 y with y(0)=43, step size h=0.9, for 7 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.77 y, so each step multiplies y by 1 - h*0.77.\nApply that update for 7 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 43.0, "rate": 0.77, "step": 0.9, "steps": 7}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(7.4)=-16.18 and f(17.2)=-42.64.\n3. The interval width is 9.8.\nFinal: {\"answer\": -288.218, \"unit\": \"area_units\"}", "dedupe_signature": "30d1c8fbdf760f2001d56114daa0e8b751d94793b26bb5d6a67d18c8253bbee8", "difficulty": "medium", "final_answer": {"answer": -288.218, "unit": "area_units"}, "id": "trapz_linear_001810_-2.7_3.8_7.4_17.2", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-2.7x+3.8 from x=7.4 to x=17.2. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(7.4)=-16.18 and f(17.2)=-42.64.\nThe interval width is 9.8.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 3.8, "slope": -2.7, "x0": 7.4, "x1": 17.200000000000003}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.16 and add it to the current value.\nFinal: {\"answer\": [2.176, 1.536, -0.756], \"unit\": \"temperature_units\"}", "dedupe_signature": "a52edce2e58f3b6bc919b2b93189e6a78258da538480e08b82783f7a7fe007cd", "difficulty": "hard", "final_answer": {"answer": [2.176, 1.536, -0.756], "unit": "temperature_units"}, "id": "heat_step_001811_0.16_-0.3_2.8_2.0_-1.7_0.5", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-0.3, right=0.5; current interior values are [2.8, 2.0, -1.7]. Use r=0.16. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.16 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [2.8, 2.0, -1.7], "left": -0.3, "r": 0.16, "right": 0.5}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kelvin equals Celsius plus 273.15.\n2. Apply the conversion factor directly to the given value.\n3. Compute 220.0 + 273.15.\nFinal: {\"answer\": 493.15, \"unit\": \"K\"}", "dedupe_signature": "1efadea7218c4d598fcdd58303e1081e1087b915b8811d2c3a5acdc2cc2812e0", "difficulty": "easy", "final_answer": {"answer": 493.15, "unit": "K"}, "id": "unit_convert_001812_c_to_k_220", "license": "Apache-2.0", "prompt": "Convert 220 degC to K. Return the converted value with unit.", "reasoning_trace": "Kelvin equals Celsius plus 273.15.\nApply the conversion factor directly to the given value.\nCompute 220.0 + 273.15.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 220.0}, "verifier": {"formula": "value + 273.15", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=135 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-290.9744, 290.9744], \"unit\": \"N\"}", "dedupe_signature": "e775c9caa4f7d2880add5552207b9e817bbfa284f65eaa8d2eda416435b0b7ac", "difficulty": "medium", "final_answer": {"answer": [-290.9744, 290.9744], "unit": "N"}, "id": "vector_components_001813_411.5_135", "license": "Apache-2.0", "prompt": "A vector has magnitude 411.5 N at 135 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=135 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 135, "magnitude": 411.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-7.55, -28.5], \"unit\": \"dimensionless\"}", "dedupe_signature": "a22f90f15c06b61f959fac8301d4dd1eef027c976a3ce4b26fdb399d942d3195", "difficulty": "medium", "final_answer": {"answer": [-7.55, -28.5], "unit": "dimensionless"}, "id": "line_two_point_001814_17.75_30.5_-7.55_-28.5", "license": "Apache-2.0", "prompt": "A line passes through points (17.75, -162.512) and (30.5, -258.775). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 17.75, "x2": 30.5, "y1": -162.5125, "y2": -258.775}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. amount times volume is not concentration\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "b576b484af021db90c62ae4e0ac03e66a8b18ca53f275b77e34089eeac177eff", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_001815_inconsistent_74ac0b02_294553", "license": "Apache-2.0", "prompt": "In sensor calibration case 294553, check dimensional consistency for C = n * V. The left side has dimensions mol/L and the right side has dimensions mol*L. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\namount times volume is not concentration\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "C = n * V"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\nimport math\n\ndef unit_vector_001816(x, y):\n    norm = math.hypot(x, y)\n    if norm == 0:\n        raise ValueError('zero vector has no direction')\n    return (x / norm, y / norm)\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"unit_vector_001816\"}", "dedupe_signature": "0571dedf5397374ad988de8c231c1222a055ab1d06c9af16b559f02cc6cc9fbc", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "unit_vector_001816"}, "id": "code_001816_unit_vector_001816", "license": "Apache-2.0", "prompt": "Write a Python function unit_vector_001816(x, y) that returns the 2D unit vector as a tuple. Raise ValueError for the zero vector. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "unit_vector_001816"}, "verifier": {"function": "unit_vector_001816", "tests": ["ux, uy = unit_vector_001816(3, 4); assert abs(ux - 0.6) < 1e-12 and abs(uy - 0.8) < 1e-12", "assert unit_vector_001816(0, 5) == (0, 1)", "try:\n    unit_vector_001816(0, 0)\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 9.5 kg and a = 0.75 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 7.125, \"unit\": \"N\"}", "dedupe_signature": "dca6309ce2dc2aef4365f1ea2edbed29413ad415941a19cd88d374c9670fc9e1", "difficulty": "easy", "final_answer": {"answer": 7.125, "unit": "N"}, "id": "force_001818_9.5_0.75", "license": "Apache-2.0", "prompt": "A cart has mass 9.5 kg and measured acceleration 0.75 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 9.5 kg and a = 0.75 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 0.75, "mass": 9.5}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=57 degrees through the sine of 2 theta.\n3. Substitute v=9.4 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 8.2284, \"unit\": \"m\"}", "dedupe_signature": "dc9c7c621fb65b8ac0f00024c2ccfe36987981a222223e563cc9a3466a255742", "difficulty": "medium", "final_answer": {"answer": 8.2284, "unit": "m"}, "id": "projectile_range_001820_9.4_57", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 9.4 m/s and angle 57 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=57 degrees through the sine of 2 theta.\nSubstitute v=9.4 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 57, "gravity": 9.81, "speed": 9.4}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 5.1 * 8.314 * 555 / 75.4.\nFinal: {\"answer\": 312.1058, \"unit\": \"kPa\"}", "dedupe_signature": "4113f71552e8f911fe74ffd098995eac45c8d714ca516a6f11fc134d1001d0b8", "difficulty": "medium", "final_answer": {"answer": 312.1058, "unit": "kPa"}, "id": "ideal_gas_001821_5.1_555_75.4", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=5.1 mol, T=555 K, and V=75.4 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 5.1 * 8.314 * 555 / 75.4.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 5.1, "temp_k": 555, "volume_l": 75.4}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1930 * 1.22 * 39.\nFinal: {\"answer\": 91829.4, \"unit\": \"J\"}", "dedupe_signature": "744958467ab093d7c5af5aa6b013d63fc3fbffdea8c3133e4090c5bd785c402d", "difficulty": "easy", "final_answer": {"answer": 91829.4, "unit": "J"}, "id": "heat_q_001822_1930_1.22_39", "license": "Apache-2.0", "prompt": "A 1930 g sample has specific heat 1.22 J/(g*K). How much heat is needed to raise its temperature by 39 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1930 * 1.22 * 39.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 39, "heat_capacity": 1.22, "mass_g": 1930}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=82.3 V and R=19.3 ohm.\nFinal: {\"answer\": 350.9477, \"unit\": \"W\"}", "dedupe_signature": "25ed31dcbbff03f0cdc4999a5a4e1ef86fb6886a50011ce4bc9019e5b9fbc48e", "difficulty": "easy", "final_answer": {"answer": 350.9477, "unit": "W"}, "id": "ohm_power_001823_82.3_19.3", "license": "Apache-2.0", "prompt": "A resistor has resistance 19.3 ohm and voltage 82.3 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=82.3 V and R=19.3 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 19.3, "voltage": 82.3}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=695.5 mg, t=254 h, and T_half=79.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 75.9479, \"unit\": \"mg\"}", "dedupe_signature": "9df7696dce99ad3511682d2f91303aaac21d15e4ff4b5c819f47496784b77d35", "difficulty": "medium", "final_answer": {"answer": 75.9479, "unit": "mg"}, "id": "half_life_001824_695.5_79.5_254", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 695.5 mg. Its half-life is 79.5 hours. How many mg remain after 254 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=695.5 mg, t=254 h, and T_half=79.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 254.0, "half_life": 79.5, "initial_amount": 695.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 2.23 mol * 100.087 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 223.194, \"unit\": \"g\"}", "dedupe_signature": "d0dde379263a0b03702918a82c4085106cdd9c8d353d320626a94fb26755ced2", "difficulty": "medium", "final_answer": {"answer": 223.194, "unit": "g"}, "id": "stoich_mass_001825_calcium_carbonate_2.23", "license": "Apache-2.0", "prompt": "A sample contains 2.23 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 2.23 mol * 100.087 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "calcium carbonate", "molar_mass": 100.087, "moles": 2.23}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 3010 mL to 3.01 L.\n3. Compute M = 4.425 / 3.01.\nFinal: {\"answer\": 1.4701, \"unit\": \"mol/L\"}", "dedupe_signature": "542b934b3e8365b026d77b4826b4ca97ec441030141cc6f7adcffbe6cefb51f2", "difficulty": "medium", "final_answer": {"answer": 1.4701, "unit": "mol/L"}, "id": "molarity_001826_4.425_3010", "license": "Apache-2.0", "prompt": "A solution contains 4.425 mol of solute in 3010 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 3010 mL to 3.01 L.\nCompute M = 4.425 / 3.01.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 4.425, "volume_ml": 3010}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-7.7)=13.07 and f(-0.6)=5.26.\n3. The interval width is 7.1.\nFinal: {\"answer\": 65.0715, \"unit\": \"area_units\"}", "dedupe_signature": "dabd7985a25807c4a5219419fe4aed5ee1295beb0e049abac0f7152488659f04", "difficulty": "medium", "final_answer": {"answer": 65.0715, "unit": "area_units"}, "id": "trapz_linear_001828_-1.1_4.6_-7.7_-0.6", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-1.1x+4.6 from x=-7.7 to x=-0.6. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-7.7)=13.07 and f(-0.6)=5.26.\nThe interval width is 7.1.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 4.6, "slope": -1.1, "x0": -7.7, "x1": -0.6000000000000005}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.2 and add it to the current value.\nFinal: {\"answer\": [0.78, -0.89, -0.82], \"unit\": \"temperature_units\"}", "dedupe_signature": "b6db84dddf4b3c385f616bd4892142940dd9a137bef60c6063b4074b2ae73dbd", "difficulty": "hard", "final_answer": {"answer": [0.78, -0.89, -0.82], "unit": "temperature_units"}, "id": "heat_step_001829_0.2_1.75_1.25_-1.6_-0.9_0.2", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.75, right=0.2; current interior values are [1.25, -1.6, -0.9]. Use r=0.2. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.2 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [1.25, -1.6, -0.9], "left": 1.75, "r": 0.2, "right": 0.2}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=57 degrees and keep the unit as newtons.\nFinal: {\"answer\": [59.0933, 90.9958], \"unit\": \"N\"}", "dedupe_signature": "def89ada70c8b78cc1ebecc3ee587dd4ca958f670e34ae1f1249c6f7d70dc3f7", "difficulty": "medium", "final_answer": {"answer": [59.0933, 90.9958], "unit": "N"}, "id": "vector_components_001831_108.5_57", "license": "Apache-2.0", "prompt": "A vector has magnitude 108.5 N at 57 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=57 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 57, "magnitude": 108.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-5.8, -26.0], \"unit\": \"dimensionless\"}", "dedupe_signature": "d645a680875032455541e487160a2dc4e635b0e16aba17410b90a73831ea16fe", "difficulty": "medium", "final_answer": {"answer": [-5.8, -26.0], "unit": "dimensionless"}, "id": "line_two_point_001832_14.25_24.25_-5.8_-26", "license": "Apache-2.0", "prompt": "A line passes through points (14.25, -108.65) and (24.25, -166.65). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 14.25, "x2": 24.25, "y1": -108.64999999999999, "y2": -166.65}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. m*v is momentum, not energy\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "70c7bb38e21afb0750b5d1278c7fb308d4aba7ac7d00f4e65430c7b4ab2b190f", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_001833_inconsistent_1e14b074_652431", "license": "Apache-2.0", "prompt": "In simulation spec case 652431, check dimensional consistency for E = m * v. The left side has dimensions kg*m^2/s^2 and the right side has dimensions kg*m/s. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nm*v is momentum, not energy\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "E = m * v"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef normalize_001834(values):\n    total = sum(values)\n    if total == 0:\n        raise ValueError('cannot normalize zero-sum values')\n    return [v / total for v in values]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"normalize_001834\"}", "dedupe_signature": "dd98abee6ee4ac7cb13c6912d72b8617ad2bd6ea3eb29365bcb4b42116c1e419", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "normalize_001834"}, "id": "code_001834_normalize_001834", "license": "Apache-2.0", "prompt": "Write a Python function normalize_001834(values) that returns a new list whose values sum to 1. Raise ValueError if the sum is zero. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "normalize_001834"}, "verifier": {"function": "normalize_001834", "tests": ["out = normalize_001834([2, 3, 5]); assert len(out) == 3", "assert abs(sum(normalize_001834([2, 3, 5])) - 1.0) < 1e-12", "assert normalize_001834([1, 1]) == [0.5, 0.5]", "try:\n    normalize_001834([1, -1])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: rate_constant, number_of_steps.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"rate_constant\", \"number_of_steps\"]}", "dedupe_signature": "1ce5ac83efe9de9799d5b34f09f684ff2b82575e76db6c2be3d13d18b475ea5e", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["rate_constant", "number_of_steps"]}, "id": "abstain_001835_rate_constant_number_of_steps", "license": "Apache-2.0", "prompt": "Use explicit Euler for dy/dt = -k y. The prompt gives y(0)=46.5 and h=0.5, but omits both k and the number of steps. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: rate_constant, number_of_steps.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["rate_constant", "number_of_steps"]}, "verifier": {"missing": ["rate_constant", "number_of_steps"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 11.05 kg and a = 8.5 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 93.925, \"unit\": \"N\"}", "dedupe_signature": "e0a9d4219e2a0bb9f21369948c3373fa9448f1a853ee9068e8954decf3b590f0", "difficulty": "easy", "final_answer": {"answer": 93.925, "unit": "N"}, "id": "force_001836_11.05_8.5", "license": "Apache-2.0", "prompt": "A cart has mass 11.05 kg and measured acceleration 8.5 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 11.05 kg and a = 8.5 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 8.5, "mass": 11.05}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=61 degrees through the sine of 2 theta.\n3. Substitute v=47.2 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 192.5908, \"unit\": \"m\"}", "dedupe_signature": "61758ec96c96a15aa1ec578052d980718ee8438ec366e6403e1f5c7070335cad", "difficulty": "medium", "final_answer": {"answer": 192.5908, "unit": "m"}, "id": "projectile_range_001838_47.2_61", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 47.2 m/s and angle 61 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=61 degrees through the sine of 2 theta.\nSubstitute v=47.2 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 61, "gravity": 9.81, "speed": 47.2}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 4.83 * 8.314 * 433 / 62.8.\nFinal: {\"answer\": 276.8761, \"unit\": \"kPa\"}", "dedupe_signature": "c2508fa59f0b85400a0ae77f9951fa33ef71569bf2b9bb431ff86ba43a704fa0", "difficulty": "medium", "final_answer": {"answer": 276.8761, "unit": "kPa"}, "id": "ideal_gas_001839_4.83_433_62.8", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=4.83 mol, T=433 K, and V=62.8 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 4.83 * 8.314 * 433 / 62.8.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 4.83, "temp_k": 433, "volume_l": 62.8}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 75 * 4.41 * 98.\nFinal: {\"answer\": 32413.5, \"unit\": \"J\"}", "dedupe_signature": "e0c536b69809158a52a08713c7b60e8f4dab7e2bb60c719037f83a28ddf37877", "difficulty": "easy", "final_answer": {"answer": 32413.5, "unit": "J"}, "id": "heat_q_001840_75_4.41_98", "license": "Apache-2.0", "prompt": "A 75 g sample has specific heat 4.41 J/(g*K). How much heat is needed to raise its temperature by 98 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 75 * 4.41 * 98.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 98, "heat_capacity": 4.41, "mass_g": 75}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=429 mg, t=156 h, and T_half=83.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 117.5044, \"unit\": \"mg\"}", "dedupe_signature": "d8a43b55ecff3aba890f7584c4ff5f5991ed1b3672952b7b8bc868a26b5bc0b9", "difficulty": "medium", "final_answer": {"answer": 117.5044, "unit": "mg"}, "id": "half_life_001842_429_83.5_156", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 429 mg. Its half-life is 83.5 hours. How many mg remain after 156 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=429 mg, t=156 h, and T_half=83.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 156.0, "half_life": 83.5, "initial_amount": 429.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 3.32 mol * 180.156 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 598.1179, \"unit\": \"g\"}", "dedupe_signature": "58eec7cf467b77b349933cf763a93b0e1678f1cdb8accfc8be42ae6d341839f7", "difficulty": "medium", "final_answer": {"answer": 598.1179, "unit": "g"}, "id": "stoich_mass_001843_glucose_3.32", "license": "Apache-2.0", "prompt": "A sample contains 3.32 mol of glucose. Using molar mass 180.156 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 3.32 mol * 180.156 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "glucose", "molar_mass": 180.156, "moles": 3.32}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 3645 mL to 3.645 L.\n3. Compute M = 4.955 / 3.645.\nFinal: {\"answer\": 1.3594, \"unit\": \"mol/L\"}", "dedupe_signature": "975075c3ebf23bbef790e992f103d20775f7549fd41026dd5279466be61c25ca", "difficulty": "medium", "final_answer": {"answer": 1.3594, "unit": "mol/L"}, "id": "molarity_001844_4.955_3645", "license": "Apache-2.0", "prompt": "A solution contains 4.955 mol of solute in 3645 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 3645 mL to 3.645 L.\nCompute M = 4.955 / 3.645.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 4.955, "volume_ml": 3645}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.53 y, so each step multiplies y by 1 - h*0.53.\n3. Apply that update for 12 steps and round the final state.\nFinal: {\"answer\": 0.0134, \"unit\": \"state_units\"}", "dedupe_signature": "4ec43617865e046ec1974db8236d127a18b5b94ed68f00b1df720cb2bf9ff393", "difficulty": "medium", "final_answer": {"answer": 0.0134, "unit": "state_units"}, "id": "euler_decay_001845_32_0.53_0.9_12", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.53 y with y(0)=32, step size h=0.9, for 12 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.53 y, so each step multiplies y by 1 - h*0.53.\nApply that update for 12 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 32.0, "rate": 0.53, "step": 0.9, "steps": 12}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-7.6)=26.76 and f(1.4)=-23.64.\n3. The interval width is 9.\nFinal: {\"answer\": 14.04, \"unit\": \"area_units\"}", "dedupe_signature": "0c3f4ae6e956cf9695da1418d08d797cb9b3a6fb2e0a4945de5add1a350510e8", "difficulty": "medium", "final_answer": {"answer": 14.04, "unit": "area_units"}, "id": "trapz_linear_001846_-5.6_-15.8_-7.6_1.4", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-5.6x+-15.8 from x=-7.6 to x=1.4. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-7.6)=26.76 and f(1.4)=-23.64.\nThe interval width is 9.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -15.8, "slope": -5.6, "x0": -7.6, "x1": 1.4000000000000004}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.14 and add it to the current value.\nFinal: {\"answer\": [1.508, 1.099, -0.732], \"unit\": \"temperature_units\"}", "dedupe_signature": "f4e8f205b1bd912b65b82d5d3c9117d6aad1410b1234d17e8fddf43afe6c1b62", "difficulty": "hard", "final_answer": {"answer": [1.508, 1.099, -0.732], "unit": "temperature_units"}, "id": "heat_step_001847_0.14_1.4_1.55_1.4_-0.9_-2.0", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.4, right=-2; current interior values are [1.55, 1.4, -0.9]. Use r=0.14. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.14 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [1.55, 1.4, -0.9], "left": 1.4, "r": 0.14, "right": -2.0}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=194 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-164.4651, -41.0058], \"unit\": \"N\"}", "dedupe_signature": "a74ffc3c00577a9a45b47e6d95c57ea02b8aad5d16b5a4340fa21a3cb748a00e", "difficulty": "medium", "final_answer": {"answer": [-164.4651, -41.0058], "unit": "N"}, "id": "vector_components_001849_169.5_194", "license": "Apache-2.0", "prompt": "A vector has magnitude 169.5 N at 194 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=194 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 194, "magnitude": 169.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-6.35, 25.0], \"unit\": \"dimensionless\"}", "dedupe_signature": "61dded042e722bbc87a00012d0b09dbb50c53c708e4c277b4f437f2f95c13e4f", "difficulty": "medium", "final_answer": {"answer": [-6.35, 25.0], "unit": "dimensionless"}, "id": "line_two_point_001850_-17.5_-13.5_-6.35_25", "license": "Apache-2.0", "prompt": "A line passes through points (-17.5, 136.125) and (-13.5, 110.725). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -17.5, "x2": -13.5, "y1": 136.125, "y2": 110.725}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. mass times acceleration has newton dimensions\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "85671cc35a7078291a5ec6f536ce93b1315e4dedfdb62bd5c10953cf59e8f3b2", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_001851_consistent_03f5e041_464965", "license": "Apache-2.0", "prompt": "In student derivation case 464965, check dimensional consistency for F = m * a. The left side has dimensions kg*m/s^2 and the right side has dimensions kg*m/s^2. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nmass times acceleration has newton dimensions\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "F = m * a"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\nimport math\n\ndef unit_vector_001852(x, y):\n    norm = math.hypot(x, y)\n    if norm == 0:\n        raise ValueError('zero vector has no direction')\n    return (x / norm, y / norm)\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"unit_vector_001852\"}", "dedupe_signature": "d2e5fdcf092d8b5a9c055da9bc81ecf855ae2ee1d7f0f22e021281e900e84420", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "unit_vector_001852"}, "id": "code_001852_unit_vector_001852", "license": "Apache-2.0", "prompt": "Write a Python function unit_vector_001852(x, y) that returns the 2D unit vector as a tuple. Raise ValueError for the zero vector. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "unit_vector_001852"}, "verifier": {"function": "unit_vector_001852", "tests": ["ux, uy = unit_vector_001852(3, 4); assert abs(ux - 0.6) < 1e-12 and abs(uy - 0.8) < 1e-12", "assert unit_vector_001852(0, 5) == (0, 1)", "try:\n    unit_vector_001852(0, 0)\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: target_schema, valid_examples.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"target_schema\", \"valid_examples\"]}", "dedupe_signature": "03a6b13b6240566b1132c7d076d9f0057487876b79ddd155ec2d95c407269fb6", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["target_schema", "valid_examples"]}, "id": "abstain_001853_target_schema_valid_examples", "license": "Apache-2.0", "prompt": "Write a parser that converts each mobile survey record from batch 721929 into the correct schema, but the prompt does not include the target schema or examples. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: target_schema, valid_examples.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["target_schema", "valid_examples"]}, "verifier": {"missing": ["target_schema", "valid_examples"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 14.5 kg and a = 13.45 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 195.025, \"unit\": \"N\"}", "dedupe_signature": "ef8041e50b0a225983a70511099912188f21a5ab78244de46bfd22beea1c7241", "difficulty": "easy", "final_answer": {"answer": 195.025, "unit": "N"}, "id": "force_001854_14.5_13.45", "license": "Apache-2.0", "prompt": "A cart has mass 14.5 kg and measured acceleration 13.45 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 14.5 kg and a = 13.45 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 13.45, "mass": 14.5}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 5.5^2 and multiply by 0.5 * 23.8.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 359.975, \"unit\": \"J\"}", "dedupe_signature": "37f12f2a32ea63250b2de52071c34f625fc2d6c5bca14650c0852dc41f03c2a0", "difficulty": "easy", "final_answer": {"answer": 359.975, "unit": "J"}, "id": "ke_001855_23.8_5.5", "license": "Apache-2.0", "prompt": "A body of mass 23.8 kg moves at 5.5 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 5.5^2 and multiply by 0.5 * 23.8.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 23.8, "velocity": 5.5}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=23 degrees through the sine of 2 theta.\n3. Substitute v=77.4 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 439.2856, \"unit\": \"m\"}", "dedupe_signature": "f857d3da29b7137c3720a1ede429cd3d34830b39123057b5d0ae6eff68d2678d", "difficulty": "medium", "final_answer": {"answer": 439.2856, "unit": "m"}, "id": "projectile_range_001856_77.4_23", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 77.4 m/s and angle 23 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=23 degrees through the sine of 2 theta.\nSubstitute v=77.4 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 23, "gravity": 9.81, "speed": 77.4}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 5.07 * 8.314 * 444 / 117.6.\nFinal: {\"answer\": 159.1452, \"unit\": \"kPa\"}", "dedupe_signature": "52600b681759252ac86d80d1ec695768e1ca1efc723c6e091cca8eb41b04c59f", "difficulty": "medium", "final_answer": {"answer": 159.1452, "unit": "kPa"}, "id": "ideal_gas_001857_5.07_444_117.6", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=5.07 mol, T=444 K, and V=117.6 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 5.07 * 8.314 * 444 / 117.6.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 5.07, "temp_k": 444, "volume_l": 117.6}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 465 * 4.31 * 112.\nFinal: {\"answer\": 224464.8, \"unit\": \"J\"}", "dedupe_signature": "f44bbc9feb922681af08d3b34aad7c1e5951c0af1bdc7713c9a170251f57a21b", "difficulty": "easy", "final_answer": {"answer": 224464.8, "unit": "J"}, "id": "heat_q_001858_465_4.31_112", "license": "Apache-2.0", "prompt": "A 465 g sample has specific heat 4.31 J/(g*K). How much heat is needed to raise its temperature by 112 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 465 * 4.31 * 112.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 112, "heat_capacity": 4.31, "mass_g": 465}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=37.4 V and R=158.8 ohm.\nFinal: {\"answer\": 8.8083, \"unit\": \"W\"}", "dedupe_signature": "b1cd80603f72498a5316181a75741144e6d73069061bf7162d4d6fc30707d9dd", "difficulty": "easy", "final_answer": {"answer": 8.8083, "unit": "W"}, "id": "ohm_power_001859_37.4_158.8", "license": "Apache-2.0", "prompt": "A resistor has resistance 158.8 ohm and voltage 37.4 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=37.4 V and R=158.8 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 158.8, "voltage": 37.4}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=711.5 mg, t=349 h, and T_half=43.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 2.7354, \"unit\": \"mg\"}", "dedupe_signature": "a6456d7b336071acb06072a11402ba745fb4049746d055e555b987cdb6488aaa", "difficulty": "medium", "final_answer": {"answer": 2.7354, "unit": "mg"}, "id": "half_life_001860_711.5_43.5_349", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 711.5 mg. Its half-life is 43.5 hours. How many mg remain after 349 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=711.5 mg, t=349 h, and T_half=43.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 349.0, "half_life": 43.5, "initial_amount": 711.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 2140 mL to 2.14 L.\n3. Compute M = 1.3 / 2.14.\nFinal: {\"answer\": 0.6075, \"unit\": \"mol/L\"}", "dedupe_signature": "73b06f68681affcaf15aebbe168fdd6792e700d56f8bfdaa604fd0102dd05e2d", "difficulty": "medium", "final_answer": {"answer": 0.6075, "unit": "mol/L"}, "id": "molarity_001862_1.3_2140", "license": "Apache-2.0", "prompt": "A solution contains 1.3 mol of solute in 2140 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 2140 mL to 2.14 L.\nCompute M = 1.3 / 2.14.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 1.3, "volume_ml": 2140}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.16 y, so each step multiplies y by 1 - h*0.16.\n3. Apply that update for 12 steps and round the final state.\nFinal: {\"answer\": 0.4951, \"unit\": \"state_units\"}", "dedupe_signature": "37a8c482749ff229b20cc8aed8168036436c26cb59d0f4774b1847eba3740151", "difficulty": "medium", "final_answer": {"answer": 0.4951, "unit": "state_units"}, "id": "euler_decay_001863_4.5_0.16_1.05_12", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.16 y with y(0)=4.5, step size h=1.05, for 12 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.16 y, so each step multiplies y by 1 - h*0.16.\nApply that update for 12 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 4.5, "rate": 0.16, "step": 1.05, "steps": 12}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-9.5)=66.9 and f(-9.2)=64.5.\n3. The interval width is 0.3.\nFinal: {\"answer\": 19.71, \"unit\": \"area_units\"}", "dedupe_signature": "229f09a520bb6a7707b3d249f3e36f1f726caaf8211fb2203fa204fc12e2b5f7", "difficulty": "medium", "final_answer": {"answer": 19.71, "unit": "area_units"}, "id": "trapz_linear_001864_-8_-9.1_-9.5_-9.2", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-8x+-9.1 from x=-9.5 to x=-9.2. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-9.5)=66.9 and f(-9.2)=64.5.\nThe interval width is 0.3.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -9.1, "slope": -8.0, "x0": -9.5, "x1": -9.2}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 44105.0 / 1000.\nFinal: {\"answer\": 44.105, \"unit\": \"kg\"}", "dedupe_signature": "efe450ead1b7d9c1eabe68d1632243c3da56e05fcf52cc96edc38174de02bc62", "difficulty": "easy", "final_answer": {"answer": 44.105, "unit": "kg"}, "id": "unit_convert_001866_g_to_kg_44105", "license": "Apache-2.0", "prompt": "Convert 44105 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 44105.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 44105.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=144 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-95.464, 69.3587], \"unit\": \"N\"}", "dedupe_signature": "6cf38561535c25b72b7a9e7896c06ded9ebb64a5b3549c1477dd512d77e685f0", "difficulty": "medium", "final_answer": {"answer": [-95.464, 69.3587], "unit": "N"}, "id": "vector_components_001867_118_144", "license": "Apache-2.0", "prompt": "A vector has magnitude 118 N at 144 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=144 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 144, "magnitude": 118.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-2.2, 25.25], \"unit\": \"dimensionless\"}", "dedupe_signature": "2bc391cca1ed0f71b2161ce342f46722c4788a06442da0f41c2f4c686cab8cda", "difficulty": "medium", "final_answer": {"answer": [-2.2, 25.25], "unit": "dimensionless"}, "id": "line_two_point_001868_10.5_23.5_-2.2_25.25", "license": "Apache-2.0", "prompt": "A line passes through points (10.5, 2.15) and (23.5, -26.45). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 10.5, "x2": 23.5, "y1": 2.1499999999999986, "y2": -26.450000000000003}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. energy divided by length is force, not spring constant\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "4b1fa8d5f65b7901793cbfb48d67877b9aa87c94a927dd4d495416efdece4a56", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_001869_inconsistent_56040f5d_62965", "license": "Apache-2.0", "prompt": "In instrument manual case 62965, check dimensional consistency for k = E / x. The left side has dimensions N/m and the right side has dimensions J/m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nenergy divided by length is force, not spring constant\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "k = E / x"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef running_total_001870(values):\n    total = 0\n    out = []\n    for value in values:\n        total += value\n        out.append(total)\n    return out\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"running_total_001870\"}", "dedupe_signature": "6e9bcb9333d2e6f017c4c428a960e8e6893c24b709a2f4dff353aa91ed081410", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "running_total_001870"}, "id": "code_001870_running_total_001870", "license": "Apache-2.0", "prompt": "Write a Python function running_total_001870(values) that returns cumulative sums as a new list. It must not mutate the input list. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "running_total_001870"}, "verifier": {"function": "running_total_001870", "tests": ["assert running_total_001870([1, 2, 3]) == [1, 3, 6]", "xs = [4, -1, 2]; assert running_total_001870(xs) == [4, 3, 5] and xs == [4, -1, 2]", "assert running_total_001870([]) == []"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: recurrence, objective, tie_breaking_rule.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"recurrence\", \"objective\", \"tie_breaking_rule\"]}", "dedupe_signature": "9e22ec12da04a98c6771e8504335c16dd81755b2fd1cd4751602109bbe2e3ecf", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["recurrence", "objective", "tie_breaking_rule"]}, "id": "abstain_001871_recurrence_objective_tie_breaking_rule", "license": "Apache-2.0", "prompt": "Write a dynamic-programming solver for a segmentation scoring problem with 2800 items and budget 55185, but the recurrence, objective, and tie-breaking rule are all absent. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: recurrence, objective, tie_breaking_rule.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["recurrence", "objective", "tie_breaking_rule"]}, "verifier": {"missing": ["recurrence", "objective", "tie_breaking_rule"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 12.45^2 and multiply by 0.5 * 8.4.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 651.0105, \"unit\": \"J\"}", "dedupe_signature": "50ab9a0cdf57d19f7af1fb157872eb0ff5ee09b61ac3e200bbc3cd9d34d0e0db", "difficulty": "easy", "final_answer": {"answer": 651.0105, "unit": "J"}, "id": "ke_001873_8.4_12.45", "license": "Apache-2.0", "prompt": "A body of mass 8.4 kg moves at 12.45 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 12.45^2 and multiply by 0.5 * 8.4.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 8.4, "velocity": 12.45}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=76 degrees through the sine of 2 theta.\n3. Substitute v=36.9 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 65.1618, \"unit\": \"m\"}", "dedupe_signature": "ce2046f5d0ebeb20c48618183752d211e8eb015ca6c70317b0dbc0fcbf61edf7", "difficulty": "medium", "final_answer": {"answer": 65.1618, "unit": "m"}, "id": "projectile_range_001874_36.9_76", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 36.9 m/s and angle 76 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=76 degrees through the sine of 2 theta.\nSubstitute v=36.9 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 76, "gravity": 9.81, "speed": 36.9}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 4.22 * 8.314 * 447 / 65.8.\nFinal: {\"answer\": 238.3439, \"unit\": \"kPa\"}", "dedupe_signature": "ed87f2f88acd63c56cebb12298ee6b701eb0c9993ed503b0ab565ab6b9b63ada", "difficulty": "medium", "final_answer": {"answer": 238.3439, "unit": "kPa"}, "id": "ideal_gas_001875_4.22_447_65.8", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=4.22 mol, T=447 K, and V=65.8 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 4.22 * 8.314 * 447 / 65.8.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 4.22, "temp_k": 447, "volume_l": 65.8}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1700 * 1.805 * 110.\nFinal: {\"answer\": 337535.0, \"unit\": \"J\"}", "dedupe_signature": "eab324847982e5001b27bde710e8d1e38153c88d9b96d6735e30d48691f8fbd0", "difficulty": "easy", "final_answer": {"answer": 337535.0, "unit": "J"}, "id": "heat_q_001876_1700_1.805_110", "license": "Apache-2.0", "prompt": "A 1700 g sample has specific heat 1.805 J/(g*K). How much heat is needed to raise its temperature by 110 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1700 * 1.805 * 110.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 110, "heat_capacity": 1.805, "mass_g": 1700}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=41.8 V and R=91.5 ohm.\nFinal: {\"answer\": 19.0955, \"unit\": \"W\"}", "dedupe_signature": "1aa98bc14dba726855ad4d9d245c5d4672876a93f580abb4b809df6981af34bd", "difficulty": "easy", "final_answer": {"answer": 19.0955, "unit": "W"}, "id": "ohm_power_001877_41.8_91.5", "license": "Apache-2.0", "prompt": "A resistor has resistance 91.5 ohm and voltage 41.8 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=41.8 V and R=91.5 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 91.5, "voltage": 41.8}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=488 mg, t=32 h, and T_half=8.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 35.903, \"unit\": \"mg\"}", "dedupe_signature": "e99f6c055b03dc61191f2c0f553b12338ae3d66520b54f193163ff5816e5849a", "difficulty": "medium", "final_answer": {"answer": 35.903, "unit": "mg"}, "id": "half_life_001878_488_8.5_32", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 488 mg. Its half-life is 8.5 hours. How many mg remain after 32 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=488 mg, t=32 h, and T_half=8.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 32.0, "half_life": 8.5, "initial_amount": 488.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 3.04 mol * 100.087 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 304.2645, \"unit\": \"g\"}", "dedupe_signature": "76e716b4a1d4b9a3538ac0f1bdc93e5b574e7b496bf69b5083b5852a1bfec3a9", "difficulty": "medium", "final_answer": {"answer": 304.2645, "unit": "g"}, "id": "stoich_mass_001879_calcium_carbonate_3.04", "license": "Apache-2.0", "prompt": "A sample contains 3.04 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 3.04 mol * 100.087 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "calcium carbonate", "molar_mass": 100.087, "moles": 3.04}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.53 y, so each step multiplies y by 1 - h*0.53.\n3. Apply that update for 6 steps and round the final state.\nFinal: {\"answer\": 30.2935, \"unit\": \"state_units\"}", "dedupe_signature": "30ebaeb3b6652004a66b94b24c4cd996ade03288361e037d4bed1c6d454ed369", "difficulty": "medium", "final_answer": {"answer": 30.2935, "unit": "state_units"}, "id": "euler_decay_001881_42_0.53_0.1_6", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.53 y with y(0)=42, step size h=0.1, for 6 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.53 y, so each step multiplies y by 1 - h*0.53.\nApply that update for 6 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 42.0, "rate": 0.53, "step": 0.1, "steps": 6}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-6.2)=59.1 and f(-0.5)=16.35.\n3. The interval width is 5.7.\nFinal: {\"answer\": 215.0325, \"unit\": \"area_units\"}", "dedupe_signature": "085da4a3a87c7b3a192b57f7f1b0eeb5cc6f98183f9843815566c1b09a4f6fb1", "difficulty": "medium", "final_answer": {"answer": 215.0325, "unit": "area_units"}, "id": "trapz_linear_001882_-7.5_12.6_-6.2_-0.5", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-7.5x+12.6 from x=-6.2 to x=-0.5. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-6.2)=59.1 and f(-0.5)=16.35.\nThe interval width is 5.7.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 12.6, "slope": -7.5, "x0": -6.2, "x1": -0.5}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=65 degrees and keep the unit as newtons.\nFinal: {\"answer\": [39.0922, 83.8335], \"unit\": \"N\"}", "dedupe_signature": "a4852484968efd00abfe186b9928617a87e0998191a93b3b6b222e5c9e1f4916", "difficulty": "medium", "final_answer": {"answer": [39.0922, 83.8335], "unit": "N"}, "id": "vector_components_001885_92.5_65", "license": "Apache-2.0", "prompt": "A vector has magnitude 92.5 N at 65 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=65 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 65, "magnitude": 92.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [8.1, 20.0], \"unit\": \"dimensionless\"}", "dedupe_signature": "bb0dfb6fa78fbcef7648acc7f1a521f9cf627b53fb7315fd65b648616a50441a", "difficulty": "medium", "final_answer": {"answer": [8.1, 20.0], "unit": "dimensionless"}, "id": "line_two_point_001886_16.75_23.75_8.1_20", "license": "Apache-2.0", "prompt": "A line passes through points (16.75, 155.675) and (23.75, 212.375). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 16.75, "x2": 23.75, "y1": 155.67499999999998, "y2": 212.375}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. mass times acceleration has newton dimensions\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "c1c3d508428ed3653f46d349fb0d2d3cfe7450cefa3eb82b05083cf233ae463b", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_001887_consistent_03f5e041_220389", "license": "Apache-2.0", "prompt": "In quality-control check case 220389, check dimensional consistency for F = m * a. The left side has dimensions kg*m/s^2 and the right side has dimensions kg*m/s^2. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nmass times acceleration has newton dimensions\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "F = m * a"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef pairwise_ratios_001888(numerators, denominators):\n    if len(numerators) != len(denominators):\n        raise ValueError('length mismatch')\n    out = []\n    for numerator, denominator in zip(numerators, denominators):\n        if denominator == 0:\n            raise ValueError('zero denominator')\n        out.append(numerator / denominator)\n    return out\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"pairwise_ratios_001888\"}", "dedupe_signature": "f873e8b424be9fc79c65fa740c6d4eb56529f57a501324ab0345f2191f66285c", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "pairwise_ratios_001888"}, "id": "code_001888_pairwise_ratios_001888", "license": "Apache-2.0", "prompt": "Write a Python function pairwise_ratios_001888(numerators, denominators) that returns a list of n/d values. Raise ValueError if lengths differ or any denominator is zero. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "pairwise_ratios_001888"}, "verifier": {"function": "pairwise_ratios_001888", "tests": ["assert pairwise_ratios_001888([2, 9], [4, 3]) == [0.5, 3.0]", "try:\n    pairwise_ratios_001888([1], [0])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass", "try:\n    pairwise_ratios_001888([1, 2], [1])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: volume.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"volume\"]}", "dedupe_signature": "d80766b1102170559b606ab15e7f1e1f5299e71c60e272044ea8ba77a3aabd78", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["volume"]}, "id": "abstain_001889_volume", "license": "Apache-2.0", "prompt": "Compute pressure from the ideal gas law. The prompt gives n=0.61 mol and T=613 K, but does not give volume. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: volume.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["volume"]}, "verifier": {"missing": ["volume"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 5.85 kg and a = 6.9 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 40.365, \"unit\": \"N\"}", "dedupe_signature": "f3814407aff1c3dfb213bbaea3da6dac20a5b585c1a80dedc72c9551da3f0c00", "difficulty": "easy", "final_answer": {"answer": 40.365, "unit": "N"}, "id": "force_001890_5.85_6.9", "license": "Apache-2.0", "prompt": "A cart has mass 5.85 kg and measured acceleration 6.9 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 5.85 kg and a = 6.9 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 6.9, "mass": 5.85}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=26 degrees through the sine of 2 theta.\n3. Substitute v=81.8 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 537.4892, \"unit\": \"m\"}", "dedupe_signature": "1ae733ea0b59e56edcc6a7abfb7c0afa7dc498f68102d962a7f830baff440a00", "difficulty": "medium", "final_answer": {"answer": 537.4892, "unit": "m"}, "id": "projectile_range_001892_81.8_26", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 81.8 m/s and angle 26 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=26 degrees through the sine of 2 theta.\nSubstitute v=81.8 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 26, "gravity": 9.81, "speed": 81.8}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 1.25 * 8.314 * 495 / 102.9.\nFinal: {\"answer\": 49.9931, \"unit\": \"kPa\"}", "dedupe_signature": "9cb8acf0f7a929985a0d23ceee26896eedec4905aaf9a1f69eabba3dc21a7ddb", "difficulty": "medium", "final_answer": {"answer": 49.9931, "unit": "kPa"}, "id": "ideal_gas_001893_1.25_495_102.9", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=1.25 mol, T=495 K, and V=102.9 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 1.25 * 8.314 * 495 / 102.9.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 1.25, "temp_k": 495, "volume_l": 102.9}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 650 * 2.08 * 45.\nFinal: {\"answer\": 60840.0, \"unit\": \"J\"}", "dedupe_signature": "f5b59face81b938320578166078a65920ef706c7bc2c2424ece944dd98862b6f", "difficulty": "easy", "final_answer": {"answer": 60840.0, "unit": "J"}, "id": "heat_q_001894_650_2.08_45", "license": "Apache-2.0", "prompt": "A 650 g sample has specific heat 2.08 J/(g*K). How much heat is needed to raise its temperature by 45 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 650 * 2.08 * 45.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 45, "heat_capacity": 2.08, "mass_g": 650}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=231.9 V and R=113.4 ohm.\nFinal: {\"answer\": 474.2294, \"unit\": \"W\"}", "dedupe_signature": "c2c88cff9041d7c0557301858e36b28fc1a027755798de90da010a272bb1ff93", "difficulty": "easy", "final_answer": {"answer": 474.2294, "unit": "W"}, "id": "ohm_power_001895_231.9_113.4", "license": "Apache-2.0", "prompt": "A resistor has resistance 113.4 ohm and voltage 231.9 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=231.9 V and R=113.4 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 113.4, "voltage": 231.9}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=33.5 mg, t=302 h, and T_half=48 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 0.4276, \"unit\": \"mg\"}", "dedupe_signature": "7369ebdc9934ac152abecf84a1d2c00770c587fc35ac3aef36e82a1b719030aa", "difficulty": "medium", "final_answer": {"answer": 0.4276, "unit": "mg"}, "id": "half_life_001896_33.5_48_302", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 33.5 mg. Its half-life is 48 hours. How many mg remain after 302 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=33.5 mg, t=302 h, and T_half=48 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 302.0, "half_life": 48.0, "initial_amount": 33.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 7.04 mol * 18.015 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 126.8256, \"unit\": \"g\"}", "dedupe_signature": "9458c2ea0338c03c97198f19a01842056a13396a3f00e4c948fd108c67deea77", "difficulty": "medium", "final_answer": {"answer": 126.8256, "unit": "g"}, "id": "stoich_mass_001897_water_7.04", "license": "Apache-2.0", "prompt": "A sample contains 7.04 mol of water. Using molar mass 18.015 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 7.04 mol * 18.015 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "water", "molar_mass": 18.015, "moles": 7.04}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.39 y, so each step multiplies y by 1 - h*0.39.\n3. Apply that update for 7 steps and round the final state.\nFinal: {\"answer\": 6.8269, \"unit\": \"state_units\"}", "dedupe_signature": "c724770b5b3be1efae1e50158616de3604dd113d67134e61c3b50bffcc2d806f", "difficulty": "medium", "final_answer": {"answer": 6.8269, "unit": "state_units"}, "id": "euler_decay_001899_37_0.39_0.55_7", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.39 y with y(0)=37, step size h=0.55, for 7 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.39 y, so each step multiplies y by 1 - h*0.39.\nApply that update for 7 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 37.0, "rate": 0.39, "step": 0.55, "steps": 7}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-1.8)=13.9 and f(2.4)=-2.9.\n3. The interval width is 4.2.\nFinal: {\"answer\": 23.1, \"unit\": \"area_units\"}", "dedupe_signature": "fcb75e9fd809c5383c7988bd84707f738ed16a7dbdeaa8a7aec56744ee47f296", "difficulty": "medium", "final_answer": {"answer": 23.1, "unit": "area_units"}, "id": "trapz_linear_001900_-4_6.7_-1.8_2.4", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-4x+6.7 from x=-1.8 to x=2.4. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-1.8)=13.9 and f(2.4)=-2.9.\nThe interval width is 4.2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 6.7, "slope": -4.0, "x0": -1.8, "x1": 2.4000000000000004}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.38 and add it to the current value.\nFinal: {\"answer\": [1.209, 0.627, 1.57], \"unit\": \"temperature_units\"}", "dedupe_signature": "b7e6f8e3fd170254f07f1d176c8ac834b3de9ff6b02467e47f6b96b1f930de10", "difficulty": "hard", "final_answer": {"answer": [1.209, 0.627, 1.57], "unit": "temperature_units"}, "id": "heat_step_001901_0.38_2.2_0.05_0.95_1.0_2.55", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=2.2, right=2.55; current interior values are [0.05, 0.95, 1.0]. Use r=0.38. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.38 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [0.05, 0.95, 1.0], "left": 2.2, "r": 0.38, "right": 2.55}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=19 degrees and keep the unit as newtons.\nFinal: {\"answer\": [72.3322, 24.906], \"unit\": \"N\"}", "dedupe_signature": "40ab5f3fa804f34fa235953fec54fd4ea9dc5cd9f23f1b597246ea5efe86547e", "difficulty": "medium", "final_answer": {"answer": [72.3322, 24.906], "unit": "N"}, "id": "vector_components_001903_76.5_19", "license": "Apache-2.0", "prompt": "A vector has magnitude 76.5 N at 19 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=19 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 19, "magnitude": 76.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [8.1, 26.5], \"unit\": \"dimensionless\"}", "dedupe_signature": "06f9d575f59a0d3216e8d6f2dbc8bb96b9212753e936b608bdbe7901049fb758", "difficulty": "medium", "final_answer": {"answer": [8.1, 26.5], "unit": "dimensionless"}, "id": "line_two_point_001904_9.25_11.5_8.1_26.5", "license": "Apache-2.0", "prompt": "A line passes through points (9.25, 101.425) and (11.5, 119.65). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 9.25, "x2": 11.5, "y1": 101.425, "y2": 119.64999999999999}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. lever arm times force has torque dimensions\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "f7f5229a5b7c2b67876b1ec32a12279e7d463de807c8ea9dc5dff031fb21e373", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_001905_consistent_5ca82cb9_542014", "license": "Apache-2.0", "prompt": "In quality-control check case 542014, check dimensional consistency for tau = r * F. The left side has dimensions N*m and the right side has dimensions N*m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nlever arm times force has torque dimensions\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "tau = r * F"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: left_boundary, right_boundary.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"left_boundary\", \"right_boundary\"]}", "dedupe_signature": "d55575465b7810fdb267b2e8b5558a4dc1e094f401ed05165f2cb04e3704545d", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["left_boundary", "right_boundary"]}, "id": "abstain_001907_left_boundary_right_boundary", "license": "Apache-2.0", "prompt": "Solve the 1D heat equation after one finite-difference step. The prompt gives r=0.26 and interior values [-1.4, 2.75, -1.2], but gives no boundary values. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: left_boundary, right_boundary.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["left_boundary", "right_boundary"]}, "verifier": {"missing": ["left_boundary", "right_boundary"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 11.05 kg and a = 11.15 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 123.2075, \"unit\": \"N\"}", "dedupe_signature": "410c65a059b2c1a61ff91168f82934cdb5404b2847ba6ffe3d674abbe867bc88", "difficulty": "easy", "final_answer": {"answer": 123.2075, "unit": "N"}, "id": "force_001908_11.05_11.15", "license": "Apache-2.0", "prompt": "A cart has mass 11.05 kg and measured acceleration 11.15 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 11.05 kg and a = 11.15 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 11.15, "mass": 11.05}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 12.25^2 and multiply by 0.5 * 14.4.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 1080.45, \"unit\": \"J\"}", "dedupe_signature": "b73b095a89948e11e695835d1bfdfe62fba53ce8ee675c5fc090b3a32ad04ab1", "difficulty": "easy", "final_answer": {"answer": 1080.45, "unit": "J"}, "id": "ke_001909_14.4_12.25", "license": "Apache-2.0", "prompt": "A body of mass 14.4 kg moves at 12.25 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 12.25^2 and multiply by 0.5 * 14.4.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 14.4, "velocity": 12.25}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=59 degrees through the sine of 2 theta.\n3. Substitute v=33.8 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 102.8251, \"unit\": \"m\"}", "dedupe_signature": "39177f8923b1881ac9a136180cd7ff136f5003d8465bd2181c2714e945ee38c4", "difficulty": "medium", "final_answer": {"answer": 102.8251, "unit": "m"}, "id": "projectile_range_001910_33.8_59", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 33.8 m/s and angle 59 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=59 degrees through the sine of 2 theta.\nSubstitute v=33.8 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 59, "gravity": 9.81, "speed": 33.8}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 5.87 * 8.314 * 568 / 7.6.\nFinal: {\"answer\": 3647.3956, \"unit\": \"kPa\"}", "dedupe_signature": "d1b34c33acb9bc66a3e84739e4bfd93edeec33e439bd87b0cedbf8f067a70a3d", "difficulty": "medium", "final_answer": {"answer": 3647.3956, "unit": "kPa"}, "id": "ideal_gas_001911_5.87_568_7.6", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=5.87 mol, T=568 K, and V=7.6 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 5.87 * 8.314 * 568 / 7.6.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 5.87, "temp_k": 568, "volume_l": 7.6}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=193.7 V and R=59.1 ohm.\nFinal: {\"answer\": 634.8509, \"unit\": \"W\"}", "dedupe_signature": "ebdb0b9e8f815b35c67ad0dc363f75d8fc1ef4c8c2db65de1de082d3f4aeb469", "difficulty": "easy", "final_answer": {"answer": 634.8509, "unit": "W"}, "id": "ohm_power_001913_193.7_59.1", "license": "Apache-2.0", "prompt": "A resistor has resistance 59.1 ohm and voltage 193.7 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=193.7 V and R=59.1 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 59.1, "voltage": 193.7}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=570.5 mg, t=225.5 h, and T_half=49.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 24.2603, \"unit\": \"mg\"}", "dedupe_signature": "41655aa295caea2305b0835be18baf057876849ef4d12416a82cc7ea9ce9bf88", "difficulty": "medium", "final_answer": {"answer": 24.2603, "unit": "mg"}, "id": "half_life_001914_570.5_49.5_225.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 570.5 mg. Its half-life is 49.5 hours. How many mg remain after 225.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=570.5 mg, t=225.5 h, and T_half=49.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 225.5, "half_life": 49.5, "initial_amount": 570.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 6.19 mol * 58.44 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 361.7436, \"unit\": \"g\"}", "dedupe_signature": "4f643312034f53bba79c7eddb73f3d69e3c96b76016185c6abf744402fc3c230", "difficulty": "medium", "final_answer": {"answer": 361.7436, "unit": "g"}, "id": "stoich_mass_001915_sodium_chloride_6.19", "license": "Apache-2.0", "prompt": "A sample contains 6.19 mol of sodium chloride. Using molar mass 58.44 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 6.19 mol * 58.44 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "sodium chloride", "molar_mass": 58.44, "moles": 6.19}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 1925 mL to 1.925 L.\n3. Compute M = 4.315 / 1.925.\nFinal: {\"answer\": 2.2416, \"unit\": \"mol/L\"}", "dedupe_signature": "cce0e6c4c72f7657ababeff9be1aab9f03c8acd9e8a80335719dffef556afc36", "difficulty": "medium", "final_answer": {"answer": 2.2416, "unit": "mol/L"}, "id": "molarity_001916_4.315_1925", "license": "Apache-2.0", "prompt": "A solution contains 4.315 mol of solute in 1925 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 1925 mL to 1.925 L.\nCompute M = 4.315 / 1.925.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 4.315, "volume_ml": 1925}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.02 y, so each step multiplies y by 1 - h*0.02.\n3. Apply that update for 6 steps and round the final state.\nFinal: {\"answer\": 5.6832, \"unit\": \"state_units\"}", "dedupe_signature": "4c24ccf2c4f7f6b5ab2b687db69ff59c0f1d769f86eb0431c313d9f8b0df3639", "difficulty": "medium", "final_answer": {"answer": 5.6832, "unit": "state_units"}, "id": "euler_decay_001917_6_0.02_0.45_6", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.02 y with y(0)=6, step size h=0.45, for 6 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.02 y, so each step multiplies y by 1 - h*0.02.\nApply that update for 6 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 6.0, "rate": 0.02, "step": 0.45, "steps": 6}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(7)=42.7 and f(8.4)=49.7.\n3. The interval width is 1.4.\nFinal: {\"answer\": 64.68, \"unit\": \"area_units\"}", "dedupe_signature": "3057b32d5c2bc0abfd3acce6bf401c430b4b4166d8b2ba38e8034b77c01afd14", "difficulty": "medium", "final_answer": {"answer": 64.68, "unit": "area_units"}, "id": "trapz_linear_001918_5_7.7_7_8.4", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=5x+7.7 from x=7 to x=8.4. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(7)=42.7 and f(8.4)=49.7.\nThe interval width is 1.4.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 7.7, "slope": 5.0, "x0": 7.0, "x1": 8.4}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.34 and add it to the current value.\nFinal: {\"answer\": [0.305, 0.72, 0.363], \"unit\": \"temperature_units\"}", "dedupe_signature": "ba9f011e347847555148bb9cf4da38410acf77226c9b6c4cf25609062151cf39", "difficulty": "hard", "final_answer": {"answer": [0.305, 0.72, 0.363], "unit": "temperature_units"}, "id": "heat_step_001919_0.34_1.25_1.75_-2.0_2.25_0.95", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.25, right=0.95; current interior values are [1.75, -2.0, 2.25]. Use r=0.34. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.34 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [1.75, -2.0, 2.25], "left": 1.25, "r": 0.34, "right": 0.95}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 100 centimeters in one meter.\n2. Apply the conversion factor directly to the given value.\n3. Compute 250.0 / 100.\nFinal: {\"answer\": 2.5, \"unit\": \"m\"}", "dedupe_signature": "498adc9267d8abcdd9e69b6653d702e939993f311635432d8df6f0cc8c0cb2c1", "difficulty": "easy", "final_answer": {"answer": 2.5, "unit": "m"}, "id": "unit_convert_001920_cm_to_m_250", "license": "Apache-2.0", "prompt": "Convert 250 cm to m. Return the converted value with unit.", "reasoning_trace": "There are 100 centimeters in one meter.\nApply the conversion factor directly to the given value.\nCompute 250.0 / 100.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 250.0}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=60 degrees and keep the unit as newtons.\nFinal: {\"answer\": [190.0, 329.0897], \"unit\": \"N\"}", "dedupe_signature": "d51b56b29d44434bc57340f0de3caa72be3b31948766a1167167b932b408c90c", "difficulty": "medium", "final_answer": {"answer": [190.0, 329.0897], "unit": "N"}, "id": "vector_components_001921_380_60", "license": "Apache-2.0", "prompt": "A vector has magnitude 380 N at 60 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=60 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 60, "magnitude": 380.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-1.15, 14.5], \"unit\": \"dimensionless\"}", "dedupe_signature": "b73e0ab3777e2b1c505a1af687d44c880cc0ecb0f39123b2accdf812452ecbaa", "difficulty": "medium", "final_answer": {"answer": [-1.15, 14.5], "unit": "dimensionless"}, "id": "line_two_point_001922_-10.25_0.5_-1.15_14.5", "license": "Apache-2.0", "prompt": "A line passes through points (-10.25, 26.2875) and (0.5, 13.925). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -10.25, "x2": 0.5, "y1": 26.2875, "y2": 13.925}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. lever arm times force has torque dimensions\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "ae0fbc5738548c43cd0f236b8adc1e28aa96c2b53dab3c9b6e55839191e5c60e", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_001923_consistent_5ca82cb9_274577", "license": "Apache-2.0", "prompt": "In lab notebook case 274577, check dimensional consistency for tau = r * F. The left side has dimensions N*m and the right side has dimensions N*m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nlever arm times force has torque dimensions\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "tau = r * F"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef safe_mean_001924(values):\n    if not values:\n        raise ValueError('safe_mean requires at least one value')\n    return sum(values) / len(values)\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"safe_mean_001924\"}", "dedupe_signature": "c3ab7c4963d17791e8a7bd1dee82dd4c20014455bf0f1ad3df469f5342f4b114", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "safe_mean_001924"}, "id": "code_001924_safe_mean_001924", "license": "Apache-2.0", "prompt": "Write a Python function safe_mean_001924(values) that returns the arithmetic mean. It must raise ValueError for an empty input and must not mutate the input list. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "safe_mean_001924"}, "verifier": {"function": "safe_mean_001924", "tests": ["assert safe_mean_001924([2, 4, 6]) == 4", "xs = [1, 2, 3]; assert safe_mean_001924(xs) == 2 and xs == [1, 2, 3]", "try:\n    safe_mean_001924([])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: volume.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"volume\"]}", "dedupe_signature": "c484468c196613a1ae655ce9529d0ff0b51f9a9415094f90846f2a14aab46bed", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["volume"]}, "id": "abstain_001925_volume", "license": "Apache-2.0", "prompt": "Compute pressure from the ideal gas law. The prompt gives n=5.61 mol and T=612 K, but does not give volume. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: volume.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["volume"]}, "verifier": {"missing": ["volume"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 20.7 kg and a = 3.65 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 75.555, \"unit\": \"N\"}", "dedupe_signature": "5c0e73e85b0fb04e0d4edbc95880422e4c21ebd70c2806a7643526f18ea29aaa", "difficulty": "easy", "final_answer": {"answer": 75.555, "unit": "N"}, "id": "force_001926_20.7_3.65", "license": "Apache-2.0", "prompt": "A cart has mass 20.7 kg and measured acceleration 3.65 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 20.7 kg and a = 3.65 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 3.65, "mass": 20.7}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 11.15^2 and multiply by 0.5 * 20.25.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 1258.7653, \"unit\": \"J\"}", "dedupe_signature": "e1dfb0993b3a243d182b6dd1b1a0d468817c6b32c423a5fb4e5e6884e4303bad", "difficulty": "easy", "final_answer": {"answer": 1258.7653, "unit": "J"}, "id": "ke_001927_20.25_11.15", "license": "Apache-2.0", "prompt": "A body of mass 20.25 kg moves at 11.15 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 11.15^2 and multiply by 0.5 * 20.25.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 20.25, "velocity": 11.15}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=64 degrees through the sine of 2 theta.\n3. Substitute v=49.4 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 196.0275, \"unit\": \"m\"}", "dedupe_signature": "e06f6f97f401f776c37ef8fe3003d874f248cedc6be199e490e58c2d045e6048", "difficulty": "medium", "final_answer": {"answer": 196.0275, "unit": "m"}, "id": "projectile_range_001928_49.4_64", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 49.4 m/s and angle 64 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=64 degrees through the sine of 2 theta.\nSubstitute v=49.4 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 64, "gravity": 9.81, "speed": 49.4}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 4.11 * 8.314 * 446 / 56.0.\nFinal: {\"answer\": 272.1439, \"unit\": \"kPa\"}", "dedupe_signature": "77fdc934c7b7a0beed2d136b5eaf126d478037882e8e6fda116bc394335805fd", "difficulty": "medium", "final_answer": {"answer": 272.1439, "unit": "kPa"}, "id": "ideal_gas_001929_4.11_446_56.0", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=4.11 mol, T=446 K, and V=56.0 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 4.11 * 8.314 * 446 / 56.0.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 4.11, "temp_k": 446, "volume_l": 56.0}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=81.6 V and R=22 ohm.\nFinal: {\"answer\": 302.6618, \"unit\": \"W\"}", "dedupe_signature": "af8db24f9ef0115f1757f7161b9d17c6ba25be512ce3adff1cc0a7ec13378f89", "difficulty": "easy", "final_answer": {"answer": 302.6618, "unit": "W"}, "id": "ohm_power_001931_81.6_22", "license": "Apache-2.0", "prompt": "A resistor has resistance 22 ohm and voltage 81.6 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=81.6 V and R=22 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 22.0, "voltage": 81.6}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=93.5 mg, t=178 h, and T_half=90 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 23.7378, \"unit\": \"mg\"}", "dedupe_signature": "7a1a9974186185d606bd9272f4cd2ccfad9947ebbde974994e3f824decf91950", "difficulty": "medium", "final_answer": {"answer": 23.7378, "unit": "mg"}, "id": "half_life_001932_93.5_90_178", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 93.5 mg. Its half-life is 90 hours. How many mg remain after 178 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=93.5 mg, t=178 h, and T_half=90 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 178.0, "half_life": 90.0, "initial_amount": 93.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 1.97 mol * 44.01 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 86.6997, \"unit\": \"g\"}", "dedupe_signature": "7ec9f33270e293b53e301240a9432761e171d5f1d3ae9b78322cf10556cd1323", "difficulty": "medium", "final_answer": {"answer": 86.6997, "unit": "g"}, "id": "stoich_mass_001933_carbon_dioxide_1.97", "license": "Apache-2.0", "prompt": "A sample contains 1.97 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 1.97 mol * 44.01 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "carbon dioxide", "molar_mass": 44.01, "moles": 1.97}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.44 and add it to the current value.\nFinal: {\"answer\": [0.524, -0.956, 0.022], \"unit\": \"temperature_units\"}", "dedupe_signature": "0d4cb8b6220bac32dbba09934c7207a37888a15d92770579a16f564072a25719", "difficulty": "hard", "final_answer": {"answer": [0.524, -0.956, 0.022], "unit": "temperature_units"}, "id": "heat_step_001937_0.44_1.9_-0.95_-0.45_-1.1_0.8", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.9, right=0.8; current interior values are [-0.95, -0.45, -1.1]. Use r=0.44. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.44 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-0.95, -0.45, -1.1], "left": 1.9, "r": 0.44, "right": 0.8}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=82 degrees and keep the unit as newtons.\nFinal: {\"answer\": [15.3786, 109.4246], \"unit\": \"N\"}", "dedupe_signature": "47eff7c6cef966fd89e80b238424d42bd0c2b0a7463a6d9717fad5226f64811e", "difficulty": "medium", "final_answer": {"answer": [15.3786, 109.4246], "unit": "N"}, "id": "vector_components_001939_110.5_82", "license": "Apache-2.0", "prompt": "A vector has magnitude 110.5 N at 82 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=82 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 82, "magnitude": 110.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-7.65, -9.5], \"unit\": \"dimensionless\"}", "dedupe_signature": "ab7d744925d16429aeb2d77363d343330f31b1959d8cd70c2f584c25833b7469", "difficulty": "medium", "final_answer": {"answer": [-7.65, -9.5], "unit": "dimensionless"}, "id": "line_two_point_001940_-19_-9.5_-7.65_-9.5", "license": "Apache-2.0", "prompt": "A line passes through points (-19, 135.85) and (-9.5, 63.175). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -19.0, "x2": -9.5, "y1": 135.85, "y2": 63.175}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. mass times acceleration has newton dimensions\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "b3ead9c73b5a249d912f02582f497c04383cdb6a622ffa41892e129383cbf436", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_001941_consistent_03f5e041_693201", "license": "Apache-2.0", "prompt": "In lab notebook case 693201, check dimensional consistency for F = m * a. The left side has dimensions kg*m/s^2 and the right side has dimensions kg*m/s^2. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nmass times acceleration has newton dimensions\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "F = m * a"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef threshold_flags_001942(values, threshold):\n    return [value >= threshold for value in values]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"threshold_flags_001942\"}", "dedupe_signature": "b692cd333933d9786f52982e48a4924b6754e12a15c1840354c1def9496ca68f", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "threshold_flags_001942"}, "id": "code_001942_threshold_flags_001942", "license": "Apache-2.0", "prompt": "Write a Python function threshold_flags_001942(values, threshold) that returns a list of booleans showing whether each value is greater than or equal to threshold. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "threshold_flags_001942"}, "verifier": {"function": "threshold_flags_001942", "tests": ["assert threshold_flags_001942([1, 2, 3], 2) == [False, True, True]", "assert threshold_flags_001942([], 5) == []", "assert threshold_flags_001942([-1, 0], 0) == [False, True]"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: rate_constant, number_of_steps.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"rate_constant\", \"number_of_steps\"]}", "dedupe_signature": "0a98b7e7cf3c1e3346df9d17966135791d9af9b9a49666e19c0bc86ecebcfe7b", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["rate_constant", "number_of_steps"]}, "id": "abstain_001943_rate_constant_number_of_steps", "license": "Apache-2.0", "prompt": "Use explicit Euler for dy/dt = -k y. The prompt gives y(0)=27.5 and h=0.1, but omits both k and the number of steps. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: rate_constant, number_of_steps.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["rate_constant", "number_of_steps"]}, "verifier": {"missing": ["rate_constant", "number_of_steps"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 15.05 kg and a = 7.55 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 113.6275, \"unit\": \"N\"}", "dedupe_signature": "76a3cbb3d8e14254854d22ead1ea6c9c0abed82b0cb84e434d8347566affd85b", "difficulty": "easy", "final_answer": {"answer": 113.6275, "unit": "N"}, "id": "force_001944_15.05_7.55", "license": "Apache-2.0", "prompt": "A cart has mass 15.05 kg and measured acceleration 7.55 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 15.05 kg and a = 7.55 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 7.55, "mass": 15.05}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 20.6^2 and multiply by 0.5 * 14.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 2970.52, \"unit\": \"J\"}", "dedupe_signature": "879587353fe37e69866e72cf5985a104fbf3083dcd66e43c47b4487f724e52ac", "difficulty": "easy", "final_answer": {"answer": 2970.52, "unit": "J"}, "id": "ke_001945_14_20.6", "license": "Apache-2.0", "prompt": "A body of mass 14 kg moves at 20.6 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 20.6^2 and multiply by 0.5 * 14.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 14.0, "velocity": 20.6}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=35 degrees through the sine of 2 theta.\n3. Substitute v=59 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 333.4424, \"unit\": \"m\"}", "dedupe_signature": "b59eaff46aaf46df86a309da5c35737122fc7a63038f169896313ecb63e3165d", "difficulty": "medium", "final_answer": {"answer": 333.4424, "unit": "m"}, "id": "projectile_range_001946_59_35", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 59 m/s and angle 35 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=35 degrees through the sine of 2 theta.\nSubstitute v=59 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 35, "gravity": 9.81, "speed": 59.0}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=18 mg, t=84 h, and T_half=73 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 8.1074, \"unit\": \"mg\"}", "dedupe_signature": "0ef243cbf564b3d107717910a09b96f0efe3048bb7a41b5ffd6bd2a76da3e717", "difficulty": "medium", "final_answer": {"answer": 8.1074, "unit": "mg"}, "id": "half_life_001950_18_73_84", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 18 mg. Its half-life is 73 hours. How many mg remain after 84 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=18 mg, t=84 h, and T_half=73 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 84.0, "half_life": 73.0, "initial_amount": 18.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 7.96 mol * 44.01 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 350.3196, \"unit\": \"g\"}", "dedupe_signature": "24d4032ed478ce3ee9b570f90401141e6a760b752f818bd2be39e914e6e35b64", "difficulty": "medium", "final_answer": {"answer": 350.3196, "unit": "g"}, "id": "stoich_mass_001951_carbon_dioxide_7.96", "license": "Apache-2.0", "prompt": "A sample contains 7.96 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 7.96 mol * 44.01 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "carbon dioxide", "molar_mass": 44.01, "moles": 7.96}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 4830 mL to 4.83 L.\n3. Compute M = 2.25 / 4.83.\nFinal: {\"answer\": 0.4658, \"unit\": \"mol/L\"}", "dedupe_signature": "3b0867b41edbc4e6db09ef52310e75c57f42d159d9681443536613073b9e3ca2", "difficulty": "medium", "final_answer": {"answer": 0.4658, "unit": "mol/L"}, "id": "molarity_001952_2.25_4830", "license": "Apache-2.0", "prompt": "A solution contains 2.25 mol of solute in 4830 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 4830 mL to 4.83 L.\nCompute M = 2.25 / 4.83.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 2.25, "volume_ml": 4830}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.42 y, so each step multiplies y by 1 - h*0.42.\n3. Apply that update for 5 steps and round the final state.\nFinal: {\"answer\": 2.8655, \"unit\": \"state_units\"}", "dedupe_signature": "5a2310e57ad217bc8b9d6e7b67a518cb91f01ec4f8be48135d49091d56f5668d", "difficulty": "medium", "final_answer": {"answer": 2.8655, "unit": "state_units"}, "id": "euler_decay_001953_19_0.42_0.75_5", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.42 y with y(0)=19, step size h=0.75, for 5 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.42 y, so each step multiplies y by 1 - h*0.42.\nApply that update for 5 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 19.0, "rate": 0.42, "step": 0.75, "steps": 5}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-3.2)=-8.14 and f(3.6)=-16.98.\n3. The interval width is 6.8.\nFinal: {\"answer\": -85.408, \"unit\": \"area_units\"}", "dedupe_signature": "d6d5c8c5dcf931c656556df1869695c9b3bae2790041291f88c9ad72610f45aa", "difficulty": "medium", "final_answer": {"answer": -85.408, "unit": "area_units"}, "id": "trapz_linear_001954_-1.3_-12.3_-3.2_3.6", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-1.3x+-12.3 from x=-3.2 to x=3.6. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-3.2)=-8.14 and f(3.6)=-16.98.\nThe interval width is 6.8.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -12.3, "slope": -1.3, "x0": -3.2, "x1": 3.5999999999999996}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.24 and add it to the current value.\nFinal: {\"answer\": [1.356, 0.888, 1.506], \"unit\": \"temperature_units\"}", "dedupe_signature": "fc0f82687b52555cd99b3c45d94571712406355c896272a42f74d665979c2d01", "difficulty": "hard", "final_answer": {"answer": [1.356, 0.888, 1.506], "unit": "temperature_units"}, "id": "heat_step_001955_0.24_0.75_2.4_-0.3_1.95_2.35", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=0.75, right=2.35; current interior values are [2.4, -0.3, 1.95]. Use r=0.24. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.24 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [2.4, -0.3, 1.95], "left": 0.75, "r": 0.24, "right": 2.35}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=306 degrees and keep the unit as newtons.\nFinal: {\"answer\": [56.1335, -77.2611], \"unit\": \"N\"}", "dedupe_signature": "2f0dd3b066778e76d8c24154ebe05eaa965e24adf871dfba2d2b612cd081162b", "difficulty": "medium", "final_answer": {"answer": [56.1335, -77.2611], "unit": "N"}, "id": "vector_components_001957_95.5_306", "license": "Apache-2.0", "prompt": "A vector has magnitude 95.5 N at 306 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=306 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 306, "magnitude": 95.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef weighted_sum_001960(values, weights):\n    if len(values) != len(weights):\n        raise ValueError('length mismatch')\n    return sum(value * weight for value, weight in zip(values, weights))\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"weighted_sum_001960\"}", "dedupe_signature": "351bc720ef6f73a1fc0365769528540c2da0a79f134e8804d1dc990d8235479e", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "weighted_sum_001960"}, "id": "code_001960_weighted_sum_001960", "license": "Apache-2.0", "prompt": "Write a Python function weighted_sum_001960(values, weights) that returns sum(value*weight). Raise ValueError when the two inputs have different lengths. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "weighted_sum_001960"}, "verifier": {"function": "weighted_sum_001960", "tests": ["assert weighted_sum_001960([2, 3], [4, 5]) == 23", "assert weighted_sum_001960([], []) == 0", "try:\n    weighted_sum_001960([1], [1, 2])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: rate_constant, number_of_steps.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"rate_constant\", \"number_of_steps\"]}", "dedupe_signature": "08edf6bbca6ea203be51223aeb25ac99e032bf834c4e48cbccb9aaf8cc4381ac", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["rate_constant", "number_of_steps"]}, "id": "abstain_001961_rate_constant_number_of_steps", "license": "Apache-2.0", "prompt": "Use explicit Euler for dy/dt = -k y. The prompt gives y(0)=25.5 and h=1.85, but omits both k and the number of steps. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: rate_constant, number_of_steps.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["rate_constant", "number_of_steps"]}, "verifier": {"missing": ["rate_constant", "number_of_steps"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 2.05 kg and a = 6 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 12.3, \"unit\": \"N\"}", "dedupe_signature": "9816aef692b52928e3f3c22e1d6b7aa80f9141dc9682acefd78f6aa40eca0e0c", "difficulty": "easy", "final_answer": {"answer": 12.3, "unit": "N"}, "id": "force_001962_2.05_6", "license": "Apache-2.0", "prompt": "A cart has mass 2.05 kg and measured acceleration 6 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 2.05 kg and a = 6 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 6.0, "mass": 2.05}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 7.85^2 and multiply by 0.5 * 19.6.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 603.9005, \"unit\": \"J\"}", "dedupe_signature": "a78a9871e722c4beb7e6248bfa279da1dd9a68e119b3ac5027ac4c21eccaf7c9", "difficulty": "easy", "final_answer": {"answer": 603.9005, "unit": "J"}, "id": "ke_001963_19.6_7.85", "license": "Apache-2.0", "prompt": "A body of mass 19.6 kg moves at 7.85 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 7.85^2 and multiply by 0.5 * 19.6.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 19.6, "velocity": 7.85}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=75 degrees through the sine of 2 theta.\n3. Substitute v=74.3 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 281.3705, \"unit\": \"m\"}", "dedupe_signature": "84bff06b52f46d72e8ba17bcd643119f514ca17ca17f909ed2c3cfcf6f327f54", "difficulty": "medium", "final_answer": {"answer": 281.3705, "unit": "m"}, "id": "projectile_range_001964_74.3_75", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 74.3 m/s and angle 75 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=75 degrees through the sine of 2 theta.\nSubstitute v=74.3 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 75, "gravity": 9.81, "speed": 74.3}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 4.07 * 8.314 * 268 / 32.4.\nFinal: {\"answer\": 279.8944, \"unit\": \"kPa\"}", "dedupe_signature": "f475e96a4925379c2339f7757b6f200fe06729f1286d1edeaa94e9876d4de8e0", "difficulty": "medium", "final_answer": {"answer": 279.8944, "unit": "kPa"}, "id": "ideal_gas_001965_4.07_268_32.4", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=4.07 mol, T=268 K, and V=32.4 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 4.07 * 8.314 * 268 / 32.4.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 4.07, "temp_k": 268, "volume_l": 32.4}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 640 * 2.43 * 118.\nFinal: {\"answer\": 183513.6, \"unit\": \"J\"}", "dedupe_signature": "a94e7bd6ac60edbc158ba2e92c7ef4022affd487b2b4235f058f4ca6f2b797d2", "difficulty": "easy", "final_answer": {"answer": 183513.6, "unit": "J"}, "id": "heat_q_001966_640_2.43_118", "license": "Apache-2.0", "prompt": "A 640 g sample has specific heat 2.43 J/(g*K). How much heat is needed to raise its temperature by 118 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 640 * 2.43 * 118.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 118, "heat_capacity": 2.43, "mass_g": 640}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=615.5 mg, t=144.5 h, and T_half=15 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 0.775, \"unit\": \"mg\"}", "dedupe_signature": "a6614293924dc5e4cf5d9d778e18b1628d3eb1d0234e7318509a8847f0a5a325", "difficulty": "medium", "final_answer": {"answer": 0.775, "unit": "mg"}, "id": "half_life_001968_615.5_15_144.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 615.5 mg. Its half-life is 15 hours. How many mg remain after 144.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=615.5 mg, t=144.5 h, and T_half=15 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 144.5, "half_life": 15.0, "initial_amount": 615.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 4485 mL to 4.485 L.\n3. Compute M = 4.065 / 4.485.\nFinal: {\"answer\": 0.9064, \"unit\": \"mol/L\"}", "dedupe_signature": "658572b4fb7c36bd01fa5b158109e309d78c9d8f9fe858310ce71dbae877eac5", "difficulty": "medium", "final_answer": {"answer": 0.9064, "unit": "mol/L"}, "id": "molarity_001970_4.065_4485", "license": "Apache-2.0", "prompt": "A solution contains 4.065 mol of solute in 4485 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 4485 mL to 4.485 L.\nCompute M = 4.065 / 4.485.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 4.065, "volume_ml": 4485}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.42 y, so each step multiplies y by 1 - h*0.42.\n3. Apply that update for 3 steps and round the final state.\nFinal: {\"answer\": 0.5665, \"unit\": \"state_units\"}", "dedupe_signature": "7b86e301a87d96601eae5841f9752c9f18c4469ec1cb28ac683a7e3ead7862a3", "difficulty": "medium", "final_answer": {"answer": 0.5665, "unit": "state_units"}, "id": "euler_decay_001971_39_0.42_1.8_3", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.42 y with y(0)=39, step size h=1.8, for 3 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.42 y, so each step multiplies y by 1 - h*0.42.\nApply that update for 3 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 39.0, "rate": 0.42, "step": 1.8, "steps": 3}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.46 and add it to the current value.\nFinal: {\"answer\": [0.398, -0.642, -0.702], \"unit\": \"temperature_units\"}", "dedupe_signature": "3052c32cdc43752d9118d568947fb0a557b843510e5f81a967615e2cde34a324", "difficulty": "hard", "final_answer": {"answer": [0.398, -0.642, -0.702], "unit": "temperature_units"}, "id": "heat_step_001973_0.46_0.3_-0.2_0.6_-1.3_-1.9", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=0.3, right=-1.9; current interior values are [-0.2, 0.6, -1.3]. Use r=0.46. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.46 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-0.2, 0.6, -1.3], "left": 0.3, "r": 0.46, "right": -1.9}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 100 centimeters in one meter.\n2. Apply the conversion factor directly to the given value.\n3. Compute 3836.5 / 100.\nFinal: {\"answer\": 38.365, \"unit\": \"m\"}", "dedupe_signature": "df3c0a0da9c661f30b49c5631344e36bfce1e8ea346d18142f757db385aafcc7", "difficulty": "easy", "final_answer": {"answer": 38.365, "unit": "m"}, "id": "unit_convert_001974_cm_to_m_3836.5", "license": "Apache-2.0", "prompt": "Convert 3836.5 cm to m. Return the converted value with unit.", "reasoning_trace": "There are 100 centimeters in one meter.\nApply the conversion factor directly to the given value.\nCompute 3836.5 / 100.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 3836.5}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=129 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-226.5553, 279.7725], \"unit\": \"N\"}", "dedupe_signature": "dd63d98c6612135ab8d6fc8c16535fce2ff23b6c5688a23acf16235a9ae4319e", "difficulty": "medium", "final_answer": {"answer": [-226.5553, 279.7725], "unit": "N"}, "id": "vector_components_001975_360_129", "license": "Apache-2.0", "prompt": "A vector has magnitude 360 N at 129 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=129 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 129, "magnitude": 360.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [8.2, -8.5], \"unit\": \"dimensionless\"}", "dedupe_signature": "34b0a77c16c407d38272cf7fa91c6f0fceadbcd99506c20d8fbd7c274be639eb", "difficulty": "medium", "final_answer": {"answer": [8.2, -8.5], "unit": "dimensionless"}, "id": "line_two_point_001976_-11.75_1_8.2_-8.5", "license": "Apache-2.0", "prompt": "A line passes through points (-11.75, -104.85) and (1, -0.3). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -11.75, "x2": 1.0, "y1": -104.85, "y2": -0.3000000000000007}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. energy divided by length is force, not spring constant\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "470a89bee3307d28cfe67f70073babdca79cf435a069fd89bd46e585f1fd0d7c", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_001977_inconsistent_56040f5d_560772", "license": "Apache-2.0", "prompt": "In sensor calibration case 560772, check dimensional consistency for k = E / x. The left side has dimensions N/m and the right side has dimensions J/m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nenergy divided by length is force, not spring constant\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "k = E / x"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\nimport math\n\ndef unit_vector_001978(x, y):\n    norm = math.hypot(x, y)\n    if norm == 0:\n        raise ValueError('zero vector has no direction')\n    return (x / norm, y / norm)\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"unit_vector_001978\"}", "dedupe_signature": "a8a07ba0be672bbd60a57ee5244bd9af94572ec8f862427608ec24ab3f3b6e72", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "unit_vector_001978"}, "id": "code_001978_unit_vector_001978", "license": "Apache-2.0", "prompt": "Write a Python function unit_vector_001978(x, y) that returns the 2D unit vector as a tuple. Raise ValueError for the zero vector. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "unit_vector_001978"}, "verifier": {"function": "unit_vector_001978", "tests": ["ux, uy = unit_vector_001978(3, 4); assert abs(ux - 0.6) < 1e-12 and abs(uy - 0.8) < 1e-12", "assert unit_vector_001978(0, 5) == (0, 1)", "try:\n    unit_vector_001978(0, 0)\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: rate_constant, number_of_steps.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"rate_constant\", \"number_of_steps\"]}", "dedupe_signature": "613b616d0a063ef1de3141126759c4b202dbf661eb868436f90cd9595fef55d9", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["rate_constant", "number_of_steps"]}, "id": "abstain_001979_rate_constant_number_of_steps", "license": "Apache-2.0", "prompt": "Use explicit Euler for dy/dt = -k y. The prompt gives y(0)=29 and h=1.65, but omits both k and the number of steps. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: rate_constant, number_of_steps.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["rate_constant", "number_of_steps"]}, "verifier": {"missing": ["rate_constant", "number_of_steps"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 10.25 kg and a = 6.3 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 64.575, \"unit\": \"N\"}", "dedupe_signature": "8d0e814084afe88d5473a47bed06598ab71f42030cebbccd5fba07f742759526", "difficulty": "easy", "final_answer": {"answer": 64.575, "unit": "N"}, "id": "force_001980_10.25_6.3", "license": "Apache-2.0", "prompt": "A cart has mass 10.25 kg and measured acceleration 6.3 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 10.25 kg and a = 6.3 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 6.3, "mass": 10.25}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 17^2 and multiply by 0.5 * 26.25.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 3793.125, \"unit\": \"J\"}", "dedupe_signature": "588aa7cd6130fbdc3439e909ab27d21c07ef1be5957a615d4001afbf9800ed49", "difficulty": "easy", "final_answer": {"answer": 3793.125, "unit": "J"}, "id": "ke_001981_26.25_17", "license": "Apache-2.0", "prompt": "A body of mass 26.25 kg moves at 17 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 17^2 and multiply by 0.5 * 26.25.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 26.25, "velocity": 17.0}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=79 degrees through the sine of 2 theta.\n3. Substitute v=30.6 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 35.756, \"unit\": \"m\"}", "dedupe_signature": "fa280e08c35c79db4bc2eb423fbbe3dae90a31fcb7c3db580d7a529b7450d77a", "difficulty": "medium", "final_answer": {"answer": 35.756, "unit": "m"}, "id": "projectile_range_001982_30.6_79", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 30.6 m/s and angle 79 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=79 degrees through the sine of 2 theta.\nSubstitute v=30.6 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 79, "gravity": 9.81, "speed": 30.6}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 1.97 * 8.314 * 574 / 90.7.\nFinal: {\"answer\": 103.6528, \"unit\": \"kPa\"}", "dedupe_signature": "895b4c3e4d1608fa3b770f8ce0fb67cbba95ed99a2a9c660e6eaf44606349a9b", "difficulty": "medium", "final_answer": {"answer": 103.6528, "unit": "kPa"}, "id": "ideal_gas_001983_1.97_574_90.7", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=1.97 mol, T=574 K, and V=90.7 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 1.97 * 8.314 * 574 / 90.7.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 1.97, "temp_k": 574, "volume_l": 90.7}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1160 * 2.655 * 63.\nFinal: {\"answer\": 194027.4, \"unit\": \"J\"}", "dedupe_signature": "71dab553063e75fd29cf797cbf9d98011a9bad63f09f033734d0e2dcd838cfe0", "difficulty": "easy", "final_answer": {"answer": 194027.4, "unit": "J"}, "id": "heat_q_001984_1160_2.655_63", "license": "Apache-2.0", "prompt": "A 1160 g sample has specific heat 2.655 J/(g*K). How much heat is needed to raise its temperature by 63 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1160 * 2.655 * 63.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 63, "heat_capacity": 2.655, "mass_g": 1160}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=36 V and R=36.6 ohm.\nFinal: {\"answer\": 35.4098, \"unit\": \"W\"}", "dedupe_signature": "7f86bcc70528c68dfb43be9d7175773ff233a69c7f6e0d1b6005af4980bcce3f", "difficulty": "easy", "final_answer": {"answer": 35.4098, "unit": "W"}, "id": "ohm_power_001985_36_36.6", "license": "Apache-2.0", "prompt": "A resistor has resistance 36.6 ohm and voltage 36 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=36 V and R=36.6 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 36.6, "voltage": 36.0}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=459 mg, t=326.5 h, and T_half=82 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 29.0536, \"unit\": \"mg\"}", "dedupe_signature": "8a70a39c6256732e2b9a7de96ccf7667048174d44376147c2929ca08783f9aed", "difficulty": "medium", "final_answer": {"answer": 29.0536, "unit": "mg"}, "id": "half_life_001986_459_82_326.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 459 mg. Its half-life is 82 hours. How many mg remain after 326.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=459 mg, t=326.5 h, and T_half=82 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 326.5, "half_life": 82.0, "initial_amount": 459.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 3950 mL to 3.95 L.\n3. Compute M = 0.04 / 3.95.\nFinal: {\"answer\": 0.0101, \"unit\": \"mol/L\"}", "dedupe_signature": "dd44316e7f61121964458d380b2864109f0755939ac22feb9e9a8e754b54ac16", "difficulty": "medium", "final_answer": {"answer": 0.0101, "unit": "mol/L"}, "id": "molarity_001988_0.04_3950", "license": "Apache-2.0", "prompt": "A solution contains 0.04 mol of solute in 3950 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 3950 mL to 3.95 L.\nCompute M = 0.04 / 3.95.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 0.04, "volume_ml": 3950}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.69 y, so each step multiplies y by 1 - h*0.69.\n3. Apply that update for 9 steps and round the final state.\nFinal: {\"answer\": -0.0001, \"unit\": \"state_units\"}", "dedupe_signature": "5f3395979baa4da3168e37374ae250422f1d6478fb87f92ad3fa0779ea519f4a", "difficulty": "medium", "final_answer": {"answer": -0.0001, "unit": "state_units"}, "id": "euler_decay_001989_78_0.69_1.75_9", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.69 y with y(0)=78, step size h=1.75, for 9 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.69 y, so each step multiplies y by 1 - h*0.69.\nApply that update for 9 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 78.0, "rate": 0.69, "step": 1.75, "steps": 9}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-0.3)=-9.29 and f(4)=-42.4.\n3. The interval width is 4.3.\nFinal: {\"answer\": -111.1335, \"unit\": \"area_units\"}", "dedupe_signature": "21c48241999306d3d0eca65e92ebca3a1672048fc64ed2ac09cb2dc65f507499", "difficulty": "medium", "final_answer": {"answer": -111.1335, "unit": "area_units"}, "id": "trapz_linear_001990_-7.7_-11.6_-0.3_4", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-7.7x+-11.6 from x=-0.3 to x=4. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-0.3)=-9.29 and f(4)=-42.4.\nThe interval width is 4.3.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -11.6, "slope": -7.7, "x0": -0.3, "x1": 4.0}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.06 and add it to the current value.\nFinal: {\"answer\": [1.774, 1.127, 2.581], \"unit\": \"temperature_units\"}", "dedupe_signature": "88b8e9808b9afef521d61d75316a9f4f242937614ff284b9f8a89ddf50927a39", "difficulty": "hard", "final_answer": {"answer": [1.774, 1.127, 2.581], "unit": "temperature_units"}, "id": "heat_step_001991_0.06_0.75_1.9_0.95_2.95_-1.2", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=0.75, right=-1.2; current interior values are [1.9, 0.95, 2.95]. Use r=0.06. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.06 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [1.9, 0.95, 2.95], "left": 0.75, "r": 0.06, "right": -1.2}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 12279.0 / 1000.\nFinal: {\"answer\": 12.279, \"unit\": \"kg\"}", "dedupe_signature": "ae1c53f07329eeace69267f6a2ba5462c86acd0e03d7bb7945d175031846f937", "difficulty": "easy", "final_answer": {"answer": 12.279, "unit": "kg"}, "id": "unit_convert_001992_g_to_kg_12279", "license": "Apache-2.0", "prompt": "Convert 12279 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 12279.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 12279.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=180 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-196.0, 0.0], \"unit\": \"N\"}", "dedupe_signature": "941052949fb976e8b1a26312b7e83406b6664e47718ce6468342a1eed0e45d4d", "difficulty": "medium", "final_answer": {"answer": [-196.0, 0.0], "unit": "N"}, "id": "vector_components_001993_196_180", "license": "Apache-2.0", "prompt": "A vector has magnitude 196 N at 180 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=180 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 180, "magnitude": 196.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-8.6, -21.25], \"unit\": \"dimensionless\"}", "dedupe_signature": "bb260c006e0ea74becf25b09296610bdd4340e65b115945b89566b3d53409511", "difficulty": "medium", "final_answer": {"answer": [-8.6, -21.25], "unit": "dimensionless"}, "id": "line_two_point_001994_-3.25_10.25_-8.6_-21.25", "license": "Apache-2.0", "prompt": "A line passes through points (-3.25, 6.7) and (10.25, -109.4). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -3.25, "x2": 10.25, "y1": 6.699999999999999, "y2": -109.39999999999999}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. grams cancel with J/(g*K), and kelvin cancels, leaving joules\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "87264808ac0b01a1ceb83fe93c75be85f564faa54b8da6a2ca99d8fd94544d3d", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_001995_consistent_4153435f_326911", "license": "Apache-2.0", "prompt": "In field worksheet case 326911, check dimensional consistency for Q = m * c * DeltaT. The left side has dimensions J and the right side has dimensions J. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\ngrams cancel with J/(g*K), and kelvin cancels, leaving joules\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "Q = m * c * DeltaT"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: recurrence, objective, tie_breaking_rule.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"recurrence\", \"objective\", \"tie_breaking_rule\"]}", "dedupe_signature": "09a58d80aa520aba980052bfc92bb9ee6c29a0b44003abcef5e677366f08e422", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["recurrence", "objective", "tie_breaking_rule"]}, "id": "abstain_001997_recurrence_objective_tie_breaking_rule", "license": "Apache-2.0", "prompt": "Write a dynamic-programming solver for a scheduler scoring problem with 3914 items and budget 19290, but the recurrence, objective, and tie-breaking rule are all absent. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: recurrence, objective, tie_breaking_rule.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["recurrence", "objective", "tie_breaking_rule"]}, "verifier": {"missing": ["recurrence", "objective", "tie_breaking_rule"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 5.9 kg and a = 15.05 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 88.795, \"unit\": \"N\"}", "dedupe_signature": "92d267ac83dc31accd445ce87cf30610c736b9bd6cc65bceaa8a7d77730513fb", "difficulty": "easy", "final_answer": {"answer": 88.795, "unit": "N"}, "id": "force_001998_5.9_15.05", "license": "Apache-2.0", "prompt": "A cart has mass 5.9 kg and measured acceleration 15.05 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 5.9 kg and a = 15.05 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 15.05, "mass": 5.9}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=8 degrees through the sine of 2 theta.\n3. Substitute v=37.4 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 39.3018, \"unit\": \"m\"}", "dedupe_signature": "d09a81fa84b6be235db516b0001dcec30fefcbc1e5978810702052f115395dd7", "difficulty": "medium", "final_answer": {"answer": 39.3018, "unit": "m"}, "id": "projectile_range_002000_37.4_8", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 37.4 m/s and angle 8 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=8 degrees through the sine of 2 theta.\nSubstitute v=37.4 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 8, "gravity": 9.81, "speed": 37.4}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1000 * 4.185 * 48.\nFinal: {\"answer\": 200880.0, \"unit\": \"J\"}", "dedupe_signature": "6e86492f6899c0f7e68dd1759db3b62e0dbca10cf17eec7f3b8a5dd3325a6957", "difficulty": "easy", "final_answer": {"answer": 200880.0, "unit": "J"}, "id": "heat_q_002002_1000_4.185_48", "license": "Apache-2.0", "prompt": "A 1000 g sample has specific heat 4.185 J/(g*K). How much heat is needed to raise its temperature by 48 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1000 * 4.185 * 48.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 48, "heat_capacity": 4.185, "mass_g": 1000}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=211.7 V and R=133.4 ohm.\nFinal: {\"answer\": 335.9587, \"unit\": \"W\"}", "dedupe_signature": "24d5015f393de691e0e968f559e2fc4815a755950db08228ae1525605d89614f", "difficulty": "easy", "final_answer": {"answer": 335.9587, "unit": "W"}, "id": "ohm_power_002003_211.7_133.4", "license": "Apache-2.0", "prompt": "A resistor has resistance 133.4 ohm and voltage 211.7 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=211.7 V and R=133.4 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 133.4, "voltage": 211.7}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=159 mg, t=55.5 h, and T_half=37 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 56.215, \"unit\": \"mg\"}", "dedupe_signature": "526dfab42f4aa6244a00ee5220a3acc9661278d96471d04b07e3c00a0614517b", "difficulty": "medium", "final_answer": {"answer": 56.215, "unit": "mg"}, "id": "half_life_002004_159_37_55.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 159 mg. Its half-life is 37 hours. How many mg remain after 55.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=159 mg, t=55.5 h, and T_half=37 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 55.5, "half_life": 37.0, "initial_amount": 159.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 1.71 mol * 100.087 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 171.1488, \"unit\": \"g\"}", "dedupe_signature": "3b409cbbd337690c15a2bd74f725ed200206c8d8785903c6341bdfec0077a2b2", "difficulty": "medium", "final_answer": {"answer": 171.1488, "unit": "g"}, "id": "stoich_mass_002005_calcium_carbonate_1.71", "license": "Apache-2.0", "prompt": "A sample contains 1.71 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 1.71 mol * 100.087 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "calcium carbonate", "molar_mass": 100.087, "moles": 1.71}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 3815 mL to 3.815 L.\n3. Compute M = 4.175 / 3.815.\nFinal: {\"answer\": 1.0944, \"unit\": \"mol/L\"}", "dedupe_signature": "8cce6d0b314395ed870fd6926b067fa2955f399c352dfd19898c1984218720ad", "difficulty": "medium", "final_answer": {"answer": 1.0944, "unit": "mol/L"}, "id": "molarity_002006_4.175_3815", "license": "Apache-2.0", "prompt": "A solution contains 4.175 mol of solute in 3815 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 3815 mL to 3.815 L.\nCompute M = 4.175 / 3.815.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 4.175, "volume_ml": 3815}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.81 y, so each step multiplies y by 1 - h*0.81.\n3. Apply that update for 11 steps and round the final state.\nFinal: {\"answer\": 2.5728, \"unit\": \"state_units\"}", "dedupe_signature": "e682568eb32b26b828892056446f49efc722ae9e04a0382e56da96c7ece539f1", "difficulty": "medium", "final_answer": {"answer": 2.5728, "unit": "state_units"}, "id": "euler_decay_002007_31_0.81_0.25_11", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.81 y with y(0)=31, step size h=0.25, for 11 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.81 y, so each step multiplies y by 1 - h*0.81.\nApply that update for 11 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 31.0, "rate": 0.81, "step": 0.25, "steps": 11}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(2.8)=-29.42 and f(7.8)=-53.92.\n3. The interval width is 5.\nFinal: {\"answer\": -208.35, \"unit\": \"area_units\"}", "dedupe_signature": "6c1c7c46a1bdcf6ad0406826d2e2a166048fb03c37478b6ea62aa86de25866df", "difficulty": "medium", "final_answer": {"answer": -208.35, "unit": "area_units"}, "id": "trapz_linear_002008_-4.9_-15.7_2.8_7.8", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-4.9x+-15.7 from x=2.8 to x=7.8. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(2.8)=-29.42 and f(7.8)=-53.92.\nThe interval width is 5.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -15.7, "slope": -4.9, "x0": 2.8, "x1": 7.8}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.48 and add it to the current value.\nFinal: {\"answer\": [2.054, 0.754, 1.53], \"unit\": \"temperature_units\"}", "dedupe_signature": "608454a53c497756dfcad0fd6675c544dc918c5afe3b6b984ca7149149a1c53c", "difficulty": "hard", "final_answer": {"answer": [2.054, 0.754, 1.53], "unit": "temperature_units"}, "id": "heat_step_002009_0.48_2.35_-1.45_2.05_2.85_0.9", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=2.35, right=0.9; current interior values are [-1.45, 2.05, 2.85]. Use r=0.48. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.48 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-1.45, 2.05, 2.85], "left": 2.35, "r": 0.48, "right": 0.9}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kelvin equals Celsius plus 273.15.\n2. Apply the conversion factor directly to the given value.\n3. Compute -13.0 + 273.15.\nFinal: {\"answer\": 260.15, \"unit\": \"K\"}", "dedupe_signature": "51bcf38fd2a680d31c91a4e37f03f05ed39a83e572d8dfb4cdb79bd1a3821170", "difficulty": "easy", "final_answer": {"answer": 260.15, "unit": "K"}, "id": "unit_convert_002010_c_to_k_-13", "license": "Apache-2.0", "prompt": "Convert -13 degC to K. Return the converted value with unit.", "reasoning_trace": "Kelvin equals Celsius plus 273.15.\nApply the conversion factor directly to the given value.\nCompute -13.0 + 273.15.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": -13.0}, "verifier": {"formula": "value + 273.15", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=202 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-426.041, -172.1317], \"unit\": \"N\"}", "dedupe_signature": "ecc06c0f14cd17cf1586feab63e9eb2c749e167f971bc02348de7e814c5ff6ad", "difficulty": "medium", "final_answer": {"answer": [-426.041, -172.1317], "unit": "N"}, "id": "vector_components_002011_459.5_202", "license": "Apache-2.0", "prompt": "A vector has magnitude 459.5 N at 202 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=202 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 202, "magnitude": 459.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-0.1, 0.25], \"unit\": \"dimensionless\"}", "dedupe_signature": "19e0ed0f9f7faee4dc31e9af9bdaa2619040b473539dbe3f9cacd9e6cf800bbf", "difficulty": "medium", "final_answer": {"answer": [-0.1, 0.25], "unit": "dimensionless"}, "id": "line_two_point_002012_-12.5_-7_-0.1_0.25", "license": "Apache-2.0", "prompt": "A line passes through points (-12.5, 1.5) and (-7, 0.95). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -12.5, "x2": -7.0, "y1": 1.5, "y2": 0.9500000000000001}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. mass times acceleration has newton dimensions\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "0a749061ad0417097c0906bda2ae0cee4054a5776aab1a48672553ba35b8a144", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_002013_consistent_03f5e041_667662", "license": "Apache-2.0", "prompt": "In instrument manual case 667662, check dimensional consistency for F = m * a. The left side has dimensions kg*m/s^2 and the right side has dimensions kg*m/s^2. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nmass times acceleration has newton dimensions\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "F = m * a"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef normalize_002014(values):\n    total = sum(values)\n    if total == 0:\n        raise ValueError('cannot normalize zero-sum values')\n    return [v / total for v in values]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"normalize_002014\"}", "dedupe_signature": "64e391bbcaf7ff9f8892b40cefdfad264a96a8299cbfbee6bcba60446600b45f", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "normalize_002014"}, "id": "code_002014_normalize_002014", "license": "Apache-2.0", "prompt": "Write a Python function normalize_002014(values) that returns a new list whose values sum to 1. Raise ValueError if the sum is zero. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "normalize_002014"}, "verifier": {"function": "normalize_002014", "tests": ["out = normalize_002014([2, 3, 5]); assert len(out) == 3", "assert abs(sum(normalize_002014([2, 3, 5])) - 1.0) < 1e-12", "assert normalize_002014([1, 1]) == [0.5, 0.5]", "try:\n    normalize_002014([1, -1])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: launch_angle_or_vertical_velocity.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"launch_angle_or_vertical_velocity\"]}", "dedupe_signature": "b5b4d0bfbde890033893c86d91bc4f59d5fb1af185f1c08b51e154cf970d8095", "difficulty": "easy", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["launch_angle_or_vertical_velocity"]}, "id": "abstain_002015_launch_angle_or_vertical_velocity", "license": "Apache-2.0", "prompt": "Compute projectile range on level ground. The prompt gives initial speed 53.2 m/s but does not give launch angle or vertical velocity. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: launch_angle_or_vertical_velocity.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["launch_angle_or_vertical_velocity"]}, "verifier": {"missing": ["launch_angle_or_vertical_velocity"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 5.65 kg and a = 12.6 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 71.19, \"unit\": \"N\"}", "dedupe_signature": "1eecf0223bc6f451d5fe6670b4898d8b2589775d83ff759931234b65fc037b59", "difficulty": "easy", "final_answer": {"answer": 71.19, "unit": "N"}, "id": "force_002016_5.65_12.6", "license": "Apache-2.0", "prompt": "A cart has mass 5.65 kg and measured acceleration 12.6 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 5.65 kg and a = 12.6 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 12.6, "mass": 5.65}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 34.8^2 and multiply by 0.5 * 19.05.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 11535.156, \"unit\": \"J\"}", "dedupe_signature": "8ec874069e872ad895a50aaf5da25b37f8044f28cf9a4aa1755e6dd72e4b3480", "difficulty": "easy", "final_answer": {"answer": 11535.156, "unit": "J"}, "id": "ke_002017_19.05_34.8", "license": "Apache-2.0", "prompt": "A body of mass 19.05 kg moves at 34.8 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 34.8^2 and multiply by 0.5 * 19.05.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 19.05, "velocity": 34.8}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=84 degrees through the sine of 2 theta.\n3. Substitute v=73 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 112.942, \"unit\": \"m\"}", "dedupe_signature": "499211f8a257df17c471281884f2062fdf5c909d62b4c8dee540fba360e728fc", "difficulty": "medium", "final_answer": {"answer": 112.942, "unit": "m"}, "id": "projectile_range_002018_73_84", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 73 m/s and angle 84 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=84 degrees through the sine of 2 theta.\nSubstitute v=73 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 84, "gravity": 9.81, "speed": 73.0}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 3.73 * 8.314 * 267 / 113.3.\nFinal: {\"answer\": 73.0803, \"unit\": \"kPa\"}", "dedupe_signature": "136875b47018585c7b568be710e4fe8b6fbdd84843cfe42776753a684a8a0a8e", "difficulty": "medium", "final_answer": {"answer": 73.0803, "unit": "kPa"}, "id": "ideal_gas_002019_3.73_267_113.3", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=3.73 mol, T=267 K, and V=113.3 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 3.73 * 8.314 * 267 / 113.3.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 3.73, "temp_k": 267, "volume_l": 113.3}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1530 * 3.755 * 16.\nFinal: {\"answer\": 91922.4, \"unit\": \"J\"}", "dedupe_signature": "23d82f7ec7f181fbdf8b39839812de4952430b93435d2c2aa158cda061ecea92", "difficulty": "easy", "final_answer": {"answer": 91922.4, "unit": "J"}, "id": "heat_q_002020_1530_3.755_16", "license": "Apache-2.0", "prompt": "A 1530 g sample has specific heat 3.755 J/(g*K). How much heat is needed to raise its temperature by 16 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1530 * 3.755 * 16.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 16, "heat_capacity": 3.755, "mass_g": 1530}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=23.4 V and R=173.6 ohm.\nFinal: {\"answer\": 3.1541, \"unit\": \"W\"}", "dedupe_signature": "c28f24b7fbe02650e7cecdad37ae97a8e2cbcb8f544fae05be918012e12eade2", "difficulty": "easy", "final_answer": {"answer": 3.1541, "unit": "W"}, "id": "ohm_power_002021_23.4_173.6", "license": "Apache-2.0", "prompt": "A resistor has resistance 173.6 ohm and voltage 23.4 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=23.4 V and R=173.6 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 173.6, "voltage": 23.4}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=890.5 mg, t=66.5 h, and T_half=48.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 344.256, \"unit\": \"mg\"}", "dedupe_signature": "aea57663d52f24173616be5f29499f1b3cabb871bac2b9d7e6345da058d6b530", "difficulty": "medium", "final_answer": {"answer": 344.256, "unit": "mg"}, "id": "half_life_002022_890.5_48.5_66.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 890.5 mg. Its half-life is 48.5 hours. How many mg remain after 66.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=890.5 mg, t=66.5 h, and T_half=48.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 66.5, "half_life": 48.5, "initial_amount": 890.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 0.51 mol * 18.015 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 9.1876, \"unit\": \"g\"}", "dedupe_signature": "151a1e65920a6a92b2bb7bdb1ad9c38d94a218471d0b509ef90fc31c02945992", "difficulty": "medium", "final_answer": {"answer": 9.1876, "unit": "g"}, "id": "stoich_mass_002023_water_0.51", "license": "Apache-2.0", "prompt": "A sample contains 0.51 mol of water. Using molar mass 18.015 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 0.51 mol * 18.015 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "water", "molar_mass": 18.015, "moles": 0.51}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 4515 mL to 4.515 L.\n3. Compute M = 2.605 / 4.515.\nFinal: {\"answer\": 0.577, \"unit\": \"mol/L\"}", "dedupe_signature": "46fe2c752f51782ed47d45d4a00ab2742d156e42429678708260ca0555029e94", "difficulty": "medium", "final_answer": {"answer": 0.577, "unit": "mol/L"}, "id": "molarity_002024_2.605_4515", "license": "Apache-2.0", "prompt": "A solution contains 2.605 mol of solute in 4515 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 4515 mL to 4.515 L.\nCompute M = 2.605 / 4.515.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 2.605, "volume_ml": 4515}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.44 and add it to the current value.\nFinal: {\"answer\": [0.072, 1.33, 2.11], \"unit\": \"temperature_units\"}", "dedupe_signature": "456f8494efbd67fb1098edaf88ecb667c5ad8b1f72d14df18f44992a8242d8ea", "difficulty": "hard", "final_answer": {"answer": [0.072, 1.33, 2.11], "unit": "temperature_units"}, "id": "heat_step_002027_0.44_-1.4_0.05_1.55_2.55_2.55", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-1.4, right=2.55; current interior values are [0.05, 1.55, 2.55]. Use r=0.44. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.44 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [0.05, 1.55, 2.55], "left": -1.4, "r": 0.44, "right": 2.55}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 100 centimeters in one meter.\n2. Apply the conversion factor directly to the given value.\n3. Compute 271.5 / 100.\nFinal: {\"answer\": 2.715, \"unit\": \"m\"}", "dedupe_signature": "e59579fd36101de94c94d6e1c8326545c2814c996004a67bcde45affc0464498", "difficulty": "easy", "final_answer": {"answer": 2.715, "unit": "m"}, "id": "unit_convert_002028_cm_to_m_271.5", "license": "Apache-2.0", "prompt": "Convert 271.5 cm to m. Return the converted value with unit.", "reasoning_trace": "There are 100 centimeters in one meter.\nApply the conversion factor directly to the given value.\nCompute 271.5 / 100.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 271.5}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=332 degrees and keep the unit as newtons.\nFinal: {\"answer\": [247.2253, -131.452], \"unit\": \"N\"}", "dedupe_signature": "b53831c71269753a1342e203015f78bcf9988928c686ab8e4c496c2b54ae1f86", "difficulty": "medium", "final_answer": {"answer": [247.2253, -131.452], "unit": "N"}, "id": "vector_components_002029_280_332", "license": "Apache-2.0", "prompt": "A vector has magnitude 280 N at 332 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=332 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 332, "magnitude": 280.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef safe_mean_002032(values):\n    if not values:\n        raise ValueError('safe_mean requires at least one value')\n    return sum(values) / len(values)\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"safe_mean_002032\"}", "dedupe_signature": "6eb139a7ee2557ed06e471874ebe7371af6f256d37269f8d3216b2b1203e4fcc", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "safe_mean_002032"}, "id": "code_002032_safe_mean_002032", "license": "Apache-2.0", "prompt": "Write a Python function safe_mean_002032(values) that returns the arithmetic mean. It must raise ValueError for an empty input and must not mutate the input list. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "safe_mean_002032"}, "verifier": {"function": "safe_mean_002032", "tests": ["assert safe_mean_002032([2, 4, 6]) == 4", "xs = [1, 2, 3]; assert safe_mean_002032(xs) == 2 and xs == [1, 2, 3]", "try:\n    safe_mean_002032([])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 23.35 kg and a = 4.35 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 101.5725, \"unit\": \"N\"}", "dedupe_signature": "59c5f1b4e1db039c82c183d38666f908d42839e229cd236b91fd9b91ab1bdcd0", "difficulty": "easy", "final_answer": {"answer": 101.5725, "unit": "N"}, "id": "force_002034_23.35_4.35", "license": "Apache-2.0", "prompt": "A cart has mass 23.35 kg and measured acceleration 4.35 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 23.35 kg and a = 4.35 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 4.35, "mass": 23.35}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 37.8^2 and multiply by 0.5 * 28.6.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 20432.412, \"unit\": \"J\"}", "dedupe_signature": "77e20519b5d47ae242f1ea7159e91aa8352a2a11351aa36b2efb6b661bb32219", "difficulty": "easy", "final_answer": {"answer": 20432.412, "unit": "J"}, "id": "ke_002035_28.6_37.8", "license": "Apache-2.0", "prompt": "A body of mass 28.6 kg moves at 37.8 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 37.8^2 and multiply by 0.5 * 28.6.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 28.6, "velocity": 37.8}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 0.5 * 8.314 * 451 / 34.4.\nFinal: {\"answer\": 54.5002, \"unit\": \"kPa\"}", "dedupe_signature": "97615749365698258a67b531fc4d2e670b6261dc135acf861208b961f1492367", "difficulty": "medium", "final_answer": {"answer": 54.5002, "unit": "kPa"}, "id": "ideal_gas_002037_0.5_451_34.4", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=0.5 mol, T=451 K, and V=34.4 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 0.5 * 8.314 * 451 / 34.4.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 0.5, "temp_k": 451, "volume_l": 34.4}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1420 * 3.9 * 81.\nFinal: {\"answer\": 448578.0, \"unit\": \"J\"}", "dedupe_signature": "0a67fd1faae7dbc0ebe8bb3d72a9cc188ad98a497713404f4ebe6ca4d68a8a3c", "difficulty": "easy", "final_answer": {"answer": 448578.0, "unit": "J"}, "id": "heat_q_002038_1420_3.9_81", "license": "Apache-2.0", "prompt": "A 1420 g sample has specific heat 3.9 J/(g*K). How much heat is needed to raise its temperature by 81 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1420 * 3.9 * 81.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 81, "heat_capacity": 3.9, "mass_g": 1420}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=204.2 V and R=28.3 ohm.\nFinal: {\"answer\": 1473.4148, \"unit\": \"W\"}", "dedupe_signature": "5c1ba8bab1adaf8db03892eb11f809a0c2213dfcdce2bf2b7261ce105dcec9a1", "difficulty": "easy", "final_answer": {"answer": 1473.4148, "unit": "W"}, "id": "ohm_power_002039_204.2_28.3", "license": "Apache-2.0", "prompt": "A resistor has resistance 28.3 ohm and voltage 204.2 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=204.2 V and R=28.3 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 28.3, "voltage": 204.2}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=154 mg, t=155.5 h, and T_half=110 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 57.8061, \"unit\": \"mg\"}", "dedupe_signature": "87d486007f37bebe8df498eb551e7e0f615a4eae95f711e2b440895b70952607", "difficulty": "medium", "final_answer": {"answer": 57.8061, "unit": "mg"}, "id": "half_life_002040_154_110_155.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 154 mg. Its half-life is 110 hours. How many mg remain after 155.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=154 mg, t=155.5 h, and T_half=110 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 155.5, "half_life": 110.0, "initial_amount": 154.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 7.2 mol * 58.44 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 420.768, \"unit\": \"g\"}", "dedupe_signature": "7e5dd6b6852a809f5a0531cd4766849662b553372b7723e0b45c9e9853db11f1", "difficulty": "medium", "final_answer": {"answer": 420.768, "unit": "g"}, "id": "stoich_mass_002041_sodium_chloride_7.2", "license": "Apache-2.0", "prompt": "A sample contains 7.2 mol of sodium chloride. Using molar mass 58.44 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 7.2 mol * 58.44 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "sodium chloride", "molar_mass": 58.44, "moles": 7.2}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 4705 mL to 4.705 L.\n3. Compute M = 2.925 / 4.705.\nFinal: {\"answer\": 0.6217, \"unit\": \"mol/L\"}", "dedupe_signature": "05860d5fceb970b8ab8f340b6ff49584de644f0c01b0ecc07448710fb3cb79c1", "difficulty": "medium", "final_answer": {"answer": 0.6217, "unit": "mol/L"}, "id": "molarity_002042_2.925_4705", "license": "Apache-2.0", "prompt": "A solution contains 2.925 mol of solute in 4705 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 4705 mL to 4.705 L.\nCompute M = 2.925 / 4.705.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 2.925, "volume_ml": 4705}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.63 y, so each step multiplies y by 1 - h*0.63.\n3. Apply that update for 10 steps and round the final state.\nFinal: {\"answer\": 0.0649, \"unit\": \"state_units\"}", "dedupe_signature": "78247e82b9eca91cbe46e63de5c8e5f992423c29b4a3717979e6447760e86403", "difficulty": "medium", "final_answer": {"answer": 0.0649, "unit": "state_units"}, "id": "euler_decay_002043_72_0.63_0.8_10", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.63 y with y(0)=72, step size h=0.8, for 10 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.63 y, so each step multiplies y by 1 - h*0.63.\nApply that update for 10 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 72.0, "rate": 0.63, "step": 0.8, "steps": 10}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(3)=-2.9 and f(7.6)=-3.36.\n3. The interval width is 4.6.\nFinal: {\"answer\": -14.398, \"unit\": \"area_units\"}", "dedupe_signature": "f80385a43b7627f15d8486cab92495627c80bc0126cafe44cf0aedd93208db42", "difficulty": "medium", "final_answer": {"answer": -14.398, "unit": "area_units"}, "id": "trapz_linear_002044_-0.1_-2.6_3_7.6", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-0.1x+-2.6 from x=3 to x=7.6. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(3)=-2.9 and f(7.6)=-3.36.\nThe interval width is 4.6.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -2.6, "slope": -0.1, "x0": 3.0, "x1": 7.6}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.26 and add it to the current value.\nFinal: {\"answer\": [1.468, 1.716, 1.415], \"unit\": \"temperature_units\"}", "dedupe_signature": "b77806819d6bbe6e7de950e88f9df1c9ef4274c99c3de12d4c3d762ddae87c58", "difficulty": "hard", "final_answer": {"answer": [1.468, 1.716, 1.415], "unit": "temperature_units"}, "id": "heat_step_002045_0.26_1.85_1.0_1.95_2.0_-0.2", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.85, right=-0.2; current interior values are [1.0, 1.95, 2.0]. Use r=0.26. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.26 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [1.0, 1.95, 2.0], "left": 1.85, "r": 0.26, "right": -0.2}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 31026.0 / 1000.\nFinal: {\"answer\": 31.026, \"unit\": \"kg\"}", "dedupe_signature": "07f72303e3e44f4a3066a8c882643b90858af1acb655e88a28cab9ea4a17e0b4", "difficulty": "easy", "final_answer": {"answer": 31.026, "unit": "kg"}, "id": "unit_convert_002046_g_to_kg_31026", "license": "Apache-2.0", "prompt": "Convert 31026 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 31026.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 31026.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=287 degrees and keep the unit as newtons.\nFinal: {\"answer\": [60.8133, -198.9114], \"unit\": \"N\"}", "dedupe_signature": "1d27fa5b46b4ab733fd403605c3e07505eeda8ab8f1dd26299d592a981322576", "difficulty": "medium", "final_answer": {"answer": [60.8133, -198.9114], "unit": "N"}, "id": "vector_components_002047_208_287", "license": "Apache-2.0", "prompt": "A vector has magnitude 208 N at 287 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=287 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 287, "magnitude": 208.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [1.55, 9.5], \"unit\": \"dimensionless\"}", "dedupe_signature": "15979b53a1f551bcd35de3148337bfcaa6487081833747af09559bceac9f04b9", "difficulty": "medium", "final_answer": {"answer": [1.55, 9.5], "unit": "dimensionless"}, "id": "line_two_point_002048_1.75_11.25_1.55_9.5", "license": "Apache-2.0", "prompt": "A line passes through points (1.75, 12.2125) and (11.25, 26.9375). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 1.75, "x2": 11.25, "y1": 12.2125, "y2": 26.9375}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. velocity divided by time is acceleration\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "5183a38b944a08814a60be0ccacadb42850d594ab94c393e8a04a9ebeae57e83", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_002049_inconsistent_c1271127_799996", "license": "Apache-2.0", "prompt": "In instrument manual case 799996, check dimensional consistency for x = v / t. The left side has dimensions m and the right side has dimensions m/s^2. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nvelocity divided by time is acceleration\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "x = v / t"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: volume.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"volume\"]}", "dedupe_signature": "cdc1af4e1c007cb0a6c79ee7c4922b4cf91be745f93b820a1fb4ff1c6450e4c0", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["volume"]}, "id": "abstain_002051_volume", "license": "Apache-2.0", "prompt": "Compute pressure from the ideal gas law. The prompt gives n=5 mol and T=406 K, but does not give volume. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: volume.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["volume"]}, "verifier": {"missing": ["volume"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 5.8 kg and a = 2.55 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 14.79, \"unit\": \"N\"}", "dedupe_signature": "748e68e72094670b900b06c9f5fd715ac99a6b03236d18c947e026510d75ad59", "difficulty": "easy", "final_answer": {"answer": 14.79, "unit": "N"}, "id": "force_002052_5.8_2.55", "license": "Apache-2.0", "prompt": "A cart has mass 5.8 kg and measured acceleration 2.55 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 5.8 kg and a = 2.55 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 2.55, "mass": 5.8}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 12.9^2 and multiply by 0.5 * 14.6.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 1214.793, \"unit\": \"J\"}", "dedupe_signature": "2e34ba24b6a51704d3247d4598550e1b107daf5cfe3f625a5e110a62829acf19", "difficulty": "easy", "final_answer": {"answer": 1214.793, "unit": "J"}, "id": "ke_002053_14.6_12.9", "license": "Apache-2.0", "prompt": "A body of mass 14.6 kg moves at 12.9 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 12.9^2 and multiply by 0.5 * 14.6.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 14.6, "velocity": 12.9}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=47 degrees through the sine of 2 theta.\n3. Substitute v=44.1 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 197.7648, \"unit\": \"m\"}", "dedupe_signature": "2584fe4c00291249e79a59a55d937bab93adc41dbfc2a64953cbf2c98f72bd75", "difficulty": "medium", "final_answer": {"answer": 197.7648, "unit": "m"}, "id": "projectile_range_002054_44.1_47", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 44.1 m/s and angle 47 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=47 degrees through the sine of 2 theta.\nSubstitute v=44.1 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 47, "gravity": 9.81, "speed": 44.1}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 5.36 * 8.314 * 552 / 66.5.\nFinal: {\"answer\": 369.9067, \"unit\": \"kPa\"}", "dedupe_signature": "c73cac3f5b43e674d84de7b6023725d054a0bef633bd37437a4073c52c0e00e2", "difficulty": "medium", "final_answer": {"answer": 369.9067, "unit": "kPa"}, "id": "ideal_gas_002055_5.36_552_66.5", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=5.36 mol, T=552 K, and V=66.5 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 5.36 * 8.314 * 552 / 66.5.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 5.36, "temp_k": 552, "volume_l": 66.5}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1640 * 0.73 * 16.\nFinal: {\"answer\": 19155.2, \"unit\": \"J\"}", "dedupe_signature": "83a6ba415f9f090da35f635e4b5849ee20e516f59a7834e63640a0512a24e1c4", "difficulty": "easy", "final_answer": {"answer": 19155.2, "unit": "J"}, "id": "heat_q_002056_1640_0.73_16", "license": "Apache-2.0", "prompt": "A 1640 g sample has specific heat 0.73 J/(g*K). How much heat is needed to raise its temperature by 16 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1640 * 0.73 * 16.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 16, "heat_capacity": 0.73, "mass_g": 1640}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=100.4 V and R=128.9 ohm.\nFinal: {\"answer\": 78.2014, \"unit\": \"W\"}", "dedupe_signature": "57e8113ab55506e750da1898274ccbfa311682c0c36bf55b21dc7e68dae14cdb", "difficulty": "easy", "final_answer": {"answer": 78.2014, "unit": "W"}, "id": "ohm_power_002057_100.4_128.9", "license": "Apache-2.0", "prompt": "A resistor has resistance 128.9 ohm and voltage 100.4 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=100.4 V and R=128.9 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 128.9, "voltage": 100.4}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=229 mg, t=33.5 h, and T_half=110.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 185.5979, \"unit\": \"mg\"}", "dedupe_signature": "1c61ada9514d8f56d215fd305558982e1fe01430f3af18780c4f17ff7b9db36c", "difficulty": "medium", "final_answer": {"answer": 185.5979, "unit": "mg"}, "id": "half_life_002058_229_110.5_33.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 229 mg. Its half-life is 110.5 hours. How many mg remain after 33.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=229 mg, t=33.5 h, and T_half=110.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 33.5, "half_life": 110.5, "initial_amount": 229.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 5.46 mol * 100.087 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 546.475, \"unit\": \"g\"}", "dedupe_signature": "43d845d6e3aef7418ef3b4f20cfbfb33e476e2f79a68048ce078c78daa6ac7d4", "difficulty": "medium", "final_answer": {"answer": 546.475, "unit": "g"}, "id": "stoich_mass_002059_calcium_carbonate_5.46", "license": "Apache-2.0", "prompt": "A sample contains 5.46 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 5.46 mol * 100.087 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "calcium carbonate", "molar_mass": 100.087, "moles": 5.46}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 3820 mL to 3.82 L.\n3. Compute M = 0.75 / 3.82.\nFinal: {\"answer\": 0.1963, \"unit\": \"mol/L\"}", "dedupe_signature": "6e60bd5a05b8cdf5a7e90bd9a0052188b2e6312d5d81eff8a5389efb372e97b4", "difficulty": "medium", "final_answer": {"answer": 0.1963, "unit": "mol/L"}, "id": "molarity_002060_0.75_3820", "license": "Apache-2.0", "prompt": "A solution contains 0.75 mol of solute in 3820 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 3820 mL to 3.82 L.\nCompute M = 0.75 / 3.82.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 0.75, "volume_ml": 3820}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.65 y, so each step multiplies y by 1 - h*0.65.\n3. Apply that update for 12 steps and round the final state.\nFinal: {\"answer\": 0.0, \"unit\": \"state_units\"}", "dedupe_signature": "b195a2fa80f6271b8c71a77bb21716e789f722b7f9dbb5f99c40731b5c032b85", "difficulty": "medium", "final_answer": {"answer": 0.0, "unit": "state_units"}, "id": "euler_decay_002061_5.5_0.65_1.1_12", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.65 y with y(0)=5.5, step size h=1.1, for 12 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.65 y, so each step multiplies y by 1 - h*0.65.\nApply that update for 12 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 5.5, "rate": 0.65, "step": 1.1, "steps": 12}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(2.8)=2.3 and f(5.3)=19.8.\n3. The interval width is 2.5.\nFinal: {\"answer\": 27.625, \"unit\": \"area_units\"}", "dedupe_signature": "6440e51df6821aa5ccb31fd4278d3244de5681ae1634cce052ba9fc36da22d05", "difficulty": "medium", "final_answer": {"answer": 27.625, "unit": "area_units"}, "id": "trapz_linear_002062_7_-17.3_2.8_5.3", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=7x+-17.3 from x=2.8 to x=5.3. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(2.8)=2.3 and f(5.3)=19.8.\nThe interval width is 2.5.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -17.3, "slope": 7.0, "x0": 2.8, "x1": 5.3}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 100 centimeters in one meter.\n2. Apply the conversion factor directly to the given value.\n3. Compute 1942.5 / 100.\nFinal: {\"answer\": 19.425, \"unit\": \"m\"}", "dedupe_signature": "8954269731f00e8dfd3b3e3679fdaca40fc9d95026778bceb7f2981317653ae4", "difficulty": "easy", "final_answer": {"answer": 19.425, "unit": "m"}, "id": "unit_convert_002064_cm_to_m_1942.5", "license": "Apache-2.0", "prompt": "Convert 1942.5 cm to m. Return the converted value with unit.", "reasoning_trace": "There are 100 centimeters in one meter.\nApply the conversion factor directly to the given value.\nCompute 1942.5 / 100.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 1942.5}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=92 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-16.839, 482.2061], \"unit\": \"N\"}", "dedupe_signature": "ea7d2bc55cb7cbda2f53b37ddb30ae77bf96d7de518d97039c7579a26a098486", "difficulty": "medium", "final_answer": {"answer": [-16.839, 482.2061], "unit": "N"}, "id": "vector_components_002065_482.5_92", "license": "Apache-2.0", "prompt": "A vector has magnitude 482.5 N at 92 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=92 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 92, "magnitude": 482.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-5.35, 17.0], \"unit\": \"dimensionless\"}", "dedupe_signature": "53bfeb95d74987e2a2ff1038aee4aeb332439dc696b3df3167f7a121f45dfdbf", "difficulty": "medium", "final_answer": {"answer": [-5.35, 17.0], "unit": "dimensionless"}, "id": "line_two_point_002066_3.75_13.75_-5.35_17", "license": "Apache-2.0", "prompt": "A line passes through points (3.75, -3.0625) and (13.75, -56.5625). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 3.75, "x2": 13.75, "y1": -3.0625, "y2": -56.5625}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. density times acceleration times height gives kg/(m*s^2), or pascal\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "b7aeac7516a2117189f491af27b9490e2ee63a0925aa43a2de04f2514cefe957", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_002067_consistent_b7d3eed1_331784", "license": "Apache-2.0", "prompt": "In quality-control check case 331784, check dimensional consistency for p = rho * g * h. The left side has dimensions Pa and the right side has dimensions Pa. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\ndensity times acceleration times height gives kg/(m*s^2), or pascal\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "p = rho * g * h"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef threshold_flags_002068(values, threshold):\n    return [value >= threshold for value in values]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"threshold_flags_002068\"}", "dedupe_signature": "7e8bbff3eca016efaa0cbd248c4317951be9b7418a0e7aa05b7bb6849cb88e2c", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "threshold_flags_002068"}, "id": "code_002068_threshold_flags_002068", "license": "Apache-2.0", "prompt": "Write a Python function threshold_flags_002068(values, threshold) that returns a list of booleans showing whether each value is greater than or equal to threshold. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "threshold_flags_002068"}, "verifier": {"function": "threshold_flags_002068", "tests": ["assert threshold_flags_002068([1, 2, 3], 2) == [False, True, True]", "assert threshold_flags_002068([], 5) == []", "assert threshold_flags_002068([-1, 0], 0) == [False, True]"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: recurrence, objective, tie_breaking_rule.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"recurrence\", \"objective\", \"tie_breaking_rule\"]}", "dedupe_signature": "7da69d9f4655deb627224a7c3ebf224a68b32d7378b2248e0fea1528c036425d", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["recurrence", "objective", "tie_breaking_rule"]}, "id": "abstain_002069_recurrence_objective_tie_breaking_rule", "license": "Apache-2.0", "prompt": "Write a dynamic-programming solver for a knapsack scoring problem with 2709 items and budget 65385, but the recurrence, objective, and tie-breaking rule are all absent. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: recurrence, objective, tie_breaking_rule.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["recurrence", "objective", "tie_breaking_rule"]}, "verifier": {"missing": ["recurrence", "objective", "tie_breaking_rule"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 16.85 kg and a = 12.15 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 204.7275, \"unit\": \"N\"}", "dedupe_signature": "289cc31251b29f1075d5cbfb0c98f2a6956cd2374a8df9363167c3babd231600", "difficulty": "easy", "final_answer": {"answer": 204.7275, "unit": "N"}, "id": "force_002070_16.85_12.15", "license": "Apache-2.0", "prompt": "A cart has mass 16.85 kg and measured acceleration 12.15 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 16.85 kg and a = 12.15 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 12.15, "mass": 16.85}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 42.25^2 and multiply by 0.5 * 15.85.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 14146.6203, \"unit\": \"J\"}", "dedupe_signature": "dab7876d55d67fa466461bd311720ff3c4483140ee2a02d10a88bcd95c508b6a", "difficulty": "easy", "final_answer": {"answer": 14146.6203, "unit": "J"}, "id": "ke_002071_15.85_42.25", "license": "Apache-2.0", "prompt": "A body of mass 15.85 kg moves at 42.25 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 42.25^2 and multiply by 0.5 * 15.85.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 15.85, "velocity": 42.25}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 3.89 * 8.314 * 293 / 13.0.\nFinal: {\"answer\": 728.9268, \"unit\": \"kPa\"}", "dedupe_signature": "99716046a83270dc22eb229ac0e489206b363854300b2a2f0719a34c32863750", "difficulty": "medium", "final_answer": {"answer": 728.9268, "unit": "kPa"}, "id": "ideal_gas_002073_3.89_293_13.0", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=3.89 mol, T=293 K, and V=13.0 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 3.89 * 8.314 * 293 / 13.0.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 3.89, "temp_k": 293, "volume_l": 13.0}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 525 * 3.745 * 101.\nFinal: {\"answer\": 198578.625, \"unit\": \"J\"}", "dedupe_signature": "c6ebc20e432a5163971cb3c27651463fda8be4e2723c2848ef31968d9bfaee4f", "difficulty": "easy", "final_answer": {"answer": 198578.625, "unit": "J"}, "id": "heat_q_002074_525_3.745_101", "license": "Apache-2.0", "prompt": "A 525 g sample has specific heat 3.745 J/(g*K). How much heat is needed to raise its temperature by 101 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 525 * 3.745 * 101.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 101, "heat_capacity": 3.745, "mass_g": 525}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=236.7 V and R=147.8 ohm.\nFinal: {\"answer\": 379.0723, \"unit\": \"W\"}", "dedupe_signature": "7d2ed04561e6a7d4cbda6d8199cb2aa60fd9349320689890e132ba5288078ade", "difficulty": "easy", "final_answer": {"answer": 379.0723, "unit": "W"}, "id": "ohm_power_002075_236.7_147.8", "license": "Apache-2.0", "prompt": "A resistor has resistance 147.8 ohm and voltage 236.7 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=236.7 V and R=147.8 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 147.8, "voltage": 236.7}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=398 mg, t=78 h, and T_half=68 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 179.7148, \"unit\": \"mg\"}", "dedupe_signature": "1411ea28504801ceaa4110e2c98d1e23b06106df733e55e7c49107ec38fd0f99", "difficulty": "medium", "final_answer": {"answer": 179.7148, "unit": "mg"}, "id": "half_life_002076_398_68_78", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 398 mg. Its half-life is 68 hours. How many mg remain after 78 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=398 mg, t=78 h, and T_half=68 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 78.0, "half_life": 68.0, "initial_amount": 398.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 3330 mL to 3.33 L.\n3. Compute M = 4.315 / 3.33.\nFinal: {\"answer\": 1.2958, \"unit\": \"mol/L\"}", "dedupe_signature": "028b99248b2550c3d99606a999bd8b28344efe7f594a069775c1943b93db07ed", "difficulty": "medium", "final_answer": {"answer": 1.2958, "unit": "mol/L"}, "id": "molarity_002078_4.315_3330", "license": "Apache-2.0", "prompt": "A solution contains 4.315 mol of solute in 3330 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 3330 mL to 3.33 L.\nCompute M = 4.315 / 3.33.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 4.315, "volume_ml": 3330}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.4 y, so each step multiplies y by 1 - h*0.4.\n3. Apply that update for 9 steps and round the final state.\nFinal: {\"answer\": 24.0201, \"unit\": \"state_units\"}", "dedupe_signature": "55d3dfa6521548c1565ce4aa644f14d408e3251e0d1410c5ee5076014cdd4ebf", "difficulty": "medium", "final_answer": {"answer": 24.0201, "unit": "state_units"}, "id": "euler_decay_002079_62_0.4_0.25_9", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.4 y with y(0)=62, step size h=0.25, for 9 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.4 y, so each step multiplies y by 1 - h*0.4.\nApply that update for 9 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 62.0, "rate": 0.4, "step": 0.25, "steps": 9}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(7.3)=-48.61 and f(16.1)=-89.97.\n3. The interval width is 8.8.\nFinal: {\"answer\": -609.752, \"unit\": \"area_units\"}", "dedupe_signature": "6fcaa8b5440b2a6118952a1fe6d8d0b086e1def6250ac11a781ad84a059dfd4f", "difficulty": "medium", "final_answer": {"answer": -609.752, "unit": "area_units"}, "id": "trapz_linear_002080_-4.7_-14.3_7.3_16.1", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-4.7x+-14.3 from x=7.3 to x=16.1. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(7.3)=-48.61 and f(16.1)=-89.97.\nThe interval width is 8.8.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -14.3, "slope": -4.7, "x0": 7.3, "x1": 16.1}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.4 and add it to the current value.\nFinal: {\"answer\": [1.98, -0.07, 0.12], \"unit\": \"temperature_units\"}", "dedupe_signature": "a2c44899b541eb41bcf47b793e3a28d357b013a47d4ae3bfd7a3fabeed94b61f", "difficulty": "hard", "final_answer": {"answer": [1.98, -0.07, 0.12], "unit": "temperature_units"}, "id": "heat_step_002081_0.4_2.15_-0.1_2.85_-1.5_-1.8", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=2.15, right=-1.8; current interior values are [-0.1, 2.85, -1.5]. Use r=0.4. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.4 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-0.1, 2.85, -1.5], "left": 2.15, "r": 0.4, "right": -1.8}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kelvin equals Celsius plus 273.15.\n2. Apply the conversion factor directly to the given value.\n3. Compute 93.0 + 273.15.\nFinal: {\"answer\": 366.15, \"unit\": \"K\"}", "dedupe_signature": "94d377fb8b1b63e786d1f6c71254278b88798044e7805e4e273b53af81640973", "difficulty": "easy", "final_answer": {"answer": 366.15, "unit": "K"}, "id": "unit_convert_002082_c_to_k_93", "license": "Apache-2.0", "prompt": "Convert 93 degC to K. Return the converted value with unit.", "reasoning_trace": "Kelvin equals Celsius plus 273.15.\nApply the conversion factor directly to the given value.\nCompute 93.0 + 273.15.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 93.0}, "verifier": {"formula": "value + 273.15", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=153 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-168.8457, 86.0312], \"unit\": \"N\"}", "dedupe_signature": "200ed519cdbe936c85f10175b6b204e8cbc9ec2d282604c52defe829376d3b1d", "difficulty": "medium", "final_answer": {"answer": [-168.8457, 86.0312], "unit": "N"}, "id": "vector_components_002083_189.5_153", "license": "Apache-2.0", "prompt": "A vector has magnitude 189.5 N at 153 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=153 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 153, "magnitude": 189.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. m*v is momentum, not energy\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "d093af42fd6ad9e25372e95b0b50bc6d80acb31e758598e12680952aa15b2aaf", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_002085_inconsistent_1e14b074_731225", "license": "Apache-2.0", "prompt": "In sensor calibration case 731225, check dimensional consistency for E = m * v. The left side has dimensions kg*m^2/s^2 and the right side has dimensions kg*m/s. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nm*v is momentum, not energy\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "E = m * v"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: target_schema, valid_examples.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"target_schema\", \"valid_examples\"]}", "dedupe_signature": "6383b82b9ac1d9d5c0df2fd2554aa271545efc9657fdba9309d89815fa6700c1", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["target_schema", "valid_examples"]}, "id": "abstain_002087_target_schema_valid_examples", "license": "Apache-2.0", "prompt": "Write a parser that converts each registry crop record from batch 384272 into the correct schema, but the prompt does not include the target schema or examples. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: target_schema, valid_examples.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["target_schema", "valid_examples"]}, "verifier": {"missing": ["target_schema", "valid_examples"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 12.45 kg and a = 14.6 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 181.77, \"unit\": \"N\"}", "dedupe_signature": "3a03a43845faf589bb1fac30dc644b6aedde5aa3c8544d80584636614d4ce20b", "difficulty": "easy", "final_answer": {"answer": 181.77, "unit": "N"}, "id": "force_002088_12.45_14.6", "license": "Apache-2.0", "prompt": "A cart has mass 12.45 kg and measured acceleration 14.6 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 12.45 kg and a = 14.6 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 14.6, "mass": 12.45}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=21 degrees through the sine of 2 theta.\n3. Substitute v=71.1 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 344.811, \"unit\": \"m\"}", "dedupe_signature": "211127d63d7438266c43961e439fbfd0fb66d3b795f3e4245e2219c801f444f1", "difficulty": "medium", "final_answer": {"answer": 344.811, "unit": "m"}, "id": "projectile_range_002090_71.1_21", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 71.1 m/s and angle 21 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=21 degrees through the sine of 2 theta.\nSubstitute v=71.1 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 21, "gravity": 9.81, "speed": 71.1}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 3.04 * 8.314 * 327 / 104.8.\nFinal: {\"answer\": 78.8624, \"unit\": \"kPa\"}", "dedupe_signature": "e1547de011be588653d9182ff20126591f8d77e8d992cad5cbd476dda79b308f", "difficulty": "medium", "final_answer": {"answer": 78.8624, "unit": "kPa"}, "id": "ideal_gas_002091_3.04_327_104.8", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=3.04 mol, T=327 K, and V=104.8 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 3.04 * 8.314 * 327 / 104.8.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 3.04, "temp_k": 327, "volume_l": 104.8}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1905 * 4.535 * 106.\nFinal: {\"answer\": 915752.55, \"unit\": \"J\"}", "dedupe_signature": "2ff3f866bdde0a6dcb87df99387e2cbb3f6953a5a2e8e57291100b9b5aee811c", "difficulty": "easy", "final_answer": {"answer": 915752.55, "unit": "J"}, "id": "heat_q_002092_1905_4.535_106", "license": "Apache-2.0", "prompt": "A 1905 g sample has specific heat 4.535 J/(g*K). How much heat is needed to raise its temperature by 106 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1905 * 4.535 * 106.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 106, "heat_capacity": 4.535, "mass_g": 1905}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=160.1 V and R=88.1 ohm.\nFinal: {\"answer\": 290.9422, \"unit\": \"W\"}", "dedupe_signature": "b0a6f0d7f0f82f5c946349ed0006be57799213050bf364c4438db53515961b1c", "difficulty": "easy", "final_answer": {"answer": 290.9422, "unit": "W"}, "id": "ohm_power_002093_160.1_88.1", "license": "Apache-2.0", "prompt": "A resistor has resistance 88.1 ohm and voltage 160.1 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=160.1 V and R=88.1 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 88.1, "voltage": 160.1}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=74 mg, t=289.5 h, and T_half=96.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 9.25, \"unit\": \"mg\"}", "dedupe_signature": "66397446aee1c14b825c6174bc0db8efe815c1e196654b0e8cfeea687a589960", "difficulty": "medium", "final_answer": {"answer": 9.25, "unit": "mg"}, "id": "half_life_002094_74_96.5_289.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 74 mg. Its half-life is 96.5 hours. How many mg remain after 289.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=74 mg, t=289.5 h, and T_half=96.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 289.5, "half_life": 96.5, "initial_amount": 74.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 2890 mL to 2.89 L.\n3. Compute M = 0.705 / 2.89.\nFinal: {\"answer\": 0.2439, \"unit\": \"mol/L\"}", "dedupe_signature": "959e09d74f13de8b68c5d325cf1f1badf988dce88c5047ae4c6a038d62b37cff", "difficulty": "medium", "final_answer": {"answer": 0.2439, "unit": "mol/L"}, "id": "molarity_002096_0.705_2890", "license": "Apache-2.0", "prompt": "A solution contains 0.705 mol of solute in 2890 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 2890 mL to 2.89 L.\nCompute M = 0.705 / 2.89.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 0.705, "volume_ml": 2890}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.85 y, so each step multiplies y by 1 - h*0.85.\n3. Apply that update for 11 steps and round the final state.\nFinal: {\"answer\": 0.3011, \"unit\": \"state_units\"}", "dedupe_signature": "495fbb1869a509396c4931c9706950edb2903c96c76c75de6ed57b8bb3ea0105", "difficulty": "medium", "final_answer": {"answer": 0.3011, "unit": "state_units"}, "id": "euler_decay_002097_60.5_0.85_0.45_11", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.85 y with y(0)=60.5, step size h=0.45, for 11 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.85 y, so each step multiplies y by 1 - h*0.85.\nApply that update for 11 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 60.5, "rate": 0.85, "step": 0.45, "steps": 11}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.2 and add it to the current value.\nFinal: {\"answer\": [0.62, 1.19, 2.22], \"unit\": \"temperature_units\"}", "dedupe_signature": "b8ef55a613366a0a35d13812bcbc6ab306b5d5430dc35ba1860985c045cbc120", "difficulty": "hard", "final_answer": {"answer": [0.62, 1.19, 2.22], "unit": "temperature_units"}, "id": "heat_step_002099_0.2_-0.15_0.8_0.85_2.6_2.45", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-0.15, right=2.45; current interior values are [0.8, 0.85, 2.6]. Use r=0.2. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.2 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [0.8, 0.85, 2.6], "left": -0.15, "r": 0.2, "right": 2.45}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=125 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-168.9183, 241.2403], \"unit\": \"N\"}", "dedupe_signature": "3af4c2adf3d26f18decaa6de3a77c86f7835a0fd300635a848a39de5d03b5a78", "difficulty": "medium", "final_answer": {"answer": [-168.9183, 241.2403], "unit": "N"}, "id": "vector_components_002101_294.5_125", "license": "Apache-2.0", "prompt": "A vector has magnitude 294.5 N at 125 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=125 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 125, "magnitude": 294.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [6.45, 11.0], \"unit\": \"dimensionless\"}", "dedupe_signature": "71423e19a5c461d24e2f3d5ec451352a313aa7663cf80fb8d173aa3a1298ec36", "difficulty": "medium", "final_answer": {"answer": [6.45, 11.0], "unit": "dimensionless"}, "id": "line_two_point_002102_-4.75_3.25_6.45_11", "license": "Apache-2.0", "prompt": "A line passes through points (-4.75, -19.6375) and (3.25, 31.9625). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -4.75, "x2": 3.25, "y1": -19.6375, "y2": 31.962500000000002}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. energy divided by length is force, not spring constant\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "8f55d51fecfac085cf3aaaa72e324f19f66144e2cbfc2cec7ad1dd1bf9b5be78", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_002103_inconsistent_56040f5d_612540", "license": "Apache-2.0", "prompt": "In field worksheet case 612540, check dimensional consistency for k = E / x. The left side has dimensions N/m and the right side has dimensions J/m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nenergy divided by length is force, not spring constant\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "k = E / x"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef safe_mean_002104(values):\n    if not values:\n        raise ValueError('safe_mean requires at least one value')\n    return sum(values) / len(values)\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"safe_mean_002104\"}", "dedupe_signature": "28b6d006ef0f7a1d0e6a6a7ceac5e56a471a4c0e3093dd2f6a95ca4dd17ed3a8", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "safe_mean_002104"}, "id": "code_002104_safe_mean_002104", "license": "Apache-2.0", "prompt": "Write a Python function safe_mean_002104(values) that returns the arithmetic mean. It must raise ValueError for an empty input and must not mutate the input list. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "safe_mean_002104"}, "verifier": {"function": "safe_mean_002104", "tests": ["assert safe_mean_002104([2, 4, 6]) == 4", "xs = [1, 2, 3]; assert safe_mean_002104(xs) == 2 and xs == [1, 2, 3]", "try:\n    safe_mean_002104([])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: launch_angle_or_vertical_velocity.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"launch_angle_or_vertical_velocity\"]}", "dedupe_signature": "606b1bbad30faba020b661d90f5095804c908e9eda4dead88870ce148ea714c6", "difficulty": "easy", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["launch_angle_or_vertical_velocity"]}, "id": "abstain_002105_launch_angle_or_vertical_velocity", "license": "Apache-2.0", "prompt": "Compute projectile range on level ground. The prompt gives initial speed 25.4 m/s but does not give launch angle or vertical velocity. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: launch_angle_or_vertical_velocity.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["launch_angle_or_vertical_velocity"]}, "verifier": {"missing": ["launch_angle_or_vertical_velocity"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 4.25 kg and a = 12.45 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 52.9125, \"unit\": \"N\"}", "dedupe_signature": "cc52aa2a4b7300aa5f75d11e4739165ac58928854eb5b05befa5b898b34debbc", "difficulty": "easy", "final_answer": {"answer": 52.9125, "unit": "N"}, "id": "force_002106_4.25_12.45", "license": "Apache-2.0", "prompt": "A cart has mass 4.25 kg and measured acceleration 12.45 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 4.25 kg and a = 12.45 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 12.45, "mass": 4.25}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 10.1^2 and multiply by 0.5 * 23.45.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 1196.0672, \"unit\": \"J\"}", "dedupe_signature": "58e7be4df3aad89567805db586b625a27e9a0d12919e1a24eebdf89a54decff5", "difficulty": "easy", "final_answer": {"answer": 1196.0672, "unit": "J"}, "id": "ke_002107_23.45_10.1", "license": "Apache-2.0", "prompt": "A body of mass 23.45 kg moves at 10.1 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 10.1^2 and multiply by 0.5 * 23.45.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 23.45, "velocity": 10.1}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=54 degrees through the sine of 2 theta.\n3. Substitute v=46.2 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 206.929, \"unit\": \"m\"}", "dedupe_signature": "a8cc3d6e7dbc52b2fd20f333904328c3768240117114747f0561911e6f2fded6", "difficulty": "medium", "final_answer": {"answer": 206.929, "unit": "m"}, "id": "projectile_range_002108_46.2_54", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 46.2 m/s and angle 54 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=54 degrees through the sine of 2 theta.\nSubstitute v=46.2 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 54, "gravity": 9.81, "speed": 46.2}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 5.47 * 8.314 * 334 / 74.9.\nFinal: {\"answer\": 202.7972, \"unit\": \"kPa\"}", "dedupe_signature": "30ccc2e9f017440b4fd7d846d2de3c0ea2d5925b52bee9a8ede038d2ca4aa6db", "difficulty": "medium", "final_answer": {"answer": 202.7972, "unit": "kPa"}, "id": "ideal_gas_002109_5.47_334_74.9", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=5.47 mol, T=334 K, and V=74.9 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 5.47 * 8.314 * 334 / 74.9.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 5.47, "temp_k": 334, "volume_l": 74.9}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=22.9 V and R=184.5 ohm.\nFinal: {\"answer\": 2.8423, \"unit\": \"W\"}", "dedupe_signature": "7f3fded45d0cf6be92c2a589f934c37020f443bd5320c638475c64af4032fb87", "difficulty": "easy", "final_answer": {"answer": 2.8423, "unit": "W"}, "id": "ohm_power_002111_22.9_184.5", "license": "Apache-2.0", "prompt": "A resistor has resistance 184.5 ohm and voltage 22.9 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=22.9 V and R=184.5 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 184.5, "voltage": 22.9}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 2.57 mol * 44.01 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 113.1057, \"unit\": \"g\"}", "dedupe_signature": "11d63c31fbc77f7c45ce8fa4f1420d9137e369930c551d10e1b4ce817b128d27", "difficulty": "medium", "final_answer": {"answer": 113.1057, "unit": "g"}, "id": "stoich_mass_002113_carbon_dioxide_2.57", "license": "Apache-2.0", "prompt": "A sample contains 2.57 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 2.57 mol * 44.01 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "carbon dioxide", "molar_mass": 44.01, "moles": 2.57}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.79 y, so each step multiplies y by 1 - h*0.79.\n3. Apply that update for 11 steps and round the final state.\nFinal: {\"answer\": 0.0804, \"unit\": \"state_units\"}", "dedupe_signature": "7734b98611c745bb0616447201a402ea5ca33f2ddbb3688077791f146682394d", "difficulty": "medium", "final_answer": {"answer": 0.0804, "unit": "state_units"}, "id": "euler_decay_002115_42.5_0.79_0.55_11", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.79 y with y(0)=42.5, step size h=0.55, for 11 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.79 y, so each step multiplies y by 1 - h*0.79.\nApply that update for 11 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 42.5, "rate": 0.79, "step": 0.55, "steps": 11}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(3)=-9.9 and f(8.3)=-3.01.\n3. The interval width is 5.3.\nFinal: {\"answer\": -34.2115, \"unit\": \"area_units\"}", "dedupe_signature": "163ee316d6c6c1caa00dd1ce3f23e70630bf600eb45dac5479b5ff01b7ab1e21", "difficulty": "medium", "final_answer": {"answer": -34.2115, "unit": "area_units"}, "id": "trapz_linear_002116_1.3_-13.8_3_8.3", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=1.3x+-13.8 from x=3 to x=8.3. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(3)=-9.9 and f(8.3)=-3.01.\nThe interval width is 5.3.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -13.8, "slope": 1.3, "x0": 3.0, "x1": 8.3}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.46 and add it to the current value.\nFinal: {\"answer\": [-0.549, -0.269, -0.408], \"unit\": \"temperature_units\"}", "dedupe_signature": "79b5f378df3ebf78abea314ca47b9e496fab1e3b77f2eafb379e018e0f39d008", "difficulty": "hard", "final_answer": {"answer": [-0.549, -0.269, -0.408], "unit": "temperature_units"}, "id": "heat_step_002117_0.46_-1.9_-1.4_0.95_0.65_-1.95", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-1.9, right=-1.95; current interior values are [-1.4, 0.95, 0.65]. Use r=0.46. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.46 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-1.4, 0.95, 0.65], "left": -1.9, "r": 0.46, "right": -1.95}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 27446.0 / 1000.\nFinal: {\"answer\": 27.446, \"unit\": \"kg\"}", "dedupe_signature": "50c856cfef74f73acf4afbce4c06c5d98c525e954cfb0a962d42a8bf76c3ac88", "difficulty": "easy", "final_answer": {"answer": 27.446, "unit": "kg"}, "id": "unit_convert_002118_g_to_kg_27446", "license": "Apache-2.0", "prompt": "Convert 27446 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 27446.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 27446.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=7 degrees and keep the unit as newtons.\nFinal: {\"answer\": [94.7882, 11.6385], \"unit\": \"N\"}", "dedupe_signature": "3b3eb38cfc64b674354a4f3f2f973286e7aeba0922fd4ca0f74873dc72f682e4", "difficulty": "medium", "final_answer": {"answer": [94.7882, 11.6385], "unit": "N"}, "id": "vector_components_002119_95.5_7", "license": "Apache-2.0", "prompt": "A vector has magnitude 95.5 N at 7 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=7 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 7, "magnitude": 95.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. lever arm times force has torque dimensions\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "e3d785f61acff99e667065eea002f2f1cbc327cc42f7df47a183bcdfc142963e", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_002121_consistent_5ca82cb9_983745", "license": "Apache-2.0", "prompt": "In student derivation case 983745, check dimensional consistency for tau = r * F. The left side has dimensions N*m and the right side has dimensions N*m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nlever arm times force has torque dimensions\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "tau = r * F"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef finite_differences_002122(values):\n    return [values[i + 1] - values[i] for i in range(len(values) - 1)]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"finite_differences_002122\"}", "dedupe_signature": "bd78aa720ca57f534f71bcd0dd999f790b4f760a7cd6df36df045aa203817e9d", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "finite_differences_002122"}, "id": "code_002122_finite_differences_002122", "license": "Apache-2.0", "prompt": "Write a Python function finite_differences_002122(values) that returns the list of successive differences values[i+1] - values[i]. It must return [] for fewer than two values. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "finite_differences_002122"}, "verifier": {"function": "finite_differences_002122", "tests": ["assert finite_differences_002122([1, 4, 9, 16]) == [3, 5, 7]", "assert finite_differences_002122([5]) == []", "assert finite_differences_002122([]) == []"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: target_schema, valid_examples.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"target_schema\", \"valid_examples\"]}", "dedupe_signature": "04e028d04ae2429dc0f81be36b9ef604f53e7f562ceb1b45df5009c1fa7e0851", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["target_schema", "valid_examples"]}, "id": "abstain_002123_target_schema_valid_examples", "license": "Apache-2.0", "prompt": "Write a parser that converts each registry crop record from batch 138513 into the correct schema, but the prompt does not include the target schema or examples. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: target_schema, valid_examples.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["target_schema", "valid_examples"]}, "verifier": {"missing": ["target_schema", "valid_examples"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 21.35 kg and a = 9.85 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 210.2975, \"unit\": \"N\"}", "dedupe_signature": "034de0485d5bddb204d872081c17161000baf713a4a06ae52ba5c70d5399310b", "difficulty": "easy", "final_answer": {"answer": 210.2975, "unit": "N"}, "id": "force_002124_21.35_9.85", "license": "Apache-2.0", "prompt": "A cart has mass 21.35 kg and measured acceleration 9.85 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 21.35 kg and a = 9.85 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 9.85, "mass": 21.35}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 28.45^2 and multiply by 0.5 * 25.55.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 10340.1169, \"unit\": \"J\"}", "dedupe_signature": "da8c93420b51bf44ae1f00e0c92e3091cd9d42b72b9b72527e8adcfbf691df6f", "difficulty": "easy", "final_answer": {"answer": 10340.1169, "unit": "J"}, "id": "ke_002125_25.55_28.45", "license": "Apache-2.0", "prompt": "A body of mass 25.55 kg moves at 28.45 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 28.45^2 and multiply by 0.5 * 25.55.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 25.55, "velocity": 28.45}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=58 degrees through the sine of 2 theta.\n3. Substitute v=44.9 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 184.7072, \"unit\": \"m\"}", "dedupe_signature": "21d008c23072dab4ca48bbd4abdada3f7ea05edd3ad8ef0a3ea728a7dfd22fc7", "difficulty": "medium", "final_answer": {"answer": 184.7072, "unit": "m"}, "id": "projectile_range_002126_44.9_58", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 44.9 m/s and angle 58 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=58 degrees through the sine of 2 theta.\nSubstitute v=44.9 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 58, "gravity": 9.81, "speed": 44.9}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 4.72 * 8.314 * 513 / 109.7.\nFinal: {\"answer\": 183.5113, \"unit\": \"kPa\"}", "dedupe_signature": "5178d829459c705365cff0cf845dca98c03380ef9af8b0ecef84270e5f0abd61", "difficulty": "medium", "final_answer": {"answer": 183.5113, "unit": "kPa"}, "id": "ideal_gas_002127_4.72_513_109.7", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=4.72 mol, T=513 K, and V=109.7 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 4.72 * 8.314 * 513 / 109.7.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 4.72, "temp_k": 513, "volume_l": 109.7}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1585 * 4.21 * 30.\nFinal: {\"answer\": 200185.5, \"unit\": \"J\"}", "dedupe_signature": "42d4b2b3cc9b5c7658a5b09c278161c5de7a17f2f44e13887941ab808f09a01e", "difficulty": "easy", "final_answer": {"answer": 200185.5, "unit": "J"}, "id": "heat_q_002128_1585_4.21_30", "license": "Apache-2.0", "prompt": "A 1585 g sample has specific heat 4.21 J/(g*K). How much heat is needed to raise its temperature by 30 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1585 * 4.21 * 30.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 30, "heat_capacity": 4.21, "mass_g": 1585}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=28.9 V and R=27.5 ohm.\nFinal: {\"answer\": 30.3713, \"unit\": \"W\"}", "dedupe_signature": "5e61682c55003b642d0938931a7a0b6de690a477f17d364067b26dbfbca2e71e", "difficulty": "easy", "final_answer": {"answer": 30.3713, "unit": "W"}, "id": "ohm_power_002129_28.9_27.5", "license": "Apache-2.0", "prompt": "A resistor has resistance 27.5 ohm and voltage 28.9 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=28.9 V and R=27.5 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 27.5, "voltage": 28.9}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=246.5 mg, t=260.5 h, and T_half=19.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 0.0235, \"unit\": \"mg\"}", "dedupe_signature": "ee56855c4ece1cf81ec0ea89b8fafdbb40c6315c575422716fb85830c69fcf80", "difficulty": "medium", "final_answer": {"answer": 0.0235, "unit": "mg"}, "id": "half_life_002130_246.5_19.5_260.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 246.5 mg. Its half-life is 19.5 hours. How many mg remain after 260.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=246.5 mg, t=260.5 h, and T_half=19.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 260.5, "half_life": 19.5, "initial_amount": 246.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 5.53 mol * 44.01 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 243.3753, \"unit\": \"g\"}", "dedupe_signature": "7b28615af7fd5e296984edfd50d22ddc363fac45f828923ca507039ff88ae7c9", "difficulty": "medium", "final_answer": {"answer": 243.3753, "unit": "g"}, "id": "stoich_mass_002131_carbon_dioxide_5.53", "license": "Apache-2.0", "prompt": "A sample contains 5.53 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 5.53 mol * 44.01 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "carbon dioxide", "molar_mass": 44.01, "moles": 5.53}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 1745 mL to 1.745 L.\n3. Compute M = 2.44 / 1.745.\nFinal: {\"answer\": 1.3983, \"unit\": \"mol/L\"}", "dedupe_signature": "2b1f12906ac2fb703ec8023a977f3a5cb3a76cc21558afb221b3c986d475d2d0", "difficulty": "medium", "final_answer": {"answer": 1.3983, "unit": "mol/L"}, "id": "molarity_002132_2.44_1745", "license": "Apache-2.0", "prompt": "A solution contains 2.44 mol of solute in 1745 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 1745 mL to 1.745 L.\nCompute M = 2.44 / 1.745.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 2.44, "volume_ml": 1745}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.45 y, so each step multiplies y by 1 - h*0.45.\n3. Apply that update for 12 steps and round the final state.\nFinal: {\"answer\": 5.6116, \"unit\": \"state_units\"}", "dedupe_signature": "a0a0da324ede10afe96d04351ead35c276126e2441d85fcb48e7e66176d859e0", "difficulty": "medium", "final_answer": {"answer": 5.6116, "unit": "state_units"}, "id": "euler_decay_002133_23.5_0.45_0.25_12", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.45 y with y(0)=23.5, step size h=0.25, for 12 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.45 y, so each step multiplies y by 1 - h*0.45.\nApply that update for 12 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 23.5, "rate": 0.45, "step": 0.25, "steps": 12}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(5.2)=-39.84 and f(8.8)=-54.96.\n3. The interval width is 3.6.\nFinal: {\"answer\": -170.64, \"unit\": \"area_units\"}", "dedupe_signature": "8bbff5817bd625d21bc4464a54c3c534cebd9206bb8268e7b6b522c9ace894e9", "difficulty": "medium", "final_answer": {"answer": -170.64, "unit": "area_units"}, "id": "trapz_linear_002134_-4.2_-18_5.2_8.8", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-4.2x+-18 from x=5.2 to x=8.8. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(5.2)=-39.84 and f(8.8)=-54.96.\nThe interval width is 3.6.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -18.0, "slope": -4.2, "x0": 5.2, "x1": 8.8}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.12 and add it to the current value.\nFinal: {\"answer\": [-1.034, 1.516, 1.832], \"unit\": \"temperature_units\"}", "dedupe_signature": "2af3ad3596d952c028f84406d56427cefae590fac80bee0fb53d634821d27817", "difficulty": "hard", "final_answer": {"answer": [-1.034, 1.516, 1.832], "unit": "temperature_units"}, "id": "heat_step_002135_0.12_0.25_-1.7_1.9_2.3_-1.2", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=0.25, right=-1.2; current interior values are [-1.7, 1.9, 2.3]. Use r=0.12. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.12 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-1.7, 1.9, 2.3], "left": 0.25, "r": 0.12, "right": -1.2}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kelvin equals Celsius plus 273.15.\n2. Apply the conversion factor directly to the given value.\n3. Compute 31.0 + 273.15.\nFinal: {\"answer\": 304.15, \"unit\": \"K\"}", "dedupe_signature": "0485e6ca407cc25576c010b3d31ba801f82070db7d8178bf974862c4cd5627e1", "difficulty": "easy", "final_answer": {"answer": 304.15, "unit": "K"}, "id": "unit_convert_002136_c_to_k_31", "license": "Apache-2.0", "prompt": "Convert 31 degC to K. Return the converted value with unit.", "reasoning_trace": "Kelvin equals Celsius plus 273.15.\nApply the conversion factor directly to the given value.\nCompute 31.0 + 273.15.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 31.0}, "verifier": {"formula": "value + 273.15", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=317 degrees and keep the unit as newtons.\nFinal: {\"answer\": [37.299, -34.7819], \"unit\": \"N\"}", "dedupe_signature": "554d911cb1fca71f5865e9feddba19e186ba7456789eb69ae8520489c2874651", "difficulty": "medium", "final_answer": {"answer": [37.299, -34.7819], "unit": "N"}, "id": "vector_components_002137_51_317", "license": "Apache-2.0", "prompt": "A vector has magnitude 51 N at 317 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=317 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 317, "magnitude": 51.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-9.2, 6.75], \"unit\": \"dimensionless\"}", "dedupe_signature": "2f6d7544ba8161e90e202479d7e067b55e8d08c2c079de889ad8228613555cd1", "difficulty": "medium", "final_answer": {"answer": [-9.2, 6.75], "unit": "dimensionless"}, "id": "line_two_point_002138_-8.25_4.75_-9.2_6.75", "license": "Apache-2.0", "prompt": "A line passes through points (-8.25, 82.65) and (4.75, -36.95). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -8.25, "x2": 4.75, "y1": 82.64999999999999, "y2": -36.949999999999996}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. amount times volume is not concentration\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "288f4b0913fb5b037d4682575caa04fa412c6d2d837fe254f5589cb8d0fe4ce5", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_002139_inconsistent_74ac0b02_371796", "license": "Apache-2.0", "prompt": "In lab notebook case 371796, check dimensional consistency for C = n * V. The left side has dimensions mol/L and the right side has dimensions mol*L. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\namount times volume is not concentration\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "C = n * V"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef finite_differences_002140(values):\n    return [values[i + 1] - values[i] for i in range(len(values) - 1)]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"finite_differences_002140\"}", "dedupe_signature": "3cdd3014befcf6a97b6dc8a0f9a4e2998387c2d77a7cddaedc044272bf6663a4", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "finite_differences_002140"}, "id": "code_002140_finite_differences_002140", "license": "Apache-2.0", "prompt": "Write a Python function finite_differences_002140(values) that returns the list of successive differences values[i+1] - values[i]. It must return [] for fewer than two values. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "finite_differences_002140"}, "verifier": {"function": "finite_differences_002140", "tests": ["assert finite_differences_002140([1, 4, 9, 16]) == [3, 5, 7]", "assert finite_differences_002140([5]) == []", "assert finite_differences_002140([]) == []"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 18.65 kg and a = 8.05 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 150.1325, \"unit\": \"N\"}", "dedupe_signature": "2914419872391e0c5be854358f1fb4a7fbb3f5ffa28d3178e2fc15f849bb2d9d", "difficulty": "easy", "final_answer": {"answer": 150.1325, "unit": "N"}, "id": "force_002142_18.65_8.05", "license": "Apache-2.0", "prompt": "A cart has mass 18.65 kg and measured acceleration 8.05 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 18.65 kg and a = 8.05 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 8.05, "mass": 18.65}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 34.2^2 and multiply by 0.5 * 1.85.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 1081.917, \"unit\": \"J\"}", "dedupe_signature": "8b2f2ea29a2d859f4309dc1dd9c28c89b29c9cd9824d71e028bb2a5e792e5de0", "difficulty": "easy", "final_answer": {"answer": 1081.917, "unit": "J"}, "id": "ke_002143_1.85_34.2", "license": "Apache-2.0", "prompt": "A body of mass 1.85 kg moves at 34.2 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 34.2^2 and multiply by 0.5 * 1.85.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 1.85, "velocity": 34.2}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 2.54 * 8.314 * 331 / 98.0.\nFinal: {\"answer\": 71.3256, \"unit\": \"kPa\"}", "dedupe_signature": "23e465f0bfce7d96a0c44cb398f292feeabdc0df4d55dc876542dff06e8c8e1c", "difficulty": "medium", "final_answer": {"answer": 71.3256, "unit": "kPa"}, "id": "ideal_gas_002145_2.54_331_98.0", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=2.54 mol, T=331 K, and V=98.0 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 2.54 * 8.314 * 331 / 98.0.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 2.54, "temp_k": 331, "volume_l": 98.0}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 60 * 1.35 * 18.\nFinal: {\"answer\": 1458.0, \"unit\": \"J\"}", "dedupe_signature": "38c3ee5fee6c8f3c38867f94c39e8b2530a485b68e53ae06d48f20cc2e97c511", "difficulty": "easy", "final_answer": {"answer": 1458.0, "unit": "J"}, "id": "heat_q_002146_60_1.35_18", "license": "Apache-2.0", "prompt": "A 60 g sample has specific heat 1.35 J/(g*K). How much heat is needed to raise its temperature by 18 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 60 * 1.35 * 18.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 18, "heat_capacity": 1.35, "mass_g": 60}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=50.7 V and R=18.9 ohm.\nFinal: {\"answer\": 136.0048, \"unit\": \"W\"}", "dedupe_signature": "4f01100f99e4257ff7e44222190d0b53df7b350cbfaedb1f8aa56f3f57ab47bb", "difficulty": "easy", "final_answer": {"answer": 136.0048, "unit": "W"}, "id": "ohm_power_002147_50.7_18.9", "license": "Apache-2.0", "prompt": "A resistor has resistance 18.9 ohm and voltage 50.7 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=50.7 V and R=18.9 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 18.9, "voltage": 50.7}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=582.5 mg, t=97 h, and T_half=100.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 298.3662, \"unit\": \"mg\"}", "dedupe_signature": "52dcc1ca883f0326b8d38d8e0238b38020f9820fe9ca07a2c6760bb869f3211d", "difficulty": "medium", "final_answer": {"answer": 298.3662, "unit": "mg"}, "id": "half_life_002148_582.5_100.5_97", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 582.5 mg. Its half-life is 100.5 hours. How many mg remain after 97 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=582.5 mg, t=97 h, and T_half=100.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 97.0, "half_life": 100.5, "initial_amount": 582.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 5.98 mol * 58.44 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 349.4712, \"unit\": \"g\"}", "dedupe_signature": "be767b52aa3372c3bfd63367ae46d632c584b866e259612bec296f3ee7106a0a", "difficulty": "medium", "final_answer": {"answer": 349.4712, "unit": "g"}, "id": "stoich_mass_002149_sodium_chloride_5.98", "license": "Apache-2.0", "prompt": "A sample contains 5.98 mol of sodium chloride. Using molar mass 58.44 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 5.98 mol * 58.44 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "sodium chloride", "molar_mass": 58.44, "moles": 5.98}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 1545 mL to 1.545 L.\n3. Compute M = 0.335 / 1.545.\nFinal: {\"answer\": 0.2168, \"unit\": \"mol/L\"}", "dedupe_signature": "73b5003b8bb64fae0a09f7b9e88fcee94d55530eaceb94d8d4554d8d533483b9", "difficulty": "medium", "final_answer": {"answer": 0.2168, "unit": "mol/L"}, "id": "molarity_002150_0.335_1545", "license": "Apache-2.0", "prompt": "A solution contains 0.335 mol of solute in 1545 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 1545 mL to 1.545 L.\nCompute M = 0.335 / 1.545.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 0.335, "volume_ml": 1545}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-3.6)=-12.38 and f(1.5)=-18.5.\n3. The interval width is 5.1.\nFinal: {\"answer\": -78.744, \"unit\": \"area_units\"}", "dedupe_signature": "27facc7c84a85fb69bf2aba6aaa981707a257bd2e24959f10c43ef8f1a3fdb59", "difficulty": "medium", "final_answer": {"answer": -78.744, "unit": "area_units"}, "id": "trapz_linear_002152_-1.2_-16.7_-3.6_1.5", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-1.2x+-16.7 from x=-3.6 to x=1.5. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-3.6)=-12.38 and f(1.5)=-18.5.\nThe interval width is 5.1.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -16.7, "slope": -1.2, "x0": -3.6, "x1": 1.4999999999999996}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.44 and add it to the current value.\nFinal: {\"answer\": [2.384, 1.838, 0.748], \"unit\": \"temperature_units\"}", "dedupe_signature": "47b2ee3f2b0d08b1b541ebd5ebae5a03bbae849215557c1e41a3934fa92f3349", "difficulty": "hard", "final_answer": {"answer": [2.384, 1.838, 0.748], "unit": "temperature_units"}, "id": "heat_step_002153_0.44_2.45_2.45_2.3_1.1_-0.9", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=2.45, right=-0.9; current interior values are [2.45, 2.3, 1.1]. Use r=0.44. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.44 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [2.45, 2.3, 1.1], "left": 2.45, "r": 0.44, "right": -0.9}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 36519.0 / 1000.\nFinal: {\"answer\": 36.519, \"unit\": \"kg\"}", "dedupe_signature": "a3782365a0bf314c2b533a6c35872c07852f4ed4700be1aa4dde1ac72c00460d", "difficulty": "easy", "final_answer": {"answer": 36.519, "unit": "kg"}, "id": "unit_convert_002154_g_to_kg_36519", "license": "Apache-2.0", "prompt": "Convert 36519 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 36519.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 36519.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=96 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-46.3584, 441.0705], \"unit\": \"N\"}", "dedupe_signature": "b59480ae3852070b136a0b75cc4cd6db9a41b2a705f47c12051d4297f0f8cd53", "difficulty": "medium", "final_answer": {"answer": [-46.3584, 441.0705], "unit": "N"}, "id": "vector_components_002155_443.5_96", "license": "Apache-2.0", "prompt": "A vector has magnitude 443.5 N at 96 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=96 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 96, "magnitude": 443.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [1.55, 15.5], \"unit\": \"dimensionless\"}", "dedupe_signature": "902ba6858dc38f6171d9ddc33308754727d3bed62be232de50fe8cd158135401", "difficulty": "medium", "final_answer": {"answer": [1.55, 15.5], "unit": "dimensionless"}, "id": "line_two_point_002156_-8.5_-2.5_1.55_15.5", "license": "Apache-2.0", "prompt": "A line passes through points (-8.5, 2.325) and (-2.5, 11.625). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -8.5, "x2": -2.5, "y1": 2.3249999999999993, "y2": 11.625}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. m*v is momentum, not energy\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "35f60da2e1f2915b48d3df49aef601576be3fafc025b05998d774d85319c6f11", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_002157_inconsistent_1e14b074_617619", "license": "Apache-2.0", "prompt": "In field worksheet case 617619, check dimensional consistency for E = m * v. The left side has dimensions kg*m^2/s^2 and the right side has dimensions kg*m/s. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nm*v is momentum, not energy\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "E = m * v"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: launch_angle_or_vertical_velocity.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"launch_angle_or_vertical_velocity\"]}", "dedupe_signature": "e3dc1d851e45cc4ba2f827f55485003144489a4f73b3e9c1d9d53c3dbe97681e", "difficulty": "easy", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["launch_angle_or_vertical_velocity"]}, "id": "abstain_002159_launch_angle_or_vertical_velocity", "license": "Apache-2.0", "prompt": "Compute projectile range on level ground. The prompt gives initial speed 34.9 m/s but does not give launch angle or vertical velocity. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: launch_angle_or_vertical_velocity.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["launch_angle_or_vertical_velocity"]}, "verifier": {"missing": ["launch_angle_or_vertical_velocity"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 18.3 kg and a = 9.4 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 172.02, \"unit\": \"N\"}", "dedupe_signature": "d78068eb12b4895da106babee6a0a5a1165472f9804fa07516f13b68b676e6d4", "difficulty": "easy", "final_answer": {"answer": 172.02, "unit": "N"}, "id": "force_002160_18.3_9.4", "license": "Apache-2.0", "prompt": "A cart has mass 18.3 kg and measured acceleration 9.4 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 18.3 kg and a = 9.4 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 9.4, "mass": 18.3}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 29.3^2 and multiply by 0.5 * 18.85.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 8091.2683, \"unit\": \"J\"}", "dedupe_signature": "22634928086fbe0ef0dcb172e55c66ba4e988d45100f20511cb1c233d3e2dfcc", "difficulty": "easy", "final_answer": {"answer": 8091.2683, "unit": "J"}, "id": "ke_002161_18.85_29.3", "license": "Apache-2.0", "prompt": "A body of mass 18.85 kg moves at 29.3 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 29.3^2 and multiply by 0.5 * 18.85.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 18.85, "velocity": 29.3}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=62 degrees through the sine of 2 theta.\n3. Substitute v=45.7 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 176.4971, \"unit\": \"m\"}", "dedupe_signature": "93dc1b6ba87e4803c4d6c7284f72308c115f3332d803e93b7f6865854097bfa3", "difficulty": "medium", "final_answer": {"answer": 176.4971, "unit": "m"}, "id": "projectile_range_002162_45.7_62", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 45.7 m/s and angle 62 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=62 degrees through the sine of 2 theta.\nSubstitute v=45.7 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 62, "gravity": 9.81, "speed": 45.7}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 5.3 * 8.314 * 280 / 87.1.\nFinal: {\"answer\": 141.653, \"unit\": \"kPa\"}", "dedupe_signature": "a558695699b65196dd00bb140c077bce137c86a9b7962f31ac19227b1209166f", "difficulty": "medium", "final_answer": {"answer": 141.653, "unit": "kPa"}, "id": "ideal_gas_002163_5.3_280_87.1", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=5.3 mol, T=280 K, and V=87.1 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 5.3 * 8.314 * 280 / 87.1.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 5.3, "temp_k": 280, "volume_l": 87.1}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 345 * 2.89 * 11.\nFinal: {\"answer\": 10967.55, \"unit\": \"J\"}", "dedupe_signature": "72b53aa005e3d26b11a68d8c0dc4535eaac2c1a2f116973d90a64ab6974a87ce", "difficulty": "easy", "final_answer": {"answer": 10967.55, "unit": "J"}, "id": "heat_q_002164_345_2.89_11", "license": "Apache-2.0", "prompt": "A 345 g sample has specific heat 2.89 J/(g*K). How much heat is needed to raise its temperature by 11 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 345 * 2.89 * 11.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 11, "heat_capacity": 2.89, "mass_g": 345}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=88.6 V and R=2.8 ohm.\nFinal: {\"answer\": 2803.5571, \"unit\": \"W\"}", "dedupe_signature": "9421f74844319537f6e864e1341c05c96fad065e9052715128fa6ca955b3965c", "difficulty": "easy", "final_answer": {"answer": 2803.5571, "unit": "W"}, "id": "ohm_power_002165_88.6_2.8", "license": "Apache-2.0", "prompt": "A resistor has resistance 2.8 ohm and voltage 88.6 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=88.6 V and R=2.8 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 2.8, "voltage": 88.6}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=5 mg, t=213.5 h, and T_half=30 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 0.036, \"unit\": \"mg\"}", "dedupe_signature": "ee525d18327cd4731f1aef488dfcd88d4ead63abb604e43b033e46297033ebf0", "difficulty": "medium", "final_answer": {"answer": 0.036, "unit": "mg"}, "id": "half_life_002166_5_30_213.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 5 mg. Its half-life is 30 hours. How many mg remain after 213.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=5 mg, t=213.5 h, and T_half=30 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 213.5, "half_life": 30.0, "initial_amount": 5.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 4.86 mol * 44.01 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 213.8886, \"unit\": \"g\"}", "dedupe_signature": "a84b907a7387fa5c232692f2f019671d68b407c1fd6d32ca280c8f104441fc1c", "difficulty": "medium", "final_answer": {"answer": 213.8886, "unit": "g"}, "id": "stoich_mass_002167_carbon_dioxide_4.86", "license": "Apache-2.0", "prompt": "A sample contains 4.86 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 4.86 mol * 44.01 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "carbon dioxide", "molar_mass": 44.01, "moles": 4.86}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 3900 mL to 3.9 L.\n3. Compute M = 4.45 / 3.9.\nFinal: {\"answer\": 1.141, \"unit\": \"mol/L\"}", "dedupe_signature": "6c9cd4ad31e64d0f7f0d9b17c182f4c8be59cebe577108ae98e75c4c0692c8db", "difficulty": "medium", "final_answer": {"answer": 1.141, "unit": "mol/L"}, "id": "molarity_002168_4.45_3900", "license": "Apache-2.0", "prompt": "A solution contains 4.45 mol of solute in 3900 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 3900 mL to 3.9 L.\nCompute M = 4.45 / 3.9.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 4.45, "volume_ml": 3900}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.5 y, so each step multiplies y by 1 - h*0.5.\n3. Apply that update for 8 steps and round the final state.\nFinal: {\"answer\": 0.0003, \"unit\": \"state_units\"}", "dedupe_signature": "c3cd25a54fcbd86dbfabdf05f973bffd0fb3dfb575e9a11760e63c61cb965947", "difficulty": "medium", "final_answer": {"answer": 0.0003, "unit": "state_units"}, "id": "euler_decay_002169_42.5_0.5_1.55_8", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.5 y with y(0)=42.5, step size h=1.55, for 8 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.5 y, so each step multiplies y by 1 - h*0.5.\nApply that update for 8 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 42.5, "rate": 0.5, "step": 1.55, "steps": 8}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.1 and add it to the current value.\nFinal: {\"answer\": [-0.685, 1.96, 0.57], \"unit\": \"temperature_units\"}", "dedupe_signature": "4b3cf3486e951dbc4c896c1d392d26911f428afc9823b32023c3ede0a1f4d44b", "difficulty": "hard", "final_answer": {"answer": [-0.685, 1.96, 0.57], "unit": "temperature_units"}, "id": "heat_step_002171_0.1_-0.95_-1.05_2.5_0.65_-2.0", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-0.95, right=-2; current interior values are [-1.05, 2.5, 0.65]. Use r=0.1. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.1 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-1.05, 2.5, 0.65], "left": -0.95, "r": 0.1, "right": -2.0}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 21022.0 / 1000.\nFinal: {\"answer\": 21.022, \"unit\": \"kg\"}", "dedupe_signature": "05df270d379cb41b326eae4df0c590e93e1bf9df543fe36e3658fc4e234ebcfa", "difficulty": "easy", "final_answer": {"answer": 21.022, "unit": "kg"}, "id": "unit_convert_002172_g_to_kg_21022", "license": "Apache-2.0", "prompt": "Convert 21022 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 21022.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 21022.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=47 degrees and keep the unit as newtons.\nFinal: {\"answer\": [7.843, 8.4106], \"unit\": \"N\"}", "dedupe_signature": "4186567e9118ae37eda291c43076ca791a87fba329f977ace2af0e93f91a43f2", "difficulty": "medium", "final_answer": {"answer": [7.843, 8.4106], "unit": "N"}, "id": "vector_components_002173_11.5_47", "license": "Apache-2.0", "prompt": "A vector has magnitude 11.5 N at 47 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=47 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 47, "magnitude": 11.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [6.2, -13.75], \"unit\": \"dimensionless\"}", "dedupe_signature": "5dd0dcb0bb0bf9cf2c156a51bde1d4e78bfaf569ebbbc24376cb71eff383a20b", "difficulty": "medium", "final_answer": {"answer": [6.2, -13.75], "unit": "dimensionless"}, "id": "line_two_point_002174_2.5_13.5_6.2_-13.75", "license": "Apache-2.0", "prompt": "A line passes through points (2.5, 1.75) and (13.5, 69.95). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 2.5, "x2": 13.5, "y1": 1.75, "y2": 69.95}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. m*v is momentum, not energy\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "fc9dd9df59ab4170f2be566e7ca0d60e85c8f8e9481dc24643f0526c5eec89f6", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_002175_inconsistent_1e14b074_385001", "license": "Apache-2.0", "prompt": "In lab notebook case 385001, check dimensional consistency for E = m * v. The left side has dimensions kg*m^2/s^2 and the right side has dimensions kg*m/s. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nm*v is momentum, not energy\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "E = m * v"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\nimport math\n\ndef unit_vector_002176(x, y):\n    norm = math.hypot(x, y)\n    if norm == 0:\n        raise ValueError('zero vector has no direction')\n    return (x / norm, y / norm)\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"unit_vector_002176\"}", "dedupe_signature": "b6ca8c12152f53aa28a08ba77dd4b9012da02d93c25825abfce3ad715d1e5bd7", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "unit_vector_002176"}, "id": "code_002176_unit_vector_002176", "license": "Apache-2.0", "prompt": "Write a Python function unit_vector_002176(x, y) that returns the 2D unit vector as a tuple. Raise ValueError for the zero vector. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "unit_vector_002176"}, "verifier": {"function": "unit_vector_002176", "tests": ["ux, uy = unit_vector_002176(3, 4); assert abs(ux - 0.6) < 1e-12 and abs(uy - 0.8) < 1e-12", "assert unit_vector_002176(0, 5) == (0, 1)", "try:\n    unit_vector_002176(0, 0)\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: volume.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"volume\"]}", "dedupe_signature": "823701bcdea6ff63c4b1e7b737ce08c1aba0db14531d0359522888ee721f9eaa", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["volume"]}, "id": "abstain_002177_volume", "license": "Apache-2.0", "prompt": "Compute pressure from the ideal gas law. The prompt gives n=4.04 mol and T=291 K, but does not give volume. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: volume.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["volume"]}, "verifier": {"missing": ["volume"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 6.05 kg and a = 10.6 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 64.13, \"unit\": \"N\"}", "dedupe_signature": "0e2ca441cd84e15713fbc9b8737e2c2fb35fd9e958384e6e7bf560f40f816527", "difficulty": "easy", "final_answer": {"answer": 64.13, "unit": "N"}, "id": "force_002178_6.05_10.6", "license": "Apache-2.0", "prompt": "A cart has mass 6.05 kg and measured acceleration 10.6 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 6.05 kg and a = 10.6 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 10.6, "mass": 6.05}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=32 degrees through the sine of 2 theta.\n3. Substitute v=49.1 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 220.8789, \"unit\": \"m\"}", "dedupe_signature": "f00fc9e219460e16d24adbd9eef9f282f0fa89cec33f057d07e638db45e0d87e", "difficulty": "medium", "final_answer": {"answer": 220.8789, "unit": "m"}, "id": "projectile_range_002180_49.1_32", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 49.1 m/s and angle 32 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=32 degrees through the sine of 2 theta.\nSubstitute v=49.1 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 32, "gravity": 9.81, "speed": 49.1}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 3.88 * 8.314 * 517 / 69.4.\nFinal: {\"answer\": 240.3105, \"unit\": \"kPa\"}", "dedupe_signature": "c31ba368ecb8046c8958211adffec6d182c59fd14264959d4e9c246189dd1ff3", "difficulty": "medium", "final_answer": {"answer": 240.3105, "unit": "kPa"}, "id": "ideal_gas_002181_3.88_517_69.4", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=3.88 mol, T=517 K, and V=69.4 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 3.88 * 8.314 * 517 / 69.4.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 3.88, "temp_k": 517, "volume_l": 69.4}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1010 * 4.315 * 105.\nFinal: {\"answer\": 457605.75, \"unit\": \"J\"}", "dedupe_signature": "b4689b15f2ad4e21af6a9c211bfc5c888f41b3900cb3aab36f8a669b1418e753", "difficulty": "easy", "final_answer": {"answer": 457605.75, "unit": "J"}, "id": "heat_q_002182_1010_4.315_105", "license": "Apache-2.0", "prompt": "A 1010 g sample has specific heat 4.315 J/(g*K). How much heat is needed to raise its temperature by 105 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1010 * 4.315 * 105.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 105, "heat_capacity": 4.315, "mass_g": 1010}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=164 V and R=127.7 ohm.\nFinal: {\"answer\": 210.6186, \"unit\": \"W\"}", "dedupe_signature": "fd683b47fa7c68f633e4de08b6c555be2598490e930d49e94721daed7d10937d", "difficulty": "easy", "final_answer": {"answer": 210.6186, "unit": "W"}, "id": "ohm_power_002183_164_127.7", "license": "Apache-2.0", "prompt": "A resistor has resistance 127.7 ohm and voltage 164 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=164 V and R=127.7 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 127.7, "voltage": 164.0}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=986.5 mg, t=174.5 h, and T_half=34.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 29.6139, \"unit\": \"mg\"}", "dedupe_signature": "74a7bb1e83ab251d285406b6c7a27a90fd11af8a4f6132464dbd369baf7db401", "difficulty": "medium", "final_answer": {"answer": 29.6139, "unit": "mg"}, "id": "half_life_002184_986.5_34.5_174.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 986.5 mg. Its half-life is 34.5 hours. How many mg remain after 174.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=986.5 mg, t=174.5 h, and T_half=34.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 174.5, "half_life": 34.5, "initial_amount": 986.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.34 y, so each step multiplies y by 1 - h*0.34.\n3. Apply that update for 2 steps and round the final state.\nFinal: {\"answer\": 8.8373, \"unit\": \"state_units\"}", "dedupe_signature": "3429287d1e301a15d9aa21b5850adab61cae469c82350e296e5d2e5e096e6e3d", "difficulty": "medium", "final_answer": {"answer": 8.8373, "unit": "state_units"}, "id": "euler_decay_002187_39.5_0.34_1.55_2", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.34 y with y(0)=39.5, step size h=1.55, for 2 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.34 y, so each step multiplies y by 1 - h*0.34.\nApply that update for 2 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 39.5, "rate": 0.34, "step": 1.55, "steps": 2}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-2.3)=-22.41 and f(7)=49.2.\n3. The interval width is 9.3.\nFinal: {\"answer\": 124.5735, \"unit\": \"area_units\"}", "dedupe_signature": "8f4fb6135cfbecd8b23e162de8a158ff16e6c7b57310884593b81b1bfa6f5e24", "difficulty": "medium", "final_answer": {"answer": 124.5735, "unit": "area_units"}, "id": "trapz_linear_002188_7.7_-4.7_-2.3_7", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=7.7x+-4.7 from x=-2.3 to x=7. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-2.3)=-22.41 and f(7)=49.2.\nThe interval width is 9.3.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -4.7, "slope": 7.7, "x0": -2.3, "x1": 7.000000000000001}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.24 and add it to the current value.\nFinal: {\"answer\": [1.428, -0.294, -0.136], \"unit\": \"temperature_units\"}", "dedupe_signature": "ad431d209a0404615bf5e97876db15c6e9b6255f21dad47db482e77edcb8c1a0", "difficulty": "hard", "final_answer": {"answer": [1.428, -0.294, -0.136], "unit": "temperature_units"}, "id": "heat_step_002189_0.24_1.45_2.7_-1.35_-1.0_2.95", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.45, right=2.95; current interior values are [2.7, -1.35, -1.0]. Use r=0.24. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.24 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [2.7, -1.35, -1.0], "left": 1.45, "r": 0.24, "right": 2.95}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kelvin equals Celsius plus 273.15.\n2. Apply the conversion factor directly to the given value.\n3. Compute 50.0 + 273.15.\nFinal: {\"answer\": 323.15, \"unit\": \"K\"}", "dedupe_signature": "dbfec23e19064cbfa50c7c068f2d151fd81f94aeceb13cc91333443dc8b2f470", "difficulty": "easy", "final_answer": {"answer": 323.15, "unit": "K"}, "id": "unit_convert_002190_c_to_k_50", "license": "Apache-2.0", "prompt": "Convert 50 degC to K. Return the converted value with unit.", "reasoning_trace": "Kelvin equals Celsius plus 273.15.\nApply the conversion factor directly to the given value.\nCompute 50.0 + 273.15.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 50.0}, "verifier": {"formula": "value + 273.15", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [0.6, -3.0], \"unit\": \"dimensionless\"}", "dedupe_signature": "d558d7ca1d5095c55495b28fa03df0ea1eff269cb3a63303a7f90b3bde3e96da", "difficulty": "medium", "final_answer": {"answer": [0.6, -3.0], "unit": "dimensionless"}, "id": "line_two_point_002192_17_19.5_0.6_-3", "license": "Apache-2.0", "prompt": "A line passes through points (17, 7.2) and (19.5, 8.7). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 17.0, "x2": 19.5, "y1": 7.199999999999999, "y2": 8.7}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef center_values_002194(values):\n    if not values:\n        raise ValueError('center_values requires at least one value')\n    mean = sum(values) / len(values)\n    return [value - mean for value in values]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"center_values_002194\"}", "dedupe_signature": "012c32c44f60316d8a0824acc81238b587c056f2a1eede87fd8f8e2dd61722a9", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "center_values_002194"}, "id": "code_002194_center_values_002194", "license": "Apache-2.0", "prompt": "Write a Python function center_values_002194(values) that subtracts the arithmetic mean from each value and returns a new list. Raise ValueError for an empty input. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "center_values_002194"}, "verifier": {"function": "center_values_002194", "tests": ["out = center_values_002194([1, 2, 3]); assert out == [-1, 0, 1]", "assert center_values_002194([5]) == [0]", "try:\n    center_values_002194([])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 23.7 kg and a = 7.2 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 170.64, \"unit\": \"N\"}", "dedupe_signature": "6f72e212fd8163ae872fd05081ee535e108ff9d11b1230f9d766834fcbdfb536", "difficulty": "easy", "final_answer": {"answer": 170.64, "unit": "N"}, "id": "force_002196_23.7_7.2", "license": "Apache-2.0", "prompt": "A cart has mass 23.7 kg and measured acceleration 7.2 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 23.7 kg and a = 7.2 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 7.2, "mass": 23.7}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=16 degrees through the sine of 2 theta.\n3. Substitute v=62 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 207.6462, \"unit\": \"m\"}", "dedupe_signature": "5c7f8ffdd9c4b972e641ada26c2e502cf7de93ce1dfa34c8bc1ab8489426b605", "difficulty": "medium", "final_answer": {"answer": 207.6462, "unit": "m"}, "id": "projectile_range_002198_62_16", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 62 m/s and angle 16 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=16 degrees through the sine of 2 theta.\nSubstitute v=62 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 16, "gravity": 9.81, "speed": 62.0}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 3.65 * 8.314 * 414 / 93.0.\nFinal: {\"answer\": 135.0891, \"unit\": \"kPa\"}", "dedupe_signature": "9e8da76fb6c2fb708b045c9a5a0531a397ad359b0d0d5293dec5232e9b0c246f", "difficulty": "medium", "final_answer": {"answer": 135.0891, "unit": "kPa"}, "id": "ideal_gas_002199_3.65_414_93.0", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=3.65 mol, T=414 K, and V=93.0 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 3.65 * 8.314 * 414 / 93.0.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 3.65, "temp_k": 414, "volume_l": 93.0}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=781 mg, t=38.5 h, and T_half=18.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 184.5794, \"unit\": \"mg\"}", "dedupe_signature": "f89010db2d83a34af70ba67004099ca81c84ec8c8447d52338aa921d2a350117", "difficulty": "medium", "final_answer": {"answer": 184.5794, "unit": "mg"}, "id": "half_life_002202_781_18.5_38.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 781 mg. Its half-life is 18.5 hours. How many mg remain after 38.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=781 mg, t=38.5 h, and T_half=18.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 38.5, "half_life": 18.5, "initial_amount": 781.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 0.5 mol * 18.015 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 9.0075, \"unit\": \"g\"}", "dedupe_signature": "1942efaa338cf1636c7454c180f0ce67a9df901664982c3a031180a225996b5d", "difficulty": "medium", "final_answer": {"answer": 9.0075, "unit": "g"}, "id": "stoich_mass_002203_water_0.5", "license": "Apache-2.0", "prompt": "A sample contains 0.5 mol of water. Using molar mass 18.015 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 0.5 mol * 18.015 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "water", "molar_mass": 18.015, "moles": 0.5}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 4530 mL to 4.53 L.\n3. Compute M = 4.08 / 4.53.\nFinal: {\"answer\": 0.9007, \"unit\": \"mol/L\"}", "dedupe_signature": "af25bf52d9ba4350d4a1813a678be015f79fc6cbdf8a2f4ed9e02fbabaa9b55b", "difficulty": "medium", "final_answer": {"answer": 0.9007, "unit": "mol/L"}, "id": "molarity_002204_4.08_4530", "license": "Apache-2.0", "prompt": "A solution contains 4.08 mol of solute in 4530 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 4530 mL to 4.53 L.\nCompute M = 4.08 / 4.53.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 4.08, "volume_ml": 4530}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.67 y, so each step multiplies y by 1 - h*0.67.\n3. Apply that update for 3 steps and round the final state.\nFinal: {\"answer\": 0.8401, \"unit\": \"state_units\"}", "dedupe_signature": "a159dc15e2f34c84e286b6492eb3c6def7fcfcf837b17b6c6d5ec37baf895e9b", "difficulty": "medium", "final_answer": {"answer": 0.8401, "unit": "state_units"}, "id": "euler_decay_002205_69.5_0.67_1.15_3", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.67 y with y(0)=69.5, step size h=1.15, for 3 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.67 y, so each step multiplies y by 1 - h*0.67.\nApply that update for 3 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 69.5, "rate": 0.67, "step": 1.15, "steps": 3}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-1.7)=16.74 and f(-0.2)=7.44.\n3. The interval width is 1.5.\nFinal: {\"answer\": 18.135, \"unit\": \"area_units\"}", "dedupe_signature": "7266b42b1318495dad0bb2dcace32b21aa8ce181abea468e3e245e3bcaf6bd6a", "difficulty": "medium", "final_answer": {"answer": 18.135, "unit": "area_units"}, "id": "trapz_linear_002206_-6.2_6.2_-1.7_-0.2", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-6.2x+6.2 from x=-1.7 to x=-0.2. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-1.7)=16.74 and f(-0.2)=7.44.\nThe interval width is 1.5.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 6.2, "slope": -6.2, "x0": -1.7, "x1": -0.19999999999999996}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.48 and add it to the current value.\nFinal: {\"answer\": [1.554, 1.146, 0.622], \"unit\": \"temperature_units\"}", "dedupe_signature": "eb0160eaf29de58b615812293d0e822f1c4256e4c8639372707b31491f6d0ef4", "difficulty": "hard", "final_answer": {"answer": [1.554, 1.146, 0.622], "unit": "temperature_units"}, "id": "heat_step_002207_0.48_0.9_1.05_2.25_1.15_-1.05", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=0.9, right=-1.05; current interior values are [1.05, 2.25, 1.15]. Use r=0.48. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.48 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [1.05, 2.25, 1.15], "left": 0.9, "r": 0.48, "right": -1.05}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 100 centimeters in one meter.\n2. Apply the conversion factor directly to the given value.\n3. Compute 739.5 / 100.\nFinal: {\"answer\": 7.395, \"unit\": \"m\"}", "dedupe_signature": "487aeaeeb29169b9f5f31af97071079d781d40b3ad2337f11712537bebb301f1", "difficulty": "easy", "final_answer": {"answer": 7.395, "unit": "m"}, "id": "unit_convert_002208_cm_to_m_739.5", "license": "Apache-2.0", "prompt": "Convert 739.5 cm to m. Return the converted value with unit.", "reasoning_trace": "There are 100 centimeters in one meter.\nApply the conversion factor directly to the given value.\nCompute 739.5 / 100.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 739.5}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=177 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-135.8136, 7.1177], \"unit\": \"N\"}", "dedupe_signature": "ea3d3873480b1c3e400184da36bf833177b9e51c41752b654db31ae650e42bbc", "difficulty": "medium", "final_answer": {"answer": [-135.8136, 7.1177], "unit": "N"}, "id": "vector_components_002209_136_177", "license": "Apache-2.0", "prompt": "A vector has magnitude 136 N at 177 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=177 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 177, "magnitude": 136.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [8.45, 7.5], \"unit\": \"dimensionless\"}", "dedupe_signature": "e94518ce1fcafaa90ee73c401e6d7834899ae1f58e3faedd215fb45a3b262e21", "difficulty": "medium", "final_answer": {"answer": [8.45, 7.5], "unit": "dimensionless"}, "id": "line_two_point_002210_-15_-8.25_8.45_7.5", "license": "Apache-2.0", "prompt": "A line passes through points (-15, -119.25) and (-8.25, -62.2125). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -15.0, "x2": -8.25, "y1": -119.24999999999999, "y2": -62.21249999999999}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. velocity divided by time is acceleration\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "f467db53e459713f4c036208b0cd7ca994ea24d13349f7e0e865c88721765bd4", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_002211_inconsistent_c1271127_104182", "license": "Apache-2.0", "prompt": "In sensor calibration case 104182, check dimensional consistency for x = v / t. The left side has dimensions m and the right side has dimensions m/s^2. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nvelocity divided by time is acceleration\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "x = v / t"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef clamp_002212(x, lo, hi):\n    if lo > hi:\n        raise ValueError('lo must be <= hi')\n    return min(max(x, lo), hi)\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"clamp_002212\"}", "dedupe_signature": "338a99fcf936284e66d30e77aaa595a12204c217e0e57f634335dc67ca732b94", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "clamp_002212"}, "id": "code_002212_clamp_002212", "license": "Apache-2.0", "prompt": "Write a Python function clamp_002212(x, lo, hi) that clips x into the inclusive interval [lo, hi]. It must raise ValueError if lo > hi. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "clamp_002212"}, "verifier": {"function": "clamp_002212", "tests": ["assert clamp_002212(5, 0, 10) == 5", "assert clamp_002212(-2, 0, 10) == 0", "assert clamp_002212(12, 0, 10) == 10", "try:\n    clamp_002212(1, 3, 2)\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: required_fields, allowed_transformations.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"required_fields\", \"allowed_transformations\"]}", "dedupe_signature": "66f8a1e5f55e57e57233273ad12314371c7f0f8ac608ac539efbd3c94a2c09b7", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["required_fields", "allowed_transformations"]}, "id": "abstain_002213_required_fields_allowed_transformations", "license": "Apache-2.0", "prompt": "Write a sanitizer for valid laboratory ledger records in release 470930, but the prompt does not state which fields are required or which transformations are allowed. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: required_fields, allowed_transformations.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["required_fields", "allowed_transformations"]}, "verifier": {"missing": ["required_fields", "allowed_transformations"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 37.6^2 and multiply by 0.5 * 0.45.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 318.096, \"unit\": \"J\"}", "dedupe_signature": "7e8d3947512246a885029a53a0409882e8f3f5ae85d2f02e53f7d2695204ea66", "difficulty": "easy", "final_answer": {"answer": 318.096, "unit": "J"}, "id": "ke_002215_0.45_37.6", "license": "Apache-2.0", "prompt": "A body of mass 0.45 kg moves at 37.6 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 37.6^2 and multiply by 0.5 * 0.45.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 0.45, "velocity": 37.6}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=40 degrees through the sine of 2 theta.\n3. Substitute v=77.2 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 598.2973, \"unit\": \"m\"}", "dedupe_signature": "444bb26567c6fc489816a05d8f9c95d4210f3a5448ae7831ddffa9e80c3ba7e9", "difficulty": "medium", "final_answer": {"answer": 598.2973, "unit": "m"}, "id": "projectile_range_002216_77.2_40", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 77.2 m/s and angle 40 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=40 degrees through the sine of 2 theta.\nSubstitute v=77.2 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 40, "gravity": 9.81, "speed": 77.2}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 3.09 * 8.314 * 478 / 83.7.\nFinal: {\"answer\": 146.7138, \"unit\": \"kPa\"}", "dedupe_signature": "2ac55b8cb88801e4a10e74ea62610294fa81b1ecd5b045362d5e14bc1c7fe55e", "difficulty": "medium", "final_answer": {"answer": 146.7138, "unit": "kPa"}, "id": "ideal_gas_002217_3.09_478_83.7", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=3.09 mol, T=478 K, and V=83.7 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 3.09 * 8.314 * 478 / 83.7.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 3.09, "temp_k": 478, "volume_l": 83.7}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1585 * 0.815 * 105.\nFinal: {\"answer\": 135636.375, \"unit\": \"J\"}", "dedupe_signature": "a825f478f4147dd654f340c7cad6f5eed9e261e28d4043665ea3375395a6648f", "difficulty": "easy", "final_answer": {"answer": 135636.375, "unit": "J"}, "id": "heat_q_002218_1585_0.815_105", "license": "Apache-2.0", "prompt": "A 1585 g sample has specific heat 0.815 J/(g*K). How much heat is needed to raise its temperature by 105 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1585 * 0.815 * 105.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 105, "heat_capacity": 0.815, "mass_g": 1585}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=901 mg, t=40.5 h, and T_half=58 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 555.2938, \"unit\": \"mg\"}", "dedupe_signature": "7d1ce124f70baf314c3c2a2a9336b0a8bfc6fced334b7fd61513b0c0c4a231d3", "difficulty": "medium", "final_answer": {"answer": 555.2938, "unit": "mg"}, "id": "half_life_002220_901_58_40.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 901 mg. Its half-life is 58 hours. How many mg remain after 40.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=901 mg, t=40.5 h, and T_half=58 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 40.5, "half_life": 58.0, "initial_amount": 901.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 3.18 mol * 18.015 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 57.2877, \"unit\": \"g\"}", "dedupe_signature": "de6ae2be8fed7f9af7706755b922930509c7044ab999dce8b8c2aee74bfea005", "difficulty": "medium", "final_answer": {"answer": 57.2877, "unit": "g"}, "id": "stoich_mass_002221_water_3.18", "license": "Apache-2.0", "prompt": "A sample contains 3.18 mol of water. Using molar mass 18.015 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 3.18 mol * 18.015 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "water", "molar_mass": 18.015, "moles": 3.18}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 705 mL to 0.705 L.\n3. Compute M = 4.26 / 0.705.\nFinal: {\"answer\": 6.0426, \"unit\": \"mol/L\"}", "dedupe_signature": "d12a7aa1baa551e6312aa68f79b7fdaf783b3efe3e6100d6a6dad866a8603ed6", "difficulty": "medium", "final_answer": {"answer": 6.0426, "unit": "mol/L"}, "id": "molarity_002222_4.26_705", "license": "Apache-2.0", "prompt": "A solution contains 4.26 mol of solute in 705 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 705 mL to 0.705 L.\nCompute M = 4.26 / 0.705.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 4.26, "volume_ml": 705}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.95 y, so each step multiplies y by 1 - h*0.95.\n3. Apply that update for 5 steps and round the final state.\nFinal: {\"answer\": -7.466, \"unit\": \"state_units\"}", "dedupe_signature": "c95fbbee7c74d19ca440008358924f397ab047df91606612e8fb63cda4d88679", "difficulty": "medium", "final_answer": {"answer": -7.466, "unit": "state_units"}, "id": "euler_decay_002223_58.5_0.95_1.75_5", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.95 y with y(0)=58.5, step size h=1.75, for 5 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.95 y, so each step multiplies y by 1 - h*0.95.\nApply that update for 5 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 58.5, "rate": 0.95, "step": 1.75, "steps": 5}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.06 and add it to the current value.\nFinal: {\"answer\": [1.919, 2.338, -1.405], \"unit\": \"temperature_units\"}", "dedupe_signature": "a917a88c38929c61022811eea92fc8b47553472de022cca3655c65907ac7cf10", "difficulty": "hard", "final_answer": {"answer": [1.919, 2.338, -1.405], "unit": "temperature_units"}, "id": "heat_step_002225_0.06_0.0_2.0_2.65_-1.9_1.8", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=0, right=1.8; current interior values are [2.0, 2.65, -1.9]. Use r=0.06. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.06 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [2.0, 2.65, -1.9], "left": 0.0, "r": 0.06, "right": 1.8}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 100 centimeters in one meter.\n2. Apply the conversion factor directly to the given value.\n3. Compute 448.5 / 100.\nFinal: {\"answer\": 4.485, \"unit\": \"m\"}", "dedupe_signature": "667480fd740ec1f5be013fb6b33020a1ea47a4fbf10ccbd2915d8c949c06df44", "difficulty": "easy", "final_answer": {"answer": 4.485, "unit": "m"}, "id": "unit_convert_002226_cm_to_m_448.5", "license": "Apache-2.0", "prompt": "Convert 448.5 cm to m. Return the converted value with unit.", "reasoning_trace": "There are 100 centimeters in one meter.\nApply the conversion factor directly to the given value.\nCompute 448.5 / 100.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 448.5}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=189 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-44.9398, -7.1178], \"unit\": \"N\"}", "dedupe_signature": "cd4589edf32e1a74845596becd02e99928d80cfdd5b65580fed1e71374ccbe43", "difficulty": "medium", "final_answer": {"answer": [-44.9398, -7.1178], "unit": "N"}, "id": "vector_components_002227_45.5_189", "license": "Apache-2.0", "prompt": "A vector has magnitude 45.5 N at 189 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=189 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 189, "magnitude": 45.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [8.1, 28.0], \"unit\": \"dimensionless\"}", "dedupe_signature": "a67546e399b419ef3abc052777bb64e4bd7737d7a6f6560b5727c80e8172cfd6", "difficulty": "medium", "final_answer": {"answer": [8.1, 28.0], "unit": "dimensionless"}, "id": "line_two_point_002228_-20_-6_8.1_28", "license": "Apache-2.0", "prompt": "A line passes through points (-20, -134) and (-6, -20.6). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -20.0, "x2": -6.0, "y1": -134.0, "y2": -20.599999999999994}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef normalize_002230(values):\n    total = sum(values)\n    if total == 0:\n        raise ValueError('cannot normalize zero-sum values')\n    return [v / total for v in values]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"normalize_002230\"}", "dedupe_signature": "ee88a7f0760155a664990583b85128f652a2df8e3074113ba5201df4be3bfe95", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "normalize_002230"}, "id": "code_002230_normalize_002230", "license": "Apache-2.0", "prompt": "Write a Python function normalize_002230(values) that returns a new list whose values sum to 1. Raise ValueError if the sum is zero. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "normalize_002230"}, "verifier": {"function": "normalize_002230", "tests": ["out = normalize_002230([2, 3, 5]); assert len(out) == 3", "assert abs(sum(normalize_002230([2, 3, 5])) - 1.0) < 1e-12", "assert normalize_002230([1, 1]) == [0.5, 0.5]", "try:\n    normalize_002230([1, -1])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 24.85 kg and a = 8.45 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 209.9825, \"unit\": \"N\"}", "dedupe_signature": "beb0b61c53f125f667854ed64535da9c77fc69625a9652fa0338f837b661c283", "difficulty": "easy", "final_answer": {"answer": 209.9825, "unit": "N"}, "id": "force_002232_24.85_8.45", "license": "Apache-2.0", "prompt": "A cart has mass 24.85 kg and measured acceleration 8.45 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 24.85 kg and a = 8.45 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 8.45, "mass": 24.85}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 1.45^2 and multiply by 0.5 * 28.65.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 30.1183, \"unit\": \"J\"}", "dedupe_signature": "b55003beebe1b4fe6dc41a34e59cb9ce9be7c8b6a11627ae891da41ac4c92cbb", "difficulty": "easy", "final_answer": {"answer": 30.1183, "unit": "J"}, "id": "ke_002233_28.65_1.45", "license": "Apache-2.0", "prompt": "A body of mass 28.65 kg moves at 1.45 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 1.45^2 and multiply by 0.5 * 28.65.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 28.65, "velocity": 1.45}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=20 degrees through the sine of 2 theta.\n3. Substitute v=48.4 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 153.4932, \"unit\": \"m\"}", "dedupe_signature": "b356f5f0d3f182e4f0a6137df383bcd99790eaa94ed08eb090eedadf8771be97", "difficulty": "medium", "final_answer": {"answer": 153.4932, "unit": "m"}, "id": "projectile_range_002234_48.4_20", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 48.4 m/s and angle 20 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=20 degrees through the sine of 2 theta.\nSubstitute v=48.4 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 20, "gravity": 9.81, "speed": 48.4}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1950 * 3.885 * 104.\nFinal: {\"answer\": 787878.0, \"unit\": \"J\"}", "dedupe_signature": "d95a78c73a56df787a963a6205e8ab92a915f39719bfc7c6915a48b7e7a482ee", "difficulty": "easy", "final_answer": {"answer": 787878.0, "unit": "J"}, "id": "heat_q_002236_1950_3.885_104", "license": "Apache-2.0", "prompt": "A 1950 g sample has specific heat 3.885 J/(g*K). How much heat is needed to raise its temperature by 104 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1950 * 3.885 * 104.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 104, "heat_capacity": 3.885, "mass_g": 1950}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=203.9 V and R=181.3 ohm.\nFinal: {\"answer\": 229.3172, \"unit\": \"W\"}", "dedupe_signature": "3bd488ca05d80b45dc7550ef0b6fc6c50cde5733c638c759d9bb11ab15194e34", "difficulty": "easy", "final_answer": {"answer": 229.3172, "unit": "W"}, "id": "ohm_power_002237_203.9_181.3", "license": "Apache-2.0", "prompt": "A resistor has resistance 181.3 ohm and voltage 203.9 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=203.9 V and R=181.3 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 181.3, "voltage": 203.9}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=767.5 mg, t=94.5 h, and T_half=115.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 435.2924, \"unit\": \"mg\"}", "dedupe_signature": "a44f8424402a3d6b7521b53c4b29be2e41804e793974caea6b46703d287a6627", "difficulty": "medium", "final_answer": {"answer": 435.2924, "unit": "mg"}, "id": "half_life_002238_767.5_115.5_94.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 767.5 mg. Its half-life is 115.5 hours. How many mg remain after 94.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=767.5 mg, t=94.5 h, and T_half=115.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 94.5, "half_life": 115.5, "initial_amount": 767.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 7.17 mol * 180.156 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 1291.7185, \"unit\": \"g\"}", "dedupe_signature": "9254e0fbe61b3d08421e7a807c61d5d08ab2ab4762c261c103d1c9a2a03f7304", "difficulty": "medium", "final_answer": {"answer": 1291.7185, "unit": "g"}, "id": "stoich_mass_002239_glucose_7.17", "license": "Apache-2.0", "prompt": "A sample contains 7.17 mol of glucose. Using molar mass 180.156 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 7.17 mol * 180.156 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "glucose", "molar_mass": 180.156, "moles": 7.17}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 255 mL to 0.255 L.\n3. Compute M = 1 / 0.255.\nFinal: {\"answer\": 3.9216, \"unit\": \"mol/L\"}", "dedupe_signature": "ad56a9eeca1712c1392035870676fbd880678d9db04435efb6bc89a05130220b", "difficulty": "medium", "final_answer": {"answer": 3.9216, "unit": "mol/L"}, "id": "molarity_002240_1_255", "license": "Apache-2.0", "prompt": "A solution contains 1 mol of solute in 255 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 255 mL to 0.255 L.\nCompute M = 1 / 0.255.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 1.0, "volume_ml": 255}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.56 y, so each step multiplies y by 1 - h*0.56.\n3. Apply that update for 6 steps and round the final state.\nFinal: {\"answer\": 26.9866, \"unit\": \"state_units\"}", "dedupe_signature": "3dba73a79497cb33e2edcec78f22a138e5fe33f82188771613dac4082bbed7a0", "difficulty": "medium", "final_answer": {"answer": 26.9866, "unit": "state_units"}, "id": "euler_decay_002241_32_0.56_0.05_6", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.56 y with y(0)=32, step size h=0.05, for 6 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.56 y, so each step multiplies y by 1 - h*0.56.\nApply that update for 6 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 32.0, "rate": 0.56, "step": 0.05, "steps": 6}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(4.9)=-0.05 and f(12.4)=26.2.\n3. The interval width is 7.5.\nFinal: {\"answer\": 98.0625, \"unit\": \"area_units\"}", "dedupe_signature": "070f62d0999b8fda20d6ca6b783b7fe71c30aac41463028bf3accf3314137478", "difficulty": "medium", "final_answer": {"answer": 98.0625, "unit": "area_units"}, "id": "trapz_linear_002242_3.5_-17.2_4.9_12.4", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=3.5x+-17.2 from x=4.9 to x=12.4. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(4.9)=-0.05 and f(12.4)=26.2.\nThe interval width is 7.5.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -17.2, "slope": 3.5, "x0": 4.9, "x1": 12.4}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.4 and add it to the current value.\nFinal: {\"answer\": [-0.09, 0.02, -0.78], \"unit\": \"temperature_units\"}", "dedupe_signature": "34d58c41af899a56d93d3e265a1bfc2dccaca1432315f2c4a09aad67c0f4bd67", "difficulty": "hard", "final_answer": {"answer": [-0.09, 0.02, -0.78], "unit": "temperature_units"}, "id": "heat_step_002243_0.4_-0.2_0.75_-0.4_-0.5_-1.3", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-0.2, right=-1.3; current interior values are [0.75, -0.4, -0.5]. Use r=0.4. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.4 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [0.75, -0.4, -0.5], "left": -0.2, "r": 0.4, "right": -1.3}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=15 degrees and keep the unit as newtons.\nFinal: {\"answer\": [8.2104, 2.2], \"unit\": \"N\"}", "dedupe_signature": "fafea32b427fcdb0e643a789dd44cc8acd870c77234e98cf9612d03ac63d1261", "difficulty": "medium", "final_answer": {"answer": [8.2104, 2.2], "unit": "N"}, "id": "vector_components_002245_8.5_15", "license": "Apache-2.0", "prompt": "A vector has magnitude 8.5 N at 15 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=15 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 15, "magnitude": 8.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [8.6, -16.5], \"unit\": \"dimensionless\"}", "dedupe_signature": "6c18a65e998cf7d38f96a1657b939256a86b7260ded95241f6aef64da71ad3b0", "difficulty": "medium", "final_answer": {"answer": [8.6, -16.5], "unit": "dimensionless"}, "id": "line_two_point_002246_16.25_22.25_8.6_-16.5", "license": "Apache-2.0", "prompt": "A line passes through points (16.25, 123.25) and (22.25, 174.85). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 16.25, "x2": 22.25, "y1": 123.25, "y2": 174.85}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. grams cancel with J/(g*K), and kelvin cancels, leaving joules\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "e0386ff9b0df9914cfd8f49a986aafb259157333cfc9b9414ae1603ed07e3012", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_002247_consistent_4153435f_542750", "license": "Apache-2.0", "prompt": "In field worksheet case 542750, check dimensional consistency for Q = m * c * DeltaT. The left side has dimensions J and the right side has dimensions J. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\ngrams cancel with J/(g*K), and kelvin cancels, leaving joules\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "Q = m * c * DeltaT"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 17.95 kg and a = 2.95 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 52.9525, \"unit\": \"N\"}", "dedupe_signature": "1adec7eb61ac0b4effff7d57e2fc5ed1b7a8a0b26995a0246520b5f065e76665", "difficulty": "easy", "final_answer": {"answer": 52.9525, "unit": "N"}, "id": "force_002250_17.95_2.95", "license": "Apache-2.0", "prompt": "A cart has mass 17.95 kg and measured acceleration 2.95 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 17.95 kg and a = 2.95 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 2.95, "mass": 17.95}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 13.2^2 and multiply by 0.5 * 2.3.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 200.376, \"unit\": \"J\"}", "dedupe_signature": "7be91012b1518d92d2884f710d5fe16356b4cda1d43dccec126a893de70dc5c4", "difficulty": "easy", "final_answer": {"answer": 200.376, "unit": "J"}, "id": "ke_002251_2.3_13.2", "license": "Apache-2.0", "prompt": "A body of mass 2.3 kg moves at 13.2 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 13.2^2 and multiply by 0.5 * 2.3.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 2.3, "velocity": 13.2}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=85 degrees through the sine of 2 theta.\n3. Substitute v=15.8 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 4.4189, \"unit\": \"m\"}", "dedupe_signature": "942530bdd2a5f9f1a6aa093382258499c5a1aef0fb31dfc360cf7a4453800689", "difficulty": "medium", "final_answer": {"answer": 4.4189, "unit": "m"}, "id": "projectile_range_002252_15.8_85", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 15.8 m/s and angle 85 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=85 degrees through the sine of 2 theta.\nSubstitute v=15.8 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 85, "gravity": 9.81, "speed": 15.8}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1555 * 1.04 * 114.\nFinal: {\"answer\": 184360.8, \"unit\": \"J\"}", "dedupe_signature": "20dc42712c173f3a41b703cd61640f259f4315b67437bb5075d14dc95bd64acc", "difficulty": "easy", "final_answer": {"answer": 184360.8, "unit": "J"}, "id": "heat_q_002254_1555_1.04_114", "license": "Apache-2.0", "prompt": "A 1555 g sample has specific heat 1.04 J/(g*K). How much heat is needed to raise its temperature by 114 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1555 * 1.04 * 114.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 114, "heat_capacity": 1.04, "mass_g": 1555}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=192.2 V and R=70.5 ohm.\nFinal: {\"answer\": 523.9835, \"unit\": \"W\"}", "dedupe_signature": "7bad098d9afd136974ac33498afd6ffd2f2ac9ec1f52f96903075092549490f9", "difficulty": "easy", "final_answer": {"answer": 523.9835, "unit": "W"}, "id": "ohm_power_002255_192.2_70.5", "license": "Apache-2.0", "prompt": "A resistor has resistance 70.5 ohm and voltage 192.2 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=192.2 V and R=70.5 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 70.5, "voltage": 192.2}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=37.5 mg, t=244 h, and T_half=1.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 0.0, \"unit\": \"mg\"}", "dedupe_signature": "bf36641e38592d52bfc162eaf79b17a999560fb82a9484c2a1235d9080b98d2d", "difficulty": "medium", "final_answer": {"answer": 0.0, "unit": "mg"}, "id": "half_life_002256_37.5_1.5_244", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 37.5 mg. Its half-life is 1.5 hours. How many mg remain after 244 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=37.5 mg, t=244 h, and T_half=1.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 244.0, "half_life": 1.5, "initial_amount": 37.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 2.67 mol * 44.01 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 117.5067, \"unit\": \"g\"}", "dedupe_signature": "15847dfe621cca0745c9518b44bd6981a35ff272b0b51d14e8967e114140a4c1", "difficulty": "medium", "final_answer": {"answer": 117.5067, "unit": "g"}, "id": "stoich_mass_002257_carbon_dioxide_2.67", "license": "Apache-2.0", "prompt": "A sample contains 2.67 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 2.67 mol * 44.01 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "carbon dioxide", "molar_mass": 44.01, "moles": 2.67}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 1110 mL to 1.11 L.\n3. Compute M = 3.04 / 1.11.\nFinal: {\"answer\": 2.7387, \"unit\": \"mol/L\"}", "dedupe_signature": "7c480116627345d7042b22aadff3f8a3d7238606e88d81c4d06e2734ca627763", "difficulty": "medium", "final_answer": {"answer": 2.7387, "unit": "mol/L"}, "id": "molarity_002258_3.04_1110", "license": "Apache-2.0", "prompt": "A solution contains 3.04 mol of solute in 1110 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 1110 mL to 1.11 L.\nCompute M = 3.04 / 1.11.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 3.04, "volume_ml": 1110}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.04 y, so each step multiplies y by 1 - h*0.04.\n3. Apply that update for 4 steps and round the final state.\nFinal: {\"answer\": 63.9387, \"unit\": \"state_units\"}", "dedupe_signature": "98a0168c3756913bbe15436a4f5a6ca6dcf6b921dd39ab0f397c3aab6447c6c4", "difficulty": "medium", "final_answer": {"answer": 63.9387, "unit": "state_units"}, "id": "euler_decay_002259_78.5_0.04_1.25_4", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.04 y with y(0)=78.5, step size h=1.25, for 4 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.04 y, so each step multiplies y by 1 - h*0.04.\nApply that update for 4 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 78.5, "rate": 0.04, "step": 1.25, "steps": 4}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(1.2)=1.28 and f(2.9)=4.51.\n3. The interval width is 1.7.\nFinal: {\"answer\": 4.9215, \"unit\": \"area_units\"}", "dedupe_signature": "80da4c2168d76634b1d9a7c31384ecc80ac03c35d8827cbc4ed74c9378e3dd77", "difficulty": "medium", "final_answer": {"answer": 4.9215, "unit": "area_units"}, "id": "trapz_linear_002260_1.9_-1_1.2_2.9", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=1.9x+-1 from x=1.2 to x=2.9. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(1.2)=1.28 and f(2.9)=4.51.\nThe interval width is 1.7.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -1.0, "slope": 1.9, "x0": 1.2, "x1": 2.9}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.18 and add it to the current value.\nFinal: {\"answer\": [0.203, 2.087, 1.886], \"unit\": \"temperature_units\"}", "dedupe_signature": "542df6e7584db89c905f8ca164b17a263f50ad0974a9289be0697f18f7ac3d6c", "difficulty": "hard", "final_answer": {"answer": [0.203, 2.087, 1.886], "unit": "temperature_units"}, "id": "heat_step_002261_0.18_-1.65_0.05_2.6_2.3_-0.3", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-1.65, right=-0.3; current interior values are [0.05, 2.6, 2.3]. Use r=0.18. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.18 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [0.05, 2.6, 2.3], "left": -1.65, "r": 0.18, "right": -0.3}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 100 centimeters in one meter.\n2. Apply the conversion factor directly to the given value.\n3. Compute 4940.0 / 100.\nFinal: {\"answer\": 49.4, \"unit\": \"m\"}", "dedupe_signature": "5dd4292cb24de3cd040719718026ee590d69a95a37a78a911427b270441107c4", "difficulty": "easy", "final_answer": {"answer": 49.4, "unit": "m"}, "id": "unit_convert_002262_cm_to_m_4940", "license": "Apache-2.0", "prompt": "Convert 4940 cm to m. Return the converted value with unit.", "reasoning_trace": "There are 100 centimeters in one meter.\nApply the conversion factor directly to the given value.\nCompute 4940.0 / 100.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 4940.0}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=27 degrees and keep the unit as newtons.\nFinal: {\"answer\": [200.4765, 102.1479], \"unit\": \"N\"}", "dedupe_signature": "038810ba9dff58d037d42cdab98347b3ee561cae287a7f54e43720526e01bab8", "difficulty": "medium", "final_answer": {"answer": [200.4765, 102.1479], "unit": "N"}, "id": "vector_components_002263_225_27", "license": "Apache-2.0", "prompt": "A vector has magnitude 225 N at 27 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=27 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 27, "magnitude": 225.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-8.75, 25.25], \"unit\": \"dimensionless\"}", "dedupe_signature": "7c2f65461c69437649f1dfacda942139f693f2340cc39f1107109a5838e1ddd2", "difficulty": "medium", "final_answer": {"answer": [-8.75, 25.25], "unit": "dimensionless"}, "id": "line_two_point_002264_2.5_6.25_-8.75_25.25", "license": "Apache-2.0", "prompt": "A line passes through points (2.5, 3.375) and (6.25, -29.4375). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 2.5, "x2": 6.25, "y1": 3.375, "y2": -29.4375}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. amount times volume is not concentration\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "9304eff586503c1dfdcfb8a8f13ce1e5ce4d179188885e1e9185ee90b7366351", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_002265_inconsistent_74ac0b02_359339", "license": "Apache-2.0", "prompt": "In simulation spec case 359339, check dimensional consistency for C = n * V. The left side has dimensions mol/L and the right side has dimensions mol*L. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\namount times volume is not concentration\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "C = n * V"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef running_total_002266(values):\n    total = 0\n    out = []\n    for value in values:\n        total += value\n        out.append(total)\n    return out\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"running_total_002266\"}", "dedupe_signature": "625158cfbc3a823c3620db9d9c5984aeb00747bba614b26dcab562daafce225c", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "running_total_002266"}, "id": "code_002266_running_total_002266", "license": "Apache-2.0", "prompt": "Write a Python function running_total_002266(values) that returns cumulative sums as a new list. It must not mutate the input list. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "running_total_002266"}, "verifier": {"function": "running_total_002266", "tests": ["assert running_total_002266([1, 2, 3]) == [1, 3, 6]", "xs = [4, -1, 2]; assert running_total_002266(xs) == [4, 3, 5] and xs == [4, -1, 2]", "assert running_total_002266([]) == []"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 23.4 kg and a = 9.75 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 228.15, \"unit\": \"N\"}", "dedupe_signature": "4ab1d3f35f250f5fde3940fd262c1f4798921c7ee6740e28281aba26f83a9761", "difficulty": "easy", "final_answer": {"answer": 228.15, "unit": "N"}, "id": "force_002268_23.4_9.75", "license": "Apache-2.0", "prompt": "A cart has mass 23.4 kg and measured acceleration 9.75 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 23.4 kg and a = 9.75 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 9.75, "mass": 23.4}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 37.2^2 and multiply by 0.5 * 25.95.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 17955.324, \"unit\": \"J\"}", "dedupe_signature": "e35b108cf7e0a4ec85d0f990d53c41989d96770d6a07c8e3347f5c46610eb369", "difficulty": "easy", "final_answer": {"answer": 17955.324, "unit": "J"}, "id": "ke_002269_25.95_37.2", "license": "Apache-2.0", "prompt": "A body of mass 25.95 kg moves at 37.2 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 37.2^2 and multiply by 0.5 * 25.95.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 25.95, "velocity": 37.2}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=47 degrees through the sine of 2 theta.\n3. Substitute v=34.9 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 123.8576, \"unit\": \"m\"}", "dedupe_signature": "f9c65162bb26e00d620c7a48e89e2703b19f51ba403cb0b27222e9c19f7b621c", "difficulty": "medium", "final_answer": {"answer": 123.8576, "unit": "m"}, "id": "projectile_range_002270_34.9_47", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 34.9 m/s and angle 47 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=47 degrees through the sine of 2 theta.\nSubstitute v=34.9 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 47, "gravity": 9.81, "speed": 34.9}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 3.73 * 8.314 * 286 / 91.5.\nFinal: {\"answer\": 96.9312, \"unit\": \"kPa\"}", "dedupe_signature": "3595cd0fa597a5596dea9d32a7ebbd42f2c3373284b6177387a962491a1a2297", "difficulty": "medium", "final_answer": {"answer": 96.9312, "unit": "kPa"}, "id": "ideal_gas_002271_3.73_286_91.5", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=3.73 mol, T=286 K, and V=91.5 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 3.73 * 8.314 * 286 / 91.5.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 3.73, "temp_k": 286, "volume_l": 91.5}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 475 * 0.715 * 119.\nFinal: {\"answer\": 40415.375, \"unit\": \"J\"}", "dedupe_signature": "3996caf17f96554a3d8edbc34b30eb0006f4a441a9f86c6cd397b1b34f7bb5a8", "difficulty": "easy", "final_answer": {"answer": 40415.375, "unit": "J"}, "id": "heat_q_002272_475_0.715_119", "license": "Apache-2.0", "prompt": "A 475 g sample has specific heat 0.715 J/(g*K). How much heat is needed to raise its temperature by 119 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 475 * 0.715 * 119.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 119, "heat_capacity": 0.715, "mass_g": 475}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=35.3 V and R=186.9 ohm.\nFinal: {\"answer\": 6.6671, \"unit\": \"W\"}", "dedupe_signature": "f5b28513349e010584b76f7b3fb05e02f8eb70f336ee0b8b2306ec04dd34b754", "difficulty": "easy", "final_answer": {"answer": 6.6671, "unit": "W"}, "id": "ohm_power_002273_35.3_186.9", "license": "Apache-2.0", "prompt": "A resistor has resistance 186.9 ohm and voltage 35.3 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=35.3 V and R=186.9 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 186.9, "voltage": 35.3}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=348.5 mg, t=356.5 h, and T_half=113 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 39.1285, \"unit\": \"mg\"}", "dedupe_signature": "d66364cd33a61f8b9e9b2dfd795cd909f7c597653f07bac9a84295524df2a0cd", "difficulty": "medium", "final_answer": {"answer": 39.1285, "unit": "mg"}, "id": "half_life_002274_348.5_113_356.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 348.5 mg. Its half-life is 113 hours. How many mg remain after 356.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=348.5 mg, t=356.5 h, and T_half=113 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 356.5, "half_life": 113.0, "initial_amount": 348.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 0.43 mol * 100.087 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 43.0374, \"unit\": \"g\"}", "dedupe_signature": "4d0cad0a328d1fb4fd54dfbc3de6c104007c90ca1b2274d044b028183c4ca3ae", "difficulty": "medium", "final_answer": {"answer": 43.0374, "unit": "g"}, "id": "stoich_mass_002275_calcium_carbonate_0.43", "license": "Apache-2.0", "prompt": "A sample contains 0.43 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 0.43 mol * 100.087 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "calcium carbonate", "molar_mass": 100.087, "moles": 0.43}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.09 y, so each step multiplies y by 1 - h*0.09.\n3. Apply that update for 10 steps and round the final state.\nFinal: {\"answer\": 18.2712, \"unit\": \"state_units\"}", "dedupe_signature": "361eee7e96b290ba9b68ed96219c1b8598872d37d1c444b74574d5cd3403624a", "difficulty": "medium", "final_answer": {"answer": 18.2712, "unit": "state_units"}, "id": "euler_decay_002277_20_0.09_0.1_10", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.09 y with y(0)=20, step size h=0.1, for 10 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.09 y, so each step multiplies y by 1 - h*0.09.\nApply that update for 10 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 20.0, "rate": 0.09, "step": 0.1, "steps": 10}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-7.2)=-71.44 and f(-4.5)=-52.\n3. The interval width is 2.7.\nFinal: {\"answer\": -166.644, \"unit\": \"area_units\"}", "dedupe_signature": "27a20010ef6c61af7cf2a3a849dc6e29c24919a34ee0b2b66eaf62825ef9ef89", "difficulty": "medium", "final_answer": {"answer": -166.644, "unit": "area_units"}, "id": "trapz_linear_002278_7.2_-19.6_-7.2_-4.5", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=7.2x+-19.6 from x=-7.2 to x=-4.5. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-7.2)=-71.44 and f(-4.5)=-52.\nThe interval width is 2.7.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -19.6, "slope": 7.2, "x0": -7.2, "x1": -4.5}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.24 and add it to the current value.\nFinal: {\"answer\": [0.654, 0.786, 1.778], \"unit\": \"temperature_units\"}", "dedupe_signature": "8b2501ed5ac46adc74789f4698beb54238ed8dfea3ba1f6bd8354fc8560aea82", "difficulty": "hard", "final_answer": {"answer": [0.654, 0.786, 1.778], "unit": "temperature_units"}, "id": "heat_step_002279_0.24_1.3_0.45_0.45_1.85_2.95", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.3, right=2.95; current interior values are [0.45, 0.45, 1.85]. Use r=0.24. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.24 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [0.45, 0.45, 1.85], "left": 1.3, "r": 0.24, "right": 2.95}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kelvin equals Celsius plus 273.15.\n2. Apply the conversion factor directly to the given value.\n3. Compute 166.0 + 273.15.\nFinal: {\"answer\": 439.15, \"unit\": \"K\"}", "dedupe_signature": "8521fe90d9f0cc8861988d6ee270edd30e86538c40361b05670cc6305f68c0a7", "difficulty": "easy", "final_answer": {"answer": 439.15, "unit": "K"}, "id": "unit_convert_002280_c_to_k_166", "license": "Apache-2.0", "prompt": "Convert 166 degC to K. Return the converted value with unit.", "reasoning_trace": "Kelvin equals Celsius plus 273.15.\nApply the conversion factor directly to the given value.\nCompute 166.0 + 273.15.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 166.0}, "verifier": {"formula": "value + 273.15", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=117 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-82.8533, 162.6087], \"unit\": \"N\"}", "dedupe_signature": "6c0a2a3eb7eaaf15a2b16f990daf99d9d5b241e91cd33e0f36897bbee1d06a3b", "difficulty": "medium", "final_answer": {"answer": [-82.8533, 162.6087], "unit": "N"}, "id": "vector_components_002281_182.5_117", "license": "Apache-2.0", "prompt": "A vector has magnitude 182.5 N at 117 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=117 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 117, "magnitude": 182.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-8.5, 17.0], \"unit\": \"dimensionless\"}", "dedupe_signature": "bd26a9da7e9cb7b86556c58edb23bc490a99c2ec05aba5eb485e1ade4ccb1384", "difficulty": "medium", "final_answer": {"answer": [-8.5, 17.0], "unit": "dimensionless"}, "id": "line_two_point_002282_-8_-5.5_-8.5_17", "license": "Apache-2.0", "prompt": "A line passes through points (-8, 85) and (-5.5, 63.75). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -8.0, "x2": -5.5, "y1": 85.0, "y2": 63.75}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. velocity divided by time is acceleration\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "6120894db1f247c756b59b8ecc735ba4755e3de7ebcedf760810277c37ebefe8", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_002283_inconsistent_c1271127_701796", "license": "Apache-2.0", "prompt": "In student derivation case 701796, check dimensional consistency for x = v / t. The left side has dimensions m and the right side has dimensions m/s^2. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nvelocity divided by time is acceleration\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "x = v / t"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef weighted_sum_002284(values, weights):\n    if len(values) != len(weights):\n        raise ValueError('length mismatch')\n    return sum(value * weight for value, weight in zip(values, weights))\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"weighted_sum_002284\"}", "dedupe_signature": "abeb2a1e77864fc96cea050a74d45d18809ac96b30f26088263eef73ee4ec880", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "weighted_sum_002284"}, "id": "code_002284_weighted_sum_002284", "license": "Apache-2.0", "prompt": "Write a Python function weighted_sum_002284(values, weights) that returns sum(value*weight). Raise ValueError when the two inputs have different lengths. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "weighted_sum_002284"}, "verifier": {"function": "weighted_sum_002284", "tests": ["assert weighted_sum_002284([2, 3], [4, 5]) == 23", "assert weighted_sum_002284([], []) == 0", "try:\n    weighted_sum_002284([1], [1, 2])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: recurrence, objective, tie_breaking_rule.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"recurrence\", \"objective\", \"tie_breaking_rule\"]}", "dedupe_signature": "6507356df80a49c7405255f36ad7c00b2a8a4df160129074d04db656076219fc", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["recurrence", "objective", "tie_breaking_rule"]}, "id": "abstain_002285_recurrence_objective_tie_breaking_rule", "license": "Apache-2.0", "prompt": "Write a dynamic-programming solver for a knapsack scoring problem with 1565 items and budget 36565, but the recurrence, objective, and tie-breaking rule are all absent. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: recurrence, objective, tie_breaking_rule.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["recurrence", "objective", "tie_breaking_rule"]}, "verifier": {"missing": ["recurrence", "objective", "tie_breaking_rule"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 21.1 kg and a = 6.3 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 132.93, \"unit\": \"N\"}", "dedupe_signature": "c4408f4501741e4f12530c7c99237cb80de1ac36eda03be656e58f47da10af6f", "difficulty": "easy", "final_answer": {"answer": 132.93, "unit": "N"}, "id": "force_002286_21.1_6.3", "license": "Apache-2.0", "prompt": "A cart has mass 21.1 kg and measured acceleration 6.3 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 21.1 kg and a = 6.3 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 6.3, "mass": 21.1}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 42.95^2 and multiply by 0.5 * 21.25.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 19599.9641, \"unit\": \"J\"}", "dedupe_signature": "1b9d36bf9a2460d13eceb3830a6de9c2d7d70e50a57aff566be5dea40daba7e2", "difficulty": "easy", "final_answer": {"answer": 19599.9641, "unit": "J"}, "id": "ke_002287_21.25_42.95", "license": "Apache-2.0", "prompt": "A body of mass 21.25 kg moves at 42.95 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 42.95^2 and multiply by 0.5 * 21.25.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 21.25, "velocity": 42.95}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=58 degrees through the sine of 2 theta.\n3. Substitute v=30.7 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 86.3511, \"unit\": \"m\"}", "dedupe_signature": "d62d0a5c4661dccc1da5c2f0182b680f1938cda11ab2acaf509f4006e01eb918", "difficulty": "medium", "final_answer": {"answer": 86.3511, "unit": "m"}, "id": "projectile_range_002288_30.7_58", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 30.7 m/s and angle 58 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=58 degrees through the sine of 2 theta.\nSubstitute v=30.7 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 58, "gravity": 9.81, "speed": 30.7}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 915 * 3.185 * 28.\nFinal: {\"answer\": 81599.7, \"unit\": \"J\"}", "dedupe_signature": "b88c626ed640fa869d06ebec697fe2de0f1a9565cd97585e4745c22fad4f9245", "difficulty": "easy", "final_answer": {"answer": 81599.7, "unit": "J"}, "id": "heat_q_002290_915_3.185_28", "license": "Apache-2.0", "prompt": "A 915 g sample has specific heat 3.185 J/(g*K). How much heat is needed to raise its temperature by 28 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 915 * 3.185 * 28.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 28, "heat_capacity": 3.185, "mass_g": 915}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=117.6 V and R=113 ohm.\nFinal: {\"answer\": 122.3873, \"unit\": \"W\"}", "dedupe_signature": "0852f2b28527320f85fcaf5e0e6b2dfc18dba873a92375383083bec8b78513aa", "difficulty": "easy", "final_answer": {"answer": 122.3873, "unit": "W"}, "id": "ohm_power_002291_117.6_113", "license": "Apache-2.0", "prompt": "A resistor has resistance 113 ohm and voltage 117.6 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=117.6 V and R=113 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 113.0, "voltage": 117.6}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=223 mg, t=67 h, and T_half=118 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 150.4461, \"unit\": \"mg\"}", "dedupe_signature": "b69842ec4da57fecc8988e9f1b8ca04c579498824ebd11df87d1f1fdec97540b", "difficulty": "medium", "final_answer": {"answer": 150.4461, "unit": "mg"}, "id": "half_life_002292_223_118_67", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 223 mg. Its half-life is 118 hours. How many mg remain after 67 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=223 mg, t=67 h, and T_half=118 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 67.0, "half_life": 118.0, "initial_amount": 223.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 7.84 mol * 58.44 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 458.1696, \"unit\": \"g\"}", "dedupe_signature": "fd7e009d4a3aaee08409589ae8b7f5aca57f1af9f97ff8ee1ae2e4932d7863d0", "difficulty": "medium", "final_answer": {"answer": 458.1696, "unit": "g"}, "id": "stoich_mass_002293_sodium_chloride_7.84", "license": "Apache-2.0", "prompt": "A sample contains 7.84 mol of sodium chloride. Using molar mass 58.44 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 7.84 mol * 58.44 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "sodium chloride", "molar_mass": 58.44, "moles": 7.84}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 3605 mL to 3.605 L.\n3. Compute M = 4.77 / 3.605.\nFinal: {\"answer\": 1.3232, \"unit\": \"mol/L\"}", "dedupe_signature": "85482f20121893dd6a7265781fc961043709208da2e973e3e4bf6c8e22cc48e1", "difficulty": "medium", "final_answer": {"answer": 1.3232, "unit": "mol/L"}, "id": "molarity_002294_4.77_3605", "license": "Apache-2.0", "prompt": "A solution contains 4.77 mol of solute in 3605 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 3605 mL to 3.605 L.\nCompute M = 4.77 / 3.605.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 4.77, "volume_ml": 3605}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.11 y, so each step multiplies y by 1 - h*0.11.\n3. Apply that update for 11 steps and round the final state.\nFinal: {\"answer\": 38.3084, \"unit\": \"state_units\"}", "dedupe_signature": "3ea45583a2e5ddef510d99cc969a28d8ee2b8c9c85783b9d7f81bdd846a81313", "difficulty": "medium", "final_answer": {"answer": 38.3084, "unit": "state_units"}, "id": "euler_decay_002295_59_0.11_0.35_11", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.11 y with y(0)=59, step size h=0.35, for 11 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.11 y, so each step multiplies y by 1 - h*0.11.\nApply that update for 11 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 59.0, "rate": 0.11, "step": 0.35, "steps": 11}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(3.1)=-8.87 and f(7.2)=-36.34.\n3. The interval width is 4.1.\nFinal: {\"answer\": -92.6805, \"unit\": \"area_units\"}", "dedupe_signature": "b0c60333b0858e1816cd2cacae7dca71958704085bc53c058251808c117d1039", "difficulty": "medium", "final_answer": {"answer": -92.6805, "unit": "area_units"}, "id": "trapz_linear_002296_-6.7_11.9_3.1_7.2", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-6.7x+11.9 from x=3.1 to x=7.2. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(3.1)=-8.87 and f(7.2)=-36.34.\nThe interval width is 4.1.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 11.9, "slope": -6.7, "x0": 3.1, "x1": 7.199999999999999}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.34 and add it to the current value.\nFinal: {\"answer\": [0.515, -0.483, -0.342], \"unit\": \"temperature_units\"}", "dedupe_signature": "7e1969e2f3ae88b5fb69a0f8bcd5d799782d5777dc1bd4e3bc33454f81e33531", "difficulty": "hard", "final_answer": {"answer": [0.515, -0.483, -0.342], "unit": "temperature_units"}, "id": "heat_step_002297_0.34_2.3_0.6_-1.35_-0.75_1.05", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=2.3, right=1.05; current interior values are [0.6, -1.35, -0.75]. Use r=0.34. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.34 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [0.6, -1.35, -0.75], "left": 2.3, "r": 0.34, "right": 1.05}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kelvin equals Celsius plus 273.15.\n2. Apply the conversion factor directly to the given value.\n3. Compute -70.5 + 273.15.\nFinal: {\"answer\": 202.65, \"unit\": \"K\"}", "dedupe_signature": "e5b729577e5bc4efc11d62566024fb790df0bebf0111379529cf4a3f230f81d5", "difficulty": "easy", "final_answer": {"answer": 202.65, "unit": "K"}, "id": "unit_convert_002298_c_to_k_-70.5", "license": "Apache-2.0", "prompt": "Convert -70.5 degC to K. Return the converted value with unit.", "reasoning_trace": "Kelvin equals Celsius plus 273.15.\nApply the conversion factor directly to the given value.\nCompute -70.5 + 273.15.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": -70.5}, "verifier": {"formula": "value + 273.15", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=96 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-17.404, 165.5879], \"unit\": \"N\"}", "dedupe_signature": "7ad45963bb5937292b94cce12d898600f4547f2d5f1d6fb8b6deca82b8c0a4c0", "difficulty": "medium", "final_answer": {"answer": [-17.404, 165.5879], "unit": "N"}, "id": "vector_components_002299_166.5_96", "license": "Apache-2.0", "prompt": "A vector has magnitude 166.5 N at 96 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=96 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 96, "magnitude": 166.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [9.05, -3.25], \"unit\": \"dimensionless\"}", "dedupe_signature": "319853e2c9da4e4e14f4b44a5f8e48b3ba1eef9347801836f13186ebf0c1ebda", "difficulty": "medium", "final_answer": {"answer": [9.05, -3.25], "unit": "dimensionless"}, "id": "line_two_point_002300_17_25.25_9.05_-3.25", "license": "Apache-2.0", "prompt": "A line passes through points (17, 150.6) and (25.25, 225.263). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 17.0, "x2": 25.25, "y1": 150.60000000000002, "y2": 225.26250000000002}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. coulomb per second is ampere\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "3482ecb123c96d068ac4a828f5b3eb7a0d275518a5c4fc20f72627443757bbc1", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_002301_consistent_8b38953d_256505", "license": "Apache-2.0", "prompt": "In simulation spec case 256505, check dimensional consistency for I = Q / t. The left side has dimensions A and the right side has dimensions A. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\ncoulomb per second is ampere\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "I = Q / t"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef running_total_002302(values):\n    total = 0\n    out = []\n    for value in values:\n        total += value\n        out.append(total)\n    return out\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"running_total_002302\"}", "dedupe_signature": "011177c53daa8fc2aeaf37dccbc1e90a3990b39432f9a51e24d6e76c53cb9673", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "running_total_002302"}, "id": "code_002302_running_total_002302", "license": "Apache-2.0", "prompt": "Write a Python function running_total_002302(values) that returns cumulative sums as a new list. It must not mutate the input list. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "running_total_002302"}, "verifier": {"function": "running_total_002302", "tests": ["assert running_total_002302([1, 2, 3]) == [1, 3, 6]", "xs = [4, -1, 2]; assert running_total_002302(xs) == [4, 3, 5] and xs == [4, -1, 2]", "assert running_total_002302([]) == []"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: volume.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"volume\"]}", "dedupe_signature": "497e71838efae7d926d1ba3d9f898279b43dd1d994a6567ca1a4e2093228caf7", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["volume"]}, "id": "abstain_002303_volume", "license": "Apache-2.0", "prompt": "Compute pressure from the ideal gas law. The prompt gives n=2.84 mol and T=380 K, but does not give volume. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: volume.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["volume"]}, "verifier": {"missing": ["volume"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 1.85 kg and a = 8.5 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 15.725, \"unit\": \"N\"}", "dedupe_signature": "9112997774b0e85844b4c861b044d3a1be15d33a60389fcf550d80f535d89f33", "difficulty": "easy", "final_answer": {"answer": 15.725, "unit": "N"}, "id": "force_002304_1.85_8.5", "license": "Apache-2.0", "prompt": "A cart has mass 1.85 kg and measured acceleration 8.5 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 1.85 kg and a = 8.5 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 8.5, "mass": 1.85}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 36.65^2 and multiply by 0.5 * 27.85.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 18704.3733, \"unit\": \"J\"}", "dedupe_signature": "4c57c00fe76d256c2bd0e9c96c898a5a1c792ced46b09dd102f58d2c6f174e4a", "difficulty": "easy", "final_answer": {"answer": 18704.3733, "unit": "J"}, "id": "ke_002305_27.85_36.65", "license": "Apache-2.0", "prompt": "A body of mass 27.85 kg moves at 36.65 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 36.65^2 and multiply by 0.5 * 27.85.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 27.85, "velocity": 36.65}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=30 degrees through the sine of 2 theta.\n3. Substitute v=27.4 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 66.277, \"unit\": \"m\"}", "dedupe_signature": "c039e5307889e6e155e8fc053c5e962c0b4da16caad8ba04946db4ae7f9233c4", "difficulty": "medium", "final_answer": {"answer": 66.277, "unit": "m"}, "id": "projectile_range_002306_27.4_30", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 27.4 m/s and angle 30 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=30 degrees through the sine of 2 theta.\nSubstitute v=27.4 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 30, "gravity": 9.81, "speed": 27.4}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 2.44 * 8.314 * 544 / 111.9.\nFinal: {\"answer\": 98.6208, \"unit\": \"kPa\"}", "dedupe_signature": "317fb6462197bc2539db3b973967514198f0a6950aaf34d33e1195541a3e350e", "difficulty": "medium", "final_answer": {"answer": 98.6208, "unit": "kPa"}, "id": "ideal_gas_002307_2.44_544_111.9", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=2.44 mol, T=544 K, and V=111.9 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 2.44 * 8.314 * 544 / 111.9.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 2.44, "temp_k": 544, "volume_l": 111.9}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=142.7 V and R=78.7 ohm.\nFinal: {\"answer\": 258.7457, \"unit\": \"W\"}", "dedupe_signature": "0b81ea71abc930cd67b7c7579402f3bf0270dc48ff81b249525b6ad87b455969", "difficulty": "easy", "final_answer": {"answer": 258.7457, "unit": "W"}, "id": "ohm_power_002309_142.7_78.7", "license": "Apache-2.0", "prompt": "A resistor has resistance 78.7 ohm and voltage 142.7 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=142.7 V and R=78.7 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 78.7, "voltage": 142.7}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=919 mg, t=24.5 h, and T_half=71 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 723.5007, \"unit\": \"mg\"}", "dedupe_signature": "a463fcbbff5d43958d409d7ed40e8cfd747a79e1afcf30596a0e89323d6c9791", "difficulty": "medium", "final_answer": {"answer": 723.5007, "unit": "mg"}, "id": "half_life_002310_919_71_24.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 919 mg. Its half-life is 71 hours. How many mg remain after 24.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=919 mg, t=24.5 h, and T_half=71 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 24.5, "half_life": 71.0, "initial_amount": 919.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 6.28 mol * 58.44 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 367.0032, \"unit\": \"g\"}", "dedupe_signature": "67deca5115537a3c519e7ff45076c144aa73ee11d160498400d0a08cc6fd91f4", "difficulty": "medium", "final_answer": {"answer": 367.0032, "unit": "g"}, "id": "stoich_mass_002311_sodium_chloride_6.28", "license": "Apache-2.0", "prompt": "A sample contains 6.28 mol of sodium chloride. Using molar mass 58.44 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 6.28 mol * 58.44 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "sodium chloride", "molar_mass": 58.44, "moles": 6.28}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-7.6)=39.88 and f(-3.9)=23.97.\n3. The interval width is 3.7.\nFinal: {\"answer\": 118.1225, \"unit\": \"area_units\"}", "dedupe_signature": "426a80ea49d3cda85e7e3b72d351280faaf3fb990e65fbeb6283e8a31384d0eb", "difficulty": "medium", "final_answer": {"answer": 118.1225, "unit": "area_units"}, "id": "trapz_linear_002314_-4.3_7.2_-7.6_-3.9", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-4.3x+7.2 from x=-7.6 to x=-3.9. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-7.6)=39.88 and f(-3.9)=23.97.\nThe interval width is 3.7.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 7.2, "slope": -4.3, "x0": -7.6, "x1": -3.8999999999999995}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.28 and add it to the current value.\nFinal: {\"answer\": [0.926, 0.858, 0.02], \"unit\": \"temperature_units\"}", "dedupe_signature": "2aa044aff9b869272b4fbde7fb07132be2d629ead9026bd0da4a3bfeff7ae8db", "difficulty": "hard", "final_answer": {"answer": [0.926, 0.858, 0.02], "unit": "temperature_units"}, "id": "heat_step_002315_0.28_-0.85_1.85_1.25_-0.75_0.0", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-0.85, right=0; current interior values are [1.85, 1.25, -0.75]. Use r=0.28. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.28 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [1.85, 1.25, -0.75], "left": -0.85, "r": 0.28, "right": 0.0}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=247 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-8.4007, -19.7909], \"unit\": \"N\"}", "dedupe_signature": "8b2bbef5bc71937cc7ad753a7eee00c4c5efe7c8e0b24c1e72f45f7fc2a0d23c", "difficulty": "medium", "final_answer": {"answer": [-8.4007, -19.7909], "unit": "N"}, "id": "vector_components_002317_21.5_247", "license": "Apache-2.0", "prompt": "A vector has magnitude 21.5 N at 247 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=247 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 247, "magnitude": 21.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-7.3, 11.25], \"unit\": \"dimensionless\"}", "dedupe_signature": "ba3b2811b6363461dbf78c1d1836bccebb75b6fdcd64bc01eeae3ce8a70911a3", "difficulty": "medium", "final_answer": {"answer": [-7.3, 11.25], "unit": "dimensionless"}, "id": "line_two_point_002318_4_14.75_-7.3_11.25", "license": "Apache-2.0", "prompt": "A line passes through points (4, -17.95) and (14.75, -96.425). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 4.0, "x2": 14.75, "y1": -17.95, "y2": -96.425}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. grams cancel with J/(g*K), and kelvin cancels, leaving joules\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "361d62e584af216683bc3ebb684ede26871e8241abbe7d7d12c697fb35c21081", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_002319_consistent_4153435f_226755", "license": "Apache-2.0", "prompt": "In student derivation case 226755, check dimensional consistency for Q = m * c * DeltaT. The left side has dimensions J and the right side has dimensions J. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\ngrams cancel with J/(g*K), and kelvin cancels, leaving joules\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "Q = m * c * DeltaT"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef finite_differences_002320(values):\n    return [values[i + 1] - values[i] for i in range(len(values) - 1)]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"finite_differences_002320\"}", "dedupe_signature": "968dfbce8d236571950f1c35d1fbe64d8b2d37ae0b9e6e4d2129cd78eba01ce8", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "finite_differences_002320"}, "id": "code_002320_finite_differences_002320", "license": "Apache-2.0", "prompt": "Write a Python function finite_differences_002320(values) that returns the list of successive differences values[i+1] - values[i]. It must return [] for fewer than two values. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "finite_differences_002320"}, "verifier": {"function": "finite_differences_002320", "tests": ["assert finite_differences_002320([1, 4, 9, 16]) == [3, 5, 7]", "assert finite_differences_002320([5]) == []", "assert finite_differences_002320([]) == []"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: recurrence, objective, tie_breaking_rule.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"recurrence\", \"objective\", \"tie_breaking_rule\"]}", "dedupe_signature": "7e55a8fa104ad75f3ffc660e03c835953a578bf94697ba41152bfcb0c1dd068c", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["recurrence", "objective", "tie_breaking_rule"]}, "id": "abstain_002321_recurrence_objective_tie_breaking_rule", "license": "Apache-2.0", "prompt": "Write a dynamic-programming solver for a segmentation scoring problem with 3183 items and budget 51285, but the recurrence, objective, and tie-breaking rule are all absent. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: recurrence, objective, tie_breaking_rule.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["recurrence", "objective", "tie_breaking_rule"]}, "verifier": {"missing": ["recurrence", "objective", "tie_breaking_rule"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 9.6 kg and a = 11.45 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 109.92, \"unit\": \"N\"}", "dedupe_signature": "d9c3270fdec81f1023a27c610f95d8c427cefbfefe91bf5a11e5b81d3564d6fc", "difficulty": "easy", "final_answer": {"answer": 109.92, "unit": "N"}, "id": "force_002322_9.6_11.45", "license": "Apache-2.0", "prompt": "A cart has mass 9.6 kg and measured acceleration 11.45 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 9.6 kg and a = 11.45 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 11.45, "mass": 9.6}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 34.15^2 and multiply by 0.5 * 10.35.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 6035.2014, \"unit\": \"J\"}", "dedupe_signature": "99bdfb3fd74e457f91dffdf9237b2b562d4e9190c95ca1656c287b3709cf0892", "difficulty": "easy", "final_answer": {"answer": 6035.2014, "unit": "J"}, "id": "ke_002323_10.35_34.15", "license": "Apache-2.0", "prompt": "A body of mass 10.35 kg moves at 34.15 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 34.15^2 and multiply by 0.5 * 10.35.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 10.35, "velocity": 34.15}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=8 degrees through the sine of 2 theta.\n3. Substitute v=60.2 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 101.8268, \"unit\": \"m\"}", "dedupe_signature": "adce0bf1e434295ef4165d01c63ec38d14a485b7c5dbfd2759d767764ec5ab3c", "difficulty": "medium", "final_answer": {"answer": 101.8268, "unit": "m"}, "id": "projectile_range_002324_60.2_8", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 60.2 m/s and angle 8 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=8 degrees through the sine of 2 theta.\nSubstitute v=60.2 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 8, "gravity": 9.81, "speed": 60.2}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 0.38 * 8.314 * 256 / 2.9.\nFinal: {\"answer\": 278.8917, \"unit\": \"kPa\"}", "dedupe_signature": "01c054a3eaf5f30fdb880fbe146bbcc5f4a10d0ec70954ca13d34708b77d4d5f", "difficulty": "medium", "final_answer": {"answer": 278.8917, "unit": "kPa"}, "id": "ideal_gas_002325_0.38_256_2.9", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=0.38 mol, T=256 K, and V=2.9 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 0.38 * 8.314 * 256 / 2.9.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 0.38, "temp_k": 256, "volume_l": 2.9}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1355 * 4.335 * 115.\nFinal: {\"answer\": 675501.375, \"unit\": \"J\"}", "dedupe_signature": "220c550c9883b03861ace38c85ee45cf42cfd6eccac28c857b20201a8cdda04f", "difficulty": "easy", "final_answer": {"answer": 675501.375, "unit": "J"}, "id": "heat_q_002326_1355_4.335_115", "license": "Apache-2.0", "prompt": "A 1355 g sample has specific heat 4.335 J/(g*K). How much heat is needed to raise its temperature by 115 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1355 * 4.335 * 115.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 115, "heat_capacity": 4.335, "mass_g": 1355}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=43.9 V and R=16.2 ohm.\nFinal: {\"answer\": 118.9636, \"unit\": \"W\"}", "dedupe_signature": "f04ecf4aa4cfbc6e8b89763481b160d585d4b59a549ed38d4c68574de75e5dbc", "difficulty": "easy", "final_answer": {"answer": 118.9636, "unit": "W"}, "id": "ohm_power_002327_43.9_16.2", "license": "Apache-2.0", "prompt": "A resistor has resistance 16.2 ohm and voltage 43.9 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=43.9 V and R=16.2 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 16.2, "voltage": 43.9}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 2.66 mol * 58.44 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 155.4504, \"unit\": \"g\"}", "dedupe_signature": "cbab971b04eefdcc6a7ea8c314d6faeba79640780e2e5c0f3734545cd0d86384", "difficulty": "medium", "final_answer": {"answer": 155.4504, "unit": "g"}, "id": "stoich_mass_002329_sodium_chloride_2.66", "license": "Apache-2.0", "prompt": "A sample contains 2.66 mol of sodium chloride. Using molar mass 58.44 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 2.66 mol * 58.44 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "sodium chloride", "molar_mass": 58.44, "moles": 2.66}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 3090 mL to 3.09 L.\n3. Compute M = 3.155 / 3.09.\nFinal: {\"answer\": 1.021, \"unit\": \"mol/L\"}", "dedupe_signature": "3ac060b30f8e5b21323247a24daac3cbfed3da26cc6dac3f094d10d47f8adfb3", "difficulty": "medium", "final_answer": {"answer": 1.021, "unit": "mol/L"}, "id": "molarity_002330_3.155_3090", "license": "Apache-2.0", "prompt": "A solution contains 3.155 mol of solute in 3090 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 3090 mL to 3.09 L.\nCompute M = 3.155 / 3.09.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 3.155, "volume_ml": 3090}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.24 y, so each step multiplies y by 1 - h*0.24.\n3. Apply that update for 11 steps and round the final state.\nFinal: {\"answer\": 0.1079, \"unit\": \"state_units\"}", "dedupe_signature": "14bb5f5093d221267cf381f2d0ada7d780f90d9b44420eff32b0b4dbb6085842", "difficulty": "medium", "final_answer": {"answer": 0.1079, "unit": "state_units"}, "id": "euler_decay_002331_18_0.24_1.55_11", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.24 y with y(0)=18, step size h=1.55, for 11 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.24 y, so each step multiplies y by 1 - h*0.24.\nApply that update for 11 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 18.0, "rate": 0.24, "step": 1.55, "steps": 11}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.32 and add it to the current value.\nFinal: {\"answer\": [1.8, 0.958, 0.754], \"unit\": \"temperature_units\"}", "dedupe_signature": "bee18fdd3c894585e24166f6f46573557c61064b17feed19fb4e30573ed7ca7a", "difficulty": "hard", "final_answer": {"answer": [1.8, 0.958, 0.754], "unit": "temperature_units"}, "id": "heat_step_002333_0.32_2.3_3.0_-0.05_0.05_2.35", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=2.3, right=2.35; current interior values are [3.0, -0.05, 0.05]. Use r=0.32. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.32 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [3.0, -0.05, 0.05], "left": 2.3, "r": 0.32, "right": 2.35}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=182 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-254.345, -8.8819], \"unit\": \"N\"}", "dedupe_signature": "9c5ca1e1d1ad7157ec2402c78f01d5318095909186b6288cf2a5c5fdee9cb086", "difficulty": "medium", "final_answer": {"answer": [-254.345, -8.8819], "unit": "N"}, "id": "vector_components_002335_254.5_182", "license": "Apache-2.0", "prompt": "A vector has magnitude 254.5 N at 182 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=182 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 182, "magnitude": 254.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. mass times acceleration has newton dimensions\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "454f3543587196398b8112ccf5bec2135b06d082d0affb93aec1c3d24598126e", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_002337_consistent_03f5e041_173257", "license": "Apache-2.0", "prompt": "In student derivation case 173257, check dimensional consistency for F = m * a. The left side has dimensions kg*m/s^2 and the right side has dimensions kg*m/s^2. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nmass times acceleration has newton dimensions\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "F = m * a"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef normalize_002338(values):\n    total = sum(values)\n    if total == 0:\n        raise ValueError('cannot normalize zero-sum values')\n    return [v / total for v in values]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"normalize_002338\"}", "dedupe_signature": "4fc88ef9516f573368ddf11df160eda467739109b21cea3339839e2cb563dcd8", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "normalize_002338"}, "id": "code_002338_normalize_002338", "license": "Apache-2.0", "prompt": "Write a Python function normalize_002338(values) that returns a new list whose values sum to 1. Raise ValueError if the sum is zero. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "normalize_002338"}, "verifier": {"function": "normalize_002338", "tests": ["out = normalize_002338([2, 3, 5]); assert len(out) == 3", "assert abs(sum(normalize_002338([2, 3, 5])) - 1.0) < 1e-12", "assert normalize_002338([1, 1]) == [0.5, 0.5]", "try:\n    normalize_002338([1, -1])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: rate_constant, number_of_steps.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"rate_constant\", \"number_of_steps\"]}", "dedupe_signature": "a2037170e0ba2465ef687592da201514eaae3b7bcfccaf99451c3913dbf75b5b", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["rate_constant", "number_of_steps"]}, "id": "abstain_002339_rate_constant_number_of_steps", "license": "Apache-2.0", "prompt": "Use explicit Euler for dy/dt = -k y. The prompt gives y(0)=61.5 and h=1.9, but omits both k and the number of steps. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: rate_constant, number_of_steps.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["rate_constant", "number_of_steps"]}, "verifier": {"missing": ["rate_constant", "number_of_steps"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 9.15 kg and a = 10.45 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 95.6175, \"unit\": \"N\"}", "dedupe_signature": "2a4a229e47cee4c39a4a866413b90665ae44dcbb7d9ce2a753891b2cf48e18ed", "difficulty": "easy", "final_answer": {"answer": 95.6175, "unit": "N"}, "id": "force_002340_9.15_10.45", "license": "Apache-2.0", "prompt": "A cart has mass 9.15 kg and measured acceleration 10.45 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 9.15 kg and a = 10.45 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 10.45, "mass": 9.15}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 11.85^2 and multiply by 0.5 * 23.95.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 1681.5594, \"unit\": \"J\"}", "dedupe_signature": "979006a1cd119a99b3c7c662910e77dd4eeca5a74851ac8821b4a43138eec8ab", "difficulty": "easy", "final_answer": {"answer": 1681.5594, "unit": "J"}, "id": "ke_002341_23.95_11.85", "license": "Apache-2.0", "prompt": "A body of mass 23.95 kg moves at 11.85 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 11.85^2 and multiply by 0.5 * 23.95.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 23.95, "velocity": 11.85}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 2.37 * 8.314 * 530 / 23.0.\nFinal: {\"answer\": 454.0528, \"unit\": \"kPa\"}", "dedupe_signature": "adba2345c64715856db884e37befd6bd0423fe211e58ffabd1758179c3ef74f4", "difficulty": "medium", "final_answer": {"answer": 454.0528, "unit": "kPa"}, "id": "ideal_gas_002343_2.37_530_23.0", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=2.37 mol, T=530 K, and V=23.0 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 2.37 * 8.314 * 530 / 23.0.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 2.37, "temp_k": 530, "volume_l": 23.0}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=214.7 V and R=191.8 ohm.\nFinal: {\"answer\": 240.3342, \"unit\": \"W\"}", "dedupe_signature": "708a56f3ad05025a9f5c55dd5edbf272bc2af736ff00ce254e2fbcae14a03c7c", "difficulty": "easy", "final_answer": {"answer": 240.3342, "unit": "W"}, "id": "ohm_power_002345_214.7_191.8", "license": "Apache-2.0", "prompt": "A resistor has resistance 191.8 ohm and voltage 214.7 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=214.7 V and R=191.8 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 191.8, "voltage": 214.7}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=856.5 mg, t=34.5 h, and T_half=96.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 668.5059, \"unit\": \"mg\"}", "dedupe_signature": "c78ef565a3517f2941b228c2c6efce095bc122628848683c0540c16ef24b1491", "difficulty": "medium", "final_answer": {"answer": 668.5059, "unit": "mg"}, "id": "half_life_002346_856.5_96.5_34.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 856.5 mg. Its half-life is 96.5 hours. How many mg remain after 34.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=856.5 mg, t=34.5 h, and T_half=96.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 34.5, "half_life": 96.5, "initial_amount": 856.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 5.42 mol * 18.015 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 97.6413, \"unit\": \"g\"}", "dedupe_signature": "60b923d8f653682baa7cc0d6afe72e411a3c2af0e5bd5b701bed6443493c3456", "difficulty": "medium", "final_answer": {"answer": 97.6413, "unit": "g"}, "id": "stoich_mass_002347_water_5.42", "license": "Apache-2.0", "prompt": "A sample contains 5.42 mol of water. Using molar mass 18.015 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 5.42 mol * 18.015 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "water", "molar_mass": 18.015, "moles": 5.42}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 2925 mL to 2.925 L.\n3. Compute M = 3.52 / 2.925.\nFinal: {\"answer\": 1.2034, \"unit\": \"mol/L\"}", "dedupe_signature": "d46a7f2575f4d05f1ec11fc91a8b3299ceb4a08cfae12b3c37f5d16fec08d120", "difficulty": "medium", "final_answer": {"answer": 1.2034, "unit": "mol/L"}, "id": "molarity_002348_3.52_2925", "license": "Apache-2.0", "prompt": "A solution contains 3.52 mol of solute in 2925 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 2925 mL to 2.925 L.\nCompute M = 3.52 / 2.925.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 3.52, "volume_ml": 2925}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(8.4)=73.06 and f(11.6)=95.14.\n3. The interval width is 3.2.\nFinal: {\"answer\": 269.12, \"unit\": \"area_units\"}", "dedupe_signature": "abcc71940b813f962f369f90fbab8c2c0751285a3128f3e3b8f0648473a0ba8e", "difficulty": "medium", "final_answer": {"answer": 269.12, "unit": "area_units"}, "id": "trapz_linear_002350_6.9_15.1_8.4_11.6", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=6.9x+15.1 from x=8.4 to x=11.6. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(8.4)=73.06 and f(11.6)=95.14.\nThe interval width is 3.2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 15.1, "slope": 6.9, "x0": 8.4, "x1": 11.600000000000001}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.06 and add it to the current value.\nFinal: {\"answer\": [1.584, 2.691, 1.391], \"unit\": \"temperature_units\"}", "dedupe_signature": "7a6453d770ee1c0cb481fca001aa07efc557344ad53d38172209a48080f11ffb", "difficulty": "hard", "final_answer": {"answer": [1.584, 2.691, 1.391], "unit": "temperature_units"}, "id": "heat_step_002351_0.06_-0.65_1.65_2.85_1.4_-0.2", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-0.65, right=-0.2; current interior values are [1.65, 2.85, 1.4]. Use r=0.06. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.06 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [1.65, 2.85, 1.4], "left": -0.65, "r": 0.06, "right": -0.2}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 45789.0 / 1000.\nFinal: {\"answer\": 45.789, \"unit\": \"kg\"}", "dedupe_signature": "cfa9782382a5969b578728a24006331c50bd2831c000b2830d88a38b9471436c", "difficulty": "easy", "final_answer": {"answer": 45.789, "unit": "kg"}, "id": "unit_convert_002352_g_to_kg_45789", "license": "Apache-2.0", "prompt": "Convert 45789 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 45789.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 45789.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=5 degrees and keep the unit as newtons.\nFinal: {\"answer\": [405.4512, 35.4724], \"unit\": \"N\"}", "dedupe_signature": "550db96f015ba56fa6123843d33c753e777e62315153fd84aace3cadd5f7f052", "difficulty": "medium", "final_answer": {"answer": [405.4512, 35.4724], "unit": "N"}, "id": "vector_components_002353_407_5", "license": "Apache-2.0", "prompt": "A vector has magnitude 407 N at 5 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=5 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 5, "magnitude": 407.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-6.7, 29.5], \"unit\": \"dimensionless\"}", "dedupe_signature": "35d8a3ffa25c9edb5c5278bcba6c249b787cdd56e4a87595d24532cc2903189c", "difficulty": "medium", "final_answer": {"answer": [-6.7, 29.5], "unit": "dimensionless"}, "id": "line_two_point_002354_-17.75_-7.75_-6.7_29.5", "license": "Apache-2.0", "prompt": "A line passes through points (-17.75, 148.425) and (-7.75, 81.425). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -17.75, "x2": -7.75, "y1": 148.425, "y2": 81.42500000000001}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. lever arm times force has torque dimensions\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "c1750dcba5ca6900023c0613b9da4d2cb955d922d60be250701c2faf1ec272f4", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_002355_consistent_5ca82cb9_431345", "license": "Apache-2.0", "prompt": "In simulation spec case 431345, check dimensional consistency for tau = r * F. The left side has dimensions N*m and the right side has dimensions N*m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nlever arm times force has torque dimensions\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "tau = r * F"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\nimport math\n\ndef unit_vector_002356(x, y):\n    norm = math.hypot(x, y)\n    if norm == 0:\n        raise ValueError('zero vector has no direction')\n    return (x / norm, y / norm)\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"unit_vector_002356\"}", "dedupe_signature": "da407dc332c53a2649926c40b5f6443db3d7a9e4e5246cd1609e428d4641681f", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "unit_vector_002356"}, "id": "code_002356_unit_vector_002356", "license": "Apache-2.0", "prompt": "Write a Python function unit_vector_002356(x, y) that returns the 2D unit vector as a tuple. Raise ValueError for the zero vector. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "unit_vector_002356"}, "verifier": {"function": "unit_vector_002356", "tests": ["ux, uy = unit_vector_002356(3, 4); assert abs(ux - 0.6) < 1e-12 and abs(uy - 0.8) < 1e-12", "assert unit_vector_002356(0, 5) == (0, 1)", "try:\n    unit_vector_002356(0, 0)\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: volume.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"volume\"]}", "dedupe_signature": "7a2d02c29fd185e0efd7e23899d8917d4ccef69c7e2b9775e3546af54b5c03e7", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["volume"]}, "id": "abstain_002357_volume", "license": "Apache-2.0", "prompt": "Compute pressure from the ideal gas law. The prompt gives n=2.92 mol and T=597 K, but does not give volume. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: volume.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["volume"]}, "verifier": {"missing": ["volume"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=54 degrees through the sine of 2 theta.\n3. Substitute v=74.5 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 538.0837, \"unit\": \"m\"}", "dedupe_signature": "f0a443b2860088fc553cdf4f687a93f978ebb871177e292a90637c2022bdec03", "difficulty": "medium", "final_answer": {"answer": 538.0837, "unit": "m"}, "id": "projectile_range_002360_74.5_54", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 74.5 m/s and angle 54 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=54 degrees through the sine of 2 theta.\nSubstitute v=74.5 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 54, "gravity": 9.81, "speed": 74.5}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 1.83 * 8.314 * 581 / 73.8.\nFinal: {\"answer\": 119.7791, \"unit\": \"kPa\"}", "dedupe_signature": "9ee6070f6ef258c5f55fa500c9d128d6fdcc8ffe68a9dbf1e24f5d4706e0f73b", "difficulty": "medium", "final_answer": {"answer": 119.7791, "unit": "kPa"}, "id": "ideal_gas_002361_1.83_581_73.8", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=1.83 mol, T=581 K, and V=73.8 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 1.83 * 8.314 * 581 / 73.8.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 1.83, "temp_k": 581, "volume_l": 73.8}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 670 * 1.49 * 77.\nFinal: {\"answer\": 76869.1, \"unit\": \"J\"}", "dedupe_signature": "b57307b897297cd4f317f4977e3285c25d87d60b5037acf91e61404267e5d0d2", "difficulty": "easy", "final_answer": {"answer": 76869.1, "unit": "J"}, "id": "heat_q_002362_670_1.49_77", "license": "Apache-2.0", "prompt": "A 670 g sample has specific heat 1.49 J/(g*K). How much heat is needed to raise its temperature by 77 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 670 * 1.49 * 77.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 77, "heat_capacity": 1.49, "mass_g": 670}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=51 V and R=48.6 ohm.\nFinal: {\"answer\": 53.5185, \"unit\": \"W\"}", "dedupe_signature": "f3cc7f4a608b5cb1175cc896795a8d79e7e900a594c911383fbc4e80f61b65b8", "difficulty": "easy", "final_answer": {"answer": 53.5185, "unit": "W"}, "id": "ohm_power_002363_51_48.6", "license": "Apache-2.0", "prompt": "A resistor has resistance 48.6 ohm and voltage 51 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=51 V and R=48.6 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 48.6, "voltage": 51.0}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=815.5 mg, t=258.5 h, and T_half=79.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 85.6255, \"unit\": \"mg\"}", "dedupe_signature": "cb26e25a941dfc9a123c1aca12d23ae9765e35494ce437342870eb8f604931ba", "difficulty": "medium", "final_answer": {"answer": 85.6255, "unit": "mg"}, "id": "half_life_002364_815.5_79.5_258.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 815.5 mg. Its half-life is 79.5 hours. How many mg remain after 258.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=815.5 mg, t=258.5 h, and T_half=79.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 258.5, "half_life": 79.5, "initial_amount": 815.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 5.92 mol * 180.156 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 1066.5235, \"unit\": \"g\"}", "dedupe_signature": "aa6597053be9056799d862f13d62d39606224b942ab950f1cd49ae832c2d12f5", "difficulty": "medium", "final_answer": {"answer": 1066.5235, "unit": "g"}, "id": "stoich_mass_002365_glucose_5.92", "license": "Apache-2.0", "prompt": "A sample contains 5.92 mol of glucose. Using molar mass 180.156 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 5.92 mol * 180.156 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "glucose", "molar_mass": 180.156, "moles": 5.92}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-6)=47.5 and f(2.6)=-0.66.\n3. The interval width is 8.6.\nFinal: {\"answer\": 201.412, \"unit\": \"area_units\"}", "dedupe_signature": "27085130c649b5568521ac5f4afe6b28149d269844e5940ad3a336a6f3dd6687", "difficulty": "medium", "final_answer": {"answer": 201.412, "unit": "area_units"}, "id": "trapz_linear_002368_-5.6_13.9_-6_2.6", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-5.6x+13.9 from x=-6 to x=2.6. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-6)=47.5 and f(2.6)=-0.66.\nThe interval width is 8.6.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 13.9, "slope": -5.6, "x0": -6.0, "x1": 2.5999999999999996}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.4 and add it to the current value.\nFinal: {\"answer\": [0.71, 0.36, -1.45], \"unit\": \"temperature_units\"}", "dedupe_signature": "caff521e5361e85c972bba4969e784436dc146c7a8f871f1dc9ef0054f44e64a", "difficulty": "hard", "final_answer": {"answer": [0.71, 0.36, -1.45], "unit": "temperature_units"}, "id": "heat_step_002369_0.4_1.95_2.85_-1.6_-1.15_-1.45", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.95, right=-1.45; current interior values are [2.85, -1.6, -1.15]. Use r=0.4. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.4 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [2.85, -1.6, -1.15], "left": 1.95, "r": 0.4, "right": -1.45}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 13863.0 / 1000.\nFinal: {\"answer\": 13.863, \"unit\": \"kg\"}", "dedupe_signature": "02cfa228fc437375294b411ff32cde7a2182edae8af278b5d5f9d060b47fbbcc", "difficulty": "easy", "final_answer": {"answer": 13.863, "unit": "kg"}, "id": "unit_convert_002370_g_to_kg_13863", "license": "Apache-2.0", "prompt": "Convert 13863 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 13863.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 13863.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=47 degrees and keep the unit as newtons.\nFinal: {\"answer\": [171.8636, 184.3011], \"unit\": \"N\"}", "dedupe_signature": "5545e5254208ebc5f641ff8f6a68828308e859f8b470baca5dff70f05fa30fc8", "difficulty": "medium", "final_answer": {"answer": [171.8636, 184.3011], "unit": "N"}, "id": "vector_components_002371_252_47", "license": "Apache-2.0", "prompt": "A vector has magnitude 252 N at 47 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=47 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 47, "magnitude": 252.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-2.0, 13.0], \"unit\": \"dimensionless\"}", "dedupe_signature": "0fd27be950ca0a64e55ac53b0523873344de4198a93a9a65d0909b4c82699f56", "difficulty": "medium", "final_answer": {"answer": [-2.0, 13.0], "unit": "dimensionless"}, "id": "line_two_point_002372_9_23.25_-2_13", "license": "Apache-2.0", "prompt": "A line passes through points (9, -5) and (23.25, -33.5). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 9.0, "x2": 23.25, "y1": -5.0, "y2": -33.5}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. mass times acceleration has newton dimensions\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "a8bd989442ef1e4024afb30e5792e83adb44e5c00afd80b33824a9b0e7730839", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_002373_consistent_03f5e041_152041", "license": "Apache-2.0", "prompt": "In quality-control check case 152041, check dimensional consistency for F = m * a. The left side has dimensions kg*m/s^2 and the right side has dimensions kg*m/s^2. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nmass times acceleration has newton dimensions\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "F = m * a"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: recurrence, objective, tie_breaking_rule.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"recurrence\", \"objective\", \"tie_breaking_rule\"]}", "dedupe_signature": "46e931085b0608b84523c46eb13d72240ab478a5571bed6f42b65e0f9f43685a", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["recurrence", "objective", "tie_breaking_rule"]}, "id": "abstain_002375_recurrence_objective_tie_breaking_rule", "license": "Apache-2.0", "prompt": "Write a dynamic-programming solver for a segmentation scoring problem with 459 items and budget 53210, but the recurrence, objective, and tie-breaking rule are all absent. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: recurrence, objective, tie_breaking_rule.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["recurrence", "objective", "tie_breaking_rule"]}, "verifier": {"missing": ["recurrence", "objective", "tie_breaking_rule"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 24.2 kg and a = 5.85 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 141.57, \"unit\": \"N\"}", "dedupe_signature": "762dfd64bcf05a1c1f1668f262651b506ccc46cf2ad17f31bbd12c237c69ecb1", "difficulty": "easy", "final_answer": {"answer": 141.57, "unit": "N"}, "id": "force_002376_24.2_5.85", "license": "Apache-2.0", "prompt": "A cart has mass 24.2 kg and measured acceleration 5.85 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 24.2 kg and a = 5.85 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 5.85, "mass": 24.2}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 2.2^2 and multiply by 0.5 * 11.55.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 27.951, \"unit\": \"J\"}", "dedupe_signature": "23d77dff343b7b2122f34e90f5d8190f356b09f14e49e847616d82b974c57c9e", "difficulty": "easy", "final_answer": {"answer": 27.951, "unit": "J"}, "id": "ke_002377_11.55_2.2", "license": "Apache-2.0", "prompt": "A body of mass 11.55 kg moves at 2.2 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 2.2^2 and multiply by 0.5 * 11.55.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 11.55, "velocity": 2.2}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=43 degrees through the sine of 2 theta.\n3. Substitute v=58.1 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 343.2607, \"unit\": \"m\"}", "dedupe_signature": "e825cc609cd52f736b15d2b4e938df69ca7cfc9b15f180bf0f25cc210e2c8a0a", "difficulty": "medium", "final_answer": {"answer": 343.2607, "unit": "m"}, "id": "projectile_range_002378_58.1_43", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 58.1 m/s and angle 43 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=43 degrees through the sine of 2 theta.\nSubstitute v=58.1 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 43, "gravity": 9.81, "speed": 58.1}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 4.86 * 8.314 * 526 / 90.3.\nFinal: {\"answer\": 235.3663, \"unit\": \"kPa\"}", "dedupe_signature": "b8d8d6191651ba94d0f1c4a930e1e1b53419fd0dc686544a1911da9f3b80f9d8", "difficulty": "medium", "final_answer": {"answer": 235.3663, "unit": "kPa"}, "id": "ideal_gas_002379_4.86_526_90.3", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=4.86 mol, T=526 K, and V=90.3 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 4.86 * 8.314 * 526 / 90.3.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 4.86, "temp_k": 526, "volume_l": 90.3}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 780 * 3.965 * 106.\nFinal: {\"answer\": 327826.2, \"unit\": \"J\"}", "dedupe_signature": "0a4dc71ff4e68c4342908389e9c6df25f2f5ae243a9abc365f84489541568671", "difficulty": "easy", "final_answer": {"answer": 327826.2, "unit": "J"}, "id": "heat_q_002380_780_3.965_106", "license": "Apache-2.0", "prompt": "A 780 g sample has specific heat 3.965 J/(g*K). How much heat is needed to raise its temperature by 106 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 780 * 3.965 * 106.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 106, "heat_capacity": 3.965, "mass_g": 780}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=188.3 V and R=93 ohm.\nFinal: {\"answer\": 381.2569, \"unit\": \"W\"}", "dedupe_signature": "29613edd8f0dffe6a133427f56378b7eb081c39846c5a3ecf6f6de726d8e106c", "difficulty": "easy", "final_answer": {"answer": 381.2569, "unit": "W"}, "id": "ohm_power_002381_188.3_93", "license": "Apache-2.0", "prompt": "A resistor has resistance 93 ohm and voltage 188.3 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=188.3 V and R=93 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 93.0, "voltage": 188.3}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=745 mg, t=170.5 h, and T_half=96 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 217.5276, \"unit\": \"mg\"}", "dedupe_signature": "d930b4b1d0653c0576b52f810e78f26b64dcb603ee6d9114ae5806db0a2840a6", "difficulty": "medium", "final_answer": {"answer": 217.5276, "unit": "mg"}, "id": "half_life_002382_745_96_170.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 745 mg. Its half-life is 96 hours. How many mg remain after 170.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=745 mg, t=170.5 h, and T_half=96 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 170.5, "half_life": 96.0, "initial_amount": 745.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 4920 mL to 4.92 L.\n3. Compute M = 0.8 / 4.92.\nFinal: {\"answer\": 0.1626, \"unit\": \"mol/L\"}", "dedupe_signature": "51e079a54531666a3b6d587de90fd723d4337e1a00048feda7fc0c5309a17d04", "difficulty": "medium", "final_answer": {"answer": 0.1626, "unit": "mol/L"}, "id": "molarity_002384_0.8_4920", "license": "Apache-2.0", "prompt": "A solution contains 0.8 mol of solute in 4920 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 4920 mL to 4.92 L.\nCompute M = 0.8 / 4.92.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 0.8, "volume_ml": 4920}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.93 y, so each step multiplies y by 1 - h*0.93.\n3. Apply that update for 9 steps and round the final state.\nFinal: {\"answer\": -0.0059, \"unit\": \"state_units\"}", "dedupe_signature": "e65609982f4e0c319ecfb2c1d76f4cb5bfb299365ba273a7d575d1e35da80f96", "difficulty": "medium", "final_answer": {"answer": -0.0059, "unit": "state_units"}, "id": "euler_decay_002385_78_0.93_1.45_9", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.93 y with y(0)=78, step size h=1.45, for 9 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.93 y, so each step multiplies y by 1 - h*0.93.\nApply that update for 9 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 78.0, "rate": 0.93, "step": 1.45, "steps": 9}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-2.6)=7.02 and f(0)=2.6.\n3. The interval width is 2.6.\nFinal: {\"answer\": 12.506, \"unit\": \"area_units\"}", "dedupe_signature": "8976e2d4c19c4cbd0d658f65a4fb3801de6ea0cf44829ca8fecfdd174b80efbc", "difficulty": "medium", "final_answer": {"answer": 12.506, "unit": "area_units"}, "id": "trapz_linear_002386_-1.7_2.6_-2.6_0", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-1.7x+2.6 from x=-2.6 to x=0. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-2.6)=7.02 and f(0)=2.6.\nThe interval width is 2.6.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 2.6, "slope": -1.7, "x0": -2.6, "x1": 0.0}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.36 and add it to the current value.\nFinal: {\"answer\": [0.556, 0.534, -0.454], \"unit\": \"temperature_units\"}", "dedupe_signature": "4408cde8057b3886d322427078b96d450df7187c5d32609835b23853746cf703", "difficulty": "hard", "final_answer": {"answer": [0.556, 0.534, -0.454], "unit": "temperature_units"}, "id": "heat_step_002387_0.36_1.2_2.95_-1.95_0.05_0.65", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.2, right=0.65; current interior values are [2.95, -1.95, 0.05]. Use r=0.36. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.36 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [2.95, -1.95, 0.05], "left": 1.2, "r": 0.36, "right": 0.65}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kelvin equals Celsius plus 273.15.\n2. Apply the conversion factor directly to the given value.\n3. Compute 139.5 + 273.15.\nFinal: {\"answer\": 412.65, \"unit\": \"K\"}", "dedupe_signature": "789192b48466f5da38e0b4ebf13f69267118cfd2d3eff75a41f6c14c4b23004d", "difficulty": "easy", "final_answer": {"answer": 412.65, "unit": "K"}, "id": "unit_convert_002388_c_to_k_139.5", "license": "Apache-2.0", "prompt": "Convert 139.5 degC to K. Return the converted value with unit.", "reasoning_trace": "Kelvin equals Celsius plus 273.15.\nApply the conversion factor directly to the given value.\nCompute 139.5 + 273.15.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 139.5}, "verifier": {"formula": "value + 273.15", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [9.05, 29.5], \"unit\": \"dimensionless\"}", "dedupe_signature": "811bb9fb93b66e3609b26c332d261215fcd6c0dc6d6038d60298f63456ffdd3a", "difficulty": "medium", "final_answer": {"answer": [9.05, 29.5], "unit": "dimensionless"}, "id": "line_two_point_002390_18_25.25_9.05_29.5", "license": "Apache-2.0", "prompt": "A line passes through points (18, 192.4) and (25.25, 258.013). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 18.0, "x2": 25.25, "y1": 192.4, "y2": 258.01250000000005}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. amount times volume is not concentration\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "28154363f726630f0a6d28af5d7f1ceed32cd3f736949d5ceec41f4f2061bf1b", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_002391_inconsistent_74ac0b02_817110", "license": "Apache-2.0", "prompt": "In lab notebook case 817110, check dimensional consistency for C = n * V. The left side has dimensions mol/L and the right side has dimensions mol*L. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\namount times volume is not concentration\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "C = n * V"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: volume.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"volume\"]}", "dedupe_signature": "f3c5feaf4b4710b785e8ca8b4621fe8efe91352b18d0f9e27d47d1b96394118f", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["volume"]}, "id": "abstain_002393_volume", "license": "Apache-2.0", "prompt": "Compute pressure from the ideal gas law. The prompt gives n=4.2 mol and T=550 K, but does not give volume. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: volume.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["volume"]}, "verifier": {"missing": ["volume"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 10.6 kg and a = 1.45 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 15.37, \"unit\": \"N\"}", "dedupe_signature": "35622ff4c44eec1bbe830c429216000cd4d3965dd334eb0cb1e15d664eddb599", "difficulty": "easy", "final_answer": {"answer": 15.37, "unit": "N"}, "id": "force_002394_10.6_1.45", "license": "Apache-2.0", "prompt": "A cart has mass 10.6 kg and measured acceleration 1.45 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 10.6 kg and a = 1.45 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 1.45, "mass": 10.6}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 39.45^2 and multiply by 0.5 * 0.85.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 661.4286, \"unit\": \"J\"}", "dedupe_signature": "cf6a36dbaeca78ee5a54ee6167f16f2a2ee26833258fd828c241dee00a550590", "difficulty": "easy", "final_answer": {"answer": 661.4286, "unit": "J"}, "id": "ke_002395_0.85_39.45", "license": "Apache-2.0", "prompt": "A body of mass 0.85 kg moves at 39.45 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 39.45^2 and multiply by 0.5 * 0.85.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 0.85, "velocity": 39.45}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 2.59 * 8.314 * 515 / 16.3.\nFinal: {\"answer\": 680.3453, \"unit\": \"kPa\"}", "dedupe_signature": "53bbfb80e1fa856d90681ed924efe17016113e98111412e620a6f545c215b7fa", "difficulty": "medium", "final_answer": {"answer": 680.3453, "unit": "kPa"}, "id": "ideal_gas_002397_2.59_515_16.3", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=2.59 mol, T=515 K, and V=16.3 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 2.59 * 8.314 * 515 / 16.3.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 2.59, "temp_k": 515, "volume_l": 16.3}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 935 * 2.44 * 33.\nFinal: {\"answer\": 75286.2, \"unit\": \"J\"}", "dedupe_signature": "bb8f8d88ada9c529bb353372db511486e65ed589fbcdb1c28c8ae0b368a86c1d", "difficulty": "easy", "final_answer": {"answer": 75286.2, "unit": "J"}, "id": "heat_q_002398_935_2.44_33", "license": "Apache-2.0", "prompt": "A 935 g sample has specific heat 2.44 J/(g*K). How much heat is needed to raise its temperature by 33 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 935 * 2.44 * 33.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 33, "heat_capacity": 2.44, "mass_g": 935}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=173.1 V and R=142.1 ohm.\nFinal: {\"answer\": 210.8628, \"unit\": \"W\"}", "dedupe_signature": "6dee6fb5ac5fda7e6c0d4927eee779ebd82b75fb2e3fced0e06a07bd4f5ed73e", "difficulty": "easy", "final_answer": {"answer": 210.8628, "unit": "W"}, "id": "ohm_power_002399_173.1_142.1", "license": "Apache-2.0", "prompt": "A resistor has resistance 142.1 ohm and voltage 173.1 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=173.1 V and R=142.1 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 142.1, "voltage": 173.1}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 0.89 mol * 18.015 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 16.0334, \"unit\": \"g\"}", "dedupe_signature": "222150dd311b736fecefe7c444aefd40761164efa22ec70f40ef289c573f6f71", "difficulty": "medium", "final_answer": {"answer": 16.0334, "unit": "g"}, "id": "stoich_mass_002401_water_0.89", "license": "Apache-2.0", "prompt": "A sample contains 0.89 mol of water. Using molar mass 18.015 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 0.89 mol * 18.015 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "water", "molar_mass": 18.015, "moles": 0.89}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 3055 mL to 3.055 L.\n3. Compute M = 2.515 / 3.055.\nFinal: {\"answer\": 0.8232, \"unit\": \"mol/L\"}", "dedupe_signature": "9e316753730096a4daa9b55ab26e55c89a9f72a02f04da0d1f64a266db649d2f", "difficulty": "medium", "final_answer": {"answer": 0.8232, "unit": "mol/L"}, "id": "molarity_002402_2.515_3055", "license": "Apache-2.0", "prompt": "A solution contains 2.515 mol of solute in 3055 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 3055 mL to 3.055 L.\nCompute M = 2.515 / 3.055.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 2.515, "volume_ml": 3055}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-8.1)=-9.05 and f(-2.2)=-12.\n3. The interval width is 5.9.\nFinal: {\"answer\": -62.0975, \"unit\": \"area_units\"}", "dedupe_signature": "9fe8a80da1c97cd9f60d31b990a05e38fa5c58ab82f968214e00bd7314a8f43d", "difficulty": "medium", "final_answer": {"answer": -62.0975, "unit": "area_units"}, "id": "trapz_linear_002404_-0.5_-13.1_-8.1_-2.2", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-0.5x+-13.1 from x=-8.1 to x=-2.2. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-8.1)=-9.05 and f(-2.2)=-12.\nThe interval width is 5.9.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -13.1, "slope": -0.5, "x0": -8.1, "x1": -2.1999999999999993}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.22 and add it to the current value.\nFinal: {\"answer\": [0.212, 0.068, 0.507], \"unit\": \"temperature_units\"}", "dedupe_signature": "2649508fe4fd0689be2100d962ffa58ba391b6aa3def43b7406b0549eb623c89", "difficulty": "hard", "final_answer": {"answer": [0.212, 0.068, 0.507], "unit": "temperature_units"}, "id": "heat_step_002405_0.22_-1.7_1.4_-0.9_1.2_0.15", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-1.7, right=0.15; current interior values are [1.4, -0.9, 1.2]. Use r=0.22. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.22 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [1.4, -0.9, 1.2], "left": -1.7, "r": 0.22, "right": 0.15}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 100 centimeters in one meter.\n2. Apply the conversion factor directly to the given value.\n3. Compute 2861.0 / 100.\nFinal: {\"answer\": 28.61, \"unit\": \"m\"}", "dedupe_signature": "439cb0fc740e4b23443f83f78ca91c00be60bcca9218e3c2911ebf929668b355", "difficulty": "easy", "final_answer": {"answer": 28.61, "unit": "m"}, "id": "unit_convert_002406_cm_to_m_2861", "license": "Apache-2.0", "prompt": "Convert 2861 cm to m. Return the converted value with unit.", "reasoning_trace": "There are 100 centimeters in one meter.\nApply the conversion factor directly to the given value.\nCompute 2861.0 / 100.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 2861.0}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=324 degrees and keep the unit as newtons.\nFinal: {\"answer\": [81.3062, -59.0724], \"unit\": \"N\"}", "dedupe_signature": "30fac9b142d01406770b92d2a1578442a4784657d39fca47579d9f38419a199e", "difficulty": "medium", "final_answer": {"answer": [81.3062, -59.0724], "unit": "N"}, "id": "vector_components_002407_100.5_324", "license": "Apache-2.0", "prompt": "A vector has magnitude 100.5 N at 324 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=324 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 324, "magnitude": 100.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [1.7, 4.0], \"unit\": \"dimensionless\"}", "dedupe_signature": "8740b71de0966334c2c1ccd1c57279f6d57764abdb8567110c20f9638f13b0ba", "difficulty": "medium", "final_answer": {"answer": [1.7, 4.0], "unit": "dimensionless"}, "id": "line_two_point_002408_4.25_17.5_1.7_4", "license": "Apache-2.0", "prompt": "A line passes through points (4.25, 11.225) and (17.5, 33.75). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 4.25, "x2": 17.5, "y1": 11.225, "y2": 33.75}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. energy divided by length is force, not spring constant\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "7c15b1b82dfb55cb6e7e6a1a5b525c8c050bf62998eae2acbbd2871b77b8b9e0", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_002409_inconsistent_56040f5d_519891", "license": "Apache-2.0", "prompt": "In field worksheet case 519891, check dimensional consistency for k = E / x. The left side has dimensions N/m and the right side has dimensions J/m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nenergy divided by length is force, not spring constant\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "k = E / x"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef normalize_002410(values):\n    total = sum(values)\n    if total == 0:\n        raise ValueError('cannot normalize zero-sum values')\n    return [v / total for v in values]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"normalize_002410\"}", "dedupe_signature": "0761168f4aad66e45a346f66ca0e6ca746a4f3e8e22cffc5d3726712c297d740", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "normalize_002410"}, "id": "code_002410_normalize_002410", "license": "Apache-2.0", "prompt": "Write a Python function normalize_002410(values) that returns a new list whose values sum to 1. Raise ValueError if the sum is zero. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "normalize_002410"}, "verifier": {"function": "normalize_002410", "tests": ["out = normalize_002410([2, 3, 5]); assert len(out) == 3", "assert abs(sum(normalize_002410([2, 3, 5])) - 1.0) < 1e-12", "assert normalize_002410([1, 1]) == [0.5, 0.5]", "try:\n    normalize_002410([1, -1])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 2.55 kg and a = 5.5 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 14.025, \"unit\": \"N\"}", "dedupe_signature": "982f3e69cb7b2754fdba3817fdb1933929cf69f04603090b57d146ffb9f374d9", "difficulty": "easy", "final_answer": {"answer": 14.025, "unit": "N"}, "id": "force_002412_2.55_5.5", "license": "Apache-2.0", "prompt": "A cart has mass 2.55 kg and measured acceleration 5.5 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 2.55 kg and a = 5.5 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 5.5, "mass": 2.55}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 43.1^2 and multiply by 0.5 * 15.05.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 13978.5153, \"unit\": \"J\"}", "dedupe_signature": "70701f521c281f3b287c407d80038573aea86e62e87f2667e895c617200671d6", "difficulty": "easy", "final_answer": {"answer": 13978.5153, "unit": "J"}, "id": "ke_002413_15.05_43.1", "license": "Apache-2.0", "prompt": "A body of mass 15.05 kg moves at 43.1 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 43.1^2 and multiply by 0.5 * 15.05.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 15.05, "velocity": 43.1}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=69 degrees through the sine of 2 theta.\n3. Substitute v=51.2 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 178.8059, \"unit\": \"m\"}", "dedupe_signature": "af7dd481f23951dd6248f0c510cd95acf79ccd0a3d03cdda9291eb5cae291c54", "difficulty": "medium", "final_answer": {"answer": 178.8059, "unit": "m"}, "id": "projectile_range_002414_51.2_69", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 51.2 m/s and angle 69 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=69 degrees through the sine of 2 theta.\nSubstitute v=51.2 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 69, "gravity": 9.81, "speed": 51.2}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1745 * 4.75 * 67.\nFinal: {\"answer\": 555346.25, \"unit\": \"J\"}", "dedupe_signature": "18a72aea774f8fc4a6c152b76ec05d37ce3a575bc78500afc01c7e4a7c5cb2de", "difficulty": "easy", "final_answer": {"answer": 555346.25, "unit": "J"}, "id": "heat_q_002416_1745_4.75_67", "license": "Apache-2.0", "prompt": "A 1745 g sample has specific heat 4.75 J/(g*K). How much heat is needed to raise its temperature by 67 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1745 * 4.75 * 67.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 67, "heat_capacity": 4.75, "mass_g": 1745}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=643.5 mg, t=181.5 h, and T_half=55.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 66.6959, \"unit\": \"mg\"}", "dedupe_signature": "1f0918fd5d447b4f0cae76eec97b5e685921ca27bac2872f1bd1df3eb8a2d868", "difficulty": "medium", "final_answer": {"answer": 66.6959, "unit": "mg"}, "id": "half_life_002418_643.5_55.5_181.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 643.5 mg. Its half-life is 55.5 hours. How many mg remain after 181.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=643.5 mg, t=181.5 h, and T_half=55.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 181.5, "half_life": 55.5, "initial_amount": 643.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 745 mL to 0.745 L.\n3. Compute M = 4.64 / 0.745.\nFinal: {\"answer\": 6.2282, \"unit\": \"mol/L\"}", "dedupe_signature": "4b659a843ef1d971a6be21c8e73d78cb4c643ce87c53969f14e434ae358eceff", "difficulty": "medium", "final_answer": {"answer": 6.2282, "unit": "mol/L"}, "id": "molarity_002420_4.64_745", "license": "Apache-2.0", "prompt": "A solution contains 4.64 mol of solute in 745 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 745 mL to 0.745 L.\nCompute M = 4.64 / 0.745.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 4.64, "volume_ml": 745}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.84 y, so each step multiplies y by 1 - h*0.84.\n3. Apply that update for 11 steps and round the final state.\nFinal: {\"answer\": 0.0, \"unit\": \"state_units\"}", "dedupe_signature": "a89d2ac8e098b305d6df60056c3372374da26453312cedf8cc849865fdff04d2", "difficulty": "medium", "final_answer": {"answer": 0.0, "unit": "state_units"}, "id": "euler_decay_002421_69_0.84_0.9_11", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.84 y with y(0)=69, step size h=0.9, for 11 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.84 y, so each step multiplies y by 1 - h*0.84.\nApply that update for 11 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 69.0, "rate": 0.84, "step": 0.9, "steps": 11}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.04 and add it to the current value.\nFinal: {\"answer\": [1.752, 1.3, 2.858], \"unit\": \"temperature_units\"}", "dedupe_signature": "87ce6d3da64783477dca1b5b1fe3dbf733697c21b8a0248d88a7a348e46526cd", "difficulty": "hard", "final_answer": {"answer": [1.752, 1.3, 2.858], "unit": "temperature_units"}, "id": "heat_step_002423_0.04_-1.1_1.9_1.2_3.0_1.25", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-1.1, right=1.25; current interior values are [1.9, 1.2, 3.0]. Use r=0.04. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.04 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [1.9, 1.2, 3.0], "left": -1.1, "r": 0.04, "right": 1.25}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 1412.0 / 1000.\nFinal: {\"answer\": 1.412, \"unit\": \"kg\"}", "dedupe_signature": "b1dd3366c7fce59ae9f72444dc691582590e79b46ec3593961a35c2b5d620012", "difficulty": "easy", "final_answer": {"answer": 1.412, "unit": "kg"}, "id": "unit_convert_002424_g_to_kg_1412", "license": "Apache-2.0", "prompt": "Convert 1412 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 1412.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 1412.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=290 degrees and keep the unit as newtons.\nFinal: {\"answer\": [66.6939, -183.2401], \"unit\": \"N\"}", "dedupe_signature": "822e0fa944e033df177a225002d6877fd90c63bbcc0808b534705f67a169404b", "difficulty": "medium", "final_answer": {"answer": [66.6939, -183.2401], "unit": "N"}, "id": "vector_components_002425_195_290", "license": "Apache-2.0", "prompt": "A vector has magnitude 195 N at 290 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=290 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 290, "magnitude": 195.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-8.7, 4.25], \"unit\": \"dimensionless\"}", "dedupe_signature": "426d021c89d739d213082e56ff206b95323b1fba640d8fa1386494f6bff38ea1", "difficulty": "medium", "final_answer": {"answer": [-8.7, 4.25], "unit": "dimensionless"}, "id": "line_two_point_002426_17.25_29.75_-8.7_4.25", "license": "Apache-2.0", "prompt": "A line passes through points (17.25, -145.825) and (29.75, -254.575). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 17.25, "x2": 29.75, "y1": -145.825, "y2": -254.575}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. m*v is momentum, not energy\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "b58af7d7b3c7e04abcb609bf14bedd5836f54538d2032537628b49942b2ba2de", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_002427_inconsistent_1e14b074_481371", "license": "Apache-2.0", "prompt": "In model card equation case 481371, check dimensional consistency for E = m * v. The left side has dimensions kg*m^2/s^2 and the right side has dimensions kg*m/s. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nm*v is momentum, not energy\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "E = m * v"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: left_boundary, right_boundary.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"left_boundary\", \"right_boundary\"]}", "dedupe_signature": "9b54084e7d50d943f2161b3c925ea242a0273aabbc5ed4b8ac1121cab49af0a2", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["left_boundary", "right_boundary"]}, "id": "abstain_002429_left_boundary_right_boundary", "license": "Apache-2.0", "prompt": "Solve the 1D heat equation after one finite-difference step. The prompt gives r=0.32 and interior values [-1.1, -0.35, -1.7], but gives no boundary values. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: left_boundary, right_boundary.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["left_boundary", "right_boundary"]}, "verifier": {"missing": ["left_boundary", "right_boundary"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 1.15 kg and a = 15.1 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 17.365, \"unit\": \"N\"}", "dedupe_signature": "c75ecd5b9fa37912011780884475c7ff7dedbcdd54e3198fb5b095f3933e88c6", "difficulty": "easy", "final_answer": {"answer": 17.365, "unit": "N"}, "id": "force_002430_1.15_15.1", "license": "Apache-2.0", "prompt": "A cart has mass 1.15 kg and measured acceleration 15.1 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 1.15 kg and a = 15.1 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 15.1, "mass": 1.15}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 17^2 and multiply by 0.5 * 12.45.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 1799.025, \"unit\": \"J\"}", "dedupe_signature": "f05aac68601235711f7cd1fb362d2e63f75845a59f11b02168b878d746c05bbd", "difficulty": "easy", "final_answer": {"answer": 1799.025, "unit": "J"}, "id": "ke_002431_12.45_17", "license": "Apache-2.0", "prompt": "A body of mass 12.45 kg moves at 17 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 17^2 and multiply by 0.5 * 12.45.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 12.45, "velocity": 17.0}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 2.97 * 8.314 * 526 / 31.6.\nFinal: {\"answer\": 411.0221, \"unit\": \"kPa\"}", "dedupe_signature": "d0184f0c3a2bb9fde81d7ca3bd9dbd8485b82534c53dc24331b0af2a1f3a73a5", "difficulty": "medium", "final_answer": {"answer": 411.0221, "unit": "kPa"}, "id": "ideal_gas_002433_2.97_526_31.6", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=2.97 mol, T=526 K, and V=31.6 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 2.97 * 8.314 * 526 / 31.6.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 2.97, "temp_k": 526, "volume_l": 31.6}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=222.5 mg, t=260.5 h, and T_half=109 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 42.4518, \"unit\": \"mg\"}", "dedupe_signature": "656e61f8f038f2669692c73fbdcb63230782828e93c98bfe0766cfad34a96ae0", "difficulty": "medium", "final_answer": {"answer": 42.4518, "unit": "mg"}, "id": "half_life_002436_222.5_109_260.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 222.5 mg. Its half-life is 109 hours. How many mg remain after 260.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=222.5 mg, t=260.5 h, and T_half=109 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 260.5, "half_life": 109.0, "initial_amount": 222.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.91 y, so each step multiplies y by 1 - h*0.91.\n3. Apply that update for 5 steps and round the final state.\nFinal: {\"answer\": 0.0521, \"unit\": \"state_units\"}", "dedupe_signature": "3a190ae96adb479c48aafa4d36e93d774adf1928c1ee069e6b75e6e700504dbe", "difficulty": "medium", "final_answer": {"answer": 0.0521, "unit": "state_units"}, "id": "euler_decay_002439_35_0.91_0.8_5", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.91 y with y(0)=35, step size h=0.8, for 5 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.91 y, so each step multiplies y by 1 - h*0.91.\nApply that update for 5 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 35.0, "rate": 0.91, "step": 0.8, "steps": 5}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(2.8)=-22 and f(9.1)=-69.25.\n3. The interval width is 6.3.\nFinal: {\"answer\": -287.4375, \"unit\": \"area_units\"}", "dedupe_signature": "0cde4ac5b4a52ef15018357e972fb4c4d8729b74f556c28af6e43330ab83ab6f", "difficulty": "medium", "final_answer": {"answer": -287.4375, "unit": "area_units"}, "id": "trapz_linear_002440_-7.5_-1_2.8_9.1", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-7.5x+-1 from x=2.8 to x=9.1. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(2.8)=-22 and f(9.1)=-69.25.\nThe interval width is 6.3.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -1.0, "slope": -7.5, "x0": 2.8, "x1": 9.1}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.46 and add it to the current value.\nFinal: {\"answer\": [2.075, 0.277, 1.403], \"unit\": \"temperature_units\"}", "dedupe_signature": "4650b708037ad46d2e28e43721f2c0f6d87adbf019204cf8c4c5ace925052bae", "difficulty": "hard", "final_answer": {"answer": [2.075, 0.277, 1.403], "unit": "temperature_units"}, "id": "heat_step_002441_0.46_2.8_1.5_1.45_-1.15_1.8", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=2.8, right=1.8; current interior values are [1.5, 1.45, -1.15]. Use r=0.46. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.46 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [1.5, 1.45, -1.15], "left": 2.8, "r": 0.46, "right": 1.8}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 44815.0 / 1000.\nFinal: {\"answer\": 44.815, \"unit\": \"kg\"}", "dedupe_signature": "839e651ab03e5614e61b0be7aaaf5d201f2047aa1de4f1276c6ec7093177f1bb", "difficulty": "easy", "final_answer": {"answer": 44.815, "unit": "kg"}, "id": "unit_convert_002442_g_to_kg_44815", "license": "Apache-2.0", "prompt": "Convert 44815 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 44815.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 44815.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=152 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-310.7976, 165.254], \"unit\": \"N\"}", "dedupe_signature": "700abfe8678166437a72ffd88ce6fee3e3eb16b220dbd095727cd84ca28558c6", "difficulty": "medium", "final_answer": {"answer": [-310.7976, 165.254], "unit": "N"}, "id": "vector_components_002443_352_152", "license": "Apache-2.0", "prompt": "A vector has magnitude 352 N at 152 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=152 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 152, "magnitude": 352.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-2.9, 30.0], \"unit\": \"dimensionless\"}", "dedupe_signature": "a8711aa62c841eb2d43f6438a4629ba8fb0b5d96aaf3ad2bf583bd514c1cb3e8", "difficulty": "medium", "final_answer": {"answer": [-2.9, 30.0], "unit": "dimensionless"}, "id": "line_two_point_002444_-1.25_9_-2.9_30", "license": "Apache-2.0", "prompt": "A line passes through points (-1.25, 33.625) and (9, 3.9). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -1.25, "x2": 9.0, "y1": 33.625, "y2": 3.900000000000002}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. density times acceleration times height gives kg/(m*s^2), or pascal\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "a871313bda8cb211c04829100bc58ef4bd8b5404bddf4bbff5206844b56b66db", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_002445_consistent_b7d3eed1_797531", "license": "Apache-2.0", "prompt": "In field worksheet case 797531, check dimensional consistency for p = rho * g * h. The left side has dimensions Pa and the right side has dimensions Pa. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\ndensity times acceleration times height gives kg/(m*s^2), or pascal\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "p = rho * g * h"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef weighted_sum_002446(values, weights):\n    if len(values) != len(weights):\n        raise ValueError('length mismatch')\n    return sum(value * weight for value, weight in zip(values, weights))\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"weighted_sum_002446\"}", "dedupe_signature": "12ec3b6f24406d653b4eaae05b54586be0227989f09fc063b8421707cba2f34b", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "weighted_sum_002446"}, "id": "code_002446_weighted_sum_002446", "license": "Apache-2.0", "prompt": "Write a Python function weighted_sum_002446(values, weights) that returns sum(value*weight). Raise ValueError when the two inputs have different lengths. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "weighted_sum_002446"}, "verifier": {"function": "weighted_sum_002446", "tests": ["assert weighted_sum_002446([2, 3], [4, 5]) == 23", "assert weighted_sum_002446([], []) == 0", "try:\n    weighted_sum_002446([1], [1, 2])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: volume.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"volume\"]}", "dedupe_signature": "929b468e5be828e4c2350bb022d7b69bd6a2ab598c504970683d178a90c9889a", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["volume"]}, "id": "abstain_002447_volume", "license": "Apache-2.0", "prompt": "Compute pressure from the ideal gas law. The prompt gives n=1.04 mol and T=369 K, but does not give volume. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: volume.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["volume"]}, "verifier": {"missing": ["volume"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 19.9^2 and multiply by 0.5 * 8.85.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 1752.3442, \"unit\": \"J\"}", "dedupe_signature": "27db07bbff9895313d94f638e328e9c1296c76aeb41e816257b1e78fdd23453c", "difficulty": "easy", "final_answer": {"answer": 1752.3442, "unit": "J"}, "id": "ke_002449_8.85_19.9", "license": "Apache-2.0", "prompt": "A body of mass 8.85 kg moves at 19.9 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 19.9^2 and multiply by 0.5 * 8.85.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 8.85, "velocity": 19.9}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=7 degrees through the sine of 2 theta.\n3. Substitute v=43.4 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 46.45, \"unit\": \"m\"}", "dedupe_signature": "d6390dc96369dd07b52ec2c77eb1e6fb2c848e57ddd0aa7ca5f8f5ef30e4dfe1", "difficulty": "medium", "final_answer": {"answer": 46.45, "unit": "m"}, "id": "projectile_range_002450_43.4_7", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 43.4 m/s and angle 7 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=7 degrees through the sine of 2 theta.\nSubstitute v=43.4 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 7, "gravity": 9.81, "speed": 43.4}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 3.19 * 8.314 * 315 / 6.5.\nFinal: {\"answer\": 1285.2804, \"unit\": \"kPa\"}", "dedupe_signature": "1defb0697955faf8f5839d5c5eee5187cf12445c7036e495c710049e8e718b54", "difficulty": "medium", "final_answer": {"answer": 1285.2804, "unit": "kPa"}, "id": "ideal_gas_002451_3.19_315_6.5", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=3.19 mol, T=315 K, and V=6.5 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 3.19 * 8.314 * 315 / 6.5.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 3.19, "temp_k": 315, "volume_l": 6.5}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 920 * 2.85 * 115.\nFinal: {\"answer\": 301530.0, \"unit\": \"J\"}", "dedupe_signature": "a3c2b4e6555f6673fc6237d34f0e4246b5a22e239f2bc11e194c91155eac4d69", "difficulty": "easy", "final_answer": {"answer": 301530.0, "unit": "J"}, "id": "heat_q_002452_920_2.85_115", "license": "Apache-2.0", "prompt": "A 920 g sample has specific heat 2.85 J/(g*K). How much heat is needed to raise its temperature by 115 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 920 * 2.85 * 115.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 115, "heat_capacity": 2.85, "mass_g": 920}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=93.8 V and R=120.9 ohm.\nFinal: {\"answer\": 72.7745, \"unit\": \"W\"}", "dedupe_signature": "aeed49705c3c4687514ec6bbef03479f213cfca909eeb3846a3694c61a063354", "difficulty": "easy", "final_answer": {"answer": 72.7745, "unit": "W"}, "id": "ohm_power_002453_93.8_120.9", "license": "Apache-2.0", "prompt": "A resistor has resistance 120.9 ohm and voltage 93.8 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=93.8 V and R=120.9 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 120.9, "voltage": 93.8}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 7.02 mol * 100.087 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 702.6107, \"unit\": \"g\"}", "dedupe_signature": "4c9f208581fae422dd1444b90851c1f1dc90e2077ccabbcd6f080d4bb4e273db", "difficulty": "medium", "final_answer": {"answer": 702.6107, "unit": "g"}, "id": "stoich_mass_002455_calcium_carbonate_7.02", "license": "Apache-2.0", "prompt": "A sample contains 7.02 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 7.02 mol * 100.087 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "calcium carbonate", "molar_mass": 100.087, "moles": 7.02}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 3730 mL to 3.73 L.\n3. Compute M = 2.46 / 3.73.\nFinal: {\"answer\": 0.6595, \"unit\": \"mol/L\"}", "dedupe_signature": "694583d7e1fe62e75c58810906d29d1508e423ef102438ceb035ebd731d8ee9a", "difficulty": "medium", "final_answer": {"answer": 0.6595, "unit": "mol/L"}, "id": "molarity_002456_2.46_3730", "license": "Apache-2.0", "prompt": "A solution contains 2.46 mol of solute in 3730 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 3730 mL to 3.73 L.\nCompute M = 2.46 / 3.73.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 2.46, "volume_ml": 3730}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.26 y, so each step multiplies y by 1 - h*0.26.\n3. Apply that update for 10 steps and round the final state.\nFinal: {\"answer\": 10.7577, \"unit\": \"state_units\"}", "dedupe_signature": "6fa8cc6fcf530bb0833609e49354257205cb332c2fde0f13cb0d37388dc6f6cf", "difficulty": "medium", "final_answer": {"answer": 10.7577, "unit": "state_units"}, "id": "euler_decay_002457_14_0.26_0.1_10", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.26 y with y(0)=14, step size h=0.1, for 10 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.26 y, so each step multiplies y by 1 - h*0.26.\nApply that update for 10 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 14.0, "rate": 0.26, "step": 0.1, "steps": 10}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(1.1)=-7.57 and f(6.4)=-27.18.\n3. The interval width is 5.3.\nFinal: {\"answer\": -92.0875, \"unit\": \"area_units\"}", "dedupe_signature": "321fa91af801a868b10eb4d1fbfd16bb73e9e9011de2880e8418dd3bfe295452", "difficulty": "medium", "final_answer": {"answer": -92.0875, "unit": "area_units"}, "id": "trapz_linear_002458_-3.7_-3.5_1.1_6.4", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-3.7x+-3.5 from x=1.1 to x=6.4. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(1.1)=-7.57 and f(6.4)=-27.18.\nThe interval width is 5.3.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -3.5, "slope": -3.7, "x0": 1.1, "x1": 6.4}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.2 and add it to the current value.\nFinal: {\"answer\": [0.77, -0.62, 0.46], \"unit\": \"temperature_units\"}", "dedupe_signature": "27b55e6517f5e995f903bd9b627b68af8186090065c3e979b6989f326db61c9c", "difficulty": "hard", "final_answer": {"answer": [0.77, -0.62, 0.46], "unit": "temperature_units"}, "id": "heat_step_002459_0.2_1.35_1.5_-2.0_1.4_0.1", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.35, right=0.1; current interior values are [1.5, -2.0, 1.4]. Use r=0.2. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.2 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [1.5, -2.0, 1.4], "left": 1.35, "r": 0.2, "right": 0.1}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kelvin equals Celsius plus 273.15.\n2. Apply the conversion factor directly to the given value.\n3. Compute 200.0 + 273.15.\nFinal: {\"answer\": 473.15, \"unit\": \"K\"}", "dedupe_signature": "6a90a5fd33eebf6fe0885795b161806f87fdcf59231080db734cd8389f380b78", "difficulty": "easy", "final_answer": {"answer": 473.15, "unit": "K"}, "id": "unit_convert_002460_c_to_k_200", "license": "Apache-2.0", "prompt": "Convert 200 degC to K. Return the converted value with unit.", "reasoning_trace": "Kelvin equals Celsius plus 273.15.\nApply the conversion factor directly to the given value.\nCompute 200.0 + 273.15.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 200.0}, "verifier": {"formula": "value + 273.15", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=211 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-140.1469, -84.2087], \"unit\": \"N\"}", "dedupe_signature": "b79576abb11393bf49b9870f08e36122bc8af8137e4b7c69b4c2a3bb505c232e", "difficulty": "medium", "final_answer": {"answer": [-140.1469, -84.2087], "unit": "N"}, "id": "vector_components_002461_163.5_211", "license": "Apache-2.0", "prompt": "A vector has magnitude 163.5 N at 211 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=211 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 211, "magnitude": 163.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [5.1, 26.75], \"unit\": \"dimensionless\"}", "dedupe_signature": "380e3386ea6c4867f7ba2a2cb576534595d18a32f34cb375452744131a48298d", "difficulty": "medium", "final_answer": {"answer": [5.1, 26.75], "unit": "dimensionless"}, "id": "line_two_point_002462_-13_0_5.1_26.75", "license": "Apache-2.0", "prompt": "A line passes through points (-13, -39.55) and (0, 26.75). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -13.0, "x2": 0.0, "y1": -39.55, "y2": 26.75}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. m*v is momentum, not energy\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "120f77e525965033450f1b7bd1ad32bf0cc6cd30d3d9fe8a2a4e3c5efb72fc27", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_002463_inconsistent_1e14b074_678744", "license": "Apache-2.0", "prompt": "In instrument manual case 678744, check dimensional consistency for E = m * v. The left side has dimensions kg*m^2/s^2 and the right side has dimensions kg*m/s. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nm*v is momentum, not energy\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "E = m * v"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef normalize_002464(values):\n    total = sum(values)\n    if total == 0:\n        raise ValueError('cannot normalize zero-sum values')\n    return [v / total for v in values]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"normalize_002464\"}", "dedupe_signature": "4861700676d2d2a3a0528b1e5ab7ea7d91d068fa323b43c71d2989838299ab71", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "normalize_002464"}, "id": "code_002464_normalize_002464", "license": "Apache-2.0", "prompt": "Write a Python function normalize_002464(values) that returns a new list whose values sum to 1. Raise ValueError if the sum is zero. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "normalize_002464"}, "verifier": {"function": "normalize_002464", "tests": ["out = normalize_002464([2, 3, 5]); assert len(out) == 3", "assert abs(sum(normalize_002464([2, 3, 5])) - 1.0) < 1e-12", "assert normalize_002464([1, 1]) == [0.5, 0.5]", "try:\n    normalize_002464([1, -1])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: left_boundary, right_boundary.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"left_boundary\", \"right_boundary\"]}", "dedupe_signature": "04bc5a41d291b17515ad59e9a9fd9e6cac728d3b20f356fe9c4df0c2cd91c3af", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["left_boundary", "right_boundary"]}, "id": "abstain_002465_left_boundary_right_boundary", "license": "Apache-2.0", "prompt": "Solve the 1D heat equation after one finite-difference step. The prompt gives r=0.38 and interior values [1.0, -1.0, -0.85], but gives no boundary values. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: left_boundary, right_boundary.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["left_boundary", "right_boundary"]}, "verifier": {"missing": ["left_boundary", "right_boundary"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 5.9 kg and a = 6.3 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 37.17, \"unit\": \"N\"}", "dedupe_signature": "eefea652b6bb063e2e815e1ce668e163b73df4a84fd05e09044f195978221cdc", "difficulty": "easy", "final_answer": {"answer": 37.17, "unit": "N"}, "id": "force_002466_5.9_6.3", "license": "Apache-2.0", "prompt": "A cart has mass 5.9 kg and measured acceleration 6.3 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 5.9 kg and a = 6.3 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 6.3, "mass": 5.9}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 22.9^2 and multiply by 0.5 * 20.6.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 5401.423, \"unit\": \"J\"}", "dedupe_signature": "2fddcc7a54fd3e19d303617cfccf44dd4d3a0e55b18d5e826f8d141c6f5659ed", "difficulty": "easy", "final_answer": {"answer": 5401.423, "unit": "J"}, "id": "ke_002467_20.6_22.9", "license": "Apache-2.0", "prompt": "A body of mass 20.6 kg moves at 22.9 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 22.9^2 and multiply by 0.5 * 20.6.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 20.6, "velocity": 22.9}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=8 degrees through the sine of 2 theta.\n3. Substitute v=8.2 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 1.8893, \"unit\": \"m\"}", "dedupe_signature": "7af31ee3fca01c36c8c08735befc364c6178bfced43485de4f1eb1c08bf7cea4", "difficulty": "medium", "final_answer": {"answer": 1.8893, "unit": "m"}, "id": "projectile_range_002468_8.2_8", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 8.2 m/s and angle 8 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=8 degrees through the sine of 2 theta.\nSubstitute v=8.2 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 8, "gravity": 9.81, "speed": 8.2}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 2.96 * 8.314 * 296 / 30.2.\nFinal: {\"answer\": 241.2051, \"unit\": \"kPa\"}", "dedupe_signature": "c20fc0dbfa14a783c1c05ee617978d7c47f1015025a1183e693a973766f9805f", "difficulty": "medium", "final_answer": {"answer": 241.2051, "unit": "kPa"}, "id": "ideal_gas_002469_2.96_296_30.2", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=2.96 mol, T=296 K, and V=30.2 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 2.96 * 8.314 * 296 / 30.2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 2.96, "temp_k": 296, "volume_l": 30.2}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=214.6 V and R=96.8 ohm.\nFinal: {\"answer\": 475.7558, \"unit\": \"W\"}", "dedupe_signature": "a76700b7340fce5c97ece00c3dd0dac472a7d966cddcc3c1c51dc9ca910f692b", "difficulty": "easy", "final_answer": {"answer": 475.7558, "unit": "W"}, "id": "ohm_power_002471_214.6_96.8", "license": "Apache-2.0", "prompt": "A resistor has resistance 96.8 ohm and voltage 214.6 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=214.6 V and R=96.8 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 96.8, "voltage": 214.6}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=528.5 mg, t=42 h, and T_half=36 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 235.42, \"unit\": \"mg\"}", "dedupe_signature": "60aff039592efb883f3991ae1c5e9626c658ace6056acbe86273e952dc75119a", "difficulty": "medium", "final_answer": {"answer": 235.42, "unit": "mg"}, "id": "half_life_002472_528.5_36_42", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 528.5 mg. Its half-life is 36 hours. How many mg remain after 42 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=528.5 mg, t=42 h, and T_half=36 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 42.0, "half_life": 36.0, "initial_amount": 528.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 1.14 mol * 100.087 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 114.0992, \"unit\": \"g\"}", "dedupe_signature": "fbf19572bfe002235a42999ad68e5bb3ff75abba999b84e9c640377c47689466", "difficulty": "medium", "final_answer": {"answer": 114.0992, "unit": "g"}, "id": "stoich_mass_002473_calcium_carbonate_1.14", "license": "Apache-2.0", "prompt": "A sample contains 1.14 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 1.14 mol * 100.087 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "calcium carbonate", "molar_mass": 100.087, "moles": 1.14}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 3875 mL to 3.875 L.\n3. Compute M = 1.995 / 3.875.\nFinal: {\"answer\": 0.5148, \"unit\": \"mol/L\"}", "dedupe_signature": "95bd0f86ffbba5882608a24917a6b10853c938800800922e4eb3e8c6e6fa08f2", "difficulty": "medium", "final_answer": {"answer": 0.5148, "unit": "mol/L"}, "id": "molarity_002474_1.995_3875", "license": "Apache-2.0", "prompt": "A solution contains 1.995 mol of solute in 3875 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 3875 mL to 3.875 L.\nCompute M = 1.995 / 3.875.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 1.995, "volume_ml": 3875}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.87 y, so each step multiplies y by 1 - h*0.87.\n3. Apply that update for 11 steps and round the final state.\nFinal: {\"answer\": 0.4308, \"unit\": \"state_units\"}", "dedupe_signature": "be744e636916ab94a4591f2661b5a80abd4fdd7ddec84ba06cc8ed586e23ebbb", "difficulty": "medium", "final_answer": {"answer": 0.4308, "unit": "state_units"}, "id": "euler_decay_002475_12_0.87_0.3_11", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.87 y with y(0)=12, step size h=0.3, for 11 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.87 y, so each step multiplies y by 1 - h*0.87.\nApply that update for 11 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 12.0, "rate": 0.87, "step": 0.3, "steps": 11}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-4.6)=-2.94 and f(5.3)=-23.73.\n3. The interval width is 9.9.\nFinal: {\"answer\": -132.0165, \"unit\": \"area_units\"}", "dedupe_signature": "8eb58862708f5e4ab3d9b24b2ec3058cb7822a848139e404d7b6543649e8021c", "difficulty": "medium", "final_answer": {"answer": -132.0165, "unit": "area_units"}, "id": "trapz_linear_002476_-2.1_-12.6_-4.6_5.3", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-2.1x+-12.6 from x=-4.6 to x=5.3. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-4.6)=-2.94 and f(5.3)=-23.73.\nThe interval width is 9.9.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -12.6, "slope": -2.1, "x0": -4.6, "x1": 5.300000000000001}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kelvin equals Celsius plus 273.15.\n2. Apply the conversion factor directly to the given value.\n3. Compute 176.0 + 273.15.\nFinal: {\"answer\": 449.15, \"unit\": \"K\"}", "dedupe_signature": "ef5a51f5a73bfcdea82b57fc6294b52688a1f37f455f39a24efedaa672bb0b22", "difficulty": "easy", "final_answer": {"answer": 449.15, "unit": "K"}, "id": "unit_convert_002478_c_to_k_176", "license": "Apache-2.0", "prompt": "Convert 176 degC to K. Return the converted value with unit.", "reasoning_trace": "Kelvin equals Celsius plus 273.15.\nApply the conversion factor directly to the given value.\nCompute 176.0 + 273.15.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 176.0}, "verifier": {"formula": "value + 273.15", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=121 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-250.8235, 417.4405], \"unit\": \"N\"}", "dedupe_signature": "55ea9900d506d23cfbbe5360fcfab3a661f8f605b07ae3b50e69e7855bad24e2", "difficulty": "medium", "final_answer": {"answer": [-250.8235, 417.4405], "unit": "N"}, "id": "vector_components_002479_487_121", "license": "Apache-2.0", "prompt": "A vector has magnitude 487 N at 121 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=121 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 121, "magnitude": 487.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-0.15, -15.0], \"unit\": \"dimensionless\"}", "dedupe_signature": "e02c3593418578375751fcca127b24c51d962bb734eb75c475ec153371f9c7c1", "difficulty": "medium", "final_answer": {"answer": [-0.15, -15.0], "unit": "dimensionless"}, "id": "line_two_point_002480_7_10_-0.15_-15", "license": "Apache-2.0", "prompt": "A line passes through points (7, -16.05) and (10, -16.5). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 7.0, "x2": 10.0, "y1": -16.05, "y2": -16.5}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. amount times volume is not concentration\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "b7e743d4f29c86ee79ec82e7aa19b36f3e1df1026f3bfc9c459525dffb0eec18", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_002481_inconsistent_74ac0b02_717643", "license": "Apache-2.0", "prompt": "In lab notebook case 717643, check dimensional consistency for C = n * V. The left side has dimensions mol/L and the right side has dimensions mol*L. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\namount times volume is not concentration\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "C = n * V"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\nimport math\n\ndef unit_vector_002482(x, y):\n    norm = math.hypot(x, y)\n    if norm == 0:\n        raise ValueError('zero vector has no direction')\n    return (x / norm, y / norm)\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"unit_vector_002482\"}", "dedupe_signature": "3d11671efe629cd296bea2c4e8241be8c76f72e3fa7b8ff7fe5b9d9dc54ec29e", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "unit_vector_002482"}, "id": "code_002482_unit_vector_002482", "license": "Apache-2.0", "prompt": "Write a Python function unit_vector_002482(x, y) that returns the 2D unit vector as a tuple. Raise ValueError for the zero vector. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "unit_vector_002482"}, "verifier": {"function": "unit_vector_002482", "tests": ["ux, uy = unit_vector_002482(3, 4); assert abs(ux - 0.6) < 1e-12 and abs(uy - 0.8) < 1e-12", "assert unit_vector_002482(0, 5) == (0, 1)", "try:\n    unit_vector_002482(0, 0)\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: left_boundary, right_boundary.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"left_boundary\", \"right_boundary\"]}", "dedupe_signature": "c2c6f93b468e933edce3daef2eeec07ed88b7f2ac10c1187ce55668290d440ff", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["left_boundary", "right_boundary"]}, "id": "abstain_002483_left_boundary_right_boundary", "license": "Apache-2.0", "prompt": "Solve the 1D heat equation after one finite-difference step. The prompt gives r=0.18 and interior values [-0.6, 0.15, 1.35], but gives no boundary values. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: left_boundary, right_boundary.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["left_boundary", "right_boundary"]}, "verifier": {"missing": ["left_boundary", "right_boundary"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 9.1 kg and a = 12.05 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 109.655, \"unit\": \"N\"}", "dedupe_signature": "8c6df200c101be7bd3d2e029e575099d8b1a05701025590ea9e994f5dabbb41f", "difficulty": "easy", "final_answer": {"answer": 109.655, "unit": "N"}, "id": "force_002484_9.1_12.05", "license": "Apache-2.0", "prompt": "A cart has mass 9.1 kg and measured acceleration 12.05 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 9.1 kg and a = 12.05 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 12.05, "mass": 9.1}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 32.05^2 and multiply by 0.5 * 13.85.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 7113.3773, \"unit\": \"J\"}", "dedupe_signature": "421d72fbe12735eb1d431414aca63a4b587f843cc43ed6d5c17ccc61ed5af802", "difficulty": "easy", "final_answer": {"answer": 7113.3773, "unit": "J"}, "id": "ke_002485_13.85_32.05", "license": "Apache-2.0", "prompt": "A body of mass 13.85 kg moves at 32.05 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 32.05^2 and multiply by 0.5 * 13.85.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 13.85, "velocity": 32.05}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 0.88 * 8.314 * 285 / 32.4.\nFinal: {\"answer\": 64.3565, \"unit\": \"kPa\"}", "dedupe_signature": "33afe488b6114801e079a9bfe2f5f5275aff4600370ddb2dc18e0cd31bf0af17", "difficulty": "medium", "final_answer": {"answer": 64.3565, "unit": "kPa"}, "id": "ideal_gas_002487_0.88_285_32.4", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=0.88 mol, T=285 K, and V=32.4 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 0.88 * 8.314 * 285 / 32.4.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 0.88, "temp_k": 285, "volume_l": 32.4}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1990 * 1.82 * 11.\nFinal: {\"answer\": 39839.8, \"unit\": \"J\"}", "dedupe_signature": "af29f256280512369ef9fb333e10c1400433a5aeb66c541ceb29a2937e1db66b", "difficulty": "easy", "final_answer": {"answer": 39839.8, "unit": "J"}, "id": "heat_q_002488_1990_1.82_11", "license": "Apache-2.0", "prompt": "A 1990 g sample has specific heat 1.82 J/(g*K). How much heat is needed to raise its temperature by 11 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1990 * 1.82 * 11.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 11, "heat_capacity": 1.82, "mass_g": 1990}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=85.3 V and R=122.5 ohm.\nFinal: {\"answer\": 59.3967, \"unit\": \"W\"}", "dedupe_signature": "16c5c7432a1699dcb972bc208499190c185c9e16bceb1758811db0ab10dcec49", "difficulty": "easy", "final_answer": {"answer": 59.3967, "unit": "W"}, "id": "ohm_power_002489_85.3_122.5", "license": "Apache-2.0", "prompt": "A resistor has resistance 122.5 ohm and voltage 85.3 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=85.3 V and R=122.5 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 122.5, "voltage": 85.3}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=882.5 mg, t=283.5 h, and T_half=40.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 6.8945, \"unit\": \"mg\"}", "dedupe_signature": "baa639260905ecdd059748a6a7dad61ca8a45ba60a02e9e7e0c2e3982bd2d53f", "difficulty": "medium", "final_answer": {"answer": 6.8945, "unit": "mg"}, "id": "half_life_002490_882.5_40.5_283.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 882.5 mg. Its half-life is 40.5 hours. How many mg remain after 283.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=882.5 mg, t=283.5 h, and T_half=40.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 283.5, "half_life": 40.5, "initial_amount": 882.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 4.7 mol * 44.01 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 206.847, \"unit\": \"g\"}", "dedupe_signature": "5070ab73c969f7fb82b2ec4b050a06d9fbcb561f5720301224101d3ad4575d3e", "difficulty": "medium", "final_answer": {"answer": 206.847, "unit": "g"}, "id": "stoich_mass_002491_carbon_dioxide_4.7", "license": "Apache-2.0", "prompt": "A sample contains 4.7 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 4.7 mol * 44.01 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "carbon dioxide", "molar_mass": 44.01, "moles": 4.7}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 4480 mL to 4.48 L.\n3. Compute M = 4.405 / 4.48.\nFinal: {\"answer\": 0.9833, \"unit\": \"mol/L\"}", "dedupe_signature": "88094feabf90822d12e9df6acf78cbeec68c63c85d2393b8a5b6256285203ae9", "difficulty": "medium", "final_answer": {"answer": 0.9833, "unit": "mol/L"}, "id": "molarity_002492_4.405_4480", "license": "Apache-2.0", "prompt": "A solution contains 4.405 mol of solute in 4480 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 4480 mL to 4.48 L.\nCompute M = 4.405 / 4.48.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 4.405, "volume_ml": 4480}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.36 y, so each step multiplies y by 1 - h*0.36.\n3. Apply that update for 4 steps and round the final state.\nFinal: {\"answer\": 1.4052, \"unit\": \"state_units\"}", "dedupe_signature": "75ec9be2cab1e7c063f3c4ed10bca04175902ce0a7e879358995779ce7261862", "difficulty": "medium", "final_answer": {"answer": 1.4052, "unit": "state_units"}, "id": "euler_decay_002493_13.5_0.36_1.2_4", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.36 y with y(0)=13.5, step size h=1.2, for 4 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.36 y, so each step multiplies y by 1 - h*0.36.\nApply that update for 4 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 13.5, "rate": 0.36, "step": 1.2, "steps": 4}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-5)=32.4 and f(0.5)=0.5.\n3. The interval width is 5.5.\nFinal: {\"answer\": 90.475, \"unit\": \"area_units\"}", "dedupe_signature": "fb2957493556d2f1fe514a426409c6c0607b978d67881f6560fa7beb8fce84e7", "difficulty": "medium", "final_answer": {"answer": 90.475, "unit": "area_units"}, "id": "trapz_linear_002494_-5.8_3.4_-5_0.5", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-5.8x+3.4 from x=-5 to x=0.5. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-5)=32.4 and f(0.5)=0.5.\nThe interval width is 5.5.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 3.4, "slope": -5.8, "x0": -5.0, "x1": 0.5}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 100 centimeters in one meter.\n2. Apply the conversion factor directly to the given value.\n3. Compute 3357.5 / 100.\nFinal: {\"answer\": 33.575, \"unit\": \"m\"}", "dedupe_signature": "6007ddaba90584551e141985817eaf95054ccb2accea5bbf09238548b72d09c2", "difficulty": "easy", "final_answer": {"answer": 33.575, "unit": "m"}, "id": "unit_convert_002496_cm_to_m_3357.5", "license": "Apache-2.0", "prompt": "Convert 3357.5 cm to m. Return the converted value with unit.", "reasoning_trace": "There are 100 centimeters in one meter.\nApply the conversion factor directly to the given value.\nCompute 3357.5 / 100.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 3357.5}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=21 degrees and keep the unit as newtons.\nFinal: {\"answer\": [285.6756, 109.6606], \"unit\": \"N\"}", "dedupe_signature": "6fb778940a9a7203ad082d3fd4314ab22c8a12fee1f6b5b876743c5d60ebda7d", "difficulty": "medium", "final_answer": {"answer": [285.6756, 109.6606], "unit": "N"}, "id": "vector_components_002497_306_21", "license": "Apache-2.0", "prompt": "A vector has magnitude 306 N at 21 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=21 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 21, "magnitude": 306.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [6.5, -10.75], \"unit\": \"dimensionless\"}", "dedupe_signature": "f8f108590d8f25a029b0602e9358642507dffc29d03f62eac3ebd4c154503600", "difficulty": "medium", "final_answer": {"answer": [6.5, -10.75], "unit": "dimensionless"}, "id": "line_two_point_002498_-9.75_-3.5_6.5_-10.75", "license": "Apache-2.0", "prompt": "A line passes through points (-9.75, -74.125) and (-3.5, -33.5). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -9.75, "x2": -3.5, "y1": -74.125, "y2": -33.5}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. energy divided by length is force, not spring constant\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "a5ad47613c9189893cb6a922ddc77eb93e6fd5c5401142192d859f972124672a", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_002499_inconsistent_56040f5d_209886", "license": "Apache-2.0", "prompt": "In student derivation case 209886, check dimensional consistency for k = E / x. The left side has dimensions N/m and the right side has dimensions J/m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nenergy divided by length is force, not spring constant\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "k = E / x"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\nimport math\n\ndef unit_vector_002500(x, y):\n    norm = math.hypot(x, y)\n    if norm == 0:\n        raise ValueError('zero vector has no direction')\n    return (x / norm, y / norm)\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"unit_vector_002500\"}", "dedupe_signature": "75cdf4bd779b4790e2a9584678c457ff27334f87db360d30719ed1a33862397a", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "unit_vector_002500"}, "id": "code_002500_unit_vector_002500", "license": "Apache-2.0", "prompt": "Write a Python function unit_vector_002500(x, y) that returns the 2D unit vector as a tuple. Raise ValueError for the zero vector. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "unit_vector_002500"}, "verifier": {"function": "unit_vector_002500", "tests": ["ux, uy = unit_vector_002500(3, 4); assert abs(ux - 0.6) < 1e-12 and abs(uy - 0.8) < 1e-12", "assert unit_vector_002500(0, 5) == (0, 1)", "try:\n    unit_vector_002500(0, 0)\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: rate_constant, number_of_steps.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"rate_constant\", \"number_of_steps\"]}", "dedupe_signature": "2be88f2b98fc83aae79e4c013111b7bd9e4d27dcaec71e2c75b1a7d485b9d2c4", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["rate_constant", "number_of_steps"]}, "id": "abstain_002501_rate_constant_number_of_steps", "license": "Apache-2.0", "prompt": "Use explicit Euler for dy/dt = -k y. The prompt gives y(0)=26.5 and h=1.55, but omits both k and the number of steps. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: rate_constant, number_of_steps.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["rate_constant", "number_of_steps"]}, "verifier": {"missing": ["rate_constant", "number_of_steps"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 18.8^2 and multiply by 0.5 * 28.2.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 4983.504, \"unit\": \"J\"}", "dedupe_signature": "0f8d8a4fda54c4631ffa3bc68feda306bf3fd1d900705070d8022093f3fc444c", "difficulty": "easy", "final_answer": {"answer": 4983.504, "unit": "J"}, "id": "ke_002503_28.2_18.8", "license": "Apache-2.0", "prompt": "A body of mass 28.2 kg moves at 18.8 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 18.8^2 and multiply by 0.5 * 28.2.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 28.2, "velocity": 18.8}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=45 degrees through the sine of 2 theta.\n3. Substitute v=66.7 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 453.5056, \"unit\": \"m\"}", "dedupe_signature": "1871d7bda8e851f5cf81ea82f18b5adbefcb4c9ab7ab3887755518a30279c69c", "difficulty": "medium", "final_answer": {"answer": 453.5056, "unit": "m"}, "id": "projectile_range_002504_66.7_45", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 66.7 m/s and angle 45 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=45 degrees through the sine of 2 theta.\nSubstitute v=66.7 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 45, "gravity": 9.81, "speed": 66.7}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 5.81 * 8.314 * 359 / 21.8.\nFinal: {\"answer\": 795.4706, \"unit\": \"kPa\"}", "dedupe_signature": "6568d564f8ca27e95f78f90d92032cb672a4b9ed0bdb48bd9beeb904e506c17b", "difficulty": "medium", "final_answer": {"answer": 795.4706, "unit": "kPa"}, "id": "ideal_gas_002505_5.81_359_21.8", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=5.81 mol, T=359 K, and V=21.8 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 5.81 * 8.314 * 359 / 21.8.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 5.81, "temp_k": 359, "volume_l": 21.8}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1760 * 1.87 * 62.\nFinal: {\"answer\": 204054.4, \"unit\": \"J\"}", "dedupe_signature": "557dac9320c53a4359c8949933bffb39363a41034712a8706a51ea5dd825fa93", "difficulty": "easy", "final_answer": {"answer": 204054.4, "unit": "J"}, "id": "heat_q_002506_1760_1.87_62", "license": "Apache-2.0", "prompt": "A 1760 g sample has specific heat 1.87 J/(g*K). How much heat is needed to raise its temperature by 62 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1760 * 1.87 * 62.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 62, "heat_capacity": 1.87, "mass_g": 1760}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=222.4 V and R=116.5 ohm.\nFinal: {\"answer\": 424.5645, \"unit\": \"W\"}", "dedupe_signature": "a6a8ce5e9eada2d7d79bf12c5a03d9c5391a38ebc1150cbbda485f8a3aa8bbac", "difficulty": "easy", "final_answer": {"answer": 424.5645, "unit": "W"}, "id": "ohm_power_002507_222.4_116.5", "license": "Apache-2.0", "prompt": "A resistor has resistance 116.5 ohm and voltage 222.4 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=222.4 V and R=116.5 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 116.5, "voltage": 222.4}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=602 mg, t=86.5 h, and T_half=53 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 194.2195, \"unit\": \"mg\"}", "dedupe_signature": "20b30dc047f8820e196848fdfdcf616c996f5bfbb4429294e6d2955b26b95b88", "difficulty": "medium", "final_answer": {"answer": 194.2195, "unit": "mg"}, "id": "half_life_002508_602_53_86.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 602 mg. Its half-life is 53 hours. How many mg remain after 86.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=602 mg, t=86.5 h, and T_half=53 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 86.5, "half_life": 53.0, "initial_amount": 602.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 2.94 mol * 44.01 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 129.3894, \"unit\": \"g\"}", "dedupe_signature": "be50afb4ddf0ad2bedd11a8711383ec332ffc8c74c445633e5136e35ff0db2c2", "difficulty": "medium", "final_answer": {"answer": 129.3894, "unit": "g"}, "id": "stoich_mass_002509_carbon_dioxide_2.94", "license": "Apache-2.0", "prompt": "A sample contains 2.94 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 2.94 mol * 44.01 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "carbon dioxide", "molar_mass": 44.01, "moles": 2.94}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 3000 mL to 3 L.\n3. Compute M = 1.165 / 3.\nFinal: {\"answer\": 0.3883, \"unit\": \"mol/L\"}", "dedupe_signature": "7577b346927f6c080cc541cbfc846a571f678db3e0524e6793d0010ad78cd403", "difficulty": "medium", "final_answer": {"answer": 0.3883, "unit": "mol/L"}, "id": "molarity_002510_1.165_3000", "license": "Apache-2.0", "prompt": "A solution contains 1.165 mol of solute in 3000 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 3000 mL to 3 L.\nCompute M = 1.165 / 3.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 1.165, "volume_ml": 3000}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.34 y, so each step multiplies y by 1 - h*0.34.\n3. Apply that update for 12 steps and round the final state.\nFinal: {\"answer\": 4.0119, \"unit\": \"state_units\"}", "dedupe_signature": "433d8530b3fce9d9093c2a5d5a556e00ad2c69facf94ed8a38574af2a964402f", "difficulty": "medium", "final_answer": {"answer": 4.0119, "unit": "state_units"}, "id": "euler_decay_002511_62_0.34_0.6_12", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.34 y with y(0)=62, step size h=0.6, for 12 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.34 y, so each step multiplies y by 1 - h*0.34.\nApply that update for 12 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 62.0, "rate": 0.34, "step": 0.6, "steps": 12}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(2.4)=-19.68 and f(7.8)=-61.26.\n3. The interval width is 5.4.\nFinal: {\"answer\": -218.538, \"unit\": \"area_units\"}", "dedupe_signature": "b43b4ba93a58ad19f05cdf17e215dcd153f9ace9c565315d255b60e940d961aa", "difficulty": "medium", "final_answer": {"answer": -218.538, "unit": "area_units"}, "id": "trapz_linear_002512_-7.7_-1.2_2.4_7.8", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-7.7x+-1.2 from x=2.4 to x=7.8. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(2.4)=-19.68 and f(7.8)=-61.26.\nThe interval width is 5.4.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -1.2, "slope": -7.7, "x0": 2.4, "x1": 7.800000000000001}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.1 and add it to the current value.\nFinal: {\"answer\": [1.24, 1.0, 1.91], \"unit\": \"temperature_units\"}", "dedupe_signature": "400f7ebc616ae769cee90a8fb4686fbde9c2c52e11721a56fdc9d33ecabde81b", "difficulty": "hard", "final_answer": {"answer": [1.24, 1.0, 1.91], "unit": "temperature_units"}, "id": "heat_step_002513_0.1_-0.35_1.5_0.75_2.5_-1.65", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-0.35, right=-1.65; current interior values are [1.5, 0.75, 2.5]. Use r=0.1. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.1 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [1.5, 0.75, 2.5], "left": -0.35, "r": 0.1, "right": -1.65}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 35801.0 / 1000.\nFinal: {\"answer\": 35.801, \"unit\": \"kg\"}", "dedupe_signature": "939bf1f01bea6a05ba6cb7a859371a9fc82556d402a4b537cb1ae010afc6308f", "difficulty": "easy", "final_answer": {"answer": 35.801, "unit": "kg"}, "id": "unit_convert_002514_g_to_kg_35801", "license": "Apache-2.0", "prompt": "Convert 35801 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 35801.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 35801.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=348 degrees and keep the unit as newtons.\nFinal: {\"answer\": [223.5067, -47.5078], \"unit\": \"N\"}", "dedupe_signature": "2b8cbcb1ee8c3e42ade00e5b9d1026fdbd8797ebe8ba9267f64894698895928e", "difficulty": "medium", "final_answer": {"answer": [223.5067, -47.5078], "unit": "N"}, "id": "vector_components_002515_228.5_348", "license": "Apache-2.0", "prompt": "A vector has magnitude 228.5 N at 348 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=348 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 348, "magnitude": 228.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [8.1, -4.75], \"unit\": \"dimensionless\"}", "dedupe_signature": "d25eb8864405cbf3abebdbc2873e8db9984914da5baa44ba2d707d12dc639120", "difficulty": "medium", "final_answer": {"answer": [8.1, -4.75], "unit": "dimensionless"}, "id": "line_two_point_002516_-16.75_-3_8.1_-4.75", "license": "Apache-2.0", "prompt": "A line passes through points (-16.75, -140.425) and (-3, -29.05). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -16.75, "x2": -3.0, "y1": -140.42499999999998, "y2": -29.049999999999997}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. density times acceleration times height gives kg/(m*s^2), or pascal\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "f71265caf2042438fca4a92fc48efff6e3d01c4e1d11cfbb2dc6981c371776b7", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_002517_consistent_b7d3eed1_647831", "license": "Apache-2.0", "prompt": "In field worksheet case 647831, check dimensional consistency for p = rho * g * h. The left side has dimensions Pa and the right side has dimensions Pa. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\ndensity times acceleration times height gives kg/(m*s^2), or pascal\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "p = rho * g * h"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef finite_differences_002518(values):\n    return [values[i + 1] - values[i] for i in range(len(values) - 1)]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"finite_differences_002518\"}", "dedupe_signature": "ad2099cdf6db4da3b6fa5c7aad7ce00e0d122eeab83b99dab75be24f5a88dd25", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "finite_differences_002518"}, "id": "code_002518_finite_differences_002518", "license": "Apache-2.0", "prompt": "Write a Python function finite_differences_002518(values) that returns the list of successive differences values[i+1] - values[i]. It must return [] for fewer than two values. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "finite_differences_002518"}, "verifier": {"function": "finite_differences_002518", "tests": ["assert finite_differences_002518([1, 4, 9, 16]) == [3, 5, 7]", "assert finite_differences_002518([5]) == []", "assert finite_differences_002518([]) == []"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: rate_constant, number_of_steps.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"rate_constant\", \"number_of_steps\"]}", "dedupe_signature": "5617daebd24d2b677512173e831d04b990999f9348e7577f716d7aadcc9f648a", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["rate_constant", "number_of_steps"]}, "id": "abstain_002519_rate_constant_number_of_steps", "license": "Apache-2.0", "prompt": "Use explicit Euler for dy/dt = -k y. The prompt gives y(0)=61.5 and h=1.25, but omits both k and the number of steps. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: rate_constant, number_of_steps.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["rate_constant", "number_of_steps"]}, "verifier": {"missing": ["rate_constant", "number_of_steps"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 17.15 kg and a = 5.05 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 86.6075, \"unit\": \"N\"}", "dedupe_signature": "11a74b68c1030c27a47406916004981848500298e0cd7269fc8fc7528bc61b1b", "difficulty": "easy", "final_answer": {"answer": 86.6075, "unit": "N"}, "id": "force_002520_17.15_5.05", "license": "Apache-2.0", "prompt": "A cart has mass 17.15 kg and measured acceleration 5.05 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 17.15 kg and a = 5.05 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 5.05, "mass": 17.15}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 25.25^2 and multiply by 0.5 * 13.25.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 4223.8516, \"unit\": \"J\"}", "dedupe_signature": "6b1645ccecd5023222553dbcced056573d1a6cc94986d33179c9a3d5a9f3187c", "difficulty": "easy", "final_answer": {"answer": 4223.8516, "unit": "J"}, "id": "ke_002521_13.25_25.25", "license": "Apache-2.0", "prompt": "A body of mass 13.25 kg moves at 25.25 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 25.25^2 and multiply by 0.5 * 13.25.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 13.25, "velocity": 25.25}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=65 degrees through the sine of 2 theta.\n3. Substitute v=16.9 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 22.3027, \"unit\": \"m\"}", "dedupe_signature": "9f19f71597513b2c4e91b309a2b0bc57424e169efe35dd2f12359984875d86d7", "difficulty": "medium", "final_answer": {"answer": 22.3027, "unit": "m"}, "id": "projectile_range_002522_16.9_65", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 16.9 m/s and angle 65 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=65 degrees through the sine of 2 theta.\nSubstitute v=16.9 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 65, "gravity": 9.81, "speed": 16.9}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 4 * 8.314 * 616 / 88.1.\nFinal: {\"answer\": 232.5278, \"unit\": \"kPa\"}", "dedupe_signature": "e7c5ed2fea07516c06bf811ef91926840707d33aa6fd7466887154d3f57e8934", "difficulty": "medium", "final_answer": {"answer": 232.5278, "unit": "kPa"}, "id": "ideal_gas_002523_4_616_88.1", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=4 mol, T=616 K, and V=88.1 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 4 * 8.314 * 616 / 88.1.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 4.0, "temp_k": 616, "volume_l": 88.1}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1335 * 4.035 * 46.\nFinal: {\"answer\": 247789.35, \"unit\": \"J\"}", "dedupe_signature": "9136555816b4b8508419fb17928f1711dad0bd91e90c7c2eb7912b7fb7f98020", "difficulty": "easy", "final_answer": {"answer": 247789.35, "unit": "J"}, "id": "heat_q_002524_1335_4.035_46", "license": "Apache-2.0", "prompt": "A 1335 g sample has specific heat 4.035 J/(g*K). How much heat is needed to raise its temperature by 46 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1335 * 4.035 * 46.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 46, "heat_capacity": 4.035, "mass_g": 1335}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=45.6 V and R=53.6 ohm.\nFinal: {\"answer\": 38.794, \"unit\": \"W\"}", "dedupe_signature": "03df0abdeb873729b2913aad5e21d6b8ebc0d1d30179872d1a4d359a023be902", "difficulty": "easy", "final_answer": {"answer": 38.794, "unit": "W"}, "id": "ohm_power_002525_45.6_53.6", "license": "Apache-2.0", "prompt": "A resistor has resistance 53.6 ohm and voltage 45.6 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=45.6 V and R=53.6 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 53.6, "voltage": 45.6}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=111 mg, t=357 h, and T_half=4.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 0.0, \"unit\": \"mg\"}", "dedupe_signature": "2e954bbce767472a0149f2686d129c5b845e7d5cbb3c5720b15554b647cb7dfa", "difficulty": "medium", "final_answer": {"answer": 0.0, "unit": "mg"}, "id": "half_life_002526_111_4.5_357", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 111 mg. Its half-life is 4.5 hours. How many mg remain after 357 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=111 mg, t=357 h, and T_half=4.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 357.0, "half_life": 4.5, "initial_amount": 111.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 5.56 mol * 180.156 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 1001.6674, \"unit\": \"g\"}", "dedupe_signature": "63f15514dfd9c056832437a0c7126a689816c2b446b77a41d4d91c61e755e0c2", "difficulty": "medium", "final_answer": {"answer": 1001.6674, "unit": "g"}, "id": "stoich_mass_002527_glucose_5.56", "license": "Apache-2.0", "prompt": "A sample contains 5.56 mol of glucose. Using molar mass 180.156 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 5.56 mol * 180.156 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "glucose", "molar_mass": 180.156, "moles": 5.56}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 890 mL to 0.89 L.\n3. Compute M = 2.195 / 0.89.\nFinal: {\"answer\": 2.4663, \"unit\": \"mol/L\"}", "dedupe_signature": "debf03e7dc7977f0f3bc76f0fed98341251b77beadd9d52fa44587d0e3f7bcb0", "difficulty": "medium", "final_answer": {"answer": 2.4663, "unit": "mol/L"}, "id": "molarity_002528_2.195_890", "license": "Apache-2.0", "prompt": "A solution contains 2.195 mol of solute in 890 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 890 mL to 0.89 L.\nCompute M = 2.195 / 0.89.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 2.195, "volume_ml": 890}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-2.1)=14.26 and f(-0.5)=13.3.\n3. The interval width is 1.6.\nFinal: {\"answer\": 22.048, \"unit\": \"area_units\"}", "dedupe_signature": "faa583625c98e9aeab6991de53a25e398d421f902034ac754eb794100ca85f92", "difficulty": "medium", "final_answer": {"answer": 22.048, "unit": "area_units"}, "id": "trapz_linear_002530_-0.6_13_-2.1_-0.5", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-0.6x+13 from x=-2.1 to x=-0.5. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-2.1)=14.26 and f(-0.5)=13.3.\nThe interval width is 1.6.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 13.0, "slope": -0.6, "x0": -2.1, "x1": -0.5}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.48 and add it to the current value.\nFinal: {\"answer\": [-1.092, 0.672, -1.056], \"unit\": \"temperature_units\"}", "dedupe_signature": "36b5d4d75b5159932e1e8c4ede916116cd348b82ff1b762d83fa952ad3d0e4cf", "difficulty": "hard", "final_answer": {"answer": [-1.092, 0.672, -1.056], "unit": "temperature_units"}, "id": "heat_step_002531_0.48_-1.3_2.7_-1.2_-1.2_-0.9", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-1.3, right=-0.9; current interior values are [2.7, -1.2, -1.2]. Use r=0.48. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.48 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [2.7, -1.2, -1.2], "left": -1.3, "r": 0.48, "right": -0.9}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 49912.0 / 1000.\nFinal: {\"answer\": 49.912, \"unit\": \"kg\"}", "dedupe_signature": "b4eb63897b0ac52bd16038388f71fa6b969761ed7c7261f97aa2c7bdde1926a3", "difficulty": "easy", "final_answer": {"answer": 49.912, "unit": "kg"}, "id": "unit_convert_002532_g_to_kg_49912", "license": "Apache-2.0", "prompt": "Convert 49912 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 49912.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 49912.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=208 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-114.7832, -61.0313], \"unit\": \"N\"}", "dedupe_signature": "eb61f1bf7e6b614c381b6807072ebed096c998556976c0013efd5de8c8cfaf77", "difficulty": "medium", "final_answer": {"answer": [-114.7832, -61.0313], "unit": "N"}, "id": "vector_components_002533_130_208", "license": "Apache-2.0", "prompt": "A vector has magnitude 130 N at 208 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=208 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 208, "magnitude": 130.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-9.75, -5.25], \"unit\": \"dimensionless\"}", "dedupe_signature": "1186269f95223b402c43228f0164fee21164112ef72bb924791eb9915a3d9e3f", "difficulty": "medium", "final_answer": {"answer": [-9.75, -5.25], "unit": "dimensionless"}, "id": "line_two_point_002534_0.5_8.25_-9.75_-5.25", "license": "Apache-2.0", "prompt": "A line passes through points (0.5, -10.125) and (8.25, -85.6875). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 0.5, "x2": 8.25, "y1": -10.125, "y2": -85.6875}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. mass times acceleration has newton dimensions\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "ea569421670ac86deceb0db5157ccd026f3a4c8f325e73810c336d5b30ea70c7", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_002535_consistent_03f5e041_919623", "license": "Apache-2.0", "prompt": "In model card equation case 919623, check dimensional consistency for F = m * a. The left side has dimensions kg*m/s^2 and the right side has dimensions kg*m/s^2. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nmass times acceleration has newton dimensions\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "F = m * a"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef finite_differences_002536(values):\n    return [values[i + 1] - values[i] for i in range(len(values) - 1)]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"finite_differences_002536\"}", "dedupe_signature": "b37e4926c2fd34e44b32d8ac55911d2e5224656b97ed839f0fdc5dc338be5561", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "finite_differences_002536"}, "id": "code_002536_finite_differences_002536", "license": "Apache-2.0", "prompt": "Write a Python function finite_differences_002536(values) that returns the list of successive differences values[i+1] - values[i]. It must return [] for fewer than two values. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "finite_differences_002536"}, "verifier": {"function": "finite_differences_002536", "tests": ["assert finite_differences_002536([1, 4, 9, 16]) == [3, 5, 7]", "assert finite_differences_002536([5]) == []", "assert finite_differences_002536([]) == []"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: target_schema, valid_examples.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"target_schema\", \"valid_examples\"]}", "dedupe_signature": "62d33ea3091af2318958d3503a530bda00bc9329f686a21fcefd3b6161c8ab6f", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["target_schema", "valid_examples"]}, "id": "abstain_002537_target_schema_valid_examples", "license": "Apache-2.0", "prompt": "Write a parser that converts each field sensor record from batch 728748 into the correct schema, but the prompt does not include the target schema or examples. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: target_schema, valid_examples.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["target_schema", "valid_examples"]}, "verifier": {"missing": ["target_schema", "valid_examples"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 22.75 kg and a = 13.2 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 300.3, \"unit\": \"N\"}", "dedupe_signature": "c056f2653dec16be940a445c01e2059eb6a0de2ff5750f0ab45a9100f493d8c0", "difficulty": "easy", "final_answer": {"answer": 300.3, "unit": "N"}, "id": "force_002538_22.75_13.2", "license": "Apache-2.0", "prompt": "A cart has mass 22.75 kg and measured acceleration 13.2 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 22.75 kg and a = 13.2 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 13.2, "mass": 22.75}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 19^2 and multiply by 0.5 * 19.25.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 3474.625, \"unit\": \"J\"}", "dedupe_signature": "8b5446cb2211526951466025f5255c40c5f2ab4bef5c4b32f68299f6e6e21b0b", "difficulty": "easy", "final_answer": {"answer": 3474.625, "unit": "J"}, "id": "ke_002539_19.25_19", "license": "Apache-2.0", "prompt": "A body of mass 19.25 kg moves at 19 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 19^2 and multiply by 0.5 * 19.25.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 19.25, "velocity": 19.0}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=67 degrees through the sine of 2 theta.\n3. Substitute v=14.2 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 14.7857, \"unit\": \"m\"}", "dedupe_signature": "c6c75f3d5866d7182e5732d0527b1639ba6b60fdbcff58524b0f9e4d6edce3c4", "difficulty": "medium", "final_answer": {"answer": 14.7857, "unit": "m"}, "id": "projectile_range_002540_14.2_67", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 14.2 m/s and angle 67 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=67 degrees through the sine of 2 theta.\nSubstitute v=14.2 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 67, "gravity": 9.81, "speed": 14.2}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 4.23 * 8.314 * 305 / 110.4.\nFinal: {\"answer\": 97.1586, \"unit\": \"kPa\"}", "dedupe_signature": "211fd7c1ad808e15f86b73b45b6393469b5fee5fb975323996c998ac284cf7e1", "difficulty": "medium", "final_answer": {"answer": 97.1586, "unit": "kPa"}, "id": "ideal_gas_002541_4.23_305_110.4", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=4.23 mol, T=305 K, and V=110.4 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 4.23 * 8.314 * 305 / 110.4.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 4.23, "temp_k": 305, "volume_l": 110.4}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 645 * 3.81 * 120.\nFinal: {\"answer\": 294894.0, \"unit\": \"J\"}", "dedupe_signature": "f2b35ff27a3e5d5528f51bccb09d71a9967b336fbd18c31810cd2213188e8b5e", "difficulty": "easy", "final_answer": {"answer": 294894.0, "unit": "J"}, "id": "heat_q_002542_645_3.81_120", "license": "Apache-2.0", "prompt": "A 645 g sample has specific heat 3.81 J/(g*K). How much heat is needed to raise its temperature by 120 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 645 * 3.81 * 120.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 120, "heat_capacity": 3.81, "mass_g": 645}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=211.9 V and R=104 ohm.\nFinal: {\"answer\": 431.7463, \"unit\": \"W\"}", "dedupe_signature": "adfa9c75c436f7b080d05ecb82948a3feae8a9f3d93783f4a753eaffbcdec17f", "difficulty": "easy", "final_answer": {"answer": 431.7463, "unit": "W"}, "id": "ohm_power_002543_211.9_104", "license": "Apache-2.0", "prompt": "A resistor has resistance 104 ohm and voltage 211.9 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=211.9 V and R=104 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 104.0, "voltage": 211.9}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 4.01 mol * 100.087 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 401.3489, \"unit\": \"g\"}", "dedupe_signature": "39b2fecf35d91efe4270a50ffc8e757132067ad00dad8dc29a77eda5f3f7b1a1", "difficulty": "medium", "final_answer": {"answer": 401.3489, "unit": "g"}, "id": "stoich_mass_002545_calcium_carbonate_4.01", "license": "Apache-2.0", "prompt": "A sample contains 4.01 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 4.01 mol * 100.087 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "calcium carbonate", "molar_mass": 100.087, "moles": 4.01}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 4240 mL to 4.24 L.\n3. Compute M = 3.685 / 4.24.\nFinal: {\"answer\": 0.8691, \"unit\": \"mol/L\"}", "dedupe_signature": "4489f5d01610eba6b35ef66fa25676311b929680d6d2ca2fb863451dfea95dbc", "difficulty": "medium", "final_answer": {"answer": 0.8691, "unit": "mol/L"}, "id": "molarity_002546_3.685_4240", "license": "Apache-2.0", "prompt": "A solution contains 3.685 mol of solute in 4240 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 4240 mL to 4.24 L.\nCompute M = 3.685 / 4.24.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 3.685, "volume_ml": 4240}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-4.6)=10.68 and f(-0.8)=-11.36.\n3. The interval width is 3.8.\nFinal: {\"answer\": -1.292, \"unit\": \"area_units\"}", "dedupe_signature": "1dc2fc55c6fa896976813f53eb6b4fb1c53e54b60f65d10ba4036e955725c1d2", "difficulty": "medium", "final_answer": {"answer": -1.292, "unit": "area_units"}, "id": "trapz_linear_002548_-5.8_-16_-4.6_-0.8", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-5.8x+-16 from x=-4.6 to x=-0.8. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-4.6)=10.68 and f(-0.8)=-11.36.\nThe interval width is 3.8.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -16.0, "slope": -5.8, "x0": -4.6, "x1": -0.7999999999999998}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.32 and add it to the current value.\nFinal: {\"answer\": [-0.53, -0.446, -0.624], \"unit\": \"temperature_units\"}", "dedupe_signature": "a76e478b3eac1f47a8ad41e2ae8348a0d15f5bb052d05f99c478a9950f9ae00a", "difficulty": "hard", "final_answer": {"answer": [-0.53, -0.446, -0.624], "unit": "temperature_units"}, "id": "heat_step_002549_0.32_-1.85_1.55_-1.55_-1.2_0.95", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-1.85, right=0.95; current interior values are [1.55, -1.55, -1.2]. Use r=0.32. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.32 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [1.55, -1.55, -1.2], "left": -1.85, "r": 0.32, "right": 0.95}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kelvin equals Celsius plus 273.15.\n2. Apply the conversion factor directly to the given value.\n3. Compute -61.5 + 273.15.\nFinal: {\"answer\": 211.65, \"unit\": \"K\"}", "dedupe_signature": "9de73bc37be02f9733e2ea4bcc505df172019ae6f951e83c24c842c5dda12889", "difficulty": "easy", "final_answer": {"answer": 211.65, "unit": "K"}, "id": "unit_convert_002550_c_to_k_-61.5", "license": "Apache-2.0", "prompt": "Convert -61.5 degC to K. Return the converted value with unit.", "reasoning_trace": "Kelvin equals Celsius plus 273.15.\nApply the conversion factor directly to the given value.\nCompute -61.5 + 273.15.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": -61.5}, "verifier": {"formula": "value + 273.15", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=355 degrees and keep the unit as newtons.\nFinal: {\"answer\": [383.0369, -33.5114], \"unit\": \"N\"}", "dedupe_signature": "a82cce4d314888b42c03e48c4652db540cf8e29dd7d7a7514d18a522c42965b1", "difficulty": "medium", "final_answer": {"answer": [383.0369, -33.5114], "unit": "N"}, "id": "vector_components_002551_384.5_355", "license": "Apache-2.0", "prompt": "A vector has magnitude 384.5 N at 355 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=355 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 355, "magnitude": 384.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-9.95, -17.75], \"unit\": \"dimensionless\"}", "dedupe_signature": "d5e31ba23096a5b2499159c88a3493b52156eb9bd6e9d4f7af54082a79a662b0", "difficulty": "medium", "final_answer": {"answer": [-9.95, -17.75], "unit": "dimensionless"}, "id": "line_two_point_002552_-14.75_-7.5_-9.95_-17.75", "license": "Apache-2.0", "prompt": "A line passes through points (-14.75, 129.012) and (-7.5, 56.875). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -14.75, "x2": -7.5, "y1": 129.0125, "y2": 56.875}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. grams cancel with J/(g*K), and kelvin cancels, leaving joules\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "67c6772e2d7ecd9241e2a3c412901f92b5d9a07e8333ce14af49c62523850f70", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_002553_consistent_4153435f_982364", "license": "Apache-2.0", "prompt": "In field worksheet case 982364, check dimensional consistency for Q = m * c * DeltaT. The left side has dimensions J and the right side has dimensions J. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\ngrams cancel with J/(g*K), and kelvin cancels, leaving joules\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "Q = m * c * DeltaT"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\nimport math\n\ndef unit_vector_002554(x, y):\n    norm = math.hypot(x, y)\n    if norm == 0:\n        raise ValueError('zero vector has no direction')\n    return (x / norm, y / norm)\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"unit_vector_002554\"}", "dedupe_signature": "20a583fb4766429b57f6ab1f950887927b751a726802e73572b8687aa98f96d1", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "unit_vector_002554"}, "id": "code_002554_unit_vector_002554", "license": "Apache-2.0", "prompt": "Write a Python function unit_vector_002554(x, y) that returns the 2D unit vector as a tuple. Raise ValueError for the zero vector. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "unit_vector_002554"}, "verifier": {"function": "unit_vector_002554", "tests": ["ux, uy = unit_vector_002554(3, 4); assert abs(ux - 0.6) < 1e-12 and abs(uy - 0.8) < 1e-12", "assert unit_vector_002554(0, 5) == (0, 1)", "try:\n    unit_vector_002554(0, 0)\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: left_boundary, right_boundary.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"left_boundary\", \"right_boundary\"]}", "dedupe_signature": "94012527e3c930e5cbff64322068c2fba4e3b0217276e90e7d93f8e4a52dcd29", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["left_boundary", "right_boundary"]}, "id": "abstain_002555_left_boundary_right_boundary", "license": "Apache-2.0", "prompt": "Solve the 1D heat equation after one finite-difference step. The prompt gives r=0.1 and interior values [1.3, 2.55, 0.85], but gives no boundary values. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: left_boundary, right_boundary.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["left_boundary", "right_boundary"]}, "verifier": {"missing": ["left_boundary", "right_boundary"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 8.35 kg and a = 14.1 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 117.735, \"unit\": \"N\"}", "dedupe_signature": "2191369bfcefe01b08d3fd31cc3ab095c1b2470a9fd1bc0aa1e090ad5bf8ae0a", "difficulty": "easy", "final_answer": {"answer": 117.735, "unit": "N"}, "id": "force_002556_8.35_14.1", "license": "Apache-2.0", "prompt": "A cart has mass 8.35 kg and measured acceleration 14.1 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 8.35 kg and a = 14.1 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 14.1, "mass": 8.35}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=28 degrees through the sine of 2 theta.\n3. Substitute v=59.9 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 303.2207, \"unit\": \"m\"}", "dedupe_signature": "d515d79ef2fee5bad1a76c8ed71962f66430a553bd5b7b9e7cb1b54bdbf4dfa5", "difficulty": "medium", "final_answer": {"answer": 303.2207, "unit": "m"}, "id": "projectile_range_002558_59.9_28", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 59.9 m/s and angle 28 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=28 degrees through the sine of 2 theta.\nSubstitute v=59.9 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 28, "gravity": 9.81, "speed": 59.9}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 3.09 * 8.314 * 533 / 33.3.\nFinal: {\"answer\": 411.1985, \"unit\": \"kPa\"}", "dedupe_signature": "fe71abe7a26ecac14eb086f0323736618a64789145b3e6f51056e1adb14a41d7", "difficulty": "medium", "final_answer": {"answer": 411.1985, "unit": "kPa"}, "id": "ideal_gas_002559_3.09_533_33.3", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=3.09 mol, T=533 K, and V=33.3 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 3.09 * 8.314 * 533 / 33.3.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 3.09, "temp_k": 533, "volume_l": 33.3}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1795 * 4.25 * 65.\nFinal: {\"answer\": 495868.75, \"unit\": \"J\"}", "dedupe_signature": "b50f76d4b322b6e3b82bbe67f17250f5b019b09943db9b4c1672e8484d5f580a", "difficulty": "easy", "final_answer": {"answer": 495868.75, "unit": "J"}, "id": "heat_q_002560_1795_4.25_65", "license": "Apache-2.0", "prompt": "A 1795 g sample has specific heat 4.25 J/(g*K). How much heat is needed to raise its temperature by 65 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1795 * 4.25 * 65.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 65, "heat_capacity": 4.25, "mass_g": 1795}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=818.5 mg, t=255 h, and T_half=2 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 0.0, \"unit\": \"mg\"}", "dedupe_signature": "370bb6a7b84e0897e7839dd274c44fd4197fa8ff4af017d2bf7a4f39ff3170ef", "difficulty": "medium", "final_answer": {"answer": 0.0, "unit": "mg"}, "id": "half_life_002562_818.5_2_255", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 818.5 mg. Its half-life is 2 hours. How many mg remain after 255 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=818.5 mg, t=255 h, and T_half=2 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 255.0, "half_life": 2.0, "initial_amount": 818.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 5.09 mol * 100.087 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 509.4428, \"unit\": \"g\"}", "dedupe_signature": "32efdc48c5e56dbd87b6cbc02864a9b12bcf386bb9ed35919cf2586012eab58c", "difficulty": "medium", "final_answer": {"answer": 509.4428, "unit": "g"}, "id": "stoich_mass_002563_calcium_carbonate_5.09", "license": "Apache-2.0", "prompt": "A sample contains 5.09 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 5.09 mol * 100.087 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "calcium carbonate", "molar_mass": 100.087, "moles": 5.09}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 2215 mL to 2.215 L.\n3. Compute M = 0.755 / 2.215.\nFinal: {\"answer\": 0.3409, \"unit\": \"mol/L\"}", "dedupe_signature": "46ee9a512079ee8eeff3a5c79eb7faf63792ae2469adbe66fcdbadb7917db850", "difficulty": "medium", "final_answer": {"answer": 0.3409, "unit": "mol/L"}, "id": "molarity_002564_0.755_2215", "license": "Apache-2.0", "prompt": "A solution contains 0.755 mol of solute in 2215 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 2215 mL to 2.215 L.\nCompute M = 0.755 / 2.215.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 0.755, "volume_ml": 2215}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.06 and add it to the current value.\nFinal: {\"answer\": [0.97, 0.052, -1.42], \"unit\": \"temperature_units\"}", "dedupe_signature": "aed6378008ad7b09401480907f5a02eaaec34e38506c2f2b21ff067a602a152f", "difficulty": "hard", "final_answer": {"answer": [0.97, 0.052, -1.42], "unit": "temperature_units"}, "id": "heat_step_002567_0.06_-0.8_1.15_0.1_-1.75_1.9", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-0.8, right=1.9; current interior values are [1.15, 0.1, -1.75]. Use r=0.06. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.06 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [1.15, 0.1, -1.75], "left": -0.8, "r": 0.06, "right": 1.9}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kelvin equals Celsius plus 273.15.\n2. Apply the conversion factor directly to the given value.\n3. Compute 186.5 + 273.15.\nFinal: {\"answer\": 459.65, \"unit\": \"K\"}", "dedupe_signature": "d88ed0b9f41e58b0c7f252f4d8ec364a30ee91022e85190c47e23ed5f515c350", "difficulty": "easy", "final_answer": {"answer": 459.65, "unit": "K"}, "id": "unit_convert_002568_c_to_k_186.5", "license": "Apache-2.0", "prompt": "Convert 186.5 degC to K. Return the converted value with unit.", "reasoning_trace": "Kelvin equals Celsius plus 273.15.\nApply the conversion factor directly to the given value.\nCompute 186.5 + 273.15.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 186.5}, "verifier": {"formula": "value + 273.15", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=177 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-205.2184, 10.755], \"unit\": \"N\"}", "dedupe_signature": "03c0793195f25a399ffb6fea950e8209e370b07747df8ce970b71b6c818de044", "difficulty": "medium", "final_answer": {"answer": [-205.2184, 10.755], "unit": "N"}, "id": "vector_components_002569_205.5_177", "license": "Apache-2.0", "prompt": "A vector has magnitude 205.5 N at 177 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=177 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 177, "magnitude": 205.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-8.45, -27.0], \"unit\": \"dimensionless\"}", "dedupe_signature": "c2468476d5b250f00f448651e3d175a90151452520984c338068bb82fba62333", "difficulty": "medium", "final_answer": {"answer": [-8.45, -27.0], "unit": "dimensionless"}, "id": "line_two_point_002570_-11.5_-3.75_-8.45_-27", "license": "Apache-2.0", "prompt": "A line passes through points (-11.5, 70.175) and (-3.75, 4.6875). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -11.5, "x2": -3.75, "y1": 70.175, "y2": 4.6874999999999964}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef pairwise_ratios_002572(numerators, denominators):\n    if len(numerators) != len(denominators):\n        raise ValueError('length mismatch')\n    out = []\n    for numerator, denominator in zip(numerators, denominators):\n        if denominator == 0:\n            raise ValueError('zero denominator')\n        out.append(numerator / denominator)\n    return out\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"pairwise_ratios_002572\"}", "dedupe_signature": "7d9f82989a7f74ee7cb18439af15c1afe12025abccb7f4c03e80f2c92f225dbd", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "pairwise_ratios_002572"}, "id": "code_002572_pairwise_ratios_002572", "license": "Apache-2.0", "prompt": "Write a Python function pairwise_ratios_002572(numerators, denominators) that returns a list of n/d values. Raise ValueError if lengths differ or any denominator is zero. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "pairwise_ratios_002572"}, "verifier": {"function": "pairwise_ratios_002572", "tests": ["assert pairwise_ratios_002572([2, 9], [4, 3]) == [0.5, 3.0]", "try:\n    pairwise_ratios_002572([1], [0])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass", "try:\n    pairwise_ratios_002572([1, 2], [1])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: rate_constant, number_of_steps.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"rate_constant\", \"number_of_steps\"]}", "dedupe_signature": "1bb5102b1b90855438851968257481cba1ada5697cb0b0270d42d89071527d11", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["rate_constant", "number_of_steps"]}, "id": "abstain_002573_rate_constant_number_of_steps", "license": "Apache-2.0", "prompt": "Use explicit Euler for dy/dt = -k y. The prompt gives y(0)=52.5 and h=0.55, but omits both k and the number of steps. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: rate_constant, number_of_steps.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["rate_constant", "number_of_steps"]}, "verifier": {"missing": ["rate_constant", "number_of_steps"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 21.05 kg and a = 12.65 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 266.2825, \"unit\": \"N\"}", "dedupe_signature": "b16d57948f6daaaf6559bf63dd5d7906987cd1d6b96ce566b47bb2bda3e0d85e", "difficulty": "easy", "final_answer": {"answer": 266.2825, "unit": "N"}, "id": "force_002574_21.05_12.65", "license": "Apache-2.0", "prompt": "A cart has mass 21.05 kg and measured acceleration 12.65 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 21.05 kg and a = 12.65 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 12.65, "mass": 21.05}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 23.4^2 and multiply by 0.5 * 19.5.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 5338.71, \"unit\": \"J\"}", "dedupe_signature": "55ef7d03b6611aafa3d31a1c294612a9ac3ab2da2b43be5f0730e8e50e8ced2b", "difficulty": "easy", "final_answer": {"answer": 5338.71, "unit": "J"}, "id": "ke_002575_19.5_23.4", "license": "Apache-2.0", "prompt": "A body of mass 19.5 kg moves at 23.4 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 23.4^2 and multiply by 0.5 * 19.5.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 19.5, "velocity": 23.4}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=15 degrees through the sine of 2 theta.\n3. Substitute v=76.8 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 300.6239, \"unit\": \"m\"}", "dedupe_signature": "a4959f461fa3a0299072b4a9848ddd2c050558ed62e15620eeefee3f7b628d4f", "difficulty": "medium", "final_answer": {"answer": 300.6239, "unit": "m"}, "id": "projectile_range_002576_76.8_15", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 76.8 m/s and angle 15 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=15 degrees through the sine of 2 theta.\nSubstitute v=76.8 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 15, "gravity": 9.81, "speed": 76.8}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 2.76 * 8.314 * 616 / 117.2.\nFinal: {\"answer\": 120.6069, \"unit\": \"kPa\"}", "dedupe_signature": "4a2e6b62266221d9855591d43d010d21e0c9faded154397947937da1769292d3", "difficulty": "medium", "final_answer": {"answer": 120.6069, "unit": "kPa"}, "id": "ideal_gas_002577_2.76_616_117.2", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=2.76 mol, T=616 K, and V=117.2 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 2.76 * 8.314 * 616 / 117.2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 2.76, "temp_k": 616, "volume_l": 117.2}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 480 * 2.81 * 88.\nFinal: {\"answer\": 118694.4, \"unit\": \"J\"}", "dedupe_signature": "8452c2beb1e76a8f348f66ae4fc54881c8de3d3a1c522cceb70f8edaf6257dc5", "difficulty": "easy", "final_answer": {"answer": 118694.4, "unit": "J"}, "id": "heat_q_002578_480_2.81_88", "license": "Apache-2.0", "prompt": "A 480 g sample has specific heat 2.81 J/(g*K). How much heat is needed to raise its temperature by 88 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 480 * 2.81 * 88.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 88, "heat_capacity": 2.81, "mass_g": 480}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=224.2 V and R=122.7 ohm.\nFinal: {\"answer\": 409.6629, \"unit\": \"W\"}", "dedupe_signature": "8326b1125f7331d0f083af2e1af068e7a843dd7c61266227d32d67488a6c4bbb", "difficulty": "easy", "final_answer": {"answer": 409.6629, "unit": "W"}, "id": "ohm_power_002579_224.2_122.7", "license": "Apache-2.0", "prompt": "A resistor has resistance 122.7 ohm and voltage 224.2 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=224.2 V and R=122.7 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 122.7, "voltage": 224.2}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=396.5 mg, t=64.5 h, and T_half=1.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 0.0, \"unit\": \"mg\"}", "dedupe_signature": "9fca46217c0064f86e9f777b3748c212b49ec5bc85e82bb4ddb816b4be095b4a", "difficulty": "medium", "final_answer": {"answer": 0.0, "unit": "mg"}, "id": "half_life_002580_396.5_1.5_64.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 396.5 mg. Its half-life is 1.5 hours. How many mg remain after 64.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=396.5 mg, t=64.5 h, and T_half=1.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 64.5, "half_life": 1.5, "initial_amount": 396.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 3.73 mol * 100.087 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 373.3245, \"unit\": \"g\"}", "dedupe_signature": "fbd7c2f758d07ec6aaaab0ff03a568bd4fa505058fc0254acf44340acb8842b4", "difficulty": "medium", "final_answer": {"answer": 373.3245, "unit": "g"}, "id": "stoich_mass_002581_calcium_carbonate_3.73", "license": "Apache-2.0", "prompt": "A sample contains 3.73 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 3.73 mol * 100.087 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "calcium carbonate", "molar_mass": 100.087, "moles": 3.73}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.55 y, so each step multiplies y by 1 - h*0.55.\n3. Apply that update for 4 steps and round the final state.\nFinal: {\"answer\": 0.0014, \"unit\": \"state_units\"}", "dedupe_signature": "d1fcad467b7ec418c416aa1ac474bbcceea29ceef357a9b9b067ff70e9d699c1", "difficulty": "medium", "final_answer": {"answer": 0.0014, "unit": "state_units"}, "id": "euler_decay_002583_78.5_0.55_1.7_4", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.55 y with y(0)=78.5, step size h=1.7, for 4 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.55 y, so each step multiplies y by 1 - h*0.55.\nApply that update for 4 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 78.5, "rate": 0.55, "step": 1.7, "steps": 4}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-6)=-22.3 and f(-0.6)=-15.82.\n3. The interval width is 5.4.\nFinal: {\"answer\": -102.924, \"unit\": \"area_units\"}", "dedupe_signature": "9bb2039acdbee6b7976f5e62dc795087372ba8b6e53255080a92599df2195d3a", "difficulty": "medium", "final_answer": {"answer": -102.924, "unit": "area_units"}, "id": "trapz_linear_002584_1.2_-15.1_-6_-0.6", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=1.2x+-15.1 from x=-6 to x=-0.6. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-6)=-22.3 and f(-0.6)=-15.82.\nThe interval width is 5.4.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -15.1, "slope": 1.2, "x0": -6.0, "x1": -0.5999999999999996}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.38 and add it to the current value.\nFinal: {\"answer\": [1.513, 0.247, 1.243], \"unit\": \"temperature_units\"}", "dedupe_signature": "298a959d06b958bb059a2419c8e3660298dfab2db018089b211affc5abdbaa59", "difficulty": "hard", "final_answer": {"answer": [1.513, 0.247, 1.243], "unit": "temperature_units"}, "id": "heat_step_002585_0.38_1.45_1.0_1.9_-1.55_2.35", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.45, right=2.35; current interior values are [1.0, 1.9, -1.55]. Use r=0.38. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.38 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [1.0, 1.9, -1.55], "left": 1.45, "r": 0.38, "right": 2.35}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=58 degrees and keep the unit as newtons.\nFinal: {\"answer\": [100.9496, 161.5532], \"unit\": \"N\"}", "dedupe_signature": "96e25978ed724c6ca70e7393a68dbded03dfc904f1c63dc6b102ba155cbd5bf3", "difficulty": "medium", "final_answer": {"answer": [100.9496, 161.5532], "unit": "N"}, "id": "vector_components_002587_190.5_58", "license": "Apache-2.0", "prompt": "A vector has magnitude 190.5 N at 58 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=58 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 58, "magnitude": 190.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [4.9, 28.5], \"unit\": \"dimensionless\"}", "dedupe_signature": "88f8c74fe73c0f1d20aa6d622e41e16f1a4bff7617cb21ed0e29987de18d02d3", "difficulty": "medium", "final_answer": {"answer": [4.9, 28.5], "unit": "dimensionless"}, "id": "line_two_point_002588_13.25_16.5_4.9_28.5", "license": "Apache-2.0", "prompt": "A line passes through points (13.25, 93.425) and (16.5, 109.35). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 13.25, "x2": 16.5, "y1": 93.42500000000001, "y2": 109.35000000000001}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. lever arm times force has torque dimensions\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "f9d93bb0b1ce9dd92465525a5a90c30d412ac8d8797b986ad18fe9e338a80e92", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_002589_consistent_5ca82cb9_991512", "license": "Apache-2.0", "prompt": "In field worksheet case 991512, check dimensional consistency for tau = r * F. The left side has dimensions N*m and the right side has dimensions N*m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nlever arm times force has torque dimensions\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "tau = r * F"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef pairwise_ratios_002590(numerators, denominators):\n    if len(numerators) != len(denominators):\n        raise ValueError('length mismatch')\n    out = []\n    for numerator, denominator in zip(numerators, denominators):\n        if denominator == 0:\n            raise ValueError('zero denominator')\n        out.append(numerator / denominator)\n    return out\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"pairwise_ratios_002590\"}", "dedupe_signature": "7f4680101b919448fa75d221ea22fb8184458578e6eff8a1d6341cda4178635c", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "pairwise_ratios_002590"}, "id": "code_002590_pairwise_ratios_002590", "license": "Apache-2.0", "prompt": "Write a Python function pairwise_ratios_002590(numerators, denominators) that returns a list of n/d values. Raise ValueError if lengths differ or any denominator is zero. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "pairwise_ratios_002590"}, "verifier": {"function": "pairwise_ratios_002590", "tests": ["assert pairwise_ratios_002590([2, 9], [4, 3]) == [0.5, 3.0]", "try:\n    pairwise_ratios_002590([1], [0])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass", "try:\n    pairwise_ratios_002590([1, 2], [1])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: volume.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"volume\"]}", "dedupe_signature": "d21ea5e5b72320d65f4333dd1e363fbc9b3ad2b643633eaf0a483984048344b7", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["volume"]}, "id": "abstain_002591_volume", "license": "Apache-2.0", "prompt": "Compute pressure from the ideal gas law. The prompt gives n=1.37 mol and T=323 K, but does not give volume. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: volume.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["volume"]}, "verifier": {"missing": ["volume"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=67 degrees through the sine of 2 theta.\n3. Substitute v=7.4 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 4.0154, \"unit\": \"m\"}", "dedupe_signature": "840ea7fe57a2ce460e3543e0dcec18242a83e13e94c7cb15fe3bc36ff3c9b00a", "difficulty": "medium", "final_answer": {"answer": 4.0154, "unit": "m"}, "id": "projectile_range_002594_7.4_67", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 7.4 m/s and angle 67 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=67 degrees through the sine of 2 theta.\nSubstitute v=7.4 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 67, "gravity": 9.81, "speed": 7.4}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 0.78 * 8.314 * 260 / 27.3.\nFinal: {\"answer\": 61.7611, \"unit\": \"kPa\"}", "dedupe_signature": "7fb9d4fa995447ef204e60b65237376979abc41caffac091b2ca35831b2ebefd", "difficulty": "medium", "final_answer": {"answer": 61.7611, "unit": "kPa"}, "id": "ideal_gas_002595_0.78_260_27.3", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=0.78 mol, T=260 K, and V=27.3 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 0.78 * 8.314 * 260 / 27.3.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 0.78, "temp_k": 260, "volume_l": 27.3}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=233.5 mg, t=46 h, and T_half=38 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 100.8979, \"unit\": \"mg\"}", "dedupe_signature": "1016e942643933c41beb9e44c5b0430bc426858739fc79bff21a0f51f45c27a2", "difficulty": "medium", "final_answer": {"answer": 100.8979, "unit": "mg"}, "id": "half_life_002598_233.5_38_46", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 233.5 mg. Its half-life is 38 hours. How many mg remain after 46 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=233.5 mg, t=46 h, and T_half=38 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 46.0, "half_life": 38.0, "initial_amount": 233.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 3.14 mol * 18.015 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 56.5671, \"unit\": \"g\"}", "dedupe_signature": "6cd0488c7e4f05289111127100b931ef8ea8462fd8f151071d7f1f872e2aa48c", "difficulty": "medium", "final_answer": {"answer": 56.5671, "unit": "g"}, "id": "stoich_mass_002599_water_3.14", "license": "Apache-2.0", "prompt": "A sample contains 3.14 mol of water. Using molar mass 18.015 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 3.14 mol * 18.015 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "water", "molar_mass": 18.015, "moles": 3.14}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 2120 mL to 2.12 L.\n3. Compute M = 0.955 / 2.12.\nFinal: {\"answer\": 0.4505, \"unit\": \"mol/L\"}", "dedupe_signature": "bbdf267b0b2dafb02c7fe4aedab937528f2c8a08d077239ab6a0791f04fd45f5", "difficulty": "medium", "final_answer": {"answer": 0.4505, "unit": "mol/L"}, "id": "molarity_002600_0.955_2120", "license": "Apache-2.0", "prompt": "A solution contains 0.955 mol of solute in 2120 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 2120 mL to 2.12 L.\nCompute M = 0.955 / 2.12.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 0.955, "volume_ml": 2120}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.32 y, so each step multiplies y by 1 - h*0.32.\n3. Apply that update for 10 steps and round the final state.\nFinal: {\"answer\": 8.8968, \"unit\": \"state_units\"}", "dedupe_signature": "91c79772797455e3f889c695f609b2c68c43d5383c6330ba4cce43308cae9106", "difficulty": "medium", "final_answer": {"answer": 8.8968, "unit": "state_units"}, "id": "euler_decay_002601_35_0.32_0.4_10", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.32 y with y(0)=35, step size h=0.4, for 10 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.32 y, so each step multiplies y by 1 - h*0.32.\nApply that update for 10 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 35.0, "rate": 0.32, "step": 0.4, "steps": 10}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-1.5)=-2.9 and f(8.5)=-62.9.\n3. The interval width is 10.\nFinal: {\"answer\": -329.0, \"unit\": \"area_units\"}", "dedupe_signature": "9f38da80e28c502003f663d2191fd06f24601577092b0513826b09187d1ab983", "difficulty": "medium", "final_answer": {"answer": -329.0, "unit": "area_units"}, "id": "trapz_linear_002602_-6_-11.9_-1.5_8.5", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-6x+-11.9 from x=-1.5 to x=8.5. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-1.5)=-2.9 and f(8.5)=-62.9.\nThe interval width is 10.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -11.9, "slope": -6.0, "x0": -1.5, "x1": 8.5}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.28 and add it to the current value.\nFinal: {\"answer\": [-0.546, -0.07, 0.596], \"unit\": \"temperature_units\"}", "dedupe_signature": "f658491897dff346e18f4c5996d5ae49297f4dd1dbb4b101825295169b190089", "difficulty": "hard", "final_answer": {"answer": [-0.546, -0.07, 0.596], "unit": "temperature_units"}, "id": "heat_step_002603_0.28_-1.55_-0.7_0.7_-0.65_2.45", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-1.55, right=2.45; current interior values are [-0.7, 0.7, -0.65]. Use r=0.28. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.28 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-0.7, 0.7, -0.65], "left": -1.55, "r": 0.28, "right": 2.45}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=306 degrees and keep the unit as newtons.\nFinal: {\"answer\": [184.5646, -254.0313], \"unit\": \"N\"}", "dedupe_signature": "5242b29bd2804e423220a73233e62cedc92af70444fbb36af89de1b861f390eb", "difficulty": "medium", "final_answer": {"answer": [184.5646, -254.0313], "unit": "N"}, "id": "vector_components_002605_314_306", "license": "Apache-2.0", "prompt": "A vector has magnitude 314 N at 306 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=306 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 306, "magnitude": 314.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. m*v is momentum, not energy\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "0c2be5760cbeaa9bb34060a54c8c10153a9aa03053696483cb91dc8caf65ef9a", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_002607_inconsistent_1e14b074_596251", "license": "Apache-2.0", "prompt": "In student derivation case 596251, check dimensional consistency for E = m * v. The left side has dimensions kg*m^2/s^2 and the right side has dimensions kg*m/s. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nm*v is momentum, not energy\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "E = m * v"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef clamp_002608(x, lo, hi):\n    if lo > hi:\n        raise ValueError('lo must be <= hi')\n    return min(max(x, lo), hi)\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"clamp_002608\"}", "dedupe_signature": "1ba019c89d7a70841d0deedce9a814a2cebdd3ba2860612b2b2be376fe629fbd", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "clamp_002608"}, "id": "code_002608_clamp_002608", "license": "Apache-2.0", "prompt": "Write a Python function clamp_002608(x, lo, hi) that clips x into the inclusive interval [lo, hi]. It must raise ValueError if lo > hi. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "clamp_002608"}, "verifier": {"function": "clamp_002608", "tests": ["assert clamp_002608(5, 0, 10) == 5", "assert clamp_002608(-2, 0, 10) == 0", "assert clamp_002608(12, 0, 10) == 10", "try:\n    clamp_002608(1, 3, 2)\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: recurrence, objective, tie_breaking_rule.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"recurrence\", \"objective\", \"tie_breaking_rule\"]}", "dedupe_signature": "aad3e78179515fc993ebce682855ac403799dc24f5322562e63fe2ade893adbf", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["recurrence", "objective", "tie_breaking_rule"]}, "id": "abstain_002609_recurrence_objective_tie_breaking_rule", "license": "Apache-2.0", "prompt": "Write a dynamic-programming solver for a segmentation scoring problem with 2249 items and budget 96735, but the recurrence, objective, and tie-breaking rule are all absent. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: recurrence, objective, tie_breaking_rule.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["recurrence", "objective", "tie_breaking_rule"]}, "verifier": {"missing": ["recurrence", "objective", "tie_breaking_rule"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 38.55^2 and multiply by 0.5 * 15.05.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 11182.9213, \"unit\": \"J\"}", "dedupe_signature": "a1d93f5a530a4cfd67dfef22f0fb91c1346f89e367f9faf47398956c366a4e6d", "difficulty": "easy", "final_answer": {"answer": 11182.9213, "unit": "J"}, "id": "ke_002611_15.05_38.55", "license": "Apache-2.0", "prompt": "A body of mass 15.05 kg moves at 38.55 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 38.55^2 and multiply by 0.5 * 15.05.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 15.05, "velocity": 38.55}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=65 degrees through the sine of 2 theta.\n3. Substitute v=61.7 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 297.2729, \"unit\": \"m\"}", "dedupe_signature": "fe517b602c124d197ba97d742b1d8d40d9721938e9b5fc6d213625462de7aa84", "difficulty": "medium", "final_answer": {"answer": 297.2729, "unit": "m"}, "id": "projectile_range_002612_61.7_65", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 61.7 m/s and angle 65 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=65 degrees through the sine of 2 theta.\nSubstitute v=61.7 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 65, "gravity": 9.81, "speed": 61.7}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1580 * 3.4 * 51.\nFinal: {\"answer\": 273972.0, \"unit\": \"J\"}", "dedupe_signature": "af0d85e1be6d6e6033fbf0cf2048e30940c9b0b265316b9fe6cf6db5f3826104", "difficulty": "easy", "final_answer": {"answer": 273972.0, "unit": "J"}, "id": "heat_q_002614_1580_3.4_51", "license": "Apache-2.0", "prompt": "A 1580 g sample has specific heat 3.4 J/(g*K). How much heat is needed to raise its temperature by 51 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1580 * 3.4 * 51.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 51, "heat_capacity": 3.4, "mass_g": 1580}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=195.1 V and R=127.3 ohm.\nFinal: {\"answer\": 299.0103, \"unit\": \"W\"}", "dedupe_signature": "25c3c460628fce5484c9f57c55018d8f4b2115d947fd06fad2ae38b423dc820d", "difficulty": "easy", "final_answer": {"answer": 299.0103, "unit": "W"}, "id": "ohm_power_002615_195.1_127.3", "license": "Apache-2.0", "prompt": "A resistor has resistance 127.3 ohm and voltage 195.1 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=195.1 V and R=127.3 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 127.3, "voltage": 195.1}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=943.5 mg, t=203.5 h, and T_half=38 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 23.0487, \"unit\": \"mg\"}", "dedupe_signature": "4b0edcaaf57ebfcf51a44ec1af24bc905e263b22665791918e7fe48042beb81d", "difficulty": "medium", "final_answer": {"answer": 23.0487, "unit": "mg"}, "id": "half_life_002616_943.5_38_203.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 943.5 mg. Its half-life is 38 hours. How many mg remain after 203.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=943.5 mg, t=203.5 h, and T_half=38 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 203.5, "half_life": 38.0, "initial_amount": 943.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 6.83 mol * 18.015 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 123.0425, \"unit\": \"g\"}", "dedupe_signature": "268932c0ed8ce2c52184329edf4e49409ec1663eb0589082d24a3da0c3b40759", "difficulty": "medium", "final_answer": {"answer": 123.0425, "unit": "g"}, "id": "stoich_mass_002617_water_6.83", "license": "Apache-2.0", "prompt": "A sample contains 6.83 mol of water. Using molar mass 18.015 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 6.83 mol * 18.015 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "water", "molar_mass": 18.015, "moles": 6.83}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 735 mL to 0.735 L.\n3. Compute M = 2.945 / 0.735.\nFinal: {\"answer\": 4.0068, \"unit\": \"mol/L\"}", "dedupe_signature": "d3ceb00626aece303e9a55c7e4112dda7c4a306e49f74101acebd1c517e1d373", "difficulty": "medium", "final_answer": {"answer": 4.0068, "unit": "mol/L"}, "id": "molarity_002618_2.945_735", "license": "Apache-2.0", "prompt": "A solution contains 2.945 mol of solute in 735 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 735 mL to 0.735 L.\nCompute M = 2.945 / 0.735.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 2.945, "volume_ml": 735}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-8.5)=-54.2 and f(-3.9)=-26.6.\n3. The interval width is 4.6.\nFinal: {\"answer\": -185.84, \"unit\": \"area_units\"}", "dedupe_signature": "6d3886404c5437cb89ca027f5140d776e856909e3160bd10fd3961b6d0617357", "difficulty": "medium", "final_answer": {"answer": -185.84, "unit": "area_units"}, "id": "trapz_linear_002620_6_-3.2_-8.5_-3.9", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=6x+-3.2 from x=-8.5 to x=-3.9. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-8.5)=-54.2 and f(-3.9)=-26.6.\nThe interval width is 4.6.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -3.2, "slope": 6.0, "x0": -8.5, "x1": -3.9000000000000004}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.28 and add it to the current value.\nFinal: {\"answer\": [-0.228, 0.794, 1.708], \"unit\": \"temperature_units\"}", "dedupe_signature": "30eaaab137503797a491e323c7e80752d4a23345f800e006e192542289134d13", "difficulty": "hard", "final_answer": {"answer": [-0.228, 0.794, 1.708], "unit": "temperature_units"}, "id": "heat_step_002621_0.28_-1.75_0.5_0.15_2.1_2.65", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-1.75, right=2.65; current interior values are [0.5, 0.15, 2.1]. Use r=0.28. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.28 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [0.5, 0.15, 2.1], "left": -1.75, "r": 0.28, "right": 2.65}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 3206.0 / 1000.\nFinal: {\"answer\": 3.206, \"unit\": \"kg\"}", "dedupe_signature": "1af334966a2363a8f5c067b37f24f227e2baa9129010ca79092d5ae835468065", "difficulty": "easy", "final_answer": {"answer": 3.206, "unit": "kg"}, "id": "unit_convert_002622_g_to_kg_3206", "license": "Apache-2.0", "prompt": "Convert 3206 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 3206.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 3206.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=131 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-295.8826, 340.374], \"unit\": \"N\"}", "dedupe_signature": "f272783e889fc4dc480d8c59119468571bfcc3ae37bfde85c75d4005023efc2a", "difficulty": "medium", "final_answer": {"answer": [-295.8826, 340.374], "unit": "N"}, "id": "vector_components_002623_451_131", "license": "Apache-2.0", "prompt": "A vector has magnitude 451 N at 131 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=131 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 131, "magnitude": 451.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. density times acceleration times height gives kg/(m*s^2), or pascal\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "970ecfbe29175e5f07ea3e51f49c00bc08b02988bb44f139c92bebca5442f921", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_002625_consistent_b7d3eed1_490565", "license": "Apache-2.0", "prompt": "In field worksheet case 490565, check dimensional consistency for p = rho * g * h. The left side has dimensions Pa and the right side has dimensions Pa. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\ndensity times acceleration times height gives kg/(m*s^2), or pascal\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "p = rho * g * h"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: rate_constant, number_of_steps.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"rate_constant\", \"number_of_steps\"]}", "dedupe_signature": "d17f22b444f58148340340259238936d514faf98fd98ce9d54ac3dbf062452c1", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["rate_constant", "number_of_steps"]}, "id": "abstain_002627_rate_constant_number_of_steps", "license": "Apache-2.0", "prompt": "Use explicit Euler for dy/dt = -k y. The prompt gives y(0)=58 and h=1.7, but omits both k and the number of steps. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: rate_constant, number_of_steps.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["rate_constant", "number_of_steps"]}, "verifier": {"missing": ["rate_constant", "number_of_steps"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 19.45 kg and a = 4.3 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 83.635, \"unit\": \"N\"}", "dedupe_signature": "8ecccd608a77d8948cd4f8d6241272a51068d53f5d0facaedf1258dbdad29f0e", "difficulty": "easy", "final_answer": {"answer": 83.635, "unit": "N"}, "id": "force_002628_19.45_4.3", "license": "Apache-2.0", "prompt": "A cart has mass 19.45 kg and measured acceleration 4.3 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 19.45 kg and a = 4.3 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 4.3, "mass": 19.45}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=59 degrees through the sine of 2 theta.\n3. Substitute v=81.5 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 597.8347, \"unit\": \"m\"}", "dedupe_signature": "36ef82ba7008a7ed2fc27e969e6605821b2486fa7debd7011d6f57fd199a0ec2", "difficulty": "medium", "final_answer": {"answer": 597.8347, "unit": "m"}, "id": "projectile_range_002630_81.5_59", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 81.5 m/s and angle 59 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=59 degrees through the sine of 2 theta.\nSubstitute v=81.5 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 59, "gravity": 9.81, "speed": 81.5}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 1.72 * 8.314 * 348 / 50.4.\nFinal: {\"answer\": 98.7386, \"unit\": \"kPa\"}", "dedupe_signature": "90e31a95d578db65eefcd338fd224d86196508949ee88ad6413670499d52133a", "difficulty": "medium", "final_answer": {"answer": 98.7386, "unit": "kPa"}, "id": "ideal_gas_002631_1.72_348_50.4", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=1.72 mol, T=348 K, and V=50.4 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 1.72 * 8.314 * 348 / 50.4.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 1.72, "temp_k": 348, "volume_l": 50.4}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=55.3 V and R=1.9 ohm.\nFinal: {\"answer\": 1609.5211, \"unit\": \"W\"}", "dedupe_signature": "e5fdddd977fe3f71cdc51cbf04cb0ec99a17e0f626df351d2c57f3d77042846c", "difficulty": "easy", "final_answer": {"answer": 1609.5211, "unit": "W"}, "id": "ohm_power_002633_55.3_1.9", "license": "Apache-2.0", "prompt": "A resistor has resistance 1.9 ohm and voltage 55.3 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=55.3 V and R=1.9 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 1.9, "voltage": 55.3}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 4780 mL to 4.78 L.\n3. Compute M = 3.54 / 4.78.\nFinal: {\"answer\": 0.7406, \"unit\": \"mol/L\"}", "dedupe_signature": "3a5051134f5dd49f525f6bcf21709ea278fdce103c483d537c27d52ff87a332f", "difficulty": "medium", "final_answer": {"answer": 0.7406, "unit": "mol/L"}, "id": "molarity_002636_3.54_4780", "license": "Apache-2.0", "prompt": "A solution contains 3.54 mol of solute in 4780 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 4780 mL to 4.78 L.\nCompute M = 3.54 / 4.78.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 3.54, "volume_ml": 4780}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.99 y, so each step multiplies y by 1 - h*0.99.\n3. Apply that update for 11 steps and round the final state.\nFinal: {\"answer\": -11.5395, \"unit\": \"state_units\"}", "dedupe_signature": "d09507fb0f127b6d88eb01baacebc4dbe2553707a30105fe1cd9c0d4a792150b", "difficulty": "medium", "final_answer": {"answer": -11.5395, "unit": "state_units"}, "id": "euler_decay_002637_46.5_0.99_1.9_11", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.99 y with y(0)=46.5, step size h=1.9, for 11 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.99 y, so each step multiplies y by 1 - h*0.99.\nApply that update for 11 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 46.5, "rate": 0.99, "step": 1.9, "steps": 11}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(1.8)=-7.4 and f(11.1)=-77.15.\n3. The interval width is 9.3.\nFinal: {\"answer\": -393.1575, \"unit\": \"area_units\"}", "dedupe_signature": "94c814da204685d646af4caf5dd45fd0be2c07eea4f6f0a8b237cd91843dda9f", "difficulty": "medium", "final_answer": {"answer": -393.1575, "unit": "area_units"}, "id": "trapz_linear_002638_-7.5_6.1_1.8_11.1", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-7.5x+6.1 from x=1.8 to x=11.1. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(1.8)=-7.4 and f(11.1)=-77.15.\nThe interval width is 9.3.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 6.1, "slope": -7.5, "x0": 1.8, "x1": 11.100000000000001}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.38 and add it to the current value.\nFinal: {\"answer\": [1.139, 0.933, 1.435], \"unit\": \"temperature_units\"}", "dedupe_signature": "2e911e769c8192dc3caf72663fee3505ca04a2fcb6a5c1dbc6b15464ac50a450", "difficulty": "hard", "final_answer": {"answer": [1.139, 0.933, 1.435], "unit": "temperature_units"}, "id": "heat_step_002639_0.38_-1.25_2.45_2.7_-1.7_2.15", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-1.25, right=2.15; current interior values are [2.45, 2.7, -1.7]. Use r=0.38. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.38 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [2.45, 2.7, -1.7], "left": -1.25, "r": 0.38, "right": 2.15}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 7770.0 / 1000.\nFinal: {\"answer\": 7.77, \"unit\": \"kg\"}", "dedupe_signature": "bdd69a00c3f4b0e8fdf97f54ffa732b60ba9ddd04c8921b8b32bc5a623ac58df", "difficulty": "easy", "final_answer": {"answer": 7.77, "unit": "kg"}, "id": "unit_convert_002640_g_to_kg_7770", "license": "Apache-2.0", "prompt": "Convert 7770 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 7770.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 7770.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=322 degrees and keep the unit as newtons.\nFinal: {\"answer\": [306.5362, -239.4923], \"unit\": \"N\"}", "dedupe_signature": "e16dc51a5c4ba433f3eab7c5acff73f093e3001bbde80f8fe5af8c7a5dba0175", "difficulty": "medium", "final_answer": {"answer": [306.5362, -239.4923], "unit": "N"}, "id": "vector_components_002641_389_322", "license": "Apache-2.0", "prompt": "A vector has magnitude 389 N at 322 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=322 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 322, "magnitude": 389.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-1.45, 29.75], \"unit\": \"dimensionless\"}", "dedupe_signature": "3b185da0436671147992ef8322c87478dfc1abbf19ab1717e1ecb7f442e680fb", "difficulty": "medium", "final_answer": {"answer": [-1.45, 29.75], "unit": "dimensionless"}, "id": "line_two_point_002642_-7.75_2_-1.45_29.75", "license": "Apache-2.0", "prompt": "A line passes through points (-7.75, 40.9875) and (2, 26.85). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -7.75, "x2": 2.0, "y1": 40.9875, "y2": 26.85}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. grams cancel with J/(g*K), and kelvin cancels, leaving joules\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "fd95c75f606b71fb9693666e867a57fa5f6801566ef70d050de98f6133856bb8", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_002643_consistent_4153435f_662902", "license": "Apache-2.0", "prompt": "In quality-control check case 662902, check dimensional consistency for Q = m * c * DeltaT. The left side has dimensions J and the right side has dimensions J. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\ngrams cancel with J/(g*K), and kelvin cancels, leaving joules\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "Q = m * c * DeltaT"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef finite_differences_002644(values):\n    return [values[i + 1] - values[i] for i in range(len(values) - 1)]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"finite_differences_002644\"}", "dedupe_signature": "65875864a819f6e0b1af19e55d5b350bcbd5b7c62bd815fdaa7ac362ca5e261b", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "finite_differences_002644"}, "id": "code_002644_finite_differences_002644", "license": "Apache-2.0", "prompt": "Write a Python function finite_differences_002644(values) that returns the list of successive differences values[i+1] - values[i]. It must return [] for fewer than two values. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "finite_differences_002644"}, "verifier": {"function": "finite_differences_002644", "tests": ["assert finite_differences_002644([1, 4, 9, 16]) == [3, 5, 7]", "assert finite_differences_002644([5]) == []", "assert finite_differences_002644([]) == []"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: rate_constant, number_of_steps.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"rate_constant\", \"number_of_steps\"]}", "dedupe_signature": "bef5b7d761a8c164ccfa3128b74115d9fcf98054917518bf2916b714b6dd3c1c", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["rate_constant", "number_of_steps"]}, "id": "abstain_002645_rate_constant_number_of_steps", "license": "Apache-2.0", "prompt": "Use explicit Euler for dy/dt = -k y. The prompt gives y(0)=11.5 and h=1.45, but omits both k and the number of steps. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: rate_constant, number_of_steps.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["rate_constant", "number_of_steps"]}, "verifier": {"missing": ["rate_constant", "number_of_steps"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 1.2 kg and a = 15.05 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 18.06, \"unit\": \"N\"}", "dedupe_signature": "14ddd002520eb768fd46b90a4df37c5e630897b696b7be890f9f27bf7d6296fb", "difficulty": "easy", "final_answer": {"answer": 18.06, "unit": "N"}, "id": "force_002646_1.2_15.05", "license": "Apache-2.0", "prompt": "A cart has mass 1.2 kg and measured acceleration 15.05 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 1.2 kg and a = 15.05 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 15.05, "mass": 1.2}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=38 degrees through the sine of 2 theta.\n3. Substitute v=31.6 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 98.7664, \"unit\": \"m\"}", "dedupe_signature": "02e40a048a287354484e299fe7391c8e22304ee310f17d4b8effbb3531bbd6b9", "difficulty": "medium", "final_answer": {"answer": 98.7664, "unit": "m"}, "id": "projectile_range_002648_31.6_38", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 31.6 m/s and angle 38 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=38 degrees through the sine of 2 theta.\nSubstitute v=31.6 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 38, "gravity": 9.81, "speed": 31.6}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1540 * 3.98 * 108.\nFinal: {\"answer\": 661953.6, \"unit\": \"J\"}", "dedupe_signature": "49031824404db236d673e5a0fec02b6555f0ab9db3775076b1b20d2021405f6a", "difficulty": "easy", "final_answer": {"answer": 661953.6, "unit": "J"}, "id": "heat_q_002650_1540_3.98_108", "license": "Apache-2.0", "prompt": "A 1540 g sample has specific heat 3.98 J/(g*K). How much heat is needed to raise its temperature by 108 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1540 * 3.98 * 108.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 108, "heat_capacity": 3.98, "mass_g": 1540}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=228.8 V and R=113.2 ohm.\nFinal: {\"answer\": 462.4509, \"unit\": \"W\"}", "dedupe_signature": "2677c815c9c6ca6e58938523e55f802613a07badca53ddfbc26d2ccf669079c6", "difficulty": "easy", "final_answer": {"answer": 462.4509, "unit": "W"}, "id": "ohm_power_002651_228.8_113.2", "license": "Apache-2.0", "prompt": "A resistor has resistance 113.2 ohm and voltage 228.8 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=228.8 V and R=113.2 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 113.2, "voltage": 228.8}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=72 mg, t=199 h, and T_half=54 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 5.5973, \"unit\": \"mg\"}", "dedupe_signature": "8c061874243a2ba5242b4d643d39a3edc6dd66769242c29e95210d8dfbbc7771", "difficulty": "medium", "final_answer": {"answer": 5.5973, "unit": "mg"}, "id": "half_life_002652_72_54_199", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 72 mg. Its half-life is 54 hours. How many mg remain after 199 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=72 mg, t=199 h, and T_half=54 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 199.0, "half_life": 54.0, "initial_amount": 72.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 2.05 mol * 44.01 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 90.2205, \"unit\": \"g\"}", "dedupe_signature": "320d8900f564d9cced6c6c26fc58c1d07231611ed8f4686837ae86d5bdca6071", "difficulty": "medium", "final_answer": {"answer": 90.2205, "unit": "g"}, "id": "stoich_mass_002653_carbon_dioxide_2.05", "license": "Apache-2.0", "prompt": "A sample contains 2.05 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 2.05 mol * 44.01 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "carbon dioxide", "molar_mass": 44.01, "moles": 2.05}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 1330 mL to 1.33 L.\n3. Compute M = 3.25 / 1.33.\nFinal: {\"answer\": 2.4436, \"unit\": \"mol/L\"}", "dedupe_signature": "4ea0dc92b9e7e50538a68819b2b2575c5deb4add4a00b3b9be424aea906ba5d2", "difficulty": "medium", "final_answer": {"answer": 2.4436, "unit": "mol/L"}, "id": "molarity_002654_3.25_1330", "license": "Apache-2.0", "prompt": "A solution contains 3.25 mol of solute in 1330 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 1330 mL to 1.33 L.\nCompute M = 3.25 / 1.33.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 3.25, "volume_ml": 1330}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.18 y, so each step multiplies y by 1 - h*0.18.\n3. Apply that update for 11 steps and round the final state.\nFinal: {\"answer\": 3.6722, \"unit\": \"state_units\"}", "dedupe_signature": "d6a64cb653dde757246c669200031457afc7b937b56e7b2aa177a22aef637cea", "difficulty": "medium", "final_answer": {"answer": 3.6722, "unit": "state_units"}, "id": "euler_decay_002655_78.5_0.18_1.35_11", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.18 y with y(0)=78.5, step size h=1.35, for 11 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.18 y, so each step multiplies y by 1 - h*0.18.\nApply that update for 11 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 78.5, "rate": 0.18, "step": 1.35, "steps": 11}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(0.3)=5.09 and f(9.8)=17.44.\n3. The interval width is 9.5.\nFinal: {\"answer\": 107.0175, \"unit\": \"area_units\"}", "dedupe_signature": "1a1fdff3dc482fb181579bfb952fe9434fab03de7984b93c9c201ef1674578d9", "difficulty": "medium", "final_answer": {"answer": 107.0175, "unit": "area_units"}, "id": "trapz_linear_002656_1.3_4.7_0.3_9.8", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=1.3x+4.7 from x=0.3 to x=9.8. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(0.3)=5.09 and f(9.8)=17.44.\nThe interval width is 9.5.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 4.7, "slope": 1.3, "x0": 0.3, "x1": 9.8}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.32 and add it to the current value.\nFinal: {\"answer\": [-0.234, -0.43, -0.314], \"unit\": \"temperature_units\"}", "dedupe_signature": "886185f8675da9150cb8655992634a9cc5998a0314a0ea16671590b914c3f680", "difficulty": "hard", "final_answer": {"answer": [-0.234, -0.43, -0.314], "unit": "temperature_units"}, "id": "heat_step_002657_0.32_-1.05_0.95_-0.75_-1.45_1.4", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-1.05, right=1.4; current interior values are [0.95, -0.75, -1.45]. Use r=0.32. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.32 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [0.95, -0.75, -1.45], "left": -1.05, "r": 0.32, "right": 1.4}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=191 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-45.1549, -8.7772], \"unit\": \"N\"}", "dedupe_signature": "704e8c4cf02f47ab2fbdaadfe499cae45acbabd9830a9d021ebb5f3b2214e959", "difficulty": "medium", "final_answer": {"answer": [-45.1549, -8.7772], "unit": "N"}, "id": "vector_components_002659_46_191", "license": "Apache-2.0", "prompt": "A vector has magnitude 46 N at 191 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=191 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 191, "magnitude": 46.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [4.75, 4.25], \"unit\": \"dimensionless\"}", "dedupe_signature": "402f7da416e6a18cbbe63b538c7451c9155b4bab75d3798fff6ca224e9b19eed", "difficulty": "medium", "final_answer": {"answer": [4.75, 4.25], "unit": "dimensionless"}, "id": "line_two_point_002660_13.75_15_4.75_4.25", "license": "Apache-2.0", "prompt": "A line passes through points (13.75, 69.5625) and (15, 75.5). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 13.75, "x2": 15.0, "y1": 69.5625, "y2": 75.5}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. m*v is momentum, not energy\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "da3724d9340502402778cf69976afe9c7cedd83409cb4c4161fd18a8429efe18", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_002661_inconsistent_1e14b074_978735", "license": "Apache-2.0", "prompt": "In lab notebook case 978735, check dimensional consistency for E = m * v. The left side has dimensions kg*m^2/s^2 and the right side has dimensions kg*m/s. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nm*v is momentum, not energy\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "E = m * v"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef finite_differences_002662(values):\n    return [values[i + 1] - values[i] for i in range(len(values) - 1)]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"finite_differences_002662\"}", "dedupe_signature": "ddb129e45a80f95d114e1b902c1d256ee7a2366838857966a954850a360138a7", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "finite_differences_002662"}, "id": "code_002662_finite_differences_002662", "license": "Apache-2.0", "prompt": "Write a Python function finite_differences_002662(values) that returns the list of successive differences values[i+1] - values[i]. It must return [] for fewer than two values. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "finite_differences_002662"}, "verifier": {"function": "finite_differences_002662", "tests": ["assert finite_differences_002662([1, 4, 9, 16]) == [3, 5, 7]", "assert finite_differences_002662([5]) == []", "assert finite_differences_002662([]) == []"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: recurrence, objective, tie_breaking_rule.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"recurrence\", \"objective\", \"tie_breaking_rule\"]}", "dedupe_signature": "a55bbd2546c10e8d951f65a2f4f485d1cc94656fef077c627ef39ab6866f2d1d", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["recurrence", "objective", "tie_breaking_rule"]}, "id": "abstain_002663_recurrence_objective_tie_breaking_rule", "license": "Apache-2.0", "prompt": "Write a dynamic-programming solver for a scheduler scoring problem with 2585 items and budget 22185, but the recurrence, objective, and tie-breaking rule are all absent. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: recurrence, objective, tie_breaking_rule.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["recurrence", "objective", "tie_breaking_rule"]}, "verifier": {"missing": ["recurrence", "objective", "tie_breaking_rule"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 18.75 kg and a = 12.1 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 226.875, \"unit\": \"N\"}", "dedupe_signature": "49c18fbfb0901067b29926e69ca589eb0e09d10f7935ac66240c394ab83409ca", "difficulty": "easy", "final_answer": {"answer": 226.875, "unit": "N"}, "id": "force_002664_18.75_12.1", "license": "Apache-2.0", "prompt": "A cart has mass 18.75 kg and measured acceleration 12.1 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 18.75 kg and a = 12.1 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 12.1, "mass": 18.75}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 18.8^2 and multiply by 0.5 * 11.8.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 2085.296, \"unit\": \"J\"}", "dedupe_signature": "f4da84230ef3cc704de38c094a6ac2d0aaa1790d6b41bf15bbc677924d53c0a0", "difficulty": "easy", "final_answer": {"answer": 2085.296, "unit": "J"}, "id": "ke_002665_11.8_18.8", "license": "Apache-2.0", "prompt": "A body of mass 11.8 kg moves at 18.8 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 18.8^2 and multiply by 0.5 * 11.8.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 11.8, "velocity": 18.8}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=15 degrees through the sine of 2 theta.\n3. Substitute v=50.4 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 129.4679, \"unit\": \"m\"}", "dedupe_signature": "2379727d3bae19112a03e89bb9f7664f700855faaac8f6067b4ed031bc1e0e66", "difficulty": "medium", "final_answer": {"answer": 129.4679, "unit": "m"}, "id": "projectile_range_002666_50.4_15", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 50.4 m/s and angle 15 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=15 degrees through the sine of 2 theta.\nSubstitute v=50.4 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 15, "gravity": 9.81, "speed": 50.4}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 0.33 * 8.314 * 269 / 84.9.\nFinal: {\"answer\": 8.693, \"unit\": \"kPa\"}", "dedupe_signature": "df203b05af430fc0529b6f3cdf5bdbc3c72e7db9f03e006ebe4e0300d4fdf1ad", "difficulty": "medium", "final_answer": {"answer": 8.693, "unit": "kPa"}, "id": "ideal_gas_002667_0.33_269_84.9", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=0.33 mol, T=269 K, and V=84.9 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 0.33 * 8.314 * 269 / 84.9.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 0.33, "temp_k": 269, "volume_l": 84.9}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 170 * 3.165 * 25.\nFinal: {\"answer\": 13451.25, \"unit\": \"J\"}", "dedupe_signature": "4396130ab024e82a243bdcd5a77384a3b87e48efa25496406634100235647bd5", "difficulty": "easy", "final_answer": {"answer": 13451.25, "unit": "J"}, "id": "heat_q_002668_170_3.165_25", "license": "Apache-2.0", "prompt": "A 170 g sample has specific heat 3.165 J/(g*K). How much heat is needed to raise its temperature by 25 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 170 * 3.165 * 25.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 25, "heat_capacity": 3.165, "mass_g": 170}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=84.2 V and R=167.8 ohm.\nFinal: {\"answer\": 42.2505, \"unit\": \"W\"}", "dedupe_signature": "b4558f49ba0db8a7138a5a11c4ed9480285e6e6355d3709a413f77ed8fca5042", "difficulty": "easy", "final_answer": {"answer": 42.2505, "unit": "W"}, "id": "ohm_power_002669_84.2_167.8", "license": "Apache-2.0", "prompt": "A resistor has resistance 167.8 ohm and voltage 84.2 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=84.2 V and R=167.8 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 167.8, "voltage": 84.2}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=447.5 mg, t=24.5 h, and T_half=108 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 382.3876, \"unit\": \"mg\"}", "dedupe_signature": "2e41824405536143aadf7f45da2c34c9974e4c8953e66e3f84647c369e450b72", "difficulty": "medium", "final_answer": {"answer": 382.3876, "unit": "mg"}, "id": "half_life_002670_447.5_108_24.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 447.5 mg. Its half-life is 108 hours. How many mg remain after 24.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=447.5 mg, t=24.5 h, and T_half=108 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 24.5, "half_life": 108.0, "initial_amount": 447.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 3.63 mol * 58.44 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 212.1372, \"unit\": \"g\"}", "dedupe_signature": "3f19ef3be81b95f7c66285c781dc064cd54981985fcb67d423c4a8cae1ce90d7", "difficulty": "medium", "final_answer": {"answer": 212.1372, "unit": "g"}, "id": "stoich_mass_002671_sodium_chloride_3.63", "license": "Apache-2.0", "prompt": "A sample contains 3.63 mol of sodium chloride. Using molar mass 58.44 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 3.63 mol * 58.44 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "sodium chloride", "molar_mass": 58.44, "moles": 3.63}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 4640 mL to 4.64 L.\n3. Compute M = 3.795 / 4.64.\nFinal: {\"answer\": 0.8179, \"unit\": \"mol/L\"}", "dedupe_signature": "fc62f3a64601b489e30bf61e94bcbfc53a1904dd260444a2e623d3460bab79b8", "difficulty": "medium", "final_answer": {"answer": 0.8179, "unit": "mol/L"}, "id": "molarity_002672_3.795_4640", "license": "Apache-2.0", "prompt": "A solution contains 3.795 mol of solute in 4640 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 4640 mL to 4.64 L.\nCompute M = 3.795 / 4.64.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 3.795, "volume_ml": 4640}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.63 y, so each step multiplies y by 1 - h*0.63.\n3. Apply that update for 3 steps and round the final state.\nFinal: {\"answer\": 0.0049, \"unit\": \"state_units\"}", "dedupe_signature": "c3f48f6b5db06c68a366933940b458acabc9507ed0c1cd5a0838aa86622808c8", "difficulty": "medium", "final_answer": {"answer": 0.0049, "unit": "state_units"}, "id": "euler_decay_002673_29.5_0.63_1.5_3", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.63 y with y(0)=29.5, step size h=1.5, for 3 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.63 y, so each step multiplies y by 1 - h*0.63.\nApply that update for 3 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 29.5, "rate": 0.63, "step": 1.5, "steps": 3}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-9.5)=-20.15 and f(-4.4)=-6.38.\n3. The interval width is 5.1.\nFinal: {\"answer\": -67.6515, \"unit\": \"area_units\"}", "dedupe_signature": "f423fcde8a2adcc12d639e463afe9ba8e3d2e0e109bd923488443a1b931d65e9", "difficulty": "medium", "final_answer": {"answer": -67.6515, "unit": "area_units"}, "id": "trapz_linear_002674_2.7_5.5_-9.5_-4.4", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=2.7x+5.5 from x=-9.5 to x=-4.4. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-9.5)=-20.15 and f(-4.4)=-6.38.\nThe interval width is 5.1.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 5.5, "slope": 2.7, "x0": -9.5, "x1": -4.4}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.12 and add it to the current value.\nFinal: {\"answer\": [-0.968, 0.654, -0.98], \"unit\": \"temperature_units\"}", "dedupe_signature": "851cbc949ae210d6adbdb7536d2a73d832a84c871a21b27f836143b0040c05a4", "difficulty": "hard", "final_answer": {"answer": [-0.968, 0.654, -0.98], "unit": "temperature_units"}, "id": "heat_step_002675_0.12_-0.55_-1.4_1.35_-1.7_1.25", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-0.55, right=1.25; current interior values are [-1.4, 1.35, -1.7]. Use r=0.12. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.12 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-1.4, 1.35, -1.7], "left": -0.55, "r": 0.12, "right": 1.25}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kelvin equals Celsius plus 273.15.\n2. Apply the conversion factor directly to the given value.\n3. Compute 146.0 + 273.15.\nFinal: {\"answer\": 419.15, \"unit\": \"K\"}", "dedupe_signature": "c44d29dc0dd1dc4fce099fe8f981dc881e5e2b489728d71213e047f4f15b0bdf", "difficulty": "easy", "final_answer": {"answer": 419.15, "unit": "K"}, "id": "unit_convert_002676_c_to_k_146", "license": "Apache-2.0", "prompt": "Convert 146 degC to K. Return the converted value with unit.", "reasoning_trace": "Kelvin equals Celsius plus 273.15.\nApply the conversion factor directly to the given value.\nCompute 146.0 + 273.15.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 146.0}, "verifier": {"formula": "value + 273.15", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=45 degrees and keep the unit as newtons.\nFinal: {\"answer\": [106.7731, 106.7731], \"unit\": \"N\"}", "dedupe_signature": "fc8d62c78d7ea53abef46ed0e2d367ac6191639ae362f0895f9527445a2958b4", "difficulty": "medium", "final_answer": {"answer": [106.7731, 106.7731], "unit": "N"}, "id": "vector_components_002677_151_45", "license": "Apache-2.0", "prompt": "A vector has magnitude 151 N at 45 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=45 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 45, "magnitude": 151.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-4.1, -21.75], \"unit\": \"dimensionless\"}", "dedupe_signature": "3d0255a4cdc7a8a44c05c2d87b70816aa7ddd8af95118516feb21db7b384441a", "difficulty": "medium", "final_answer": {"answer": [-4.1, -21.75], "unit": "dimensionless"}, "id": "line_two_point_002678_-7.75_3.75_-4.1_-21.75", "license": "Apache-2.0", "prompt": "A line passes through points (-7.75, 10.025) and (3.75, -37.125). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -7.75, "x2": 3.75, "y1": 10.024999999999999, "y2": -37.125}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. amount times volume is not concentration\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "ba1e44d6b7380c14e6a53a64ab0d07349de0f684912c081a7ad17b8f07ab2308", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_002679_inconsistent_74ac0b02_970201", "license": "Apache-2.0", "prompt": "In sensor calibration case 970201, check dimensional consistency for C = n * V. The left side has dimensions mol/L and the right side has dimensions mol*L. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\namount times volume is not concentration\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "C = n * V"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef running_total_002680(values):\n    total = 0\n    out = []\n    for value in values:\n        total += value\n        out.append(total)\n    return out\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"running_total_002680\"}", "dedupe_signature": "6bda3c8140e28ad6fe6cfd60b14107cdef3ab6a71b66618d6f55e83a7fbe2d72", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "running_total_002680"}, "id": "code_002680_running_total_002680", "license": "Apache-2.0", "prompt": "Write a Python function running_total_002680(values) that returns cumulative sums as a new list. It must not mutate the input list. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "running_total_002680"}, "verifier": {"function": "running_total_002680", "tests": ["assert running_total_002680([1, 2, 3]) == [1, 3, 6]", "xs = [4, -1, 2]; assert running_total_002680(xs) == [4, 3, 5] and xs == [4, -1, 2]", "assert running_total_002680([]) == []"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: recurrence, objective, tie_breaking_rule.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"recurrence\", \"objective\", \"tie_breaking_rule\"]}", "dedupe_signature": "17dd45ab5ed9656b8270a2ebee46dc5792b2225de2b32c3ceb38311af48ff9b7", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["recurrence", "objective", "tie_breaking_rule"]}, "id": "abstain_002681_recurrence_objective_tie_breaking_rule", "license": "Apache-2.0", "prompt": "Write a dynamic-programming solver for a scheduler scoring problem with 2429 items and budget 54415, but the recurrence, objective, and tie-breaking rule are all absent. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: recurrence, objective, tie_breaking_rule.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["recurrence", "objective", "tie_breaking_rule"]}, "verifier": {"missing": ["recurrence", "objective", "tie_breaking_rule"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 39.05^2 and multiply by 0.5 * 15.3.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 11665.5041, \"unit\": \"J\"}", "dedupe_signature": "60ad739b36c4acd37d989585ac8c87fedcf0f1cb479baa0dd38eb21df3d69bb3", "difficulty": "easy", "final_answer": {"answer": 11665.5041, "unit": "J"}, "id": "ke_002683_15.3_39.05", "license": "Apache-2.0", "prompt": "A body of mass 15.3 kg moves at 39.05 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 39.05^2 and multiply by 0.5 * 15.3.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 15.3, "velocity": 39.05}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=29 degrees through the sine of 2 theta.\n3. Substitute v=27.2 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 63.9572, \"unit\": \"m\"}", "dedupe_signature": "5a1dc9885eff6d3cdbc751c417525528211c651477ff8c2db59f798ec7c0c0f1", "difficulty": "medium", "final_answer": {"answer": 63.9572, "unit": "m"}, "id": "projectile_range_002684_27.2_29", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 27.2 m/s and angle 29 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=29 degrees through the sine of 2 theta.\nSubstitute v=27.2 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 29, "gravity": 9.81, "speed": 27.2}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=63.2 V and R=115.5 ohm.\nFinal: {\"answer\": 34.5822, \"unit\": \"W\"}", "dedupe_signature": "918ecccc69cff2445a079cbdf8386a81a7a425c0a413b2950b92580b44c0483c", "difficulty": "easy", "final_answer": {"answer": 34.5822, "unit": "W"}, "id": "ohm_power_002687_63.2_115.5", "license": "Apache-2.0", "prompt": "A resistor has resistance 115.5 ohm and voltage 63.2 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=63.2 V and R=115.5 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 115.5, "voltage": 63.2}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=170 mg, t=321 h, and T_half=38 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 0.487, \"unit\": \"mg\"}", "dedupe_signature": "8b6d1b7122b3285cdb360911c95148ff6dc16fd028743843330a29fca57811f4", "difficulty": "medium", "final_answer": {"answer": 0.487, "unit": "mg"}, "id": "half_life_002688_170_38_321", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 170 mg. Its half-life is 38 hours. How many mg remain after 321 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=170 mg, t=321 h, and T_half=38 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 321.0, "half_life": 38.0, "initial_amount": 170.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 4815 mL to 4.815 L.\n3. Compute M = 4.295 / 4.815.\nFinal: {\"answer\": 0.892, \"unit\": \"mol/L\"}", "dedupe_signature": "56e71485bf41964e86c840cb2d4e8df870d83abcf2191eab571658254e7235c9", "difficulty": "medium", "final_answer": {"answer": 0.892, "unit": "mol/L"}, "id": "molarity_002690_4.295_4815", "license": "Apache-2.0", "prompt": "A solution contains 4.295 mol of solute in 4815 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 4815 mL to 4.815 L.\nCompute M = 4.295 / 4.815.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 4.295, "volume_ml": 4815}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.99 y, so each step multiplies y by 1 - h*0.99.\n3. Apply that update for 4 steps and round the final state.\nFinal: {\"answer\": 28.9164, \"unit\": \"state_units\"}", "dedupe_signature": "64a684ff4eded479c4f6d9ca5850ad24bb54be45ac6077ceb16e88694bc0d568", "difficulty": "medium", "final_answer": {"answer": 28.9164, "unit": "state_units"}, "id": "euler_decay_002691_48_0.99_1.9_4", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.99 y with y(0)=48, step size h=1.9, for 4 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.99 y, so each step multiplies y by 1 - h*0.99.\nApply that update for 4 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 48.0, "rate": 0.99, "step": 1.9, "steps": 4}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.26 and add it to the current value.\nFinal: {\"answer\": [2.401, 1.259, -0.419], \"unit\": \"temperature_units\"}", "dedupe_signature": "3943965f7a1f353dff6a2b8c0324f018bc95da96343942aaf9079ca75ae062ec", "difficulty": "hard", "final_answer": {"answer": [2.401, 1.259, -0.419], "unit": "temperature_units"}, "id": "heat_step_002693_0.26_2.25_2.7_2.0_-1.55_-0.75", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=2.25, right=-0.75; current interior values are [2.7, 2.0, -1.55]. Use r=0.26. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.26 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [2.7, 2.0, -1.55], "left": 2.25, "r": 0.26, "right": -0.75}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kelvin equals Celsius plus 273.15.\n2. Apply the conversion factor directly to the given value.\n3. Compute 235.5 + 273.15.\nFinal: {\"answer\": 508.65, \"unit\": \"K\"}", "dedupe_signature": "c89e6165a7163fd802765f671d12a9b5b3e1d74c058ac3fff36431f4f84ef760", "difficulty": "easy", "final_answer": {"answer": 508.65, "unit": "K"}, "id": "unit_convert_002694_c_to_k_235.5", "license": "Apache-2.0", "prompt": "Convert 235.5 degC to K. Return the converted value with unit.", "reasoning_trace": "Kelvin equals Celsius plus 273.15.\nApply the conversion factor directly to the given value.\nCompute 235.5 + 273.15.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 235.5}, "verifier": {"formula": "value + 273.15", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=188 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-111.4052, -15.657], \"unit\": \"N\"}", "dedupe_signature": "80fa198be964a23057d34f39f4a9af3d247cc0702ea55df1ee7d1f33437f660d", "difficulty": "medium", "final_answer": {"answer": [-111.4052, -15.657], "unit": "N"}, "id": "vector_components_002695_112.5_188", "license": "Apache-2.0", "prompt": "A vector has magnitude 112.5 N at 188 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=188 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 188, "magnitude": 112.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. lever arm times force has torque dimensions\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "7c5ff9bd07f457f6fc8cea3264ebbe4ffbec4eeba71efb1eabacd4a5faf4434c", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_002697_consistent_5ca82cb9_444283", "license": "Apache-2.0", "prompt": "In sensor calibration case 444283, check dimensional consistency for tau = r * F. The left side has dimensions N*m and the right side has dimensions N*m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nlever arm times force has torque dimensions\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "tau = r * F"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef pairwise_ratios_002698(numerators, denominators):\n    if len(numerators) != len(denominators):\n        raise ValueError('length mismatch')\n    out = []\n    for numerator, denominator in zip(numerators, denominators):\n        if denominator == 0:\n            raise ValueError('zero denominator')\n        out.append(numerator / denominator)\n    return out\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"pairwise_ratios_002698\"}", "dedupe_signature": "d3dcd159cac6152fac78cce46d132bfc4ad0ed9f066ada80dd1fbd867df97cf3", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "pairwise_ratios_002698"}, "id": "code_002698_pairwise_ratios_002698", "license": "Apache-2.0", "prompt": "Write a Python function pairwise_ratios_002698(numerators, denominators) that returns a list of n/d values. Raise ValueError if lengths differ or any denominator is zero. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "pairwise_ratios_002698"}, "verifier": {"function": "pairwise_ratios_002698", "tests": ["assert pairwise_ratios_002698([2, 9], [4, 3]) == [0.5, 3.0]", "try:\n    pairwise_ratios_002698([1], [0])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass", "try:\n    pairwise_ratios_002698([1, 2], [1])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: required_fields, allowed_transformations.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"required_fields\", \"allowed_transformations\"]}", "dedupe_signature": "6f1fed3f6bf17efdcec585b953d129f6b6ad35983feb4e4934d03559060f8a78", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["required_fields", "allowed_transformations"]}, "id": "abstain_002699_required_fields_allowed_transformations", "license": "Apache-2.0", "prompt": "Write a sanitizer for valid mobile clinical records in release 286042, but the prompt does not state which fields are required or which transformations are allowed. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: required_fields, allowed_transformations.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["required_fields", "allowed_transformations"]}, "verifier": {"missing": ["required_fields", "allowed_transformations"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 0.5 kg and a = 12.3 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 6.15, \"unit\": \"N\"}", "dedupe_signature": "377bd36c2f3a6d46eb15029d7a95c4fc691f42482361978fd3ccdfb2039fc767", "difficulty": "easy", "final_answer": {"answer": 6.15, "unit": "N"}, "id": "force_002700_0.5_12.3", "license": "Apache-2.0", "prompt": "A cart has mass 0.5 kg and measured acceleration 12.3 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 0.5 kg and a = 12.3 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 12.3, "mass": 0.5}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 19.25^2 and multiply by 0.5 * 29.85.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 5530.6453, \"unit\": \"J\"}", "dedupe_signature": "d186877f8650a701c50a256767faf87a3f461e85f9032aa8c20bb2cee84d6bd8", "difficulty": "easy", "final_answer": {"answer": 5530.6453, "unit": "J"}, "id": "ke_002701_29.85_19.25", "license": "Apache-2.0", "prompt": "A body of mass 29.85 kg moves at 19.25 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 19.25^2 and multiply by 0.5 * 29.85.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 29.85, "velocity": 19.25}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=68 degrees through the sine of 2 theta.\n3. Substitute v=5.6 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 2.2206, \"unit\": \"m\"}", "dedupe_signature": "d8f80ede4fb040edc1b87f5557fa1bbe54c1df0592f23c97399f12568fb02d2b", "difficulty": "medium", "final_answer": {"answer": 2.2206, "unit": "m"}, "id": "projectile_range_002702_5.6_68", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 5.6 m/s and angle 68 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=68 degrees through the sine of 2 theta.\nSubstitute v=5.6 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 68, "gravity": 9.81, "speed": 5.6}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=104.8 V and R=97.5 ohm.\nFinal: {\"answer\": 112.6466, \"unit\": \"W\"}", "dedupe_signature": "bf75399d3a2c9e89a9731a84983cd3c839338dbe6f4c2b75439d3250c7f00276", "difficulty": "easy", "final_answer": {"answer": 112.6466, "unit": "W"}, "id": "ohm_power_002705_104.8_97.5", "license": "Apache-2.0", "prompt": "A resistor has resistance 97.5 ohm and voltage 104.8 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=104.8 V and R=97.5 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 97.5, "voltage": 104.8}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=382.5 mg, t=226.5 h, and T_half=11.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 0.0005, \"unit\": \"mg\"}", "dedupe_signature": "fd98075bf1723b1a910d4c192405bd214126e61356e6a9066d5986c8a629f3e3", "difficulty": "medium", "final_answer": {"answer": 0.0005, "unit": "mg"}, "id": "half_life_002706_382.5_11.5_226.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 382.5 mg. Its half-life is 11.5 hours. How many mg remain after 226.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=382.5 mg, t=226.5 h, and T_half=11.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 226.5, "half_life": 11.5, "initial_amount": 382.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 2.35 mol * 100.087 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 235.2045, \"unit\": \"g\"}", "dedupe_signature": "2b2ff7ea156af2cad13a8bb7516a3b3b6a259df70d37f1d77977fcf98306ce9c", "difficulty": "medium", "final_answer": {"answer": 235.2045, "unit": "g"}, "id": "stoich_mass_002707_calcium_carbonate_2.35", "license": "Apache-2.0", "prompt": "A sample contains 2.35 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 2.35 mol * 100.087 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "calcium carbonate", "molar_mass": 100.087, "moles": 2.35}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 1690 mL to 1.69 L.\n3. Compute M = 3.35 / 1.69.\nFinal: {\"answer\": 1.9822, \"unit\": \"mol/L\"}", "dedupe_signature": "71257c725d473bdef82536763e036dd4bf60a04c5720b40fa07e813c82138404", "difficulty": "medium", "final_answer": {"answer": 1.9822, "unit": "mol/L"}, "id": "molarity_002708_3.35_1690", "license": "Apache-2.0", "prompt": "A solution contains 3.35 mol of solute in 1690 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 1690 mL to 1.69 L.\nCompute M = 3.35 / 1.69.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 3.35, "volume_ml": 1690}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.2 y, so each step multiplies y by 1 - h*0.2.\n3. Apply that update for 2 steps and round the final state.\nFinal: {\"answer\": 13.005, \"unit\": \"state_units\"}", "dedupe_signature": "1ff1146571a09a430c21e3d1316ffdcee36e6be9de0ded15762bc1a0443d1947", "difficulty": "medium", "final_answer": {"answer": 13.005, "unit": "state_units"}, "id": "euler_decay_002709_18_0.2_0.75_2", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.2 y with y(0)=18, step size h=0.75, for 2 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.2 y, so each step multiplies y by 1 - h*0.2.\nApply that update for 2 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 18.0, "rate": 0.2, "step": 0.75, "steps": 2}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-1)=4.6 and f(6.7)=-16.19.\n3. The interval width is 7.7.\nFinal: {\"answer\": -44.6215, \"unit\": \"area_units\"}", "dedupe_signature": "574726993e8530d45d23264a91d30a4b1f33f0466dfa559585a197a1295094b6", "difficulty": "medium", "final_answer": {"answer": -44.6215, "unit": "area_units"}, "id": "trapz_linear_002710_-2.7_1.9_-1_6.7", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-2.7x+1.9 from x=-1 to x=6.7. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-1)=4.6 and f(6.7)=-16.19.\nThe interval width is 7.7.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 1.9, "slope": -2.7, "x0": -1.0, "x1": 6.7}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.34 and add it to the current value.\nFinal: {\"answer\": [0.525, -0.108, -0.953], \"unit\": \"temperature_units\"}", "dedupe_signature": "77d3a75e044afe46b69b9f83a4924e7f0e3458fe9dda5d2d2883be55a93e12f9", "difficulty": "hard", "final_answer": {"answer": [0.525, -0.108, -0.953], "unit": "temperature_units"}, "id": "heat_step_002711_0.34_0.45_2.65_-1.4_-1.65_0.15", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=0.45, right=0.15; current interior values are [2.65, -1.4, -1.65]. Use r=0.34. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.34 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [2.65, -1.4, -1.65], "left": 0.45, "r": 0.34, "right": 0.15}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=196 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-133.6154, -38.3136], \"unit\": \"N\"}", "dedupe_signature": "c3b7f3081cb6f0606ef16e24576b6f804bcb950219f7d76a15451db0d550e9e9", "difficulty": "medium", "final_answer": {"answer": [-133.6154, -38.3136], "unit": "N"}, "id": "vector_components_002713_139_196", "license": "Apache-2.0", "prompt": "A vector has magnitude 139 N at 196 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=196 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 196, "magnitude": 139.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-7.75, 15.0], \"unit\": \"dimensionless\"}", "dedupe_signature": "026de6e87e09516e574527b72764a5dfae48264cf317e3276cb852d38ff1ae0a", "difficulty": "medium", "final_answer": {"answer": [-7.75, 15.0], "unit": "dimensionless"}, "id": "line_two_point_002714_9.75_17.25_-7.75_15", "license": "Apache-2.0", "prompt": "A line passes through points (9.75, -60.5625) and (17.25, -118.688). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 9.75, "x2": 17.25, "y1": -60.5625, "y2": -118.6875}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. amount times volume is not concentration\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "a1cf0b7a2c633583d39c35f1cb231cdce737745fec8c35d661f6511ff6482a30", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_002715_inconsistent_74ac0b02_21672", "license": "Apache-2.0", "prompt": "In quality-control check case 21672, check dimensional consistency for C = n * V. The left side has dimensions mol/L and the right side has dimensions mol*L. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\namount times volume is not concentration\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "C = n * V"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: volume.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"volume\"]}", "dedupe_signature": "9d26f1e6ca5be231286f09a1c8b4969cbbff7e33b9f2aa851ae5f4e2898af383", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["volume"]}, "id": "abstain_002717_volume", "license": "Apache-2.0", "prompt": "Compute pressure from the ideal gas law. The prompt gives n=4.98 mol and T=394 K, but does not give volume. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: volume.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["volume"]}, "verifier": {"missing": ["volume"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 11.75 kg and a = 2.3 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 27.025, \"unit\": \"N\"}", "dedupe_signature": "e8fb56b388ab66d96be5a128c174c87b9c844e7fe4129c68290397b912e64c97", "difficulty": "easy", "final_answer": {"answer": 27.025, "unit": "N"}, "id": "force_002718_11.75_2.3", "license": "Apache-2.0", "prompt": "A cart has mass 11.75 kg and measured acceleration 2.3 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 11.75 kg and a = 2.3 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 2.3, "mass": 11.75}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 13.75^2 and multiply by 0.5 * 5.75.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 543.5547, \"unit\": \"J\"}", "dedupe_signature": "3779f8a28ebcdecef7a3fb985e139ebc182556926f87953895b7abe7fdfc28ce", "difficulty": "easy", "final_answer": {"answer": 543.5547, "unit": "J"}, "id": "ke_002719_5.75_13.75", "license": "Apache-2.0", "prompt": "A body of mass 5.75 kg moves at 13.75 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 13.75^2 and multiply by 0.5 * 5.75.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 5.75, "velocity": 13.75}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 5.02 * 8.314 * 470 / 3.6.\nFinal: {\"answer\": 5448.9032, \"unit\": \"kPa\"}", "dedupe_signature": "6262f959e6c3b4fc31f600b9b4f4f9109adbdf2bd6c2bf11fb593f44e97e1734", "difficulty": "medium", "final_answer": {"answer": 5448.9032, "unit": "kPa"}, "id": "ideal_gas_002721_5.02_470_3.6", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=5.02 mol, T=470 K, and V=3.6 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 5.02 * 8.314 * 470 / 3.6.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 5.02, "temp_k": 470, "volume_l": 3.6}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=63.9 V and R=180.3 ohm.\nFinal: {\"answer\": 22.6468, \"unit\": \"W\"}", "dedupe_signature": "3944f2eb1f10a0812244d470e9e1a9c5cf23402c4f54d4abbca543b002c208f6", "difficulty": "easy", "final_answer": {"answer": 22.6468, "unit": "W"}, "id": "ohm_power_002723_63.9_180.3", "license": "Apache-2.0", "prompt": "A resistor has resistance 180.3 ohm and voltage 63.9 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=63.9 V and R=180.3 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 180.3, "voltage": 63.9}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=917 mg, t=17.5 h, and T_half=54 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 732.5096, \"unit\": \"mg\"}", "dedupe_signature": "c3c2fd2f4b1bf44b9f711fe8b6e61436c2c7d2cccc2d16311258652fb86acd57", "difficulty": "medium", "final_answer": {"answer": 732.5096, "unit": "mg"}, "id": "half_life_002724_917_54_17.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 917 mg. Its half-life is 54 hours. How many mg remain after 17.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=917 mg, t=17.5 h, and T_half=54 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 17.5, "half_life": 54.0, "initial_amount": 917.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 7.96 mol * 58.44 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 465.1824, \"unit\": \"g\"}", "dedupe_signature": "5a3532a5f076e20bda2f37393ace73de9b482b4947ff496b1f6811bd78b53544", "difficulty": "medium", "final_answer": {"answer": 465.1824, "unit": "g"}, "id": "stoich_mass_002725_sodium_chloride_7.96", "license": "Apache-2.0", "prompt": "A sample contains 7.96 mol of sodium chloride. Using molar mass 58.44 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 7.96 mol * 58.44 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "sodium chloride", "molar_mass": 58.44, "moles": 7.96}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.63 y, so each step multiplies y by 1 - h*0.63.\n3. Apply that update for 6 steps and round the final state.\nFinal: {\"answer\": 0.0, \"unit\": \"state_units\"}", "dedupe_signature": "a0f4920a3e2a63c4e39ef505816388a37e783e5947b4b79f2bb59ae2b7cc058e", "difficulty": "medium", "final_answer": {"answer": 0.0, "unit": "state_units"}, "id": "euler_decay_002727_19.5_0.63_1.5_6", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.63 y with y(0)=19.5, step size h=1.5, for 6 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.63 y, so each step multiplies y by 1 - h*0.63.\nApply that update for 6 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 19.5, "rate": 0.63, "step": 1.5, "steps": 6}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-9)=-85.6 and f(-4.7)=-51.2.\n3. The interval width is 4.3.\nFinal: {\"answer\": -294.12, \"unit\": \"area_units\"}", "dedupe_signature": "b36f4d4add43247de035b0794884b696bf69aefb57bd1072ce545003beeca97b", "difficulty": "medium", "final_answer": {"answer": -294.12, "unit": "area_units"}, "id": "trapz_linear_002728_8_-13.6_-9_-4.7", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=8x+-13.6 from x=-9 to x=-4.7. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-9)=-85.6 and f(-4.7)=-51.2.\nThe interval width is 4.3.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -13.6, "slope": 8.0, "x0": -9.0, "x1": -4.7}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 8071.0 / 1000.\nFinal: {\"answer\": 8.071, \"unit\": \"kg\"}", "dedupe_signature": "581f43383882413defaac22ebdb7e7c9dab24fc7db42f38bac82c8d05b229125", "difficulty": "easy", "final_answer": {"answer": 8.071, "unit": "kg"}, "id": "unit_convert_002730_g_to_kg_8071", "license": "Apache-2.0", "prompt": "Convert 8071 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 8071.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 8071.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=147 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-0.4193, 0.2723], \"unit\": \"N\"}", "dedupe_signature": "7a5465b0fe73a7e7c9359bb3565fcef0fff044e3207a4e743f0dd561d0609661", "difficulty": "medium", "final_answer": {"answer": [-0.4193, 0.2723], "unit": "N"}, "id": "vector_components_002731_0.5_147", "license": "Apache-2.0", "prompt": "A vector has magnitude 0.5 N at 147 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=147 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 147, "magnitude": 0.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [1.0, 6.5], \"unit\": \"dimensionless\"}", "dedupe_signature": "f8c7280cc624b24a46b37d96ff61c2cb41519b63397665a9da9cfe2ad1a56316", "difficulty": "medium", "final_answer": {"answer": [1.0, 6.5], "unit": "dimensionless"}, "id": "line_two_point_002732_-6.25_-3.5_1_6.5", "license": "Apache-2.0", "prompt": "A line passes through points (-6.25, 0.25) and (-3.5, 3). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -6.25, "x2": -3.5, "y1": 0.25, "y2": 3.0}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. m*v is momentum, not energy\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "485d1b5e273d8e6c8a979eb124d2c295964b471a8e712b05147f595dcdfc67c6", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_002733_inconsistent_1e14b074_667439", "license": "Apache-2.0", "prompt": "In instrument manual case 667439, check dimensional consistency for E = m * v. The left side has dimensions kg*m^2/s^2 and the right side has dimensions kg*m/s. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nm*v is momentum, not energy\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "E = m * v"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef finite_differences_002734(values):\n    return [values[i + 1] - values[i] for i in range(len(values) - 1)]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"finite_differences_002734\"}", "dedupe_signature": "8d293ef4a48d5b560b14630cf9596d2e76b55ad396ded3116928660677089a10", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "finite_differences_002734"}, "id": "code_002734_finite_differences_002734", "license": "Apache-2.0", "prompt": "Write a Python function finite_differences_002734(values) that returns the list of successive differences values[i+1] - values[i]. It must return [] for fewer than two values. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "finite_differences_002734"}, "verifier": {"function": "finite_differences_002734", "tests": ["assert finite_differences_002734([1, 4, 9, 16]) == [3, 5, 7]", "assert finite_differences_002734([5]) == []", "assert finite_differences_002734([]) == []"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: rate_constant, number_of_steps.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"rate_constant\", \"number_of_steps\"]}", "dedupe_signature": "9838c0019c3d238b80d66fc1f69c756650e9c5e628b783a013063a24fec94750", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["rate_constant", "number_of_steps"]}, "id": "abstain_002735_rate_constant_number_of_steps", "license": "Apache-2.0", "prompt": "Use explicit Euler for dy/dt = -k y. The prompt gives y(0)=70.5 and h=1.2, but omits both k and the number of steps. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: rate_constant, number_of_steps.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["rate_constant", "number_of_steps"]}, "verifier": {"missing": ["rate_constant", "number_of_steps"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 4.9 kg and a = 6.4 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 31.36, \"unit\": \"N\"}", "dedupe_signature": "fd6a689321207e4b303f7d12c4228da0644a2efcaee7913b7788cf6c15aa92fe", "difficulty": "easy", "final_answer": {"answer": 31.36, "unit": "N"}, "id": "force_002736_4.9_6.4", "license": "Apache-2.0", "prompt": "A cart has mass 4.9 kg and measured acceleration 6.4 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 4.9 kg and a = 6.4 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 6.4, "mass": 4.9}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 32.8^2 and multiply by 0.5 * 21.4.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 11511.488, \"unit\": \"J\"}", "dedupe_signature": "caa1b01f16c0578e11d66a3f38d348d670e2ccbb558573b57a31d1f8ec9ca59f", "difficulty": "easy", "final_answer": {"answer": 11511.488, "unit": "J"}, "id": "ke_002737_21.4_32.8", "license": "Apache-2.0", "prompt": "A body of mass 21.4 kg moves at 32.8 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 32.8^2 and multiply by 0.5 * 21.4.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 21.4, "velocity": 32.8}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=16 degrees through the sine of 2 theta.\n3. Substitute v=38 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 78.0024, \"unit\": \"m\"}", "dedupe_signature": "a5e3c3595365b316e3fd853f9ef6f29c4d128f3ce91932bd88ef5cfe45628f70", "difficulty": "medium", "final_answer": {"answer": 78.0024, "unit": "m"}, "id": "projectile_range_002738_38_16", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 38 m/s and angle 16 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=16 degrees through the sine of 2 theta.\nSubstitute v=38 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 16, "gravity": 9.81, "speed": 38.0}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 4.39 * 8.314 * 488 / 18.3.\nFinal: {\"answer\": 973.2923, \"unit\": \"kPa\"}", "dedupe_signature": "ad9990c779190ad2a1fb800d409af50293ed378d1eedd24294121090e40f172d", "difficulty": "medium", "final_answer": {"answer": 973.2923, "unit": "kPa"}, "id": "ideal_gas_002739_4.39_488_18.3", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=4.39 mol, T=488 K, and V=18.3 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 4.39 * 8.314 * 488 / 18.3.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 4.39, "temp_k": 488, "volume_l": 18.3}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1050 * 2.37 * 1.\nFinal: {\"answer\": 2488.5, \"unit\": \"J\"}", "dedupe_signature": "a7a31e1e8c419782f5891922299b22f5e76382d0d5ef0085f13397811fe1fa69", "difficulty": "easy", "final_answer": {"answer": 2488.5, "unit": "J"}, "id": "heat_q_002740_1050_2.37_1", "license": "Apache-2.0", "prompt": "A 1050 g sample has specific heat 2.37 J/(g*K). How much heat is needed to raise its temperature by 1 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1050 * 2.37 * 1.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 1, "heat_capacity": 2.37, "mass_g": 1050}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=79.7 V and R=74.9 ohm.\nFinal: {\"answer\": 84.8076, \"unit\": \"W\"}", "dedupe_signature": "3d9bdee9c7ae8770b9cc513df55c3bec7734cfe3b23f7deef4f2541264a477d5", "difficulty": "easy", "final_answer": {"answer": 84.8076, "unit": "W"}, "id": "ohm_power_002741_79.7_74.9", "license": "Apache-2.0", "prompt": "A resistor has resistance 74.9 ohm and voltage 79.7 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=79.7 V and R=74.9 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 74.9, "voltage": 79.7}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=839 mg, t=99.5 h, and T_half=26.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 62.1555, \"unit\": \"mg\"}", "dedupe_signature": "ba65dc09d54148b3a0cd36b9569ad78da12bf691fc120f52a37861a2514f790b", "difficulty": "medium", "final_answer": {"answer": 62.1555, "unit": "mg"}, "id": "half_life_002742_839_26.5_99.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 839 mg. Its half-life is 26.5 hours. How many mg remain after 99.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=839 mg, t=99.5 h, and T_half=26.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 99.5, "half_life": 26.5, "initial_amount": 839.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 6.22 mol * 44.01 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 273.7422, \"unit\": \"g\"}", "dedupe_signature": "4c90c8f69ab8795e91bbfa99649cf293dd8bf48c7fc5efbc6dc9c39cbe6d27e4", "difficulty": "medium", "final_answer": {"answer": 273.7422, "unit": "g"}, "id": "stoich_mass_002743_carbon_dioxide_6.22", "license": "Apache-2.0", "prompt": "A sample contains 6.22 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 6.22 mol * 44.01 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "carbon dioxide", "molar_mass": 44.01, "moles": 6.22}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 1125 mL to 1.125 L.\n3. Compute M = 2.545 / 1.125.\nFinal: {\"answer\": 2.2622, \"unit\": \"mol/L\"}", "dedupe_signature": "3586c79aeec12fd46875cbb936f451488a7b09097ba34ba621df31787a6adc8a", "difficulty": "medium", "final_answer": {"answer": 2.2622, "unit": "mol/L"}, "id": "molarity_002744_2.545_1125", "license": "Apache-2.0", "prompt": "A solution contains 2.545 mol of solute in 1125 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 1125 mL to 1.125 L.\nCompute M = 2.545 / 1.125.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 2.545, "volume_ml": 1125}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-7.6)=44.74 and f(-1.4)=23.66.\n3. The interval width is 6.2.\nFinal: {\"answer\": 212.04, \"unit\": \"area_units\"}", "dedupe_signature": "9569206a9b6befe1a7b38246cfeb3ade14d8ef7ce893fe28940cf8bccf6aa690", "difficulty": "medium", "final_answer": {"answer": 212.04, "unit": "area_units"}, "id": "trapz_linear_002746_-3.4_18.9_-7.6_-1.4", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-3.4x+18.9 from x=-7.6 to x=-1.4. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-7.6)=44.74 and f(-1.4)=23.66.\nThe interval width is 6.2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 18.9, "slope": -3.4, "x0": -7.6, "x1": -1.3999999999999995}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.44 and add it to the current value.\nFinal: {\"answer\": [1.208, 0.06, 0.894], \"unit\": \"temperature_units\"}", "dedupe_signature": "a323c66ff7ffe4eaf0a92b36a2fc32cf3ff1276ece2bb46d814d398dcdc5bb43", "difficulty": "hard", "final_answer": {"answer": [1.208, 0.06, 0.894], "unit": "temperature_units"}, "id": "heat_step_002747_0.44_0.95_-1.3_2.15_0.85_-0.35", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=0.95, right=-0.35; current interior values are [-1.3, 2.15, 0.85]. Use r=0.44. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.44 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-1.3, 2.15, 0.85], "left": 0.95, "r": 0.44, "right": -0.35}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 6667.0 / 1000.\nFinal: {\"answer\": 6.667, \"unit\": \"kg\"}", "dedupe_signature": "96793ae07ec5ec2208f0787cdbaa04fbe7204012213b60894382d8701d67c69b", "difficulty": "easy", "final_answer": {"answer": 6.667, "unit": "kg"}, "id": "unit_convert_002748_g_to_kg_6667", "license": "Apache-2.0", "prompt": "Convert 6667 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 6667.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 6667.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=222 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-357.4527, -321.8518], \"unit\": \"N\"}", "dedupe_signature": "8e7a339a4a61160bdade2d7728f3ef5afb3da7df58c01d06217fb1471af4a954", "difficulty": "medium", "final_answer": {"answer": [-357.4527, -321.8518], "unit": "N"}, "id": "vector_components_002749_481_222", "license": "Apache-2.0", "prompt": "A vector has magnitude 481 N at 222 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=222 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 222, "magnitude": 481.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. mass times acceleration has newton dimensions\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "eb8b6165e60a8df3e20e5960ffbf21180bdba5ae70bcc6cf613f4aef40d752d5", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_002751_consistent_03f5e041_846799", "license": "Apache-2.0", "prompt": "In lab notebook case 846799, check dimensional consistency for F = m * a. The left side has dimensions kg*m/s^2 and the right side has dimensions kg*m/s^2. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nmass times acceleration has newton dimensions\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "F = m * a"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef running_total_002752(values):\n    total = 0\n    out = []\n    for value in values:\n        total += value\n        out.append(total)\n    return out\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"running_total_002752\"}", "dedupe_signature": "106d8b798ffbad5f544c42a9a1ab86aae34e32a95dc9cf702a638a5897028ee6", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "running_total_002752"}, "id": "code_002752_running_total_002752", "license": "Apache-2.0", "prompt": "Write a Python function running_total_002752(values) that returns cumulative sums as a new list. It must not mutate the input list. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "running_total_002752"}, "verifier": {"function": "running_total_002752", "tests": ["assert running_total_002752([1, 2, 3]) == [1, 3, 6]", "xs = [4, -1, 2]; assert running_total_002752(xs) == [4, 3, 5] and xs == [4, -1, 2]", "assert running_total_002752([]) == []"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 10^2 and multiply by 0.5 * 29.45.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 1472.5, \"unit\": \"J\"}", "dedupe_signature": "54d23ad56e3b2c19adbb62a9f5183bf2887a7a01182ca0de5c1106009d7bed30", "difficulty": "easy", "final_answer": {"answer": 1472.5, "unit": "J"}, "id": "ke_002755_29.45_10", "license": "Apache-2.0", "prompt": "A body of mass 29.45 kg moves at 10 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 10^2 and multiply by 0.5 * 29.45.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 29.45, "velocity": 10.0}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=32 degrees through the sine of 2 theta.\n3. Substitute v=60.9 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 339.8019, \"unit\": \"m\"}", "dedupe_signature": "4afc3bae165e2f9e96a88a8f1dbd0dbaba1ca767226a963b29fa49ef03649bf1", "difficulty": "medium", "final_answer": {"answer": 339.8019, "unit": "m"}, "id": "projectile_range_002756_60.9_32", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 60.9 m/s and angle 32 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=32 degrees through the sine of 2 theta.\nSubstitute v=60.9 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 32, "gravity": 9.81, "speed": 60.9}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 205 * 1.86 * 90.\nFinal: {\"answer\": 34317.0, \"unit\": \"J\"}", "dedupe_signature": "ff863f6e47a1fe6cf10c08757aa8d0a83ad3fa79d255031b60775a455ec692f3", "difficulty": "easy", "final_answer": {"answer": 34317.0, "unit": "J"}, "id": "heat_q_002758_205_1.86_90", "license": "Apache-2.0", "prompt": "A 205 g sample has specific heat 1.86 J/(g*K). How much heat is needed to raise its temperature by 90 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 205 * 1.86 * 90.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 90, "heat_capacity": 1.86, "mass_g": 205}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=212.9 V and R=120.6 ohm.\nFinal: {\"answer\": 375.8409, \"unit\": \"W\"}", "dedupe_signature": "c1b8bc0cd72f4ca2c51d06721827b1c14b5a9b956ac367385df001c2fd27a96c", "difficulty": "easy", "final_answer": {"answer": 375.8409, "unit": "W"}, "id": "ohm_power_002759_212.9_120.6", "license": "Apache-2.0", "prompt": "A resistor has resistance 120.6 ohm and voltage 212.9 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=212.9 V and R=120.6 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 120.6, "voltage": 212.9}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.21 y, so each step multiplies y by 1 - h*0.21.\n3. Apply that update for 12 steps and round the final state.\nFinal: {\"answer\": 0.0705, \"unit\": \"state_units\"}", "dedupe_signature": "9892e8033cf4e3ffd2a20a65283827e2493f63639f87bdcc4672cdf164979fc5", "difficulty": "medium", "final_answer": {"answer": 0.0705, "unit": "state_units"}, "id": "euler_decay_002763_5.5_0.21_1.45_12", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.21 y with y(0)=5.5, step size h=1.45, for 12 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.21 y, so each step multiplies y by 1 - h*0.21.\nApply that update for 12 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 5.5, "rate": 0.21, "step": 1.45, "steps": 12}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(8.7)=-53.08 and f(13)=-84.9.\n3. The interval width is 4.3.\nFinal: {\"answer\": -296.657, \"unit\": \"area_units\"}", "dedupe_signature": "c86a6965ee5d1aceed0e1f033d4e5585efd0da62f5e138fb82357b6692cd603d", "difficulty": "medium", "final_answer": {"answer": -296.657, "unit": "area_units"}, "id": "trapz_linear_002764_-7.4_11.3_8.7_13", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-7.4x+11.3 from x=8.7 to x=13. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(8.7)=-53.08 and f(13)=-84.9.\nThe interval width is 4.3.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 11.3, "slope": -7.4, "x0": 8.7, "x1": 13.0}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.14 and add it to the current value.\nFinal: {\"answer\": [-0.461, -0.801, -0.294], \"unit\": \"temperature_units\"}", "dedupe_signature": "56b119cee51d18284c330c97eb7dc53fba61b78d6cdc51f2f9fd0fd192ef2580", "difficulty": "hard", "final_answer": {"answer": [-0.461, -0.801, -0.294], "unit": "temperature_units"}, "id": "heat_step_002765_0.14_2.7_-1.0_-0.85_-0.35_0.55", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=2.7, right=0.55; current interior values are [-1.0, -0.85, -0.35]. Use r=0.14. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.14 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-1.0, -0.85, -0.35], "left": 2.7, "r": 0.14, "right": 0.55}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=254 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-15.0222, -52.3888], \"unit\": \"N\"}", "dedupe_signature": "3dec0fbce631496a1f6233507048c7c987eb91c2d8d0be0db91f7ea83bc9972c", "difficulty": "medium", "final_answer": {"answer": [-15.0222, -52.3888], "unit": "N"}, "id": "vector_components_002767_54.5_254", "license": "Apache-2.0", "prompt": "A vector has magnitude 54.5 N at 254 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=254 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 254, "magnitude": 54.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: target_schema, valid_examples.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"target_schema\", \"valid_examples\"]}", "dedupe_signature": "a7d09703d388f91dbd7709a682caf0c5493e4e2ff1dc7ca676f62089e4a61b0e", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["target_schema", "valid_examples"]}, "id": "abstain_002771_target_schema_valid_examples", "license": "Apache-2.0", "prompt": "Write a parser that converts each billing survey record from batch 476214 into the correct schema, but the prompt does not include the target schema or examples. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: target_schema, valid_examples.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["target_schema", "valid_examples"]}, "verifier": {"missing": ["target_schema", "valid_examples"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 36.85^2 and multiply by 0.5 * 6.8.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 4616.9365, \"unit\": \"J\"}", "dedupe_signature": "a1be95bb35243006b8479ec8cc77a0774cf2c56989843e20d16bc7f6280a5f1e", "difficulty": "easy", "final_answer": {"answer": 4616.9365, "unit": "J"}, "id": "ke_002773_6.8_36.85", "license": "Apache-2.0", "prompt": "A body of mass 6.8 kg moves at 36.85 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 36.85^2 and multiply by 0.5 * 6.8.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 6.8, "velocity": 36.85}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=13 degrees through the sine of 2 theta.\n3. Substitute v=20 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 17.8745, \"unit\": \"m\"}", "dedupe_signature": "707bce6073751ee0c979278cc416edb4abff94366dd31aaeddfbadb8e29cbb74", "difficulty": "medium", "final_answer": {"answer": 17.8745, "unit": "m"}, "id": "projectile_range_002774_20_13", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 20 m/s and angle 13 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=13 degrees through the sine of 2 theta.\nSubstitute v=20 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 13, "gravity": 9.81, "speed": 20.0}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 5.82 * 8.314 * 448 / 93.4.\nFinal: {\"answer\": 232.0941, \"unit\": \"kPa\"}", "dedupe_signature": "6177b1a11013f5bec786e35fefa86c783a12d148aad7a8826f4201a7dc6d79a0", "difficulty": "medium", "final_answer": {"answer": 232.0941, "unit": "kPa"}, "id": "ideal_gas_002775_5.82_448_93.4", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=5.82 mol, T=448 K, and V=93.4 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 5.82 * 8.314 * 448 / 93.4.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 5.82, "temp_k": 448, "volume_l": 93.4}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1370 * 2.625 * 114.\nFinal: {\"answer\": 409972.5, \"unit\": \"J\"}", "dedupe_signature": "935390c6262793977e764f909364546232b8364a0daf5564ed4526388324f79a", "difficulty": "easy", "final_answer": {"answer": 409972.5, "unit": "J"}, "id": "heat_q_002776_1370_2.625_114", "license": "Apache-2.0", "prompt": "A 1370 g sample has specific heat 2.625 J/(g*K). How much heat is needed to raise its temperature by 114 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1370 * 2.625 * 114.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 114, "heat_capacity": 2.625, "mass_g": 1370}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=83.7 V and R=123.9 ohm.\nFinal: {\"answer\": 56.5431, \"unit\": \"W\"}", "dedupe_signature": "a45f88250609b2791ceedaaa0e24e51984ade2b7824d37dedad2f240526e29db", "difficulty": "easy", "final_answer": {"answer": 56.5431, "unit": "W"}, "id": "ohm_power_002777_83.7_123.9", "license": "Apache-2.0", "prompt": "A resistor has resistance 123.9 ohm and voltage 83.7 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=83.7 V and R=123.9 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 123.9, "voltage": 83.7}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=887.5 mg, t=44.5 h, and T_half=14.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 105.7591, \"unit\": \"mg\"}", "dedupe_signature": "fb1aa8767083dd465f8a227bf04e128fe7c4c26699430306c4a29a57101c0431", "difficulty": "medium", "final_answer": {"answer": 105.7591, "unit": "mg"}, "id": "half_life_002778_887.5_14.5_44.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 887.5 mg. Its half-life is 14.5 hours. How many mg remain after 44.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=887.5 mg, t=44.5 h, and T_half=14.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 44.5, "half_life": 14.5, "initial_amount": 887.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 7.11 mol * 44.01 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 312.9111, \"unit\": \"g\"}", "dedupe_signature": "1fa6e68e752ab8e6690b0043a04f99fec9078a88fb8997b0e317be0d1af93c86", "difficulty": "medium", "final_answer": {"answer": 312.9111, "unit": "g"}, "id": "stoich_mass_002779_carbon_dioxide_7.11", "license": "Apache-2.0", "prompt": "A sample contains 7.11 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 7.11 mol * 44.01 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "carbon dioxide", "molar_mass": 44.01, "moles": 7.11}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.81 y, so each step multiplies y by 1 - h*0.81.\n3. Apply that update for 10 steps and round the final state.\nFinal: {\"answer\": 0.0, \"unit\": \"state_units\"}", "dedupe_signature": "7cc0adc1d1d3d93682b939ed879a3ca064a0f9351057e96051ebffb0e1238b1d", "difficulty": "medium", "final_answer": {"answer": 0.0, "unit": "state_units"}, "id": "euler_decay_002781_36.5_0.81_1.05_10", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.81 y with y(0)=36.5, step size h=1.05, for 10 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.81 y, so each step multiplies y by 1 - h*0.81.\nApply that update for 10 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 36.5, "rate": 0.81, "step": 1.05, "steps": 10}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-7.6)=50.36 and f(1.7)=-11.02.\n3. The interval width is 9.3.\nFinal: {\"answer\": 182.931, \"unit\": \"area_units\"}", "dedupe_signature": "e5ddddae2b303ca06a7decaa6763d9f9442a9e9395854c709dcbfa71da3c771b", "difficulty": "medium", "final_answer": {"answer": 182.931, "unit": "area_units"}, "id": "trapz_linear_002782_-6.6_0.2_-7.6_1.7", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-6.6x+0.2 from x=-7.6 to x=1.7. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-7.6)=50.36 and f(1.7)=-11.02.\nThe interval width is 9.3.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 0.2, "slope": -6.6, "x0": -7.6, "x1": 1.700000000000001}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.38 and add it to the current value.\nFinal: {\"answer\": [0.907, 0.916, 0.097], \"unit\": \"temperature_units\"}", "dedupe_signature": "2e32a91979ed469ff71ad762785d04ac92a7edd0b57a18deb0a1724aea8b7ad2", "difficulty": "hard", "final_answer": {"answer": [0.907, 0.916, 0.097], "unit": "temperature_units"}, "id": "heat_step_002783_0.38_2.75_-0.1_-0.3_2.7_-1.15", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=2.75, right=-1.15; current interior values are [-0.1, -0.3, 2.7]. Use r=0.38. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.38 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-0.1, -0.3, 2.7], "left": 2.75, "r": 0.38, "right": -1.15}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 12774.0 / 1000.\nFinal: {\"answer\": 12.774, \"unit\": \"kg\"}", "dedupe_signature": "5db654d95ec836c296f29132a448eb2dbb68748f41ae10f3a5f569cf2cdca2a9", "difficulty": "easy", "final_answer": {"answer": 12.774, "unit": "kg"}, "id": "unit_convert_002784_g_to_kg_12774", "license": "Apache-2.0", "prompt": "Convert 12774 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 12774.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 12774.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-5.8, 19.75], \"unit\": \"dimensionless\"}", "dedupe_signature": "1c0f69815d3d9d54224d96d9720c7bdd3d76529f6f7bb80af4abc95bc5312a9a", "difficulty": "medium", "final_answer": {"answer": [-5.8, 19.75], "unit": "dimensionless"}, "id": "line_two_point_002786_7.5_16.25_-5.8_19.75", "license": "Apache-2.0", "prompt": "A line passes through points (7.5, -23.75) and (16.25, -74.5). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 7.5, "x2": 16.25, "y1": -23.75, "y2": -74.5}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\nimport math\n\ndef unit_vector_002788(x, y):\n    norm = math.hypot(x, y)\n    if norm == 0:\n        raise ValueError('zero vector has no direction')\n    return (x / norm, y / norm)\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"unit_vector_002788\"}", "dedupe_signature": "ce07aca8088fccede42e08b09be63a5fdbd7fe041868322d0c861dbddcb5c1b0", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "unit_vector_002788"}, "id": "code_002788_unit_vector_002788", "license": "Apache-2.0", "prompt": "Write a Python function unit_vector_002788(x, y) that returns the 2D unit vector as a tuple. Raise ValueError for the zero vector. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "unit_vector_002788"}, "verifier": {"function": "unit_vector_002788", "tests": ["ux, uy = unit_vector_002788(3, 4); assert abs(ux - 0.6) < 1e-12 and abs(uy - 0.8) < 1e-12", "assert unit_vector_002788(0, 5) == (0, 1)", "try:\n    unit_vector_002788(0, 0)\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: left_boundary, right_boundary.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"left_boundary\", \"right_boundary\"]}", "dedupe_signature": "952e0e7d81d9d1a5dca9a986e5bd4f939e7d8e224698e62f8d4b28d92bcfddee", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["left_boundary", "right_boundary"]}, "id": "abstain_002789_left_boundary_right_boundary", "license": "Apache-2.0", "prompt": "Solve the 1D heat equation after one finite-difference step. The prompt gives r=0.38 and interior values [1.9, 2.3, 2.6], but gives no boundary values. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: left_boundary, right_boundary.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["left_boundary", "right_boundary"]}, "verifier": {"missing": ["left_boundary", "right_boundary"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 22.6 kg and a = 6.4 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 144.64, \"unit\": \"N\"}", "dedupe_signature": "3b5aee4f5f3d49178c947ba4fc8d9f5f6e50982673b3163911d5dce45b0754c8", "difficulty": "easy", "final_answer": {"answer": 144.64, "unit": "N"}, "id": "force_002790_22.6_6.4", "license": "Apache-2.0", "prompt": "A cart has mass 22.6 kg and measured acceleration 6.4 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 22.6 kg and a = 6.4 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 6.4, "mass": 22.6}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 17.1^2 and multiply by 0.5 * 12.75.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 1864.1138, \"unit\": \"J\"}", "dedupe_signature": "f4effd903de18dafc9c01fa1ea2cd1c3be3c22a0eb08fe2c9b2aed68392937bc", "difficulty": "easy", "final_answer": {"answer": 1864.1138, "unit": "J"}, "id": "ke_002791_12.75_17.1", "license": "Apache-2.0", "prompt": "A body of mass 12.75 kg moves at 17.1 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 17.1^2 and multiply by 0.5 * 12.75.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 12.75, "velocity": 17.1}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1640 * 4.925 * 93.\nFinal: {\"answer\": 751161.0, \"unit\": \"J\"}", "dedupe_signature": "d1436f363ccf56e6a7a0ddfad45f9407beb5f48db923f1213d2ba8e28d045aed", "difficulty": "easy", "final_answer": {"answer": 751161.0, "unit": "J"}, "id": "heat_q_002794_1640_4.925_93", "license": "Apache-2.0", "prompt": "A 1640 g sample has specific heat 4.925 J/(g*K). How much heat is needed to raise its temperature by 93 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1640 * 4.925 * 93.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 93, "heat_capacity": 4.925, "mass_g": 1640}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=28.5 mg, t=289 h, and T_half=105.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 4.268, \"unit\": \"mg\"}", "dedupe_signature": "123edf07e44a337dd5e76dc93bd0ef541aa159a67479a3359231a51dc859134c", "difficulty": "medium", "final_answer": {"answer": 4.268, "unit": "mg"}, "id": "half_life_002796_28.5_105.5_289", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 28.5 mg. Its half-life is 105.5 hours. How many mg remain after 289 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=28.5 mg, t=289 h, and T_half=105.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 289.0, "half_life": 105.5, "initial_amount": 28.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 3715 mL to 3.715 L.\n3. Compute M = 4.185 / 3.715.\nFinal: {\"answer\": 1.1265, \"unit\": \"mol/L\"}", "dedupe_signature": "92e8dafec8c349989ed47777b78373cfbf50358a40b5bf3b65a6d38400090905", "difficulty": "medium", "final_answer": {"answer": 1.1265, "unit": "mol/L"}, "id": "molarity_002798_4.185_3715", "license": "Apache-2.0", "prompt": "A solution contains 4.185 mol of solute in 3715 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 3715 mL to 3.715 L.\nCompute M = 4.185 / 3.715.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 4.185, "volume_ml": 3715}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(3)=-15.7 and f(8.3)=-47.5.\n3. The interval width is 5.3.\nFinal: {\"answer\": -167.48, \"unit\": \"area_units\"}", "dedupe_signature": "6d2e6ee056dc48666aa80f133e8b126d411878d8ca7c33b32d86ef859ad5a346", "difficulty": "medium", "final_answer": {"answer": -167.48, "unit": "area_units"}, "id": "trapz_linear_002800_-6_2.3_3_8.3", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-6x+2.3 from x=3 to x=8.3. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(3)=-15.7 and f(8.3)=-47.5.\nThe interval width is 5.3.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 2.3, "slope": -6.0, "x0": 3.0, "x1": 8.3}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.2 and add it to the current value.\nFinal: {\"answer\": [-1.38, -0.52, 0.0], \"unit\": \"temperature_units\"}", "dedupe_signature": "0724b060947e7e4fd8abc02b32cc86130f61be79793b196022cc90907cc0e80d", "difficulty": "hard", "final_answer": {"answer": [-1.38, -0.52, 0.0], "unit": "temperature_units"}, "id": "heat_step_002801_0.2_-0.8_-1.9_-0.4_0.5_-1.1", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-0.8, right=-1.1; current interior values are [-1.9, -0.4, 0.5]. Use r=0.2. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.2 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-1.9, -0.4, 0.5], "left": -0.8, "r": 0.2, "right": -1.1}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=324 degrees and keep the unit as newtons.\nFinal: {\"answer\": [244.3231, -177.5111], \"unit\": \"N\"}", "dedupe_signature": "7bceb77e4aa461fc226b43382d1cb1dc4ec393ae8fa25a3648629935632b7759", "difficulty": "medium", "final_answer": {"answer": [244.3231, -177.5111], "unit": "N"}, "id": "vector_components_002803_302_324", "license": "Apache-2.0", "prompt": "A vector has magnitude 302 N at 324 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=324 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 324, "magnitude": 302.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-0.8, -20.5], \"unit\": \"dimensionless\"}", "dedupe_signature": "c382b778d503cd2ada4157889fac2e1a1538fff729f97ba1265edcfea2c02988", "difficulty": "medium", "final_answer": {"answer": [-0.8, -20.5], "unit": "dimensionless"}, "id": "line_two_point_002804_11.5_16.25_-0.8_-20.5", "license": "Apache-2.0", "prompt": "A line passes through points (11.5, -29.7) and (16.25, -33.5). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 11.5, "x2": 16.25, "y1": -29.700000000000003, "y2": -33.5}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. velocity divided by time is acceleration\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "d4bd3a84820447b343117e2f3e61061bacdadd7275e4a95a4448ab45a19ed0ba", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_002805_inconsistent_c1271127_778535", "license": "Apache-2.0", "prompt": "In student derivation case 778535, check dimensional consistency for x = v / t. The left side has dimensions m and the right side has dimensions m/s^2. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nvelocity divided by time is acceleration\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "x = v / t"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef weighted_sum_002806(values, weights):\n    if len(values) != len(weights):\n        raise ValueError('length mismatch')\n    return sum(value * weight for value, weight in zip(values, weights))\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"weighted_sum_002806\"}", "dedupe_signature": "0984fd226839f74c021be8ae2b98ae1eed1be416f704e5b57580549f2bad67c6", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "weighted_sum_002806"}, "id": "code_002806_weighted_sum_002806", "license": "Apache-2.0", "prompt": "Write a Python function weighted_sum_002806(values, weights) that returns sum(value*weight). Raise ValueError when the two inputs have different lengths. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "weighted_sum_002806"}, "verifier": {"function": "weighted_sum_002806", "tests": ["assert weighted_sum_002806([2, 3], [4, 5]) == 23", "assert weighted_sum_002806([], []) == 0", "try:\n    weighted_sum_002806([1], [1, 2])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: rate_constant, number_of_steps.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"rate_constant\", \"number_of_steps\"]}", "dedupe_signature": "d4793da2abcf1e4d857417db8a51dbf8933f974d28330b6ee45f7885c7603906", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["rate_constant", "number_of_steps"]}, "id": "abstain_002807_rate_constant_number_of_steps", "license": "Apache-2.0", "prompt": "Use explicit Euler for dy/dt = -k y. The prompt gives y(0)=4 and h=2, but omits both k and the number of steps. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: rate_constant, number_of_steps.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["rate_constant", "number_of_steps"]}, "verifier": {"missing": ["rate_constant", "number_of_steps"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 44.5^2 and multiply by 0.5 * 8.4.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 8317.05, \"unit\": \"J\"}", "dedupe_signature": "c503ededaf47ed346447a8eb2092db7a06acc125ef0f8b7b8cdaabb0395e6489", "difficulty": "easy", "final_answer": {"answer": 8317.05, "unit": "J"}, "id": "ke_002809_8.4_44.5", "license": "Apache-2.0", "prompt": "A body of mass 8.4 kg moves at 44.5 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 44.5^2 and multiply by 0.5 * 8.4.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 8.4, "velocity": 44.5}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=60 degrees through the sine of 2 theta.\n3. Substitute v=67.2 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 398.6577, \"unit\": \"m\"}", "dedupe_signature": "bebc621eb6ab1abbaa3b09d6fc39771f6cf132d986a0e2750c636b3ab148e48c", "difficulty": "medium", "final_answer": {"answer": 398.6577, "unit": "m"}, "id": "projectile_range_002810_67.2_60", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 67.2 m/s and angle 60 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=60 degrees through the sine of 2 theta.\nSubstitute v=67.2 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 60, "gravity": 9.81, "speed": 67.2}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 2.15 * 8.314 * 413 / 75.0.\nFinal: {\"answer\": 98.4322, \"unit\": \"kPa\"}", "dedupe_signature": "d84751d81608c979a76c5f40b17718281bf777c29bea7cfd083557e6be28b936", "difficulty": "medium", "final_answer": {"answer": 98.4322, "unit": "kPa"}, "id": "ideal_gas_002811_2.15_413_75.0", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=2.15 mol, T=413 K, and V=75.0 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 2.15 * 8.314 * 413 / 75.0.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 2.15, "temp_k": 413, "volume_l": 75.0}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1345 * 3.705 * 46.\nFinal: {\"answer\": 229228.35, \"unit\": \"J\"}", "dedupe_signature": "e8526025f8f7161c16977eac8e505a961a52939630b8e9bdd52c746228131a60", "difficulty": "easy", "final_answer": {"answer": 229228.35, "unit": "J"}, "id": "heat_q_002812_1345_3.705_46", "license": "Apache-2.0", "prompt": "A 1345 g sample has specific heat 3.705 J/(g*K). How much heat is needed to raise its temperature by 46 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1345 * 3.705 * 46.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 46, "heat_capacity": 3.705, "mass_g": 1345}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=800.5 mg, t=133.5 h, and T_half=19.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 6.9577, \"unit\": \"mg\"}", "dedupe_signature": "904cb1badf79aeb98c845b0161f4fffffe37e0ac03a77b7a8543d1f781c6ea00", "difficulty": "medium", "final_answer": {"answer": 6.9577, "unit": "mg"}, "id": "half_life_002814_800.5_19.5_133.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 800.5 mg. Its half-life is 19.5 hours. How many mg remain after 133.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=800.5 mg, t=133.5 h, and T_half=19.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 133.5, "half_life": 19.5, "initial_amount": 800.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 1.55 mol * 100.087 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 155.1349, \"unit\": \"g\"}", "dedupe_signature": "c4ad9b7ebd87c394482c9bafee8d23054feed2424daf5f51575cba1ccad5e4eb", "difficulty": "medium", "final_answer": {"answer": 155.1349, "unit": "g"}, "id": "stoich_mass_002815_calcium_carbonate_1.55", "license": "Apache-2.0", "prompt": "A sample contains 1.55 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 1.55 mol * 100.087 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "calcium carbonate", "molar_mass": 100.087, "moles": 1.55}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 3435 mL to 3.435 L.\n3. Compute M = 0.305 / 3.435.\nFinal: {\"answer\": 0.0888, \"unit\": \"mol/L\"}", "dedupe_signature": "6285b6d03b5e3c521a3801739e959baac5cf9d006484eb64a50463fd20035a2a", "difficulty": "medium", "final_answer": {"answer": 0.0888, "unit": "mol/L"}, "id": "molarity_002816_0.305_3435", "license": "Apache-2.0", "prompt": "A solution contains 0.305 mol of solute in 3435 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 3435 mL to 3.435 L.\nCompute M = 0.305 / 3.435.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 0.305, "volume_ml": 3435}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-0.5)=-11.3 and f(4.5)=-51.3.\n3. The interval width is 5.\nFinal: {\"answer\": -156.5, \"unit\": \"area_units\"}", "dedupe_signature": "4e6ae17df8cf007c68db4354edd09a5e798b9cc8baab082ca34474963c415f33", "difficulty": "medium", "final_answer": {"answer": -156.5, "unit": "area_units"}, "id": "trapz_linear_002818_-8_-15.3_-0.5_4.5", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-8x+-15.3 from x=-0.5 to x=4.5. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-0.5)=-11.3 and f(4.5)=-51.3.\nThe interval width is 5.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -15.3, "slope": -8.0, "x0": -0.5, "x1": 4.5}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.36 and add it to the current value.\nFinal: {\"answer\": [1.012, 0.402, 1.476], \"unit\": \"temperature_units\"}", "dedupe_signature": "12ede79ebe0ca1b89bea39302749d2d0d74301f75fd92fe3d96e497b2b907a8e", "difficulty": "hard", "final_answer": {"answer": [1.012, 0.402, 1.476], "unit": "temperature_units"}, "id": "heat_step_002819_0.36_2.4_-1.4_1.5_1.35_1.55", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=2.4, right=1.55; current interior values are [-1.4, 1.5, 1.35]. Use r=0.36. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.36 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-1.4, 1.5, 1.35], "left": 2.4, "r": 0.36, "right": 1.55}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 33175.0 / 1000.\nFinal: {\"answer\": 33.175, \"unit\": \"kg\"}", "dedupe_signature": "879c5b4a0bcaefe34d73648149ff8bd5155b05cf3b2898fc579b23941618de44", "difficulty": "easy", "final_answer": {"answer": 33.175, "unit": "kg"}, "id": "unit_convert_002820_g_to_kg_33175", "license": "Apache-2.0", "prompt": "Convert 33175 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 33175.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 33175.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [9.65, -18.75], \"unit\": \"dimensionless\"}", "dedupe_signature": "2b792af111c68299127d9fcaef9ca1cfa0d1dab4d72c42cc18b39b35bb78bbb6", "difficulty": "medium", "final_answer": {"answer": [9.65, -18.75], "unit": "dimensionless"}, "id": "line_two_point_002822_-19.25_-8.5_9.65_-18.75", "license": "Apache-2.0", "prompt": "A line passes through points (-19.25, -204.513) and (-8.5, -100.775). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -19.25, "x2": -8.5, "y1": -204.51250000000002, "y2": -100.775}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. density times acceleration times height gives kg/(m*s^2), or pascal\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "175c57487b5250a9470f08257a9b610d2918bd5ba97754ae24ce82b2b84cda9a", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_002823_consistent_b7d3eed1_141156", "license": "Apache-2.0", "prompt": "In quality-control check case 141156, check dimensional consistency for p = rho * g * h. The left side has dimensions Pa and the right side has dimensions Pa. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\ndensity times acceleration times height gives kg/(m*s^2), or pascal\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "p = rho * g * h"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef safe_mean_002824(values):\n    if not values:\n        raise ValueError('safe_mean requires at least one value')\n    return sum(values) / len(values)\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"safe_mean_002824\"}", "dedupe_signature": "ba3d4bf78a03eddf8d52144f767e6bdbfe0c2494022d3601f5bc566edb86bf89", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "safe_mean_002824"}, "id": "code_002824_safe_mean_002824", "license": "Apache-2.0", "prompt": "Write a Python function safe_mean_002824(values) that returns the arithmetic mean. It must raise ValueError for an empty input and must not mutate the input list. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "safe_mean_002824"}, "verifier": {"function": "safe_mean_002824", "tests": ["assert safe_mean_002824([2, 4, 6]) == 4", "xs = [1, 2, 3]; assert safe_mean_002824(xs) == 2 and xs == [1, 2, 3]", "try:\n    safe_mean_002824([])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 7.65 kg and a = 1.65 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 12.6225, \"unit\": \"N\"}", "dedupe_signature": "a1fd5dcfad2ef5ee8161264cc8458b23797c2fd61dd46631527465079ee029b4", "difficulty": "easy", "final_answer": {"answer": 12.6225, "unit": "N"}, "id": "force_002826_7.65_1.65", "license": "Apache-2.0", "prompt": "A cart has mass 7.65 kg and measured acceleration 1.65 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 7.65 kg and a = 1.65 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 1.65, "mass": 7.65}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 1.35^2 and multiply by 0.5 * 11.65.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 10.6161, \"unit\": \"J\"}", "dedupe_signature": "7c5d6a4eea70feb7214ca221519a26717fd36743427ce6b413424670bb77d0fc", "difficulty": "easy", "final_answer": {"answer": 10.6161, "unit": "J"}, "id": "ke_002827_11.65_1.35", "license": "Apache-2.0", "prompt": "A body of mass 11.65 kg moves at 1.35 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 1.35^2 and multiply by 0.5 * 11.65.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 11.65, "velocity": 1.35}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=16 degrees through the sine of 2 theta.\n3. Substitute v=44.3 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 106.0103, \"unit\": \"m\"}", "dedupe_signature": "c73b37c32c46f9a4f1a6ad922a7eb3c8c04ac87d8a81ff63879a97d5f7ae1a4a", "difficulty": "medium", "final_answer": {"answer": 106.0103, "unit": "m"}, "id": "projectile_range_002828_44.3_16", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 44.3 m/s and angle 16 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=16 degrees through the sine of 2 theta.\nSubstitute v=44.3 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 16, "gravity": 9.81, "speed": 44.3}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 1 * 8.314 * 542 / 103.6.\nFinal: {\"answer\": 43.496, \"unit\": \"kPa\"}", "dedupe_signature": "ea7d5738e62aa705692a9f92110b41bb8a9636ac75f8d405608708f7aa5239e8", "difficulty": "medium", "final_answer": {"answer": 43.496, "unit": "kPa"}, "id": "ideal_gas_002829_1_542_103.6", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=1 mol, T=542 K, and V=103.6 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 1 * 8.314 * 542 / 103.6.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 1.0, "temp_k": 542, "volume_l": 103.6}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 790 * 0.515 * 57.\nFinal: {\"answer\": 23190.45, \"unit\": \"J\"}", "dedupe_signature": "cb20fb924e67361888ea050f191ab7125ca2b7cedc09daae0da91d0b4ded1ef3", "difficulty": "easy", "final_answer": {"answer": 23190.45, "unit": "J"}, "id": "heat_q_002830_790_0.515_57", "license": "Apache-2.0", "prompt": "A 790 g sample has specific heat 0.515 J/(g*K). How much heat is needed to raise its temperature by 57 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 790 * 0.515 * 57.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 57, "heat_capacity": 0.515, "mass_g": 790}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=140.7 V and R=194.4 ohm.\nFinal: {\"answer\": 101.8338, \"unit\": \"W\"}", "dedupe_signature": "3697a580e0ee096c4e4d916f247abe56daa4958063071d66fecddaeb2bddbc5b", "difficulty": "easy", "final_answer": {"answer": 101.8338, "unit": "W"}, "id": "ohm_power_002831_140.7_194.4", "license": "Apache-2.0", "prompt": "A resistor has resistance 194.4 ohm and voltage 140.7 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=140.7 V and R=194.4 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 194.4, "voltage": 140.7}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=142.5 mg, t=313 h, and T_half=82.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 10.2737, \"unit\": \"mg\"}", "dedupe_signature": "ebda87444faf5b2bcbe38a941bc030e0d1cab23f8a616a0448c0a301e454fd44", "difficulty": "medium", "final_answer": {"answer": 10.2737, "unit": "mg"}, "id": "half_life_002832_142.5_82.5_313", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 142.5 mg. Its half-life is 82.5 hours. How many mg remain after 313 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=142.5 mg, t=313 h, and T_half=82.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 313.0, "half_life": 82.5, "initial_amount": 142.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 8 mol * 180.156 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 1441.248, \"unit\": \"g\"}", "dedupe_signature": "7abbd3616682984d468c2af6a6861a7378196ba58134ad56ef9b3f05465f45a6", "difficulty": "medium", "final_answer": {"answer": 1441.248, "unit": "g"}, "id": "stoich_mass_002833_glucose_8", "license": "Apache-2.0", "prompt": "A sample contains 8 mol of glucose. Using molar mass 180.156 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 8 mol * 180.156 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "glucose", "molar_mass": 180.156, "moles": 8.0}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 2400 mL to 2.4 L.\n3. Compute M = 1.88 / 2.4.\nFinal: {\"answer\": 0.7833, \"unit\": \"mol/L\"}", "dedupe_signature": "7efc7cfe9fe6097fc745c9b77650749578c7fa56fae183ea68280bab065bb9d9", "difficulty": "medium", "final_answer": {"answer": 0.7833, "unit": "mol/L"}, "id": "molarity_002834_1.88_2400", "license": "Apache-2.0", "prompt": "A solution contains 1.88 mol of solute in 2400 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 2400 mL to 2.4 L.\nCompute M = 1.88 / 2.4.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 1.88, "volume_ml": 2400}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.09 y, so each step multiplies y by 1 - h*0.09.\n3. Apply that update for 8 steps and round the final state.\nFinal: {\"answer\": 5.9798, \"unit\": \"state_units\"}", "dedupe_signature": "81ccc1eee5c3b8c15a3c914ab085c1f5272abe13e885d6c33165839bbf9bcb34", "difficulty": "medium", "final_answer": {"answer": 5.9798, "unit": "state_units"}, "id": "euler_decay_002835_28_0.09_1.95_8", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.09 y with y(0)=28, step size h=1.95, for 8 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.09 y, so each step multiplies y by 1 - h*0.09.\nApply that update for 8 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 28.0, "rate": 0.09, "step": 1.95, "steps": 8}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(9.8)=5 and f(12.9)=9.65.\n3. The interval width is 3.1.\nFinal: {\"answer\": 22.7075, \"unit\": \"area_units\"}", "dedupe_signature": "74a5c0f2ba0eba5c3b8280a60319a1c51e2d50d1986df27979f56e36a6031bc2", "difficulty": "medium", "final_answer": {"answer": 22.7075, "unit": "area_units"}, "id": "trapz_linear_002836_1.5_-9.7_9.8_12.9", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=1.5x+-9.7 from x=9.8 to x=12.9. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(9.8)=5 and f(12.9)=9.65.\nThe interval width is 3.1.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -9.7, "slope": 1.5, "x0": 9.8, "x1": 12.9}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.4 and add it to the current value.\nFinal: {\"answer\": [-0.05, 0.2, -1.16], \"unit\": \"temperature_units\"}", "dedupe_signature": "4223654de9cfc62500bf2318de89ebc33560928c6baaf176a07bfe66ae8e6ab5", "difficulty": "hard", "final_answer": {"answer": [-0.05, 0.2, -1.16], "unit": "temperature_units"}, "id": "heat_step_002837_0.4_0.7_2.15_-1.9_-0.7_-0.65", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=0.7, right=-0.65; current interior values are [2.15, -1.9, -0.7]. Use r=0.4. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.4 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [2.15, -1.9, -0.7], "left": 0.7, "r": 0.4, "right": -0.65}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 22346.0 / 1000.\nFinal: {\"answer\": 22.346, \"unit\": \"kg\"}", "dedupe_signature": "5abe7ba7ca767e757a76773a14b646e544ab1fb98ffc96e556e45d1538a76e05", "difficulty": "easy", "final_answer": {"answer": 22.346, "unit": "kg"}, "id": "unit_convert_002838_g_to_kg_22346", "license": "Apache-2.0", "prompt": "Convert 22346 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 22346.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 22346.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=137 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-273.5263, 255.0674], \"unit\": \"N\"}", "dedupe_signature": "e7775da34ed36bd99b00d63cca97103d32ab5d8682dbbcb8bdf0d4f1745785c9", "difficulty": "medium", "final_answer": {"answer": [-273.5263, 255.0674], "unit": "N"}, "id": "vector_components_002839_374_137", "license": "Apache-2.0", "prompt": "A vector has magnitude 374 N at 137 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=137 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 137, "magnitude": 374.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-5.4, -11.0], \"unit\": \"dimensionless\"}", "dedupe_signature": "2d8d96b31e8451f7ba232c813a830659c204ad1cdf9b8bbbd5d88c2f6aae8494", "difficulty": "medium", "final_answer": {"answer": [-5.4, -11.0], "unit": "dimensionless"}, "id": "line_two_point_002840_10.25_15.25_-5.4_-11", "license": "Apache-2.0", "prompt": "A line passes through points (10.25, -66.35) and (15.25, -93.35). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 10.25, "x2": 15.25, "y1": -66.35, "y2": -93.35000000000001}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. energy divided by length is force, not spring constant\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "0de74f9fb9eb794ab33e1c016bf8a1990eb68e0f550b24b9cc5669df063894af", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_002841_inconsistent_56040f5d_707097", "license": "Apache-2.0", "prompt": "In quality-control check case 707097, check dimensional consistency for k = E / x. The left side has dimensions N/m and the right side has dimensions J/m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nenergy divided by length is force, not spring constant\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "k = E / x"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: volume.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"volume\"]}", "dedupe_signature": "71fc05c8d432e1d97c75278ad6323cdb610026cf4ede643851f300ef695bc363", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["volume"]}, "id": "abstain_002843_volume", "license": "Apache-2.0", "prompt": "Compute pressure from the ideal gas law. The prompt gives n=3.2 mol and T=613 K, but does not give volume. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: volume.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["volume"]}, "verifier": {"missing": ["volume"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 3.8 kg and a = 10.25 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 38.95, \"unit\": \"N\"}", "dedupe_signature": "5b483e2a8f1473d4eb89a8400b89104468c620767a33457cc4dc1bad98a3aef1", "difficulty": "easy", "final_answer": {"answer": 38.95, "unit": "N"}, "id": "force_002844_3.8_10.25", "license": "Apache-2.0", "prompt": "A cart has mass 3.8 kg and measured acceleration 10.25 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 3.8 kg and a = 10.25 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 10.25, "mass": 3.8}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 34.65^2 and multiply by 0.5 * 27.3.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 16388.4971, \"unit\": \"J\"}", "dedupe_signature": "2f89db002d8d0684b40e008a322783c8e049cc8620b24a1ba037fdcb6adf0506", "difficulty": "easy", "final_answer": {"answer": 16388.4971, "unit": "J"}, "id": "ke_002845_27.3_34.65", "license": "Apache-2.0", "prompt": "A body of mass 27.3 kg moves at 34.65 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 34.65^2 and multiply by 0.5 * 27.3.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 27.3, "velocity": 34.65}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=60 degrees through the sine of 2 theta.\n3. Substitute v=30.5 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 82.1223, \"unit\": \"m\"}", "dedupe_signature": "00b1c25778c1449fcb0c74d0eae0acb53e6670e443c3db1d0a40304cfe340459", "difficulty": "medium", "final_answer": {"answer": 82.1223, "unit": "m"}, "id": "projectile_range_002846_30.5_60", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 30.5 m/s and angle 60 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=60 degrees through the sine of 2 theta.\nSubstitute v=30.5 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 60, "gravity": 9.81, "speed": 30.5}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 4.87 * 8.314 * 530 / 22.7.\nFinal: {\"answer\": 945.3421, \"unit\": \"kPa\"}", "dedupe_signature": "989505b2b841e12d2d6dcdbf6e2e8b260f5d773c965b16b396208da8bdaeb5b2", "difficulty": "medium", "final_answer": {"answer": 945.3421, "unit": "kPa"}, "id": "ideal_gas_002847_4.87_530_22.7", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=4.87 mol, T=530 K, and V=22.7 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 4.87 * 8.314 * 530 / 22.7.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 4.87, "temp_k": 530, "volume_l": 22.7}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1645 * 2.305 * 60.\nFinal: {\"answer\": 227503.5, \"unit\": \"J\"}", "dedupe_signature": "db09bfe0eb644d0dd4e18117fe783b1c61a6c58a7a81ca73c73c4acce273a8bf", "difficulty": "easy", "final_answer": {"answer": 227503.5, "unit": "J"}, "id": "heat_q_002848_1645_2.305_60", "license": "Apache-2.0", "prompt": "A 1645 g sample has specific heat 2.305 J/(g*K). How much heat is needed to raise its temperature by 60 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1645 * 2.305 * 60.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 60, "heat_capacity": 2.305, "mass_g": 1645}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=2.4 V and R=139.6 ohm.\nFinal: {\"answer\": 0.0413, \"unit\": \"W\"}", "dedupe_signature": "55b3a6104607402d2117f63aebd3706f172d9e39061ebd11dcf391285a76a80b", "difficulty": "easy", "final_answer": {"answer": 0.0413, "unit": "W"}, "id": "ohm_power_002849_2.4_139.6", "license": "Apache-2.0", "prompt": "A resistor has resistance 139.6 ohm and voltage 2.4 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=2.4 V and R=139.6 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 139.6, "voltage": 2.4}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=732.5 mg, t=106.5 h, and T_half=112 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 378.9312, \"unit\": \"mg\"}", "dedupe_signature": "3e3519aeb6ae58eb672fae1117a84d1f9dca4072f50ef9a8cbaee134e146dce4", "difficulty": "medium", "final_answer": {"answer": 378.9312, "unit": "mg"}, "id": "half_life_002850_732.5_112_106.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 732.5 mg. Its half-life is 112 hours. How many mg remain after 106.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=732.5 mg, t=106.5 h, and T_half=112 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 106.5, "half_life": 112.0, "initial_amount": 732.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 7.89 mol * 44.01 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 347.2389, \"unit\": \"g\"}", "dedupe_signature": "5e89cdd948e8f6dc9fb27919a84f15326603f289e61046061bc7d436ce69266f", "difficulty": "medium", "final_answer": {"answer": 347.2389, "unit": "g"}, "id": "stoich_mass_002851_carbon_dioxide_7.89", "license": "Apache-2.0", "prompt": "A sample contains 7.89 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 7.89 mol * 44.01 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "carbon dioxide", "molar_mass": 44.01, "moles": 7.89}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 4295 mL to 4.295 L.\n3. Compute M = 1.015 / 4.295.\nFinal: {\"answer\": 0.2363, \"unit\": \"mol/L\"}", "dedupe_signature": "6322fa749c2b9a76b418780b3188ae9fd69ff68f18b8cefe45068a9b180d4e22", "difficulty": "medium", "final_answer": {"answer": 0.2363, "unit": "mol/L"}, "id": "molarity_002852_1.015_4295", "license": "Apache-2.0", "prompt": "A solution contains 1.015 mol of solute in 4295 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 4295 mL to 4.295 L.\nCompute M = 1.015 / 4.295.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 1.015, "volume_ml": 4295}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.34 y, so each step multiplies y by 1 - h*0.34.\n3. Apply that update for 9 steps and round the final state.\nFinal: {\"answer\": 0.029, \"unit\": \"state_units\"}", "dedupe_signature": "691795d836f857d81ec626a371b98b8e63562f5006ad87ad94a02ad87a8669a7", "difficulty": "medium", "final_answer": {"answer": 0.029, "unit": "state_units"}, "id": "euler_decay_002853_34_0.34_1.6_9", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.34 y with y(0)=34, step size h=1.6, for 9 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.34 y, so each step multiplies y by 1 - h*0.34.\nApply that update for 9 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 34.0, "rate": 0.34, "step": 1.6, "steps": 9}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.4 and add it to the current value.\nFinal: {\"answer\": [1.0, -0.35, 1.21], \"unit\": \"temperature_units\"}", "dedupe_signature": "08326cb6b4e6bf8c08bf35bc09b9606ed570af8328bf54a512d2d42147d4a763", "difficulty": "hard", "final_answer": {"answer": [1.0, -0.35, 1.21], "unit": "temperature_units"}, "id": "heat_step_002855_0.4_0.75_-1.6_2.55_-0.55_0.75", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=0.75, right=0.75; current interior values are [-1.6, 2.55, -0.55]. Use r=0.4. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.4 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-1.6, 2.55, -0.55], "left": 0.75, "r": 0.4, "right": 0.75}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=9 degrees and keep the unit as newtons.\nFinal: {\"answer\": [406.4338, 64.3728], \"unit\": \"N\"}", "dedupe_signature": "e853da7288a390939de2324586cfe8c9bf8e054222e2283463b635c7cce0bff5", "difficulty": "medium", "final_answer": {"answer": [406.4338, 64.3728], "unit": "N"}, "id": "vector_components_002857_411.5_9", "license": "Apache-2.0", "prompt": "A vector has magnitude 411.5 N at 9 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=9 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 9, "magnitude": 411.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. volt squared divided by ohm is watt\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "c8814422f8fc9c7376f7991ed0b27c7b3391cffb910a76cef23d57a03c2a0b58", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_002859_consistent_82e93f3d_664451", "license": "Apache-2.0", "prompt": "In simulation spec case 664451, check dimensional consistency for P = V^2 / R. The left side has dimensions W and the right side has dimensions W. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nvolt squared divided by ohm is watt\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "P = V^2 / R"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef safe_mean_002860(values):\n    if not values:\n        raise ValueError('safe_mean requires at least one value')\n    return sum(values) / len(values)\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"safe_mean_002860\"}", "dedupe_signature": "bb4c141ed61f4bb739e2cc499966b19429d26e90cebaab082106e5203f14c506", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "safe_mean_002860"}, "id": "code_002860_safe_mean_002860", "license": "Apache-2.0", "prompt": "Write a Python function safe_mean_002860(values) that returns the arithmetic mean. It must raise ValueError for an empty input and must not mutate the input list. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "safe_mean_002860"}, "verifier": {"function": "safe_mean_002860", "tests": ["assert safe_mean_002860([2, 4, 6]) == 4", "xs = [1, 2, 3]; assert safe_mean_002860(xs) == 2 and xs == [1, 2, 3]", "try:\n    safe_mean_002860([])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: required_fields, allowed_transformations.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"required_fields\", \"allowed_transformations\"]}", "dedupe_signature": "84642706e84399e0600e434e672963fc1b20cbd94205d499da1f9f5621c51c22", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["required_fields", "allowed_transformations"]}, "id": "abstain_002861_required_fields_allowed_transformations", "license": "Apache-2.0", "prompt": "Write a sanitizer for valid mobile sensor records in release 624648, but the prompt does not state which fields are required or which transformations are allowed. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: required_fields, allowed_transformations.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["required_fields", "allowed_transformations"]}, "verifier": {"missing": ["required_fields", "allowed_transformations"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 24.45 kg and a = 14.2 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 347.19, \"unit\": \"N\"}", "dedupe_signature": "712a1de7f6b7400629f1e40a18e6f892517ad638d884b4789ea806aaae2b4d50", "difficulty": "easy", "final_answer": {"answer": 347.19, "unit": "N"}, "id": "force_002862_24.45_14.2", "license": "Apache-2.0", "prompt": "A cart has mass 24.45 kg and measured acceleration 14.2 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 24.45 kg and a = 14.2 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 14.2, "mass": 24.45}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=34 degrees through the sine of 2 theta.\n3. Substitute v=37.7 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 134.332, \"unit\": \"m\"}", "dedupe_signature": "ea77ec9433eef53eaa64f837242ad14c42f9ca7adf0a75088c331a897c54d1e5", "difficulty": "medium", "final_answer": {"answer": 134.332, "unit": "m"}, "id": "projectile_range_002864_37.7_34", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 37.7 m/s and angle 34 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=34 degrees through the sine of 2 theta.\nSubstitute v=37.7 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 34, "gravity": 9.81, "speed": 37.7}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 30 * 4.81 * 11.\nFinal: {\"answer\": 1587.3, \"unit\": \"J\"}", "dedupe_signature": "4170433dde83f186cc273a9ee02902b69873c3d6226c85b505610c809961bb69", "difficulty": "easy", "final_answer": {"answer": 1587.3, "unit": "J"}, "id": "heat_q_002866_30_4.81_11", "license": "Apache-2.0", "prompt": "A 30 g sample has specific heat 4.81 J/(g*K). How much heat is needed to raise its temperature by 11 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 30 * 4.81 * 11.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 11, "heat_capacity": 4.81, "mass_g": 30}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=14.4 V and R=126 ohm.\nFinal: {\"answer\": 1.6457, \"unit\": \"W\"}", "dedupe_signature": "e5cd55143778aff21975c350c86b19d47479ffe3265e6638cf3edcb7b637cbcb", "difficulty": "easy", "final_answer": {"answer": 1.6457, "unit": "W"}, "id": "ohm_power_002867_14.4_126", "license": "Apache-2.0", "prompt": "A resistor has resistance 126 ohm and voltage 14.4 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=14.4 V and R=126 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 126.0, "voltage": 14.4}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 2055 mL to 2.055 L.\n3. Compute M = 2.36 / 2.055.\nFinal: {\"answer\": 1.1484, \"unit\": \"mol/L\"}", "dedupe_signature": "359338fd8c8e6a85afccfd55c62a88222c04d438257f4d56589963ad3c834faf", "difficulty": "medium", "final_answer": {"answer": 1.1484, "unit": "mol/L"}, "id": "molarity_002870_2.36_2055", "license": "Apache-2.0", "prompt": "A solution contains 2.36 mol of solute in 2055 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 2055 mL to 2.055 L.\nCompute M = 2.36 / 2.055.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 2.36, "volume_ml": 2055}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.56 y, so each step multiplies y by 1 - h*0.56.\n3. Apply that update for 3 steps and round the final state.\nFinal: {\"answer\": 0.0088, \"unit\": \"state_units\"}", "dedupe_signature": "c88475c4a1b38bc8445b2808a68e6bfd0963f0ee992d0c49caa09d06a7cc03f3", "difficulty": "medium", "final_answer": {"answer": 0.0088, "unit": "state_units"}, "id": "euler_decay_002871_79.5_0.56_1.7_3", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.56 y with y(0)=79.5, step size h=1.7, for 3 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.56 y, so each step multiplies y by 1 - h*0.56.\nApply that update for 3 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 79.5, "rate": 0.56, "step": 1.7, "steps": 3}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(9.5)=20.2 and f(17.5)=45.8.\n3. The interval width is 8.\nFinal: {\"answer\": 264.0, \"unit\": \"area_units\"}", "dedupe_signature": "dba7a9d1eddb20975ed96a10ee9859d9b27d6e96ab586f62c87a3449de298e94", "difficulty": "medium", "final_answer": {"answer": 264.0, "unit": "area_units"}, "id": "trapz_linear_002872_3.2_-10.2_9.5_17.5", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=3.2x+-10.2 from x=9.5 to x=17.5. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(9.5)=20.2 and f(17.5)=45.8.\nThe interval width is 8.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -10.2, "slope": 3.2, "x0": 9.5, "x1": 17.5}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.14 and add it to the current value.\nFinal: {\"answer\": [0.543, 0.021, 0.518], \"unit\": \"temperature_units\"}", "dedupe_signature": "af18c1799c9ec2fc6d79b1fc53ceeb5857224e771d541e8a3897c3fdbc1c8424", "difficulty": "hard", "final_answer": {"answer": [0.543, 0.021, 0.518], "unit": "temperature_units"}, "id": "heat_step_002873_0.14_-0.4_0.9_-0.35_1.05_-1.35", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-0.4, right=-1.35; current interior values are [0.9, -0.35, 1.05]. Use r=0.14. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.14 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [0.9, -0.35, 1.05], "left": -0.4, "r": 0.14, "right": -1.35}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=10 degrees and keep the unit as newtons.\nFinal: {\"answer\": [44.8088, 7.901], \"unit\": \"N\"}", "dedupe_signature": "4dbe655796f4ac0d21b9f4a89e2b2453269e35ddb6ddda366d71ba52ed6bacf4", "difficulty": "medium", "final_answer": {"answer": [44.8088, 7.901], "unit": "N"}, "id": "vector_components_002875_45.5_10", "license": "Apache-2.0", "prompt": "A vector has magnitude 45.5 N at 10 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=10 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 10, "magnitude": 45.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. amount times volume is not concentration\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "da29482df87da9b6cc2586bfeac6a05f05219d11033bfc421a9bf497ccd6fba0", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_002877_inconsistent_74ac0b02_780435", "license": "Apache-2.0", "prompt": "In student derivation case 780435, check dimensional consistency for C = n * V. The left side has dimensions mol/L and the right side has dimensions mol*L. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\namount times volume is not concentration\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "C = n * V"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef finite_differences_002878(values):\n    return [values[i + 1] - values[i] for i in range(len(values) - 1)]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"finite_differences_002878\"}", "dedupe_signature": "e59d4fe289c26a413c0be1d06358eb6e58dec8cb9eb509977c74d5781cbc9814", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "finite_differences_002878"}, "id": "code_002878_finite_differences_002878", "license": "Apache-2.0", "prompt": "Write a Python function finite_differences_002878(values) that returns the list of successive differences values[i+1] - values[i]. It must return [] for fewer than two values. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "finite_differences_002878"}, "verifier": {"function": "finite_differences_002878", "tests": ["assert finite_differences_002878([1, 4, 9, 16]) == [3, 5, 7]", "assert finite_differences_002878([5]) == []", "assert finite_differences_002878([]) == []"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: rate_constant, number_of_steps.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"rate_constant\", \"number_of_steps\"]}", "dedupe_signature": "856d442cf525491b1a68eae0b37f48394f3d9b7a1b4f74701fd3802d63170ef7", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["rate_constant", "number_of_steps"]}, "id": "abstain_002879_rate_constant_number_of_steps", "license": "Apache-2.0", "prompt": "Use explicit Euler for dy/dt = -k y. The prompt gives y(0)=21.5 and h=0.85, but omits both k and the number of steps. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: rate_constant, number_of_steps.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["rate_constant", "number_of_steps"]}, "verifier": {"missing": ["rate_constant", "number_of_steps"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 11.5 kg and a = 4.9 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 56.35, \"unit\": \"N\"}", "dedupe_signature": "b1d80a01cdfab1fef2f9afb7554f30810c2c1743ddb2136012be937939500769", "difficulty": "easy", "final_answer": {"answer": 56.35, "unit": "N"}, "id": "force_002880_11.5_4.9", "license": "Apache-2.0", "prompt": "A cart has mass 11.5 kg and measured acceleration 4.9 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 11.5 kg and a = 4.9 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 4.9, "mass": 11.5}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 14.35^2 and multiply by 0.5 * 6.1.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 628.0636, \"unit\": \"J\"}", "dedupe_signature": "7dac5b6efa7b362aee7e6892e0ae6a441f8142f300de7c09ba5957f8ad9d171f", "difficulty": "easy", "final_answer": {"answer": 628.0636, "unit": "J"}, "id": "ke_002881_6.1_14.35", "license": "Apache-2.0", "prompt": "A body of mass 6.1 kg moves at 14.35 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 14.35^2 and multiply by 0.5 * 6.1.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 6.1, "velocity": 14.35}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=66 degrees through the sine of 2 theta.\n3. Substitute v=37.8 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 108.2401, \"unit\": \"m\"}", "dedupe_signature": "5bc2d4150f6bdfd831228954ab98c32b75a20e81e002be51dc40c47240aff1ba", "difficulty": "medium", "final_answer": {"answer": 108.2401, "unit": "m"}, "id": "projectile_range_002882_37.8_66", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 37.8 m/s and angle 66 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=66 degrees through the sine of 2 theta.\nSubstitute v=37.8 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 66, "gravity": 9.81, "speed": 37.8}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 3.52 * 8.314 * 281 / 84.7.\nFinal: {\"answer\": 97.0902, \"unit\": \"kPa\"}", "dedupe_signature": "dbcf2aced2cefcebc67fc9aa4b383008f91e5c104b47bfe7fe06d78e93f9d6de", "difficulty": "medium", "final_answer": {"answer": 97.0902, "unit": "kPa"}, "id": "ideal_gas_002883_3.52_281_84.7", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=3.52 mol, T=281 K, and V=84.7 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 3.52 * 8.314 * 281 / 84.7.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 3.52, "temp_k": 281, "volume_l": 84.7}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=219.3 V and R=54 ohm.\nFinal: {\"answer\": 890.6017, \"unit\": \"W\"}", "dedupe_signature": "418775ad49b7f15f00081d18a4c9071760aaffaafa34b02bc5da173e86722d49", "difficulty": "easy", "final_answer": {"answer": 890.6017, "unit": "W"}, "id": "ohm_power_002885_219.3_54", "license": "Apache-2.0", "prompt": "A resistor has resistance 54 ohm and voltage 219.3 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=219.3 V and R=54 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 54.0, "voltage": 219.3}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=986.5 mg, t=198.5 h, and T_half=57.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 90.1341, \"unit\": \"mg\"}", "dedupe_signature": "bcd974a6dbcbf57721a9eb12779c09a7d260023ada1cf41a51158c7b18866f7f", "difficulty": "medium", "final_answer": {"answer": 90.1341, "unit": "mg"}, "id": "half_life_002886_986.5_57.5_198.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 986.5 mg. Its half-life is 57.5 hours. How many mg remain after 198.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=986.5 mg, t=198.5 h, and T_half=57.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 198.5, "half_life": 57.5, "initial_amount": 986.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 3600 mL to 3.6 L.\n3. Compute M = 3.705 / 3.6.\nFinal: {\"answer\": 1.0292, \"unit\": \"mol/L\"}", "dedupe_signature": "483f81ab8d9b5c54351792ba50f492d837c45e3437f59a31477d09ebe346112f", "difficulty": "medium", "final_answer": {"answer": 1.0292, "unit": "mol/L"}, "id": "molarity_002888_3.705_3600", "license": "Apache-2.0", "prompt": "A solution contains 3.705 mol of solute in 3600 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 3600 mL to 3.6 L.\nCompute M = 3.705 / 3.6.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 3.705, "volume_ml": 3600}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(6.2)=38.92 and f(7.3)=46.18.\n3. The interval width is 1.1.\nFinal: {\"answer\": 46.805, \"unit\": \"area_units\"}", "dedupe_signature": "a003eba88a2a10d723ac359f85b5e7e08364587abfcf0ff948fea1d7bf1fcea4", "difficulty": "medium", "final_answer": {"answer": 46.805, "unit": "area_units"}, "id": "trapz_linear_002890_6.6_-2_6.2_7.3", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=6.6x+-2 from x=6.2 to x=7.3. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(6.2)=38.92 and f(7.3)=46.18.\nThe interval width is 1.1.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -2.0, "slope": 6.6, "x0": 6.2, "x1": 7.300000000000001}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.3 and add it to the current value.\nFinal: {\"answer\": [1.045, 0.53, -0.49], \"unit\": \"temperature_units\"}", "dedupe_signature": "f9f3031d931d05f7f288ded1d58e9c2420fed242cbd1f783ef0e5fbb349a620a", "difficulty": "hard", "final_answer": {"answer": [1.045, 0.53, -0.49], "unit": "temperature_units"}, "id": "heat_step_002891_0.3_1.1_2.65_-1.15_0.65_-1.35", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.1, right=-1.35; current interior values are [2.65, -1.15, 0.65]. Use r=0.3. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.3 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [2.65, -1.15, 0.65], "left": 1.1, "r": 0.3, "right": -1.35}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=218 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-1.576, -1.2313], \"unit\": \"N\"}", "dedupe_signature": "d80e4157fb04573d69e09a1f34679a34fddaf25105c949db8cabb18fc06ef670", "difficulty": "medium", "final_answer": {"answer": [-1.576, -1.2313], "unit": "N"}, "id": "vector_components_002893_2_218", "license": "Apache-2.0", "prompt": "A vector has magnitude 2 N at 218 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=218 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 218, "magnitude": 2.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. velocity times time gives distance, not acceleration\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "c251d95dd320ccd7f65ca26163de7e75b3e1b9eea67e2c06ae6454fb36781d89", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_002895_inconsistent_7481c798_959047", "license": "Apache-2.0", "prompt": "In field worksheet case 959047, check dimensional consistency for a = v * t. The left side has dimensions m/s^2 and the right side has dimensions m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nvelocity times time gives distance, not acceleration\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "a = v * t"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef finite_differences_002896(values):\n    return [values[i + 1] - values[i] for i in range(len(values) - 1)]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"finite_differences_002896\"}", "dedupe_signature": "0d3fbf00e8d1563ec675b4b1e6e5d493f53b7bf22df8084a12b25074a0b560f9", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "finite_differences_002896"}, "id": "code_002896_finite_differences_002896", "license": "Apache-2.0", "prompt": "Write a Python function finite_differences_002896(values) that returns the list of successive differences values[i+1] - values[i]. It must return [] for fewer than two values. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "finite_differences_002896"}, "verifier": {"function": "finite_differences_002896", "tests": ["assert finite_differences_002896([1, 4, 9, 16]) == [3, 5, 7]", "assert finite_differences_002896([5]) == []", "assert finite_differences_002896([]) == []"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: required_fields, allowed_transformations.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"required_fields\", \"allowed_transformations\"]}", "dedupe_signature": "20fce2dd72208497575fe543490ebc41b9d33a5f8a24b2ef1f1de35146e7ac85", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["required_fields", "allowed_transformations"]}, "id": "abstain_002897_required_fields_allowed_transformations", "license": "Apache-2.0", "prompt": "Write a sanitizer for valid billing sensor records in release 920031, but the prompt does not state which fields are required or which transformations are allowed. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: required_fields, allowed_transformations.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["required_fields", "allowed_transformations"]}, "verifier": {"missing": ["required_fields", "allowed_transformations"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 2.9 kg and a = 6.35 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 18.415, \"unit\": \"N\"}", "dedupe_signature": "f18fc19bed82db18d3cacd2c7039f61149ec2b28f2a2ab4c83f1628e80a1151c", "difficulty": "easy", "final_answer": {"answer": 18.415, "unit": "N"}, "id": "force_002898_2.9_6.35", "license": "Apache-2.0", "prompt": "A cart has mass 2.9 kg and measured acceleration 6.35 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 2.9 kg and a = 6.35 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 6.35, "mass": 2.9}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 23.5^2 and multiply by 0.5 * 22.75.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 6281.8438, \"unit\": \"J\"}", "dedupe_signature": "9b8f2d1722bed5f47d98e7c20a317407cff7aebe3c06bcde308e7b6e2039cf70", "difficulty": "easy", "final_answer": {"answer": 6281.8438, "unit": "J"}, "id": "ke_002899_22.75_23.5", "license": "Apache-2.0", "prompt": "A body of mass 22.75 kg moves at 23.5 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 23.5^2 and multiply by 0.5 * 22.75.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 22.75, "velocity": 23.5}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=41 degrees through the sine of 2 theta.\n3. Substitute v=68.6 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 475.042, \"unit\": \"m\"}", "dedupe_signature": "f72cedcd59da21e6d6a40ba9c6a994925451d4a8b26a6688d50b64767970fc20", "difficulty": "medium", "final_answer": {"answer": 475.042, "unit": "m"}, "id": "projectile_range_002900_68.6_41", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 68.6 m/s and angle 41 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=41 degrees through the sine of 2 theta.\nSubstitute v=68.6 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 41, "gravity": 9.81, "speed": 68.6}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 0.38 * 8.314 * 501 / 66.2.\nFinal: {\"answer\": 23.9097, \"unit\": \"kPa\"}", "dedupe_signature": "22f854c39c2640e50a728d77994fa77a26d5a1f558c142fbfe85eca009b42bba", "difficulty": "medium", "final_answer": {"answer": 23.9097, "unit": "kPa"}, "id": "ideal_gas_002901_0.38_501_66.2", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=0.38 mol, T=501 K, and V=66.2 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 0.38 * 8.314 * 501 / 66.2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 0.38, "temp_k": 501, "volume_l": 66.2}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1780 * 4.275 * 33.\nFinal: {\"answer\": 251113.5, \"unit\": \"J\"}", "dedupe_signature": "836ae57daaec3bba2788d2d5ef75dadf8bb4b5d8023860b4eeb6abff60345afc", "difficulty": "easy", "final_answer": {"answer": 251113.5, "unit": "J"}, "id": "heat_q_002902_1780_4.275_33", "license": "Apache-2.0", "prompt": "A 1780 g sample has specific heat 4.275 J/(g*K). How much heat is needed to raise its temperature by 33 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1780 * 4.275 * 33.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 33, "heat_capacity": 4.275, "mass_g": 1780}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=171.7 V and R=169 ohm.\nFinal: {\"answer\": 174.4431, \"unit\": \"W\"}", "dedupe_signature": "2d20be009b390133d753c9536eb78464e34574c20a3a44c4ec51c4204c3110c8", "difficulty": "easy", "final_answer": {"answer": 174.4431, "unit": "W"}, "id": "ohm_power_002903_171.7_169", "license": "Apache-2.0", "prompt": "A resistor has resistance 169 ohm and voltage 171.7 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=171.7 V and R=169 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 169.0, "voltage": 171.7}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=897.5 mg, t=349.5 h, and T_half=55.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 11.4119, \"unit\": \"mg\"}", "dedupe_signature": "b628d8636b84bd3c9aca4b4def0cac78336256bc3f070d32be301ddb0f7109e4", "difficulty": "medium", "final_answer": {"answer": 11.4119, "unit": "mg"}, "id": "half_life_002904_897.5_55.5_349.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 897.5 mg. Its half-life is 55.5 hours. How many mg remain after 349.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=897.5 mg, t=349.5 h, and T_half=55.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 349.5, "half_life": 55.5, "initial_amount": 897.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 4.94 mol * 44.01 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 217.4094, \"unit\": \"g\"}", "dedupe_signature": "6c0f3dcfc9f5f5286ba8a5573bd41aaee7e81bc2771208c153f5422b8ef77c2f", "difficulty": "medium", "final_answer": {"answer": 217.4094, "unit": "g"}, "id": "stoich_mass_002905_carbon_dioxide_4.94", "license": "Apache-2.0", "prompt": "A sample contains 4.94 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 4.94 mol * 44.01 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "carbon dioxide", "molar_mass": 44.01, "moles": 4.94}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 2065 mL to 2.065 L.\n3. Compute M = 4.685 / 2.065.\nFinal: {\"answer\": 2.2688, \"unit\": \"mol/L\"}", "dedupe_signature": "b670e5d0abf34bb947a88387913f3b5eff4366715b981dcfc5783a0ba3bb040d", "difficulty": "medium", "final_answer": {"answer": 2.2688, "unit": "mol/L"}, "id": "molarity_002906_4.685_2065", "license": "Apache-2.0", "prompt": "A solution contains 4.685 mol of solute in 2065 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 2065 mL to 2.065 L.\nCompute M = 4.685 / 2.065.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 4.685, "volume_ml": 2065}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.75 y, so each step multiplies y by 1 - h*0.75.\n3. Apply that update for 9 steps and round the final state.\nFinal: {\"answer\": 0.0, \"unit\": \"state_units\"}", "dedupe_signature": "516cff65d137165cf16d8d543512b999ff0dc117184b4092eb55db1f50ae1042", "difficulty": "medium", "final_answer": {"answer": 0.0, "unit": "state_units"}, "id": "euler_decay_002907_78_0.75_1.25_9", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.75 y with y(0)=78, step size h=1.25, for 9 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.75 y, so each step multiplies y by 1 - h*0.75.\nApply that update for 9 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 78.0, "rate": 0.75, "step": 1.25, "steps": 9}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(2.1)=-18.19 and f(8.4)=-23.86.\n3. The interval width is 6.3.\nFinal: {\"answer\": -132.4575, \"unit\": \"area_units\"}", "dedupe_signature": "e1af8ccf36ca4b6c79ebe0ae218591bf999a5d72c99d5a2eb44f2fabb614a705", "difficulty": "medium", "final_answer": {"answer": -132.4575, "unit": "area_units"}, "id": "trapz_linear_002908_-0.9_-16.3_2.1_8.4", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-0.9x+-16.3 from x=2.1 to x=8.4. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(2.1)=-18.19 and f(8.4)=-23.86.\nThe interval width is 6.3.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -16.3, "slope": -0.9, "x0": 2.1, "x1": 8.4}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 9507.0 / 1000.\nFinal: {\"answer\": 9.507, \"unit\": \"kg\"}", "dedupe_signature": "64d1b7a8cc56796e8746383891c05efb4830ec6ce9b8a0627bf90ad39bd68421", "difficulty": "easy", "final_answer": {"answer": 9.507, "unit": "kg"}, "id": "unit_convert_002910_g_to_kg_9507", "license": "Apache-2.0", "prompt": "Convert 9507 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 9507.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 9507.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=177 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-14.4801, 0.7589], \"unit\": \"N\"}", "dedupe_signature": "3d4ff69e07d98e47fda69efaad583beb6b1293a1e94280f445a97f4e68d45fb3", "difficulty": "medium", "final_answer": {"answer": [-14.4801, 0.7589], "unit": "N"}, "id": "vector_components_002911_14.5_177", "license": "Apache-2.0", "prompt": "A vector has magnitude 14.5 N at 177 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=177 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 177, "magnitude": 14.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [0.2, -8.75], \"unit\": \"dimensionless\"}", "dedupe_signature": "b4978036848cc23f1c5bfe2af21cbe50f0499c768c339d4e859347bad6dfc74f", "difficulty": "medium", "final_answer": {"answer": [0.2, -8.75], "unit": "dimensionless"}, "id": "line_two_point_002912_-8.75_-8.25_0.2_-8.75", "license": "Apache-2.0", "prompt": "A line passes through points (-8.75, -10.5) and (-8.25, -10.4). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -8.75, "x2": -8.25, "y1": -10.5, "y2": -10.4}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef finite_differences_002914(values):\n    return [values[i + 1] - values[i] for i in range(len(values) - 1)]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"finite_differences_002914\"}", "dedupe_signature": "242db6cb2a54d8052835c196b146db11f887ded102c65a288d354eeab2103dc6", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "finite_differences_002914"}, "id": "code_002914_finite_differences_002914", "license": "Apache-2.0", "prompt": "Write a Python function finite_differences_002914(values) that returns the list of successive differences values[i+1] - values[i]. It must return [] for fewer than two values. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "finite_differences_002914"}, "verifier": {"function": "finite_differences_002914", "tests": ["assert finite_differences_002914([1, 4, 9, 16]) == [3, 5, 7]", "assert finite_differences_002914([5]) == []", "assert finite_differences_002914([]) == []"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: required_fields, allowed_transformations.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"required_fields\", \"allowed_transformations\"]}", "dedupe_signature": "0888916bf9c38ba1e33647a32c29d2f4e06594be747b5a50ac24c8b2a5f4a662", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["required_fields", "allowed_transformations"]}, "id": "abstain_002915_required_fields_allowed_transformations", "license": "Apache-2.0", "prompt": "Write a sanitizer for valid registry clinical records in release 292671, but the prompt does not state which fields are required or which transformations are allowed. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: required_fields, allowed_transformations.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["required_fields", "allowed_transformations"]}, "verifier": {"missing": ["required_fields", "allowed_transformations"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 17.55 kg and a = 8.2 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 143.91, \"unit\": \"N\"}", "dedupe_signature": "d82590710d7da95c3c3f67df9e431de398e91206ae61efc9b4d03f7c85b4dbd5", "difficulty": "easy", "final_answer": {"answer": 143.91, "unit": "N"}, "id": "force_002916_17.55_8.2", "license": "Apache-2.0", "prompt": "A cart has mass 17.55 kg and measured acceleration 8.2 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 17.55 kg and a = 8.2 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 8.2, "mass": 17.55}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 2.54 * 8.314 * 314 / 64.6.\nFinal: {\"answer\": 102.6457, \"unit\": \"kPa\"}", "dedupe_signature": "faa1458020c06eaf1f0449b4dd715ba400fc5fd3ceb2aef97af033c7a9c16848", "difficulty": "medium", "final_answer": {"answer": 102.6457, "unit": "kPa"}, "id": "ideal_gas_002919_2.54_314_64.6", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=2.54 mol, T=314 K, and V=64.6 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 2.54 * 8.314 * 314 / 64.6.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 2.54, "temp_k": 314, "volume_l": 64.6}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1135 * 3.06 * 104.\nFinal: {\"answer\": 361202.4, \"unit\": \"J\"}", "dedupe_signature": "d37bdda23f87b8b57434721b00b135ab0e07b654ed0de8dda4bc071b2a9ae38b", "difficulty": "easy", "final_answer": {"answer": 361202.4, "unit": "J"}, "id": "heat_q_002920_1135_3.06_104", "license": "Apache-2.0", "prompt": "A 1135 g sample has specific heat 3.06 J/(g*K). How much heat is needed to raise its temperature by 104 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1135 * 3.06 * 104.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 104, "heat_capacity": 3.06, "mass_g": 1135}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=215.2 V and R=129.2 ohm.\nFinal: {\"answer\": 358.4446, \"unit\": \"W\"}", "dedupe_signature": "0d3563cdc489a811c23bf61694d1144473a161238e342cfe8c81d1c553be5ded", "difficulty": "easy", "final_answer": {"answer": 358.4446, "unit": "W"}, "id": "ohm_power_002921_215.2_129.2", "license": "Apache-2.0", "prompt": "A resistor has resistance 129.2 ohm and voltage 215.2 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=215.2 V and R=129.2 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 129.2, "voltage": 215.2}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=936.5 mg, t=33.5 h, and T_half=24.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 362.9906, \"unit\": \"mg\"}", "dedupe_signature": "0767f14917cc652eac5b87b9c3ca9221b62c4d470da627e5cc336045e0da9de9", "difficulty": "medium", "final_answer": {"answer": 362.9906, "unit": "mg"}, "id": "half_life_002922_936.5_24.5_33.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 936.5 mg. Its half-life is 24.5 hours. How many mg remain after 33.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=936.5 mg, t=33.5 h, and T_half=24.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 33.5, "half_life": 24.5, "initial_amount": 936.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 3.97 mol * 18.015 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 71.5196, \"unit\": \"g\"}", "dedupe_signature": "7449af49e171bbf8c7b5972464f8d9beba96c2c994625a854dc24c132ba9d723", "difficulty": "medium", "final_answer": {"answer": 71.5196, "unit": "g"}, "id": "stoich_mass_002923_water_3.97", "license": "Apache-2.0", "prompt": "A sample contains 3.97 mol of water. Using molar mass 18.015 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 3.97 mol * 18.015 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "water", "molar_mass": 18.015, "moles": 3.97}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 3205 mL to 3.205 L.\n3. Compute M = 0.78 / 3.205.\nFinal: {\"answer\": 0.2434, \"unit\": \"mol/L\"}", "dedupe_signature": "bbe4fc9c09c0e80ac71346a9fa4f030ee5dfda1bab2e20e2fbb18f60c486f1ce", "difficulty": "medium", "final_answer": {"answer": 0.2434, "unit": "mol/L"}, "id": "molarity_002924_0.78_3205", "license": "Apache-2.0", "prompt": "A solution contains 0.78 mol of solute in 3205 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 3205 mL to 3.205 L.\nCompute M = 0.78 / 3.205.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 0.78, "volume_ml": 3205}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.09 y, so each step multiplies y by 1 - h*0.09.\n3. Apply that update for 2 steps and round the final state.\nFinal: {\"answer\": 12.177, \"unit\": \"state_units\"}", "dedupe_signature": "10cf648a3615106ae7b5f1cdd2a728d12b846690630afd6175a05c48dc4a587d", "difficulty": "medium", "final_answer": {"answer": 12.177, "unit": "state_units"}, "id": "euler_decay_002925_15_0.09_1.1_2", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.09 y with y(0)=15, step size h=1.1, for 2 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.09 y, so each step multiplies y by 1 - h*0.09.\nApply that update for 2 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 15.0, "rate": 0.09, "step": 1.1, "steps": 2}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-7.2)=-22 and f(-3.5)=-18.3.\n3. The interval width is 3.7.\nFinal: {\"answer\": -74.555, \"unit\": \"area_units\"}", "dedupe_signature": "8b76adfa80921d443c5c38c05a092d1f438afcdebbaa2d24391f86f40933f062", "difficulty": "medium", "final_answer": {"answer": -74.555, "unit": "area_units"}, "id": "trapz_linear_002926_1_-14.8_-7.2_-3.5", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=1x+-14.8 from x=-7.2 to x=-3.5. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-7.2)=-22 and f(-3.5)=-18.3.\nThe interval width is 3.7.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -14.8, "slope": 1.0, "x0": -7.2, "x1": -3.5}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kelvin equals Celsius plus 273.15.\n2. Apply the conversion factor directly to the given value.\n3. Compute 128.0 + 273.15.\nFinal: {\"answer\": 401.15, \"unit\": \"K\"}", "dedupe_signature": "990250bb64e65612464a2046f6bab32a5ff7f2c674350d765f1b20c72d92dc42", "difficulty": "easy", "final_answer": {"answer": 401.15, "unit": "K"}, "id": "unit_convert_002928_c_to_k_128", "license": "Apache-2.0", "prompt": "Convert 128 degC to K. Return the converted value with unit.", "reasoning_trace": "Kelvin equals Celsius plus 273.15.\nApply the conversion factor directly to the given value.\nCompute 128.0 + 273.15.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 128.0}, "verifier": {"formula": "value + 273.15", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [3.9, -23.25], \"unit\": \"dimensionless\"}", "dedupe_signature": "3b9ff776742255173800e571fca41367bd1df4774d0df1da88af08df9d2bd68c", "difficulty": "medium", "final_answer": {"answer": [3.9, -23.25], "unit": "dimensionless"}, "id": "line_two_point_002930_-5.75_1.75_3.9_-23.25", "license": "Apache-2.0", "prompt": "A line passes through points (-5.75, -45.675) and (1.75, -16.425). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -5.75, "x2": 1.75, "y1": -45.675, "y2": -16.425}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. grams cancel with J/(g*K), and kelvin cancels, leaving joules\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "93c70f6bb97988d85791edaa574e479e6adee79bd74383324adc3244f9468de0", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_002931_consistent_4153435f_166696", "license": "Apache-2.0", "prompt": "In field worksheet case 166696, check dimensional consistency for Q = m * c * DeltaT. The left side has dimensions J and the right side has dimensions J. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\ngrams cancel with J/(g*K), and kelvin cancels, leaving joules\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "Q = m * c * DeltaT"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef pairwise_ratios_002932(numerators, denominators):\n    if len(numerators) != len(denominators):\n        raise ValueError('length mismatch')\n    out = []\n    for numerator, denominator in zip(numerators, denominators):\n        if denominator == 0:\n            raise ValueError('zero denominator')\n        out.append(numerator / denominator)\n    return out\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"pairwise_ratios_002932\"}", "dedupe_signature": "536d2f4131ad7b33ef4e1f3e5702942b4241508763d9e20d77f4089974ed3f12", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "pairwise_ratios_002932"}, "id": "code_002932_pairwise_ratios_002932", "license": "Apache-2.0", "prompt": "Write a Python function pairwise_ratios_002932(numerators, denominators) that returns a list of n/d values. Raise ValueError if lengths differ or any denominator is zero. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "pairwise_ratios_002932"}, "verifier": {"function": "pairwise_ratios_002932", "tests": ["assert pairwise_ratios_002932([2, 9], [4, 3]) == [0.5, 3.0]", "try:\n    pairwise_ratios_002932([1], [0])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass", "try:\n    pairwise_ratios_002932([1, 2], [1])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: launch_angle_or_vertical_velocity.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"launch_angle_or_vertical_velocity\"]}", "dedupe_signature": "b11f07d6dad12b44ff60535be6e870319cb65b4c473a2a49f07c6b2f24cd3084", "difficulty": "easy", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["launch_angle_or_vertical_velocity"]}, "id": "abstain_002933_launch_angle_or_vertical_velocity", "license": "Apache-2.0", "prompt": "Compute projectile range on level ground. The prompt gives initial speed 81.4 m/s but does not give launch angle or vertical velocity. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: launch_angle_or_vertical_velocity.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["launch_angle_or_vertical_velocity"]}, "verifier": {"missing": ["launch_angle_or_vertical_velocity"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 6.05 kg and a = 5.1 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 30.855, \"unit\": \"N\"}", "dedupe_signature": "bcf9f978fb42ff017c08e896844a77b2eea8a83e8c2cf445b792a52ac1cb69db", "difficulty": "easy", "final_answer": {"answer": 30.855, "unit": "N"}, "id": "force_002934_6.05_5.1", "license": "Apache-2.0", "prompt": "A cart has mass 6.05 kg and measured acceleration 5.1 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 6.05 kg and a = 5.1 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 5.1, "mass": 6.05}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 1.05^2 and multiply by 0.5 * 19.4.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 10.6943, \"unit\": \"J\"}", "dedupe_signature": "b76463781300f11c8f3667d421a0dd49aa32d34cf3c72b261ec3628972aea6bd", "difficulty": "easy", "final_answer": {"answer": 10.6943, "unit": "J"}, "id": "ke_002935_19.4_1.05", "license": "Apache-2.0", "prompt": "A body of mass 19.4 kg moves at 1.05 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 1.05^2 and multiply by 0.5 * 19.4.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 19.4, "velocity": 1.05}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=22 degrees through the sine of 2 theta.\n3. Substitute v=78.9 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 440.8149, \"unit\": \"m\"}", "dedupe_signature": "628ba24c9bcc51724d8d8f5967f7e7349ad83f67324c5087598f270a4402cb8e", "difficulty": "medium", "final_answer": {"answer": 440.8149, "unit": "m"}, "id": "projectile_range_002936_78.9_22", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 78.9 m/s and angle 22 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=22 degrees through the sine of 2 theta.\nSubstitute v=78.9 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 22, "gravity": 9.81, "speed": 78.9}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 1.63 * 8.314 * 616 / 3.2.\nFinal: {\"answer\": 2608.7253, \"unit\": \"kPa\"}", "dedupe_signature": "147d87fa2ef8bbac15e24ce42aea392b8c490a8a6b0029fda2ef676b99c4f92f", "difficulty": "medium", "final_answer": {"answer": 2608.7253, "unit": "kPa"}, "id": "ideal_gas_002937_1.63_616_3.2", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=1.63 mol, T=616 K, and V=3.2 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 1.63 * 8.314 * 616 / 3.2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 1.63, "temp_k": 616, "volume_l": 3.2}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 830 * 0.9 * 111.\nFinal: {\"answer\": 82917.0, \"unit\": \"J\"}", "dedupe_signature": "05e66b0ab4b90b0cdcd22bd966acf196cd6a5eed8f06da23e3219142ac37df5b", "difficulty": "easy", "final_answer": {"answer": 82917.0, "unit": "J"}, "id": "heat_q_002938_830_0.9_111", "license": "Apache-2.0", "prompt": "A 830 g sample has specific heat 0.9 J/(g*K). How much heat is needed to raise its temperature by 111 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 830 * 0.9 * 111.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 111, "heat_capacity": 0.9, "mass_g": 830}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=129.9 V and R=116.7 ohm.\nFinal: {\"answer\": 144.5931, \"unit\": \"W\"}", "dedupe_signature": "ad4c5b68eba80eee5be44e8fea0d6d50c71505c16d477e339495aebc326381ee", "difficulty": "easy", "final_answer": {"answer": 144.5931, "unit": "W"}, "id": "ohm_power_002939_129.9_116.7", "license": "Apache-2.0", "prompt": "A resistor has resistance 116.7 ohm and voltage 129.9 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=129.9 V and R=116.7 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 116.7, "voltage": 129.9}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=697 mg, t=6 h, and T_half=95 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 667.1452, \"unit\": \"mg\"}", "dedupe_signature": "7d6b2b33ab7d43485751cce85e42ebdc4eb998e612c6b0f13eda9d9a8267e231", "difficulty": "medium", "final_answer": {"answer": 667.1452, "unit": "mg"}, "id": "half_life_002940_697_95_6", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 697 mg. Its half-life is 95 hours. How many mg remain after 6 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=697 mg, t=6 h, and T_half=95 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 6.0, "half_life": 95.0, "initial_amount": 697.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 4.81 mol * 180.156 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 866.5504, \"unit\": \"g\"}", "dedupe_signature": "e952e1e9f543c498c5d1b201ca3ecff9eee287d45884358f4bb1c088d7f76a2b", "difficulty": "medium", "final_answer": {"answer": 866.5504, "unit": "g"}, "id": "stoich_mass_002941_glucose_4.81", "license": "Apache-2.0", "prompt": "A sample contains 4.81 mol of glucose. Using molar mass 180.156 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 4.81 mol * 180.156 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "glucose", "molar_mass": 180.156, "moles": 4.81}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 185 mL to 0.185 L.\n3. Compute M = 1.825 / 0.185.\nFinal: {\"answer\": 9.8649, \"unit\": \"mol/L\"}", "dedupe_signature": "c3d18387cfe7754d5a454f67545eb9e90dbfc3d155bc4e5d13cbab35e44fba0a", "difficulty": "medium", "final_answer": {"answer": 9.8649, "unit": "mol/L"}, "id": "molarity_002942_1.825_185", "license": "Apache-2.0", "prompt": "A solution contains 1.825 mol of solute in 185 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 185 mL to 0.185 L.\nCompute M = 1.825 / 0.185.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 1.825, "volume_ml": 185}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.88 y, so each step multiplies y by 1 - h*0.88.\n3. Apply that update for 11 steps and round the final state.\nFinal: {\"answer\": 0.0, \"unit\": \"state_units\"}", "dedupe_signature": "3b0080155b385a271b33b150a6cc6e46bc9c0b424aebc7f1745fde5c5dea5018", "difficulty": "medium", "final_answer": {"answer": 0.0, "unit": "state_units"}, "id": "euler_decay_002943_29_0.88_1.4_11", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.88 y with y(0)=29, step size h=1.4, for 11 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.88 y, so each step multiplies y by 1 - h*0.88.\nApply that update for 11 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 29.0, "rate": 0.88, "step": 1.4, "steps": 11}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.18 and add it to the current value.\nFinal: {\"answer\": [1.474, 2.06, 2.281], \"unit\": \"temperature_units\"}", "dedupe_signature": "bb4a6f0e06985e5cc466c87c4f6310b6f5a9241767e083c93aafcad9d2e8cda5", "difficulty": "hard", "final_answer": {"answer": [1.474, 2.06, 2.281], "unit": "temperature_units"}, "id": "heat_step_002945_0.18_1.95_1.15_2.15_2.65_1.1", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.95, right=1.1; current interior values are [1.15, 2.15, 2.65]. Use r=0.18. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.18 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [1.15, 2.15, 2.65], "left": 1.95, "r": 0.18, "right": 1.1}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kelvin equals Celsius plus 273.15.\n2. Apply the conversion factor directly to the given value.\n3. Compute 120.0 + 273.15.\nFinal: {\"answer\": 393.15, \"unit\": \"K\"}", "dedupe_signature": "a43d1db9a5da24e13d09f8f0a549682caec2fcdfa8a5979f2f8f27474248f87e", "difficulty": "easy", "final_answer": {"answer": 393.15, "unit": "K"}, "id": "unit_convert_002946_c_to_k_120", "license": "Apache-2.0", "prompt": "Convert 120 degC to K. Return the converted value with unit.", "reasoning_trace": "Kelvin equals Celsius plus 273.15.\nApply the conversion factor directly to the given value.\nCompute 120.0 + 273.15.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 120.0}, "verifier": {"formula": "value + 273.15", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=46 degrees and keep the unit as newtons.\nFinal: {\"answer\": [254.5923, 263.638], \"unit\": \"N\"}", "dedupe_signature": "99f0428d76a7aa6f3ed8ac9959629ef4a2540d1c975423dd81493bdc149f6c6e", "difficulty": "medium", "final_answer": {"answer": [254.5923, 263.638], "unit": "N"}, "id": "vector_components_002947_366.5_46", "license": "Apache-2.0", "prompt": "A vector has magnitude 366.5 N at 46 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=46 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 46, "magnitude": 366.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [7.65, -25.25], \"unit\": \"dimensionless\"}", "dedupe_signature": "ac8b79befe23564383c7fc9a8834680303575e746d8ab29bab7495dfaf31f734", "difficulty": "medium", "final_answer": {"answer": [7.65, -25.25], "unit": "dimensionless"}, "id": "line_two_point_002948_-3_6.5_7.65_-25.25", "license": "Apache-2.0", "prompt": "A line passes through points (-3, -48.2) and (6.5, 24.475). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -3.0, "x2": 6.5, "y1": -48.2, "y2": 24.475}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. speed squared over acceleration has units of meters\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "eccd3e8b5681258e723b0d3d063c4e59f42221994a2f6b4b646910f1ebcbe6ab", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_002949_consistent_741d4e34_169246", "license": "Apache-2.0", "prompt": "In model card equation case 169246, check dimensional consistency for R = v^2 * sin(theta) / g. The left side has dimensions m and the right side has dimensions m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nspeed squared over acceleration has units of meters\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "R = v^2 * sin(theta) / g"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\nimport math\n\ndef unit_vector_002950(x, y):\n    norm = math.hypot(x, y)\n    if norm == 0:\n        raise ValueError('zero vector has no direction')\n    return (x / norm, y / norm)\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"unit_vector_002950\"}", "dedupe_signature": "7596fe36819e0e17fd242c3750e3653a01f60ae3b355dc1c67445c4d46953d97", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "unit_vector_002950"}, "id": "code_002950_unit_vector_002950", "license": "Apache-2.0", "prompt": "Write a Python function unit_vector_002950(x, y) that returns the 2D unit vector as a tuple. Raise ValueError for the zero vector. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "unit_vector_002950"}, "verifier": {"function": "unit_vector_002950", "tests": ["ux, uy = unit_vector_002950(3, 4); assert abs(ux - 0.6) < 1e-12 and abs(uy - 0.8) < 1e-12", "assert unit_vector_002950(0, 5) == (0, 1)", "try:\n    unit_vector_002950(0, 0)\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: launch_angle_or_vertical_velocity.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"launch_angle_or_vertical_velocity\"]}", "dedupe_signature": "1f32159873b639393ef1bc68307acfede3759e1a3d79ea33afc897e29a8e5d59", "difficulty": "easy", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["launch_angle_or_vertical_velocity"]}, "id": "abstain_002951_launch_angle_or_vertical_velocity", "license": "Apache-2.0", "prompt": "Compute projectile range on level ground. The prompt gives initial speed 59.1 m/s but does not give launch angle or vertical velocity. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: launch_angle_or_vertical_velocity.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["launch_angle_or_vertical_velocity"]}, "verifier": {"missing": ["launch_angle_or_vertical_velocity"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 24.05 kg and a = 9.65 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 232.0825, \"unit\": \"N\"}", "dedupe_signature": "cd6533bbb9975f40ab199cf920c9afd2786392f5aecdd5ed626b08f8bc779818", "difficulty": "easy", "final_answer": {"answer": 232.0825, "unit": "N"}, "id": "force_002952_24.05_9.65", "license": "Apache-2.0", "prompt": "A cart has mass 24.05 kg and measured acceleration 9.65 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 24.05 kg and a = 9.65 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 9.65, "mass": 24.05}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 35.8^2 and multiply by 0.5 * 28.7.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 18391.534, \"unit\": \"J\"}", "dedupe_signature": "3c0aebc951145ee01a338d4011c9fa538c6772a42703c913c4a1a8785b6ad2b7", "difficulty": "easy", "final_answer": {"answer": 18391.534, "unit": "J"}, "id": "ke_002953_28.7_35.8", "license": "Apache-2.0", "prompt": "A body of mass 28.7 kg moves at 35.8 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 35.8^2 and multiply by 0.5 * 28.7.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 28.7, "velocity": 35.8}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 2.04 * 8.314 * 255 / 17.1.\nFinal: {\"answer\": 252.9206, \"unit\": \"kPa\"}", "dedupe_signature": "072c547f47f51b9d04ce53d1ca729973b31c6241770e9e8eb98e90b75a6cda74", "difficulty": "medium", "final_answer": {"answer": 252.9206, "unit": "kPa"}, "id": "ideal_gas_002955_2.04_255_17.1", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=2.04 mol, T=255 K, and V=17.1 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 2.04 * 8.314 * 255 / 17.1.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 2.04, "temp_k": 255, "volume_l": 17.1}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1120 * 1.975 * 77.\nFinal: {\"answer\": 170324.0, \"unit\": \"J\"}", "dedupe_signature": "fc54f3eeec0f98ff9f4f97c0be5a129a912e5163cbd2922c96029d38a597898d", "difficulty": "easy", "final_answer": {"answer": 170324.0, "unit": "J"}, "id": "heat_q_002956_1120_1.975_77", "license": "Apache-2.0", "prompt": "A 1120 g sample has specific heat 1.975 J/(g*K). How much heat is needed to raise its temperature by 77 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1120 * 1.975 * 77.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 77, "heat_capacity": 1.975, "mass_g": 1120}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=117.1 V and R=15.1 ohm.\nFinal: {\"answer\": 908.1066, \"unit\": \"W\"}", "dedupe_signature": "abc86062daef4b71831562c1a5c752d7fcaf809775916a2d9c98553d193ac603", "difficulty": "easy", "final_answer": {"answer": 908.1066, "unit": "W"}, "id": "ohm_power_002957_117.1_15.1", "license": "Apache-2.0", "prompt": "A resistor has resistance 15.1 ohm and voltage 117.1 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=117.1 V and R=15.1 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 15.1, "voltage": 117.1}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=900.5 mg, t=273 h, and T_half=54.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 27.9622, \"unit\": \"mg\"}", "dedupe_signature": "78d3f29eaa6a963f9ad9af92e31466e9170558e65871709a91547bd2556aeb1e", "difficulty": "medium", "final_answer": {"answer": 27.9622, "unit": "mg"}, "id": "half_life_002958_900.5_54.5_273", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 900.5 mg. Its half-life is 54.5 hours. How many mg remain after 273 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=900.5 mg, t=273 h, and T_half=54.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 273.0, "half_life": 54.5, "initial_amount": 900.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 1.2 mol * 100.087 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 120.1044, \"unit\": \"g\"}", "dedupe_signature": "202a8937ed6c0c8ff1f9eb1a47aa7e0880ba4cc4d1ae51be67fbdc6c85b43518", "difficulty": "medium", "final_answer": {"answer": 120.1044, "unit": "g"}, "id": "stoich_mass_002959_calcium_carbonate_1.2", "license": "Apache-2.0", "prompt": "A sample contains 1.2 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 1.2 mol * 100.087 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "calcium carbonate", "molar_mass": 100.087, "moles": 1.2}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 3795 mL to 3.795 L.\n3. Compute M = 2.19 / 3.795.\nFinal: {\"answer\": 0.5771, \"unit\": \"mol/L\"}", "dedupe_signature": "6092496755748d75a12b01512410dd03bcbd2b14939062eca340dd68ddb9ab57", "difficulty": "medium", "final_answer": {"answer": 0.5771, "unit": "mol/L"}, "id": "molarity_002960_2.19_3795", "license": "Apache-2.0", "prompt": "A solution contains 2.19 mol of solute in 3795 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 3795 mL to 3.795 L.\nCompute M = 2.19 / 3.795.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 2.19, "volume_ml": 3795}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.64 y, so each step multiplies y by 1 - h*0.64.\n3. Apply that update for 10 steps and round the final state.\nFinal: {\"answer\": 0.0578, \"unit\": \"state_units\"}", "dedupe_signature": "c9780ca47e750e0e496243ca43aaf7d5d7e68f31454838d26172f19c873c0014", "difficulty": "medium", "final_answer": {"answer": 0.0578, "unit": "state_units"}, "id": "euler_decay_002961_22_0.64_0.7_10", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.64 y with y(0)=22, step size h=0.7, for 10 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.64 y, so each step multiplies y by 1 - h*0.64.\nApply that update for 10 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 22.0, "rate": 0.64, "step": 0.7, "steps": 10}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(7.4)=34.62 and f(15.4)=73.02.\n3. The interval width is 8.\nFinal: {\"answer\": 430.56, \"unit\": \"area_units\"}", "dedupe_signature": "644e68be886c7eebbecd6cd0e1e11da881aca2487e8f65b2d9aeb640a2a573cd", "difficulty": "medium", "final_answer": {"answer": 430.56, "unit": "area_units"}, "id": "trapz_linear_002962_4.8_-0.9_7.4_15.4", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=4.8x+-0.9 from x=7.4 to x=15.4. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(7.4)=34.62 and f(15.4)=73.02.\nThe interval width is 8.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -0.9, "slope": 4.8, "x0": 7.4, "x1": 15.4}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.36 and add it to the current value.\nFinal: {\"answer\": [1.348, -0.128, 1.3], \"unit\": \"temperature_units\"}", "dedupe_signature": "fed6ef66d6191408911cabe5af6bedfcefda4e2674ffd9660c073cf124f66de6", "difficulty": "hard", "final_answer": {"answer": [1.348, -0.128, 1.3], "unit": "temperature_units"}, "id": "heat_step_002963_0.36_2.65_-0.65_1.6_-0.95_2.75", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=2.65, right=2.75; current interior values are [-0.65, 1.6, -0.95]. Use r=0.36. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.36 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-0.65, 1.6, -0.95], "left": 2.65, "r": 0.36, "right": 2.75}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 100 centimeters in one meter.\n2. Apply the conversion factor directly to the given value.\n3. Compute 2544.5 / 100.\nFinal: {\"answer\": 25.445, \"unit\": \"m\"}", "dedupe_signature": "059fbf6789fb380f17a08a2b76789d89ee897fa315feb9b32912cb06a8c8caae", "difficulty": "easy", "final_answer": {"answer": 25.445, "unit": "m"}, "id": "unit_convert_002964_cm_to_m_2544.5", "license": "Apache-2.0", "prompt": "Convert 2544.5 cm to m. Return the converted value with unit.", "reasoning_trace": "There are 100 centimeters in one meter.\nApply the conversion factor directly to the given value.\nCompute 2544.5 / 100.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 2544.5}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=356 degrees and keep the unit as newtons.\nFinal: {\"answer\": [297.2741, -20.7874], \"unit\": \"N\"}", "dedupe_signature": "21ab78653fe1d5d74cbe6864043d8888c56644f78190f85f683d4d5c8bb863b8", "difficulty": "medium", "final_answer": {"answer": [297.2741, -20.7874], "unit": "N"}, "id": "vector_components_002965_298_356", "license": "Apache-2.0", "prompt": "A vector has magnitude 298 N at 356 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=356 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 356, "magnitude": 298.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [4.25, 12.75], \"unit\": \"dimensionless\"}", "dedupe_signature": "77eb35a11a74e1f7ed2c7f826b5c34148b428c2c46c018a959225bd0788a864f", "difficulty": "medium", "final_answer": {"answer": [4.25, 12.75], "unit": "dimensionless"}, "id": "line_two_point_002966_-10_-1_4.25_12.75", "license": "Apache-2.0", "prompt": "A line passes through points (-10, -29.75) and (-1, 8.5). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -10.0, "x2": -1.0, "y1": -29.75, "y2": 8.5}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. speed squared over acceleration has units of meters\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "3cbd3f5c26d8cbd071aeb470fd98e33c16e618b35daaccfada5cc65dbc94425f", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_002967_consistent_741d4e34_654509", "license": "Apache-2.0", "prompt": "In sensor calibration case 654509, check dimensional consistency for R = v^2 * sin(theta) / g. The left side has dimensions m and the right side has dimensions m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nspeed squared over acceleration has units of meters\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "R = v^2 * sin(theta) / g"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef center_values_002968(values):\n    if not values:\n        raise ValueError('center_values requires at least one value')\n    mean = sum(values) / len(values)\n    return [value - mean for value in values]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"center_values_002968\"}", "dedupe_signature": "7702941945e1f1edb6567d741f2820bd1598b8957b87cc1ec768c91afa37ee84", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "center_values_002968"}, "id": "code_002968_center_values_002968", "license": "Apache-2.0", "prompt": "Write a Python function center_values_002968(values) that subtracts the arithmetic mean from each value and returns a new list. Raise ValueError for an empty input. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "center_values_002968"}, "verifier": {"function": "center_values_002968", "tests": ["out = center_values_002968([1, 2, 3]); assert out == [-1, 0, 1]", "assert center_values_002968([5]) == [0]", "try:\n    center_values_002968([])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: recurrence, objective, tie_breaking_rule.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"recurrence\", \"objective\", \"tie_breaking_rule\"]}", "dedupe_signature": "a70e3c423367690f90ba310bb4b899c5dc262a6ae942378ebe78422adc71eb4b", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["recurrence", "objective", "tie_breaking_rule"]}, "id": "abstain_002969_recurrence_objective_tie_breaking_rule", "license": "Apache-2.0", "prompt": "Write a dynamic-programming solver for a scheduler scoring problem with 4176 items and budget 56695, but the recurrence, objective, and tie-breaking rule are all absent. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: recurrence, objective, tie_breaking_rule.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["recurrence", "objective", "tie_breaking_rule"]}, "verifier": {"missing": ["recurrence", "objective", "tie_breaking_rule"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 4.65 kg and a = 1.3 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 6.045, \"unit\": \"N\"}", "dedupe_signature": "c470086e94789e9b5d59a0fccd057978fb6f142886a5985489cd3b36cb42d929", "difficulty": "easy", "final_answer": {"answer": 6.045, "unit": "N"}, "id": "force_002970_4.65_1.3", "license": "Apache-2.0", "prompt": "A cart has mass 4.65 kg and measured acceleration 1.3 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 4.65 kg and a = 1.3 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 1.3, "mass": 4.65}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 41.7^2 and multiply by 0.5 * 3.2.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 2782.224, \"unit\": \"J\"}", "dedupe_signature": "7e4e08dc3b53624f28c376ced313e97682cc3daef5dfa590f371b44e3e5d33ec", "difficulty": "easy", "final_answer": {"answer": 2782.224, "unit": "J"}, "id": "ke_002971_3.2_41.7", "license": "Apache-2.0", "prompt": "A body of mass 3.2 kg moves at 41.7 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 41.7^2 and multiply by 0.5 * 3.2.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 3.2, "velocity": 41.7}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=8 degrees through the sine of 2 theta.\n3. Substitute v=21.5 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 12.9881, \"unit\": \"m\"}", "dedupe_signature": "d0d69c96b5355c0eff3d78c6b7d994b747b6889f33446fe2827c8cc21b7d7ddd", "difficulty": "medium", "final_answer": {"answer": 12.9881, "unit": "m"}, "id": "projectile_range_002972_21.5_8", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 21.5 m/s and angle 8 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=8 degrees through the sine of 2 theta.\nSubstitute v=21.5 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 8, "gravity": 9.81, "speed": 21.5}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 4.19 * 8.314 * 584 / 83.6.\nFinal: {\"answer\": 243.3496, \"unit\": \"kPa\"}", "dedupe_signature": "2660d2305b7014ac4cb3e2ef7b5559a2bc6a8d624c209e550ce1ea37ade74459", "difficulty": "medium", "final_answer": {"answer": 243.3496, "unit": "kPa"}, "id": "ideal_gas_002973_4.19_584_83.6", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=4.19 mol, T=584 K, and V=83.6 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 4.19 * 8.314 * 584 / 83.6.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 4.19, "temp_k": 584, "volume_l": 83.6}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1990 * 3.28 * 66.\nFinal: {\"answer\": 430795.2, \"unit\": \"J\"}", "dedupe_signature": "fc2d14230a400f4fb646bc137e7fecf2d3185a2ee1e6a9dc21af44f6752a8529", "difficulty": "easy", "final_answer": {"answer": 430795.2, "unit": "J"}, "id": "heat_q_002974_1990_3.28_66", "license": "Apache-2.0", "prompt": "A 1990 g sample has specific heat 3.28 J/(g*K). How much heat is needed to raise its temperature by 66 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1990 * 3.28 * 66.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 66, "heat_capacity": 3.28, "mass_g": 1990}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=53.5 V and R=182.2 ohm.\nFinal: {\"answer\": 15.7094, \"unit\": \"W\"}", "dedupe_signature": "4f8b783da224b6bc360bc5ab326bfa90ec875fc92f619ebea794683218240c01", "difficulty": "easy", "final_answer": {"answer": 15.7094, "unit": "W"}, "id": "ohm_power_002975_53.5_182.2", "license": "Apache-2.0", "prompt": "A resistor has resistance 182.2 ohm and voltage 53.5 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=53.5 V and R=182.2 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 182.2, "voltage": 53.5}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=89 mg, t=358.5 h, and T_half=110.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 9.3917, \"unit\": \"mg\"}", "dedupe_signature": "0dc9cff28dc3eb0c650c9094e772679180376612868a04493e6765d37900ea7b", "difficulty": "medium", "final_answer": {"answer": 9.3917, "unit": "mg"}, "id": "half_life_002976_89_110.5_358.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 89 mg. Its half-life is 110.5 hours. How many mg remain after 358.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=89 mg, t=358.5 h, and T_half=110.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 358.5, "half_life": 110.5, "initial_amount": 89.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 6.6 mol * 180.156 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 1189.0296, \"unit\": \"g\"}", "dedupe_signature": "4434af16ae8e1ade70cd114d6d3fe223bbe062d9c6e325c9247789e97c6d4f1a", "difficulty": "medium", "final_answer": {"answer": 1189.0296, "unit": "g"}, "id": "stoich_mass_002977_glucose_6.6", "license": "Apache-2.0", "prompt": "A sample contains 6.6 mol of glucose. Using molar mass 180.156 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 6.6 mol * 180.156 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "glucose", "molar_mass": 180.156, "moles": 6.6}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(4.6)=3.68 and f(12)=13.3.\n3. The interval width is 7.4.\nFinal: {\"answer\": 62.826, \"unit\": \"area_units\"}", "dedupe_signature": "9479823ef4e415f1c0a8c428110ce5864f3e769e9844b741ac07ed8eb2896c04", "difficulty": "medium", "final_answer": {"answer": 62.826, "unit": "area_units"}, "id": "trapz_linear_002980_1.3_-2.3_4.6_12", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=1.3x+-2.3 from x=4.6 to x=12. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(4.6)=3.68 and f(12)=13.3.\nThe interval width is 7.4.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -2.3, "slope": 1.3, "x0": 4.6, "x1": 12.0}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 100 centimeters in one meter.\n2. Apply the conversion factor directly to the given value.\n3. Compute 3452.5 / 100.\nFinal: {\"answer\": 34.525, \"unit\": \"m\"}", "dedupe_signature": "912dc3a4aa46d3101ff8a39e864007dd0a4a531e7399cafeaa600c641379a51c", "difficulty": "easy", "final_answer": {"answer": 34.525, "unit": "m"}, "id": "unit_convert_002982_cm_to_m_3452.5", "license": "Apache-2.0", "prompt": "Convert 3452.5 cm to m. Return the converted value with unit.", "reasoning_trace": "There are 100 centimeters in one meter.\nApply the conversion factor directly to the given value.\nCompute 3452.5 / 100.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 3452.5}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=213 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-164.3794, -106.7493], \"unit\": \"N\"}", "dedupe_signature": "84ff266a3c4495be2c9cbedadf3da9160be102a1954a60320e760a716261ac7d", "difficulty": "medium", "final_answer": {"answer": [-164.3794, -106.7493], "unit": "N"}, "id": "vector_components_002983_196_213", "license": "Apache-2.0", "prompt": "A vector has magnitude 196 N at 213 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=213 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 213, "magnitude": 196.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [2.0, -16.25], \"unit\": \"dimensionless\"}", "dedupe_signature": "5bb609f884dfe2c456ffb8e31c367188db1d1c0e5785c80bb78593c72083cd05", "difficulty": "medium", "final_answer": {"answer": [2.0, -16.25], "unit": "dimensionless"}, "id": "line_two_point_002984_-12.5_2.5_2_-16.25", "license": "Apache-2.0", "prompt": "A line passes through points (-12.5, -41.25) and (2.5, -11.25). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -12.5, "x2": 2.5, "y1": -41.25, "y2": -11.25}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef normalize_002986(values):\n    total = sum(values)\n    if total == 0:\n        raise ValueError('cannot normalize zero-sum values')\n    return [v / total for v in values]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"normalize_002986\"}", "dedupe_signature": "7863171e3216617e44de1a1909f5dcc88bf16e4e8d4a2f8f84f173892ac17fb6", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "normalize_002986"}, "id": "code_002986_normalize_002986", "license": "Apache-2.0", "prompt": "Write a Python function normalize_002986(values) that returns a new list whose values sum to 1. Raise ValueError if the sum is zero. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "normalize_002986"}, "verifier": {"function": "normalize_002986", "tests": ["out = normalize_002986([2, 3, 5]); assert len(out) == 3", "assert abs(sum(normalize_002986([2, 3, 5])) - 1.0) < 1e-12", "assert normalize_002986([1, 1]) == [0.5, 0.5]", "try:\n    normalize_002986([1, -1])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: recurrence, objective, tie_breaking_rule.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"recurrence\", \"objective\", \"tie_breaking_rule\"]}", "dedupe_signature": "fd5413c00e4bd8709b0f2e24d696fb6ce08e39e734ab449286ddee11739a8c57", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["recurrence", "objective", "tie_breaking_rule"]}, "id": "abstain_002987_recurrence_objective_tie_breaking_rule", "license": "Apache-2.0", "prompt": "Write a dynamic-programming solver for a scheduler scoring problem with 1766 items and budget 28575, but the recurrence, objective, and tie-breaking rule are all absent. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: recurrence, objective, tie_breaking_rule.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["recurrence", "objective", "tie_breaking_rule"]}, "verifier": {"missing": ["recurrence", "objective", "tie_breaking_rule"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 11.55 kg and a = 4 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 46.2, \"unit\": \"N\"}", "dedupe_signature": "c8b84ee30427ed6081d0f69ea4678dbe7b1428345876b893dee35ff8c95b430e", "difficulty": "easy", "final_answer": {"answer": 46.2, "unit": "N"}, "id": "force_002988_11.55_4", "license": "Apache-2.0", "prompt": "A cart has mass 11.55 kg and measured acceleration 4 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 11.55 kg and a = 4 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 4.0, "mass": 11.55}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 41.5^2 and multiply by 0.5 * 5.9.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 5080.6375, \"unit\": \"J\"}", "dedupe_signature": "ad7f17322edaa834bc823c4ec017f0097df39c5aaab688c0359f6249d8666fb5", "difficulty": "easy", "final_answer": {"answer": 5080.6375, "unit": "J"}, "id": "ke_002989_5.9_41.5", "license": "Apache-2.0", "prompt": "A body of mass 5.9 kg moves at 41.5 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 41.5^2 and multiply by 0.5 * 5.9.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 5.9, "velocity": 41.5}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=16 degrees through the sine of 2 theta.\n3. Substitute v=13.9 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 10.4369, \"unit\": \"m\"}", "dedupe_signature": "606bab66bb7bb9e5707194d67c719e3ca5c9b1e13eb8460fc60f7dd309934216", "difficulty": "medium", "final_answer": {"answer": 10.4369, "unit": "m"}, "id": "projectile_range_002990_13.9_16", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 13.9 m/s and angle 16 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=16 degrees through the sine of 2 theta.\nSubstitute v=13.9 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 16, "gravity": 9.81, "speed": 13.9}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 5.71 * 8.314 * 466 / 57.1.\nFinal: {\"answer\": 387.4324, \"unit\": \"kPa\"}", "dedupe_signature": "4b2b28c13c8fe8f393f18a49b7a23d2619f10a9b57993d887180384585800bc3", "difficulty": "medium", "final_answer": {"answer": 387.4324, "unit": "kPa"}, "id": "ideal_gas_002991_5.71_466_57.1", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=5.71 mol, T=466 K, and V=57.1 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 5.71 * 8.314 * 466 / 57.1.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 5.71, "temp_k": 466, "volume_l": 57.1}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1965 * 0.79 * 54.\nFinal: {\"answer\": 83826.9, \"unit\": \"J\"}", "dedupe_signature": "8e29e1134cd69b547f6f5a229260c36f5c46e3f59e61a27ffaef2e358872148f", "difficulty": "easy", "final_answer": {"answer": 83826.9, "unit": "J"}, "id": "heat_q_002992_1965_0.79_54", "license": "Apache-2.0", "prompt": "A 1965 g sample has specific heat 0.79 J/(g*K). How much heat is needed to raise its temperature by 54 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1965 * 0.79 * 54.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 54, "heat_capacity": 0.79, "mass_g": 1965}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=182.2 V and R=104.9 ohm.\nFinal: {\"answer\": 316.4618, \"unit\": \"W\"}", "dedupe_signature": "f12c16414c16236455e5849c2b42f76ed15fd37da512629647c3b1efbe19324c", "difficulty": "easy", "final_answer": {"answer": 316.4618, "unit": "W"}, "id": "ohm_power_002993_182.2_104.9", "license": "Apache-2.0", "prompt": "A resistor has resistance 104.9 ohm and voltage 182.2 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=182.2 V and R=104.9 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 104.9, "voltage": 182.2}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=80 mg, t=251 h, and T_half=34.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 0.5164, \"unit\": \"mg\"}", "dedupe_signature": "6a6c5775232db7f2a0e7c4ea340ff96dcd5e5df8fe93bc15165440e16eb2f4f7", "difficulty": "medium", "final_answer": {"answer": 0.5164, "unit": "mg"}, "id": "half_life_002994_80_34.5_251", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 80 mg. Its half-life is 34.5 hours. How many mg remain after 251 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=80 mg, t=251 h, and T_half=34.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 251.0, "half_life": 34.5, "initial_amount": 80.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 6.99 mol * 100.087 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 699.6081, \"unit\": \"g\"}", "dedupe_signature": "ff10788de678d2e7724af87d5e43d015974d797445c641227a0afd4babd0bc56", "difficulty": "medium", "final_answer": {"answer": 699.6081, "unit": "g"}, "id": "stoich_mass_002995_calcium_carbonate_6.99", "license": "Apache-2.0", "prompt": "A sample contains 6.99 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 6.99 mol * 100.087 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "calcium carbonate", "molar_mass": 100.087, "moles": 6.99}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 4330 mL to 4.33 L.\n3. Compute M = 0.35 / 4.33.\nFinal: {\"answer\": 0.0808, \"unit\": \"mol/L\"}", "dedupe_signature": "c56488bf7eebdc3a71aa9fb7fc8ee7f8bd8757b00c0f8d837be8dea622124407", "difficulty": "medium", "final_answer": {"answer": 0.0808, "unit": "mol/L"}, "id": "molarity_002996_0.35_4330", "license": "Apache-2.0", "prompt": "A solution contains 0.35 mol of solute in 4330 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 4330 mL to 4.33 L.\nCompute M = 0.35 / 4.33.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 0.35, "volume_ml": 4330}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.85 y, so each step multiplies y by 1 - h*0.85.\n3. Apply that update for 6 steps and round the final state.\nFinal: {\"answer\": 3.3933, \"unit\": \"state_units\"}", "dedupe_signature": "fbd42ca67ccae2e26460cf53d044638d6a4e4af4a4ba6569bb155d319a2e93da", "difficulty": "medium", "final_answer": {"answer": 3.3933, "unit": "state_units"}, "id": "euler_decay_002997_42_0.85_1.95_6", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.85 y with y(0)=42, step size h=1.95, for 6 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.85 y, so each step multiplies y by 1 - h*0.85.\nApply that update for 6 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 42.0, "rate": 0.85, "step": 1.95, "steps": 6}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-0.5)=-8.3 and f(3)=-26.5.\n3. The interval width is 3.5.\nFinal: {\"answer\": -60.9, \"unit\": \"area_units\"}", "dedupe_signature": "8c8d1ba9d94eb82f5a20141812c1b1750a876a32583b493f2552230f70f3d21d", "difficulty": "medium", "final_answer": {"answer": -60.9, "unit": "area_units"}, "id": "trapz_linear_002998_-5.2_-10.9_-0.5_3", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-5.2x+-10.9 from x=-0.5 to x=3. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-0.5)=-8.3 and f(3)=-26.5.\nThe interval width is 3.5.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -10.9, "slope": -5.2, "x0": -0.5, "x1": 3.0}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.24 and add it to the current value.\nFinal: {\"answer\": [-0.458, 0.57, 1.6], \"unit\": \"temperature_units\"}", "dedupe_signature": "3ab8a6cec64a0e7325627ebb4ded54f429a0ab7a9f466cf2bc9af272b0ddcc90", "difficulty": "hard", "final_answer": {"answer": [-0.458, 0.57, 1.6], "unit": "temperature_units"}, "id": "heat_step_002999_0.24_0.75_-1.85_1.35_1.3_2.5", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=0.75, right=2.5; current interior values are [-1.85, 1.35, 1.3]. Use r=0.24. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.24 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-1.85, 1.35, 1.3], "left": 0.75, "r": 0.24, "right": 2.5}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kelvin equals Celsius plus 273.15.\n2. Apply the conversion factor directly to the given value.\n3. Compute 27.0 + 273.15.\nFinal: {\"answer\": 300.15, \"unit\": \"K\"}", "dedupe_signature": "f54005c0c9e94206089d8bd87fc4c7408b6eada3c05c89969c1bb680434c6c9a", "difficulty": "easy", "final_answer": {"answer": 300.15, "unit": "K"}, "id": "unit_convert_003000_c_to_k_27", "license": "Apache-2.0", "prompt": "Convert 27 degC to K. Return the converted value with unit.", "reasoning_trace": "Kelvin equals Celsius plus 273.15.\nApply the conversion factor directly to the given value.\nCompute 27.0 + 273.15.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 27.0}, "verifier": {"formula": "value + 273.15", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [0.3, 23.0], \"unit\": \"dimensionless\"}", "dedupe_signature": "a2a048da26d4a0bd6a7491c500b8897b0beca7e0bb5842af48dd3d91658e38ea", "difficulty": "medium", "final_answer": {"answer": [0.3, 23.0], "unit": "dimensionless"}, "id": "line_two_point_003002_7.5_13.75_0.3_23", "license": "Apache-2.0", "prompt": "A line passes through points (7.5, 25.25) and (13.75, 27.125). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 7.5, "x2": 13.75, "y1": 25.25, "y2": 27.125}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. velocity times time gives distance, not acceleration\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "32b6ede9e50a4cbff11c15b5d4b93186f9a811c6c6b19b1ecfc8d81124827845", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_003003_inconsistent_7481c798_118785", "license": "Apache-2.0", "prompt": "In field worksheet case 118785, check dimensional consistency for a = v * t. The left side has dimensions m/s^2 and the right side has dimensions m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nvelocity times time gives distance, not acceleration\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "a = v * t"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef threshold_flags_003004(values, threshold):\n    return [value >= threshold for value in values]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"threshold_flags_003004\"}", "dedupe_signature": "0c47b10dc9f5ae99ac287139a233605493c2bbb343a307abd0b9c072e022f8c5", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "threshold_flags_003004"}, "id": "code_003004_threshold_flags_003004", "license": "Apache-2.0", "prompt": "Write a Python function threshold_flags_003004(values, threshold) that returns a list of booleans showing whether each value is greater than or equal to threshold. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "threshold_flags_003004"}, "verifier": {"function": "threshold_flags_003004", "tests": ["assert threshold_flags_003004([1, 2, 3], 2) == [False, True, True]", "assert threshold_flags_003004([], 5) == []", "assert threshold_flags_003004([-1, 0], 0) == [False, True]"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: launch_angle_or_vertical_velocity.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"launch_angle_or_vertical_velocity\"]}", "dedupe_signature": "4a2c892d69fd79a8b05a4f0c9bae4a80a75bf42cb6ef263e56d6e5f426128184", "difficulty": "easy", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["launch_angle_or_vertical_velocity"]}, "id": "abstain_003005_launch_angle_or_vertical_velocity", "license": "Apache-2.0", "prompt": "Compute projectile range on level ground. The prompt gives initial speed 61.7 m/s but does not give launch angle or vertical velocity. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: launch_angle_or_vertical_velocity.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["launch_angle_or_vertical_velocity"]}, "verifier": {"missing": ["launch_angle_or_vertical_velocity"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 2.8 kg and a = 12.55 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 35.14, \"unit\": \"N\"}", "dedupe_signature": "873e2373dd7de133dcdcb84ecd2446958b91fd14ce98ad04677b59b8e855e862", "difficulty": "easy", "final_answer": {"answer": 35.14, "unit": "N"}, "id": "force_003006_2.8_12.55", "license": "Apache-2.0", "prompt": "A cart has mass 2.8 kg and measured acceleration 12.55 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 2.8 kg and a = 12.55 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 12.55, "mass": 2.8}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 2.85^2 and multiply by 0.5 * 11.9.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 48.3289, \"unit\": \"J\"}", "dedupe_signature": "de79eedfd497723c8abeef97ba0da6c0513c5432a9620fd2050e6c5d6f4eedc4", "difficulty": "easy", "final_answer": {"answer": 48.3289, "unit": "J"}, "id": "ke_003007_11.9_2.85", "license": "Apache-2.0", "prompt": "A body of mass 11.9 kg moves at 2.85 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 2.85^2 and multiply by 0.5 * 11.9.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 11.9, "velocity": 2.85}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=82 degrees through the sine of 2 theta.\n3. Substitute v=38.3 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 41.2161, \"unit\": \"m\"}", "dedupe_signature": "1e3defb1921144e37913a80148bded30a223b4c447f0acd1883027921cf8d7e3", "difficulty": "medium", "final_answer": {"answer": 41.2161, "unit": "m"}, "id": "projectile_range_003008_38.3_82", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 38.3 m/s and angle 82 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=82 degrees through the sine of 2 theta.\nSubstitute v=38.3 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 82, "gravity": 9.81, "speed": 38.3}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=40.6 V and R=43 ohm.\nFinal: {\"answer\": 38.334, \"unit\": \"W\"}", "dedupe_signature": "903e0a2bf5569bfff3d82986739f55dd9ba718374088a7ad6a932e3bd05ba9c5", "difficulty": "easy", "final_answer": {"answer": 38.334, "unit": "W"}, "id": "ohm_power_003011_40.6_43", "license": "Apache-2.0", "prompt": "A resistor has resistance 43 ohm and voltage 40.6 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=40.6 V and R=43 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 43.0, "voltage": 40.6}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=840.5 mg, t=171 h, and T_half=64.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 133.8006, \"unit\": \"mg\"}", "dedupe_signature": "c2c5a31bec894df66925b68ccd8ae47d12df02a78b0158807bd88dc0588610c5", "difficulty": "medium", "final_answer": {"answer": 133.8006, "unit": "mg"}, "id": "half_life_003012_840.5_64.5_171", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 840.5 mg. Its half-life is 64.5 hours. How many mg remain after 171 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=840.5 mg, t=171 h, and T_half=64.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 171.0, "half_life": 64.5, "initial_amount": 840.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 3.94 mol * 44.01 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 173.3994, \"unit\": \"g\"}", "dedupe_signature": "c5b7620d16d53e4f5bcda4c34ee043ec625a8ea6e5e74b5eee82345ed8ef1432", "difficulty": "medium", "final_answer": {"answer": 173.3994, "unit": "g"}, "id": "stoich_mass_003013_carbon_dioxide_3.94", "license": "Apache-2.0", "prompt": "A sample contains 3.94 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 3.94 mol * 44.01 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "carbon dioxide", "molar_mass": 44.01, "moles": 3.94}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 4845 mL to 4.845 L.\n3. Compute M = 2.96 / 4.845.\nFinal: {\"answer\": 0.6109, \"unit\": \"mol/L\"}", "dedupe_signature": "0ec459cf7ce5f6810588959f29f81333b972542fc89ae738811776094dd5bbc9", "difficulty": "medium", "final_answer": {"answer": 0.6109, "unit": "mol/L"}, "id": "molarity_003014_2.96_4845", "license": "Apache-2.0", "prompt": "A solution contains 2.96 mol of solute in 4845 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 4845 mL to 4.845 L.\nCompute M = 2.96 / 4.845.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 2.96, "volume_ml": 4845}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.13 y, so each step multiplies y by 1 - h*0.13.\n3. Apply that update for 3 steps and round the final state.\nFinal: {\"answer\": 10.5567, \"unit\": \"state_units\"}", "dedupe_signature": "f652ddb49346ef80e93d34a16409b7d4ed5adbda40800810f454bae049b6046f", "difficulty": "medium", "final_answer": {"answer": 10.5567, "unit": "state_units"}, "id": "euler_decay_003015_15_0.13_0.85_3", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.13 y with y(0)=15, step size h=0.85, for 3 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.13 y, so each step multiplies y by 1 - h*0.13.\nApply that update for 3 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 15.0, "rate": 0.13, "step": 0.85, "steps": 3}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-4.3)=2.87 and f(3)=-32.9.\n3. The interval width is 7.3.\nFinal: {\"answer\": -109.6095, \"unit\": \"area_units\"}", "dedupe_signature": "5be7849f79105635808c8801c50f9d8b1ec7f3f7947e59e55361e96e6b830c36", "difficulty": "medium", "final_answer": {"answer": -109.6095, "unit": "area_units"}, "id": "trapz_linear_003016_-4.9_-18.2_-4.3_3", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-4.9x+-18.2 from x=-4.3 to x=3. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-4.3)=2.87 and f(3)=-32.9.\nThe interval width is 7.3.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -18.2, "slope": -4.9, "x0": -4.3, "x1": 3.0}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.08 and add it to the current value.\nFinal: {\"answer\": [-1.038, -1.03, -1.65], \"unit\": \"temperature_units\"}", "dedupe_signature": "b615134c7d0faa398000cddae3308caed06b54bae0d22b635c26b3f96d3babd2", "difficulty": "hard", "final_answer": {"answer": [-1.038, -1.03, -1.65], "unit": "temperature_units"}, "id": "heat_step_003017_0.08_0.05_-1.15_-0.95_-1.75_-1.3", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=0.05, right=-1.3; current interior values are [-1.15, -0.95, -1.75]. Use r=0.08. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.08 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-1.15, -0.95, -1.75], "left": 0.05, "r": 0.08, "right": -1.3}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kelvin equals Celsius plus 273.15.\n2. Apply the conversion factor directly to the given value.\n3. Compute 197.5 + 273.15.\nFinal: {\"answer\": 470.65, \"unit\": \"K\"}", "dedupe_signature": "ea779fe7e07921cbf460453fa314e2ef9282ad9e1d92201189492483d8b36367", "difficulty": "easy", "final_answer": {"answer": 470.65, "unit": "K"}, "id": "unit_convert_003018_c_to_k_197.5", "license": "Apache-2.0", "prompt": "Convert 197.5 degC to K. Return the converted value with unit.", "reasoning_trace": "Kelvin equals Celsius plus 273.15.\nApply the conversion factor directly to the given value.\nCompute 197.5 + 273.15.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 197.5}, "verifier": {"formula": "value + 273.15", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=16 degrees and keep the unit as newtons.\nFinal: {\"answer\": [12.977, 3.7211], \"unit\": \"N\"}", "dedupe_signature": "137364a5c1255b589cf2fc5261360d10c01f35d6b22fc9901921f3a18b5af64b", "difficulty": "medium", "final_answer": {"answer": [12.977, 3.7211], "unit": "N"}, "id": "vector_components_003019_13.5_16", "license": "Apache-2.0", "prompt": "A vector has magnitude 13.5 N at 16 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=16 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 16, "magnitude": 13.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [4.35, 3.0], \"unit\": \"dimensionless\"}", "dedupe_signature": "a9c537b98ad5acd215826b06e0da3b131da1303c8809cbe9da80be7833dd1184", "difficulty": "medium", "final_answer": {"answer": [4.35, 3.0], "unit": "dimensionless"}, "id": "line_two_point_003020_14.75_15.5_4.35_3", "license": "Apache-2.0", "prompt": "A line passes through points (14.75, 67.1625) and (15.5, 70.425). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 14.75, "x2": 15.5, "y1": 67.1625, "y2": 70.425}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. amount times volume is not concentration\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "880b7cdafe173f00305b4a8fc6199658aa1cef6518fdadc92d139b7baa707bda", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_003021_inconsistent_74ac0b02_435984", "license": "Apache-2.0", "prompt": "In student derivation case 435984, check dimensional consistency for C = n * V. The left side has dimensions mol/L and the right side has dimensions mol*L. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\namount times volume is not concentration\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "C = n * V"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef normalize_003022(values):\n    total = sum(values)\n    if total == 0:\n        raise ValueError('cannot normalize zero-sum values')\n    return [v / total for v in values]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"normalize_003022\"}", "dedupe_signature": "b301d26dacf8943b671bdb1caee8e29c054f85560bdc4cf33fa8748559c75edf", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "normalize_003022"}, "id": "code_003022_normalize_003022", "license": "Apache-2.0", "prompt": "Write a Python function normalize_003022(values) that returns a new list whose values sum to 1. Raise ValueError if the sum is zero. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "normalize_003022"}, "verifier": {"function": "normalize_003022", "tests": ["out = normalize_003022([2, 3, 5]); assert len(out) == 3", "assert abs(sum(normalize_003022([2, 3, 5])) - 1.0) < 1e-12", "assert normalize_003022([1, 1]) == [0.5, 0.5]", "try:\n    normalize_003022([1, -1])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: recurrence, objective, tie_breaking_rule.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"recurrence\", \"objective\", \"tie_breaking_rule\"]}", "dedupe_signature": "b3ba8a3bb7d7118d214adecbc755cd78f05eab43bd2d7069b0e871d16a60c111", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["recurrence", "objective", "tie_breaking_rule"]}, "id": "abstain_003023_recurrence_objective_tie_breaking_rule", "license": "Apache-2.0", "prompt": "Write a dynamic-programming solver for a scheduler scoring problem with 49 items and budget 70905, but the recurrence, objective, and tie-breaking rule are all absent. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: recurrence, objective, tie_breaking_rule.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["recurrence", "objective", "tie_breaking_rule"]}, "verifier": {"missing": ["recurrence", "objective", "tie_breaking_rule"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 4.6 kg and a = 6.85 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 31.51, \"unit\": \"N\"}", "dedupe_signature": "0397d3a30e3ac3e60ea66d51edf0562cf738d956a7e093f5148394d11d32b44d", "difficulty": "easy", "final_answer": {"answer": 31.51, "unit": "N"}, "id": "force_003024_4.6_6.85", "license": "Apache-2.0", "prompt": "A cart has mass 4.6 kg and measured acceleration 6.85 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 4.6 kg and a = 6.85 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 6.85, "mass": 4.6}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 7.85^2 and multiply by 0.5 * 21.3.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 656.2796, \"unit\": \"J\"}", "dedupe_signature": "53a2bd070cd7fd977a98a074f4a40e7bf3f3a809499065ca3720e42e0e60afd9", "difficulty": "easy", "final_answer": {"answer": 656.2796, "unit": "J"}, "id": "ke_003025_21.3_7.85", "license": "Apache-2.0", "prompt": "A body of mass 21.3 kg moves at 7.85 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 7.85^2 and multiply by 0.5 * 21.3.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 21.3, "velocity": 7.85}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=36 degrees through the sine of 2 theta.\n3. Substitute v=31 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 93.1667, \"unit\": \"m\"}", "dedupe_signature": "825739879656b3df97e4959c0d188e5675059003668403c689dac0277dd0df68", "difficulty": "medium", "final_answer": {"answer": 93.1667, "unit": "m"}, "id": "projectile_range_003026_31_36", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 31 m/s and angle 36 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=36 degrees through the sine of 2 theta.\nSubstitute v=31 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 36, "gravity": 9.81, "speed": 31.0}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 0.99 * 8.314 * 456 / 57.8.\nFinal: {\"answer\": 64.9355, \"unit\": \"kPa\"}", "dedupe_signature": "8f97ac1ad5c3cf62749ac2814776d35d97386cad3cef873d4efc550167b7957d", "difficulty": "medium", "final_answer": {"answer": 64.9355, "unit": "kPa"}, "id": "ideal_gas_003027_0.99_456_57.8", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=0.99 mol, T=456 K, and V=57.8 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 0.99 * 8.314 * 456 / 57.8.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 0.99, "temp_k": 456, "volume_l": 57.8}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1085 * 2.755 * 116.\nFinal: {\"answer\": 346744.3, \"unit\": \"J\"}", "dedupe_signature": "e8270db03c589b01ffaf7723128fcd90ce37c758303028933e3e79bc94a92bca", "difficulty": "easy", "final_answer": {"answer": 346744.3, "unit": "J"}, "id": "heat_q_003028_1085_2.755_116", "license": "Apache-2.0", "prompt": "A 1085 g sample has specific heat 2.755 J/(g*K). How much heat is needed to raise its temperature by 116 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1085 * 2.755 * 116.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 116, "heat_capacity": 2.755, "mass_g": 1085}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=94 mg, t=202 h, and T_half=87 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 18.8012, \"unit\": \"mg\"}", "dedupe_signature": "2160b7b2569b04ed11c1f21dcd0da235f5eb4770f90eab4613d3146b56087ab2", "difficulty": "medium", "final_answer": {"answer": 18.8012, "unit": "mg"}, "id": "half_life_003030_94_87_202", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 94 mg. Its half-life is 87 hours. How many mg remain after 202 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=94 mg, t=202 h, and T_half=87 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 202.0, "half_life": 87.0, "initial_amount": 94.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 1.18 mol * 180.156 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 212.5841, \"unit\": \"g\"}", "dedupe_signature": "dc3da19ecba6fc7ca0273c4da64de10c76f7596b78ac2bacf379f2022a650c39", "difficulty": "medium", "final_answer": {"answer": 212.5841, "unit": "g"}, "id": "stoich_mass_003031_glucose_1.18", "license": "Apache-2.0", "prompt": "A sample contains 1.18 mol of glucose. Using molar mass 180.156 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 1.18 mol * 180.156 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "glucose", "molar_mass": 180.156, "moles": 1.18}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 3455 mL to 3.455 L.\n3. Compute M = 4.18 / 3.455.\nFinal: {\"answer\": 1.2098, \"unit\": \"mol/L\"}", "dedupe_signature": "ec0631fcef440f3a9d9c715b9ee602ae7bf9d3bb0acb2251ec8fe0b046b2d4d7", "difficulty": "medium", "final_answer": {"answer": 1.2098, "unit": "mol/L"}, "id": "molarity_003032_4.18_3455", "license": "Apache-2.0", "prompt": "A solution contains 4.18 mol of solute in 3455 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 3455 mL to 3.455 L.\nCompute M = 4.18 / 3.455.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 4.18, "volume_ml": 3455}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.85 y, so each step multiplies y by 1 - h*0.85.\n3. Apply that update for 3 steps and round the final state.\nFinal: {\"answer\": 0.8636, \"unit\": \"state_units\"}", "dedupe_signature": "5c97402f494e00403816d40a863b1769741b7ff1db919338f90ac31625a1c7da", "difficulty": "medium", "final_answer": {"answer": 0.8636, "unit": "state_units"}, "id": "euler_decay_003033_13_0.85_0.7_3", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.85 y with y(0)=13, step size h=0.7, for 3 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.85 y, so each step multiplies y by 1 - h*0.85.\nApply that update for 3 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 13.0, "rate": 0.85, "step": 0.7, "steps": 3}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(8.5)=-10.5 and f(11.2)=-9.96.\n3. The interval width is 2.7.\nFinal: {\"answer\": -27.621, \"unit\": \"area_units\"}", "dedupe_signature": "9382c64c1178a0fcc11450681ceac275f7f9a13738c3ef0547cf267a337b8ea2", "difficulty": "medium", "final_answer": {"answer": -27.621, "unit": "area_units"}, "id": "trapz_linear_003034_0.2_-12.2_8.5_11.2", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=0.2x+-12.2 from x=8.5 to x=11.2. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(8.5)=-10.5 and f(11.2)=-9.96.\nThe interval width is 2.7.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -12.2, "slope": 0.2, "x0": 8.5, "x1": 11.2}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.2 and add it to the current value.\nFinal: {\"answer\": [-0.69, 1.91, 1.96], \"unit\": \"temperature_units\"}", "dedupe_signature": "2d89914bd5983fc4dde7ab9614f91f2785913da49467307ece703274754cdb97", "difficulty": "hard", "final_answer": {"answer": [-0.69, 1.91, 1.96], "unit": "temperature_units"}, "id": "heat_step_003035_0.2_-1.15_-1.7_2.8_2.85_-1.55", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-1.15, right=-1.55; current interior values are [-1.7, 2.8, 2.85]. Use r=0.2. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.2 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-1.7, 2.8, 2.85], "left": -1.15, "r": 0.2, "right": -1.55}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 100 centimeters in one meter.\n2. Apply the conversion factor directly to the given value.\n3. Compute 4776.0 / 100.\nFinal: {\"answer\": 47.76, \"unit\": \"m\"}", "dedupe_signature": "7095ab35bc59a3e36767aed1a5528137949309fa9118746123ff738888f71895", "difficulty": "easy", "final_answer": {"answer": 47.76, "unit": "m"}, "id": "unit_convert_003036_cm_to_m_4776", "license": "Apache-2.0", "prompt": "Convert 4776 cm to m. Return the converted value with unit.", "reasoning_trace": "There are 100 centimeters in one meter.\nApply the conversion factor directly to the given value.\nCompute 4776.0 / 100.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 4776.0}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=37 degrees and keep the unit as newtons.\nFinal: {\"answer\": [262.3518, 197.6962], \"unit\": \"N\"}", "dedupe_signature": "e831769d6c63bf8b5d8e7c995d7c598add37314e722beba5239a940be7e872f7", "difficulty": "medium", "final_answer": {"answer": [262.3518, 197.6962], "unit": "N"}, "id": "vector_components_003037_328.5_37", "license": "Apache-2.0", "prompt": "A vector has magnitude 328.5 N at 37 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=37 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 37, "magnitude": 328.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [6.4, -29.5], \"unit\": \"dimensionless\"}", "dedupe_signature": "046ea1001d1a7920aa5d168356e464967dfa63d9404760c5b427190e00ab0ec9", "difficulty": "medium", "final_answer": {"answer": [6.4, -29.5], "unit": "dimensionless"}, "id": "line_two_point_003038_5.5_11.25_6.4_-29.5", "license": "Apache-2.0", "prompt": "A line passes through points (5.5, 5.7) and (11.25, 42.5). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 5.5, "x2": 11.25, "y1": 5.700000000000003, "y2": 42.5}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: left_boundary, right_boundary.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"left_boundary\", \"right_boundary\"]}", "dedupe_signature": "6f95cac2d725c3a98c85f4dea71855c65089c61d2f8a9aa4bbbf062a39557f73", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["left_boundary", "right_boundary"]}, "id": "abstain_003041_left_boundary_right_boundary", "license": "Apache-2.0", "prompt": "Solve the 1D heat equation after one finite-difference step. The prompt gives r=0.48 and interior values [-0.2, -1.05, 0.55], but gives no boundary values. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: left_boundary, right_boundary.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["left_boundary", "right_boundary"]}, "verifier": {"missing": ["left_boundary", "right_boundary"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 9.5 kg and a = 10.9 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 103.55, \"unit\": \"N\"}", "dedupe_signature": "5fee0eecb6065b4683265615fbf2714609395b76c7ce7edce009ce30af60b378", "difficulty": "easy", "final_answer": {"answer": 103.55, "unit": "N"}, "id": "force_003042_9.5_10.9", "license": "Apache-2.0", "prompt": "A cart has mass 9.5 kg and measured acceleration 10.9 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 9.5 kg and a = 10.9 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 10.9, "mass": 9.5}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 2.68 * 8.314 * 534 / 5.8.\nFinal: {\"answer\": 2051.4365, \"unit\": \"kPa\"}", "dedupe_signature": "21e90ad1eb13e055b93428e27546934dece4f9ac0766bb97fbc0dc91db9fd93c", "difficulty": "medium", "final_answer": {"answer": 2051.4365, "unit": "kPa"}, "id": "ideal_gas_003045_2.68_534_5.8", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=2.68 mol, T=534 K, and V=5.8 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 2.68 * 8.314 * 534 / 5.8.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 2.68, "temp_k": 534, "volume_l": 5.8}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 770 * 1.23 * 85.\nFinal: {\"answer\": 80503.5, \"unit\": \"J\"}", "dedupe_signature": "8a205521006fbc71958392d0ba30d1f28ac81b0da4a6ef83448b25474bf1e127", "difficulty": "easy", "final_answer": {"answer": 80503.5, "unit": "J"}, "id": "heat_q_003046_770_1.23_85", "license": "Apache-2.0", "prompt": "A 770 g sample has specific heat 1.23 J/(g*K). How much heat is needed to raise its temperature by 85 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 770 * 1.23 * 85.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 85, "heat_capacity": 1.23, "mass_g": 770}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=193.1 V and R=195.4 ohm.\nFinal: {\"answer\": 190.8271, \"unit\": \"W\"}", "dedupe_signature": "351262efbbf786c23581b2e83d2d567896b1faad695ae2517c456abfcd27bf74", "difficulty": "easy", "final_answer": {"answer": 190.8271, "unit": "W"}, "id": "ohm_power_003047_193.1_195.4", "license": "Apache-2.0", "prompt": "A resistor has resistance 195.4 ohm and voltage 193.1 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=193.1 V and R=195.4 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 195.4, "voltage": 193.1}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=975 mg, t=354.5 h, and T_half=37.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 1.3908, \"unit\": \"mg\"}", "dedupe_signature": "25681245331fc1c455128e0143dbc6c87ee8ccf2c6c8857aef393d12c93b209d", "difficulty": "medium", "final_answer": {"answer": 1.3908, "unit": "mg"}, "id": "half_life_003048_975_37.5_354.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 975 mg. Its half-life is 37.5 hours. How many mg remain after 354.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=975 mg, t=354.5 h, and T_half=37.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 354.5, "half_life": 37.5, "initial_amount": 975.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 6.71 mol * 58.44 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 392.1324, \"unit\": \"g\"}", "dedupe_signature": "6409a1e731987c8f7704655b04e37105e00e3122a8df3f673c6ce3dd692e1cb8", "difficulty": "medium", "final_answer": {"answer": 392.1324, "unit": "g"}, "id": "stoich_mass_003049_sodium_chloride_6.71", "license": "Apache-2.0", "prompt": "A sample contains 6.71 mol of sodium chloride. Using molar mass 58.44 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 6.71 mol * 58.44 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "sodium chloride", "molar_mass": 58.44, "moles": 6.71}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.47 y, so each step multiplies y by 1 - h*0.47.\n3. Apply that update for 9 steps and round the final state.\nFinal: {\"answer\": 0.026, \"unit\": \"state_units\"}", "dedupe_signature": "8400ab342150b33f5da11f3f5db2a545f9335d74eb504edd9694be4442c8dfd1", "difficulty": "medium", "final_answer": {"answer": 0.026, "unit": "state_units"}, "id": "euler_decay_003051_28.5_0.47_1.15_9", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.47 y with y(0)=28.5, step size h=1.15, for 9 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.47 y, so each step multiplies y by 1 - h*0.47.\nApply that update for 9 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 28.5, "rate": 0.47, "step": 1.15, "steps": 9}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.46 and add it to the current value.\nFinal: {\"answer\": [1.252, 0.823, 0.129], \"unit\": \"temperature_units\"}", "dedupe_signature": "e666e9e84065fe48aba0c7f201d83980b993161f61357bc7e08f864af08c9365", "difficulty": "hard", "final_answer": {"answer": [1.252, 0.823, 0.129], "unit": "temperature_units"}, "id": "heat_step_003053_0.46_0.85_-0.45_1.95_1.9_-2.0", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=0.85, right=-2; current interior values are [-0.45, 1.95, 1.9]. Use r=0.46. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.46 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-0.45, 1.95, 1.9], "left": 0.85, "r": 0.46, "right": -2.0}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 39030.0 / 1000.\nFinal: {\"answer\": 39.03, \"unit\": \"kg\"}", "dedupe_signature": "0563dcac1a163099e4281c3744da954986656b435efab9bfd10022eb07938eb5", "difficulty": "easy", "final_answer": {"answer": 39.03, "unit": "kg"}, "id": "unit_convert_003054_g_to_kg_39030", "license": "Apache-2.0", "prompt": "Convert 39030 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 39030.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 39030.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=93 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-14.5756, 278.1183], \"unit\": \"N\"}", "dedupe_signature": "ab52fc3909735d51c95f6b6c3181f230422da5ec90b37f7c1f5b45a5eaafc051", "difficulty": "medium", "final_answer": {"answer": [-14.5756, 278.1183], "unit": "N"}, "id": "vector_components_003055_278.5_93", "license": "Apache-2.0", "prompt": "A vector has magnitude 278.5 N at 93 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=93 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 93, "magnitude": 278.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [3.3, 27.75], \"unit\": \"dimensionless\"}", "dedupe_signature": "780d0c0d9e7885016f57175648ec00c1a6f0d78becb166f0f388d54e7055ea7b", "difficulty": "medium", "final_answer": {"answer": [3.3, 27.75], "unit": "dimensionless"}, "id": "line_two_point_003056_4.75_6.25_3.3_27.75", "license": "Apache-2.0", "prompt": "A line passes through points (4.75, 43.425) and (6.25, 48.375). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 4.75, "x2": 6.25, "y1": 43.425, "y2": 48.375}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. grams cancel with J/(g*K), and kelvin cancels, leaving joules\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "4ea1a957d782fa8825bdf4ec14c0371c832407919236fd89cb1e19d82b366b1d", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_003057_consistent_4153435f_16400", "license": "Apache-2.0", "prompt": "In sensor calibration case 16400, check dimensional consistency for Q = m * c * DeltaT. The left side has dimensions J and the right side has dimensions J. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\ngrams cancel with J/(g*K), and kelvin cancels, leaving joules\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "Q = m * c * DeltaT"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef running_total_003058(values):\n    total = 0\n    out = []\n    for value in values:\n        total += value\n        out.append(total)\n    return out\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"running_total_003058\"}", "dedupe_signature": "53f4b5b73a7ddeea71f77c3883be704487eff633f375eab5929a5ee86a8ad5fe", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "running_total_003058"}, "id": "code_003058_running_total_003058", "license": "Apache-2.0", "prompt": "Write a Python function running_total_003058(values) that returns cumulative sums as a new list. It must not mutate the input list. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "running_total_003058"}, "verifier": {"function": "running_total_003058", "tests": ["assert running_total_003058([1, 2, 3]) == [1, 3, 6]", "xs = [4, -1, 2]; assert running_total_003058(xs) == [4, 3, 5] and xs == [4, -1, 2]", "assert running_total_003058([]) == []"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: launch_angle_or_vertical_velocity.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"launch_angle_or_vertical_velocity\"]}", "dedupe_signature": "352ad8b9c0665f762cbee8ea9821eb5fbeed8eeae59e74c936aa27d3e055fa1e", "difficulty": "easy", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["launch_angle_or_vertical_velocity"]}, "id": "abstain_003059_launch_angle_or_vertical_velocity", "license": "Apache-2.0", "prompt": "Compute projectile range on level ground. The prompt gives initial speed 57.6 m/s but does not give launch angle or vertical velocity. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: launch_angle_or_vertical_velocity.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["launch_angle_or_vertical_velocity"]}, "verifier": {"missing": ["launch_angle_or_vertical_velocity"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 20.9 kg and a = 2.5 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 52.25, \"unit\": \"N\"}", "dedupe_signature": "9a9493a7123e720e11b752fd3343a6b9e90541338e63b3382d427ee5a30062a7", "difficulty": "easy", "final_answer": {"answer": 52.25, "unit": "N"}, "id": "force_003060_20.9_2.5", "license": "Apache-2.0", "prompt": "A cart has mass 20.9 kg and measured acceleration 2.5 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 20.9 kg and a = 2.5 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 2.5, "mass": 20.9}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 26.9^2 and multiply by 0.5 * 17.95.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 6494.3997, \"unit\": \"J\"}", "dedupe_signature": "0f91315b1e2a188032d49000b6ca211ea64794fae97acbe9887d9138f93472ed", "difficulty": "easy", "final_answer": {"answer": 6494.3997, "unit": "J"}, "id": "ke_003061_17.95_26.9", "license": "Apache-2.0", "prompt": "A body of mass 17.95 kg moves at 26.9 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 26.9^2 and multiply by 0.5 * 17.95.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 17.95, "velocity": 26.9}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=80 degrees through the sine of 2 theta.\n3. Substitute v=55.9 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 108.9447, \"unit\": \"m\"}", "dedupe_signature": "837ca6dcd88abd5bcccad6ec613ae3d42970397844d94f247136c7497bec2023", "difficulty": "medium", "final_answer": {"answer": 108.9447, "unit": "m"}, "id": "projectile_range_003062_55.9_80", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 55.9 m/s and angle 80 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=80 degrees through the sine of 2 theta.\nSubstitute v=55.9 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 80, "gravity": 9.81, "speed": 55.9}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1310 * 2.76 * 26.\nFinal: {\"answer\": 94005.6, \"unit\": \"J\"}", "dedupe_signature": "031c4a4b99eb126a2902d4efa240abdf9a50c9bdefa2edc4590b1e39a4b286ee", "difficulty": "easy", "final_answer": {"answer": 94005.6, "unit": "J"}, "id": "heat_q_003064_1310_2.76_26", "license": "Apache-2.0", "prompt": "A 1310 g sample has specific heat 2.76 J/(g*K). How much heat is needed to raise its temperature by 26 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1310 * 2.76 * 26.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 26, "heat_capacity": 2.76, "mass_g": 1310}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=87.2 V and R=122.7 ohm.\nFinal: {\"answer\": 61.971, \"unit\": \"W\"}", "dedupe_signature": "63b1f4ae0bebd3040618fd44cbcbe536bd0a38bf2b3e385d334122a374ac398b", "difficulty": "easy", "final_answer": {"answer": 61.971, "unit": "W"}, "id": "ohm_power_003065_87.2_122.7", "license": "Apache-2.0", "prompt": "A resistor has resistance 122.7 ohm and voltage 87.2 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=87.2 V and R=122.7 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 122.7, "voltage": 87.2}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=897.5 mg, t=357 h, and T_half=75 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 33.1232, \"unit\": \"mg\"}", "dedupe_signature": "c3d47a4a99501dd0cd3f8d7d6d8a78f381b2a6bf29275293d2c02e32fc70f87f", "difficulty": "medium", "final_answer": {"answer": 33.1232, "unit": "mg"}, "id": "half_life_003066_897.5_75_357", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 897.5 mg. Its half-life is 75 hours. How many mg remain after 357 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=897.5 mg, t=357 h, and T_half=75 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 357.0, "half_life": 75.0, "initial_amount": 897.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 4655 mL to 4.655 L.\n3. Compute M = 4.385 / 4.655.\nFinal: {\"answer\": 0.942, \"unit\": \"mol/L\"}", "dedupe_signature": "def108875e59bac0c498f3b41a6e47b939a0ecad9d1e17f93c7da2428f803239", "difficulty": "medium", "final_answer": {"answer": 0.942, "unit": "mol/L"}, "id": "molarity_003068_4.385_4655", "license": "Apache-2.0", "prompt": "A solution contains 4.385 mol of solute in 4655 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 4655 mL to 4.655 L.\nCompute M = 4.385 / 4.655.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 4.385, "volume_ml": 4655}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.45 y, so each step multiplies y by 1 - h*0.45.\n3. Apply that update for 5 steps and round the final state.\nFinal: {\"answer\": 0.8678, \"unit\": \"state_units\"}", "dedupe_signature": "5c1c128c84d97e317a6381577212fe757c3c75ab465d616a1197fe00196b9aed", "difficulty": "medium", "final_answer": {"answer": 0.8678, "unit": "state_units"}, "id": "euler_decay_003069_70.5_0.45_1.3_5", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.45 y with y(0)=70.5, step size h=1.3, for 5 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.45 y, so each step multiplies y by 1 - h*0.45.\nApply that update for 5 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 70.5, "rate": 0.45, "step": 1.3, "steps": 5}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(8.5)=-59.65 and f(16.6)=-104.2.\n3. The interval width is 8.1.\nFinal: {\"answer\": -663.5925, \"unit\": \"area_units\"}", "dedupe_signature": "494e6119f77d15c9ca4f2e505115140dec0e69ab28fbbe6f7abff71b19a9d749", "difficulty": "medium", "final_answer": {"answer": -663.5925, "unit": "area_units"}, "id": "trapz_linear_003070_-5.5_-12.9_8.5_16.6", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-5.5x+-12.9 from x=8.5 to x=16.6. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(8.5)=-59.65 and f(16.6)=-104.2.\nThe interval width is 8.1.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -12.9, "slope": -5.5, "x0": 8.5, "x1": 16.6}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kelvin equals Celsius plus 273.15.\n2. Apply the conversion factor directly to the given value.\n3. Compute 22.5 + 273.15.\nFinal: {\"answer\": 295.65, \"unit\": \"K\"}", "dedupe_signature": "1624b6a4bbf727a4576b40c46f89bb70f8b43378406e1b28eae889fe91b4e67d", "difficulty": "easy", "final_answer": {"answer": 295.65, "unit": "K"}, "id": "unit_convert_003072_c_to_k_22.5", "license": "Apache-2.0", "prompt": "Convert 22.5 degC to K. Return the converted value with unit.", "reasoning_trace": "Kelvin equals Celsius plus 273.15.\nApply the conversion factor directly to the given value.\nCompute 22.5 + 273.15.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 22.5}, "verifier": {"formula": "value + 273.15", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [6.25, -27.0], \"unit\": \"dimensionless\"}", "dedupe_signature": "cfafdb06850b18f99f4feec6114457ffe4d1aebd10c59da5b0e1b5be841a8455", "difficulty": "medium", "final_answer": {"answer": [6.25, -27.0], "unit": "dimensionless"}, "id": "line_two_point_003074_-15.25_-1.75_6.25_-27", "license": "Apache-2.0", "prompt": "A line passes through points (-15.25, -122.312) and (-1.75, -37.9375). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -15.25, "x2": -1.75, "y1": -122.3125, "y2": -37.9375}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. velocity divided by time is acceleration\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "b0d5c0a2249e0abd9a7236b71774ec9a57a0ebd6c2ac0287a4a7598ecfbdda51", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_003075_inconsistent_c1271127_67004", "license": "Apache-2.0", "prompt": "In simulation spec case 67004, check dimensional consistency for x = v / t. The left side has dimensions m and the right side has dimensions m/s^2. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nvelocity divided by time is acceleration\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "x = v / t"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef running_total_003076(values):\n    total = 0\n    out = []\n    for value in values:\n        total += value\n        out.append(total)\n    return out\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"running_total_003076\"}", "dedupe_signature": "cb998baf641e3ce923391a758f7734ef3543bc6be3e1030892685cd701b13abc", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "running_total_003076"}, "id": "code_003076_running_total_003076", "license": "Apache-2.0", "prompt": "Write a Python function running_total_003076(values) that returns cumulative sums as a new list. It must not mutate the input list. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "running_total_003076"}, "verifier": {"function": "running_total_003076", "tests": ["assert running_total_003076([1, 2, 3]) == [1, 3, 6]", "xs = [4, -1, 2]; assert running_total_003076(xs) == [4, 3, 5] and xs == [4, -1, 2]", "assert running_total_003076([]) == []"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: recurrence, objective, tie_breaking_rule.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"recurrence\", \"objective\", \"tie_breaking_rule\"]}", "dedupe_signature": "edfc4fea2b0886e35780a00cc5878759ca7fc326c3d956cd6a01d214914b8fbc", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["recurrence", "objective", "tie_breaking_rule"]}, "id": "abstain_003077_recurrence_objective_tie_breaking_rule", "license": "Apache-2.0", "prompt": "Write a dynamic-programming solver for a scheduler scoring problem with 2157 items and budget 58565, but the recurrence, objective, and tie-breaking rule are all absent. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: recurrence, objective, tie_breaking_rule.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["recurrence", "objective", "tie_breaking_rule"]}, "verifier": {"missing": ["recurrence", "objective", "tie_breaking_rule"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 21 kg and a = 5.45 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 114.45, \"unit\": \"N\"}", "dedupe_signature": "da088c5540650d50b1c90ac0c4b3fae22e241c34bbe33e89d0e8e6c96154e166", "difficulty": "easy", "final_answer": {"answer": 114.45, "unit": "N"}, "id": "force_003078_21_5.45", "license": "Apache-2.0", "prompt": "A cart has mass 21 kg and measured acceleration 5.45 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 21 kg and a = 5.45 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 5.45, "mass": 21.0}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 20.85^2 and multiply by 0.5 * 24.6.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 5347.0868, \"unit\": \"J\"}", "dedupe_signature": "03869c5aff4bf7733dd03288fd30262b7f6413f3ac7463685dec698e03d8f48f", "difficulty": "easy", "final_answer": {"answer": 5347.0868, "unit": "J"}, "id": "ke_003079_24.6_20.85", "license": "Apache-2.0", "prompt": "A body of mass 24.6 kg moves at 20.85 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 20.85^2 and multiply by 0.5 * 24.6.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 24.6, "velocity": 20.85}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=31 degrees through the sine of 2 theta.\n3. Substitute v=76.7 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 529.4886, \"unit\": \"m\"}", "dedupe_signature": "d1bc9a126cbe59a8e0c6781d59ccd84fdf9ca36e9e75ebad86ea3c099d297495", "difficulty": "medium", "final_answer": {"answer": 529.4886, "unit": "m"}, "id": "projectile_range_003080_76.7_31", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 76.7 m/s and angle 31 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=31 degrees through the sine of 2 theta.\nSubstitute v=76.7 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 31, "gravity": 9.81, "speed": 76.7}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=391.5 mg, t=112.5 h, and T_half=35 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 42.1828, \"unit\": \"mg\"}", "dedupe_signature": "9960d2f584a2a312147195c710a357ef727728d328b2b0ec3d1f8cdaa1b3fb96", "difficulty": "medium", "final_answer": {"answer": 42.1828, "unit": "mg"}, "id": "half_life_003084_391.5_35_112.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 391.5 mg. Its half-life is 35 hours. How many mg remain after 112.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=391.5 mg, t=112.5 h, and T_half=35 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 112.5, "half_life": 35.0, "initial_amount": 391.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 3.05 mol * 18.015 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 54.9457, \"unit\": \"g\"}", "dedupe_signature": "f92ec6c71246c1ea139dcb35048020cd62795266d65a3db9f9d667be61eadba0", "difficulty": "medium", "final_answer": {"answer": 54.9457, "unit": "g"}, "id": "stoich_mass_003085_water_3.05", "license": "Apache-2.0", "prompt": "A sample contains 3.05 mol of water. Using molar mass 18.015 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 3.05 mol * 18.015 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "water", "molar_mass": 18.015, "moles": 3.05}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 2740 mL to 2.74 L.\n3. Compute M = 2.02 / 2.74.\nFinal: {\"answer\": 0.7372, \"unit\": \"mol/L\"}", "dedupe_signature": "6e87ea1b115db0384e11cb2cc9facc91d8a6113067b2251d1f19b8f353bf1d15", "difficulty": "medium", "final_answer": {"answer": 0.7372, "unit": "mol/L"}, "id": "molarity_003086_2.02_2740", "license": "Apache-2.0", "prompt": "A solution contains 2.02 mol of solute in 2740 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 2740 mL to 2.74 L.\nCompute M = 2.02 / 2.74.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 2.02, "volume_ml": 2740}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.98 y, so each step multiplies y by 1 - h*0.98.\n3. Apply that update for 10 steps and round the final state.\nFinal: {\"answer\": 0.0, \"unit\": \"state_units\"}", "dedupe_signature": "7153927c6a91e40a4c3438a4331a27ac1f6e151004b83cacb06956876f35bd7d", "difficulty": "medium", "final_answer": {"answer": 0.0, "unit": "state_units"}, "id": "euler_decay_003087_44_0.98_1.2_10", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.98 y with y(0)=44, step size h=1.2, for 10 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.98 y, so each step multiplies y by 1 - h*0.98.\nApply that update for 10 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 44.0, "rate": 0.98, "step": 1.2, "steps": 10}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-7.4)=-31.96 and f(0.3)=-5.78.\n3. The interval width is 7.7.\nFinal: {\"answer\": -145.299, \"unit\": \"area_units\"}", "dedupe_signature": "654925261f52927720dc7ffb2bf42c5551af14d38b7fceb7c9e04bf5e77edf49", "difficulty": "medium", "final_answer": {"answer": -145.299, "unit": "area_units"}, "id": "trapz_linear_003088_3.4_-6.8_-7.4_0.3", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=3.4x+-6.8 from x=-7.4 to x=0.3. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-7.4)=-31.96 and f(0.3)=-5.78.\nThe interval width is 7.7.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -6.8, "slope": 3.4, "x0": -7.4, "x1": 0.2999999999999998}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.2 and add it to the current value.\nFinal: {\"answer\": [1.3, 1.35, -0.28], \"unit\": \"temperature_units\"}", "dedupe_signature": "9830c9f1b5ff3ee6eb30ec4ff8a933bee41a03fed3ac8b1596aaaa9fad308904", "difficulty": "hard", "final_answer": {"answer": [1.3, 1.35, -0.28], "unit": "temperature_units"}, "id": "heat_step_003089_0.2_0.05_1.4_2.25_-1.4_0.55", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=0.05, right=0.55; current interior values are [1.4, 2.25, -1.4]. Use r=0.2. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.2 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [1.4, 2.25, -1.4], "left": 0.05, "r": 0.2, "right": 0.55}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 35142.0 / 1000.\nFinal: {\"answer\": 35.142, \"unit\": \"kg\"}", "dedupe_signature": "e6aa6613c766f228ddabe3aba4d9852ebffc8839364707c47877c406899ca1ec", "difficulty": "easy", "final_answer": {"answer": 35.142, "unit": "kg"}, "id": "unit_convert_003090_g_to_kg_35142", "license": "Apache-2.0", "prompt": "Convert 35142 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 35142.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 35142.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=94 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-23.9265, 342.1645], \"unit\": \"N\"}", "dedupe_signature": "df946f7bef849e8a6301eef4e6edceee64c1f43552d677458c56b5dadf2ec279", "difficulty": "medium", "final_answer": {"answer": [-23.9265, 342.1645], "unit": "N"}, "id": "vector_components_003091_343_94", "license": "Apache-2.0", "prompt": "A vector has magnitude 343 N at 94 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=94 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 94, "magnitude": 343.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [4.25, -9.25], \"unit\": \"dimensionless\"}", "dedupe_signature": "a749a00a38389c7fe396023684a37efea7286b0ef235d44321f51f007dfc8187", "difficulty": "medium", "final_answer": {"answer": [4.25, -9.25], "unit": "dimensionless"}, "id": "line_two_point_003092_11.5_13_4.25_-9.25", "license": "Apache-2.0", "prompt": "A line passes through points (11.5, 39.625) and (13, 46). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 11.5, "x2": 13.0, "y1": 39.625, "y2": 46.0}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. amount times volume is not concentration\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "de013501ab2dd947df17721fceb9e4fa27a6c20b07778bdcfc904722ca68a60d", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_003093_inconsistent_74ac0b02_226409", "license": "Apache-2.0", "prompt": "In field worksheet case 226409, check dimensional consistency for C = n * V. The left side has dimensions mol/L and the right side has dimensions mol*L. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\namount times volume is not concentration\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "C = n * V"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef clamp_003094(x, lo, hi):\n    if lo > hi:\n        raise ValueError('lo must be <= hi')\n    return min(max(x, lo), hi)\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"clamp_003094\"}", "dedupe_signature": "f2e3d0def19429e1529a41e552e0f4300c0bcdc4a2582dc08d465c7bb411e754", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "clamp_003094"}, "id": "code_003094_clamp_003094", "license": "Apache-2.0", "prompt": "Write a Python function clamp_003094(x, lo, hi) that clips x into the inclusive interval [lo, hi]. It must raise ValueError if lo > hi. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "clamp_003094"}, "verifier": {"function": "clamp_003094", "tests": ["assert clamp_003094(5, 0, 10) == 5", "assert clamp_003094(-2, 0, 10) == 0", "assert clamp_003094(12, 0, 10) == 10", "try:\n    clamp_003094(1, 3, 2)\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: required_fields, allowed_transformations.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"required_fields\", \"allowed_transformations\"]}", "dedupe_signature": "0ecefdf23ee7a9e898170a1fd1454ff991599a49e19970d50f3a1bf80ce6f06e", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["required_fields", "allowed_transformations"]}, "id": "abstain_003095_required_fields_allowed_transformations", "license": "Apache-2.0", "prompt": "Write a sanitizer for valid laboratory invoice records in release 365033, but the prompt does not state which fields are required or which transformations are allowed. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: required_fields, allowed_transformations.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["required_fields", "allowed_transformations"]}, "verifier": {"missing": ["required_fields", "allowed_transformations"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 9.5 kg and a = 14.1 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 133.95, \"unit\": \"N\"}", "dedupe_signature": "474ebe2f61bcc02f022637a93bf01e4970cb6d2ade85a3e78b0654f572be14f2", "difficulty": "easy", "final_answer": {"answer": 133.95, "unit": "N"}, "id": "force_003096_9.5_14.1", "license": "Apache-2.0", "prompt": "A cart has mass 9.5 kg and measured acceleration 14.1 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 9.5 kg and a = 14.1 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 14.1, "mass": 9.5}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 330 * 2.445 * 5.\nFinal: {\"answer\": 4034.25, \"unit\": \"J\"}", "dedupe_signature": "3dc11152dbe764b7ab9bc47cc2d9f2d136122413b19020988e4e92b74b316c3c", "difficulty": "easy", "final_answer": {"answer": 4034.25, "unit": "J"}, "id": "heat_q_003100_330_2.445_5", "license": "Apache-2.0", "prompt": "A 330 g sample has specific heat 2.445 J/(g*K). How much heat is needed to raise its temperature by 5 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 330 * 2.445 * 5.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 5, "heat_capacity": 2.445, "mass_g": 330}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=201.6 V and R=67.1 ohm.\nFinal: {\"answer\": 605.7013, \"unit\": \"W\"}", "dedupe_signature": "bb2745dba0ebe862fb9f24c8ad6292ec110ef3d32898c9e45daad85e75d31b7f", "difficulty": "easy", "final_answer": {"answer": 605.7013, "unit": "W"}, "id": "ohm_power_003101_201.6_67.1", "license": "Apache-2.0", "prompt": "A resistor has resistance 67.1 ohm and voltage 201.6 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=201.6 V and R=67.1 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 67.1, "voltage": 201.6}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=399.5 mg, t=76 h, and T_half=104 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 240.7317, \"unit\": \"mg\"}", "dedupe_signature": "ca466dd35e9977309be5b012ec8c0af09b67eb7446beb728c9701da06d967adb", "difficulty": "medium", "final_answer": {"answer": 240.7317, "unit": "mg"}, "id": "half_life_003102_399.5_104_76", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 399.5 mg. Its half-life is 104 hours. How many mg remain after 76 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=399.5 mg, t=76 h, and T_half=104 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 76.0, "half_life": 104.0, "initial_amount": 399.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 0.26 mol * 180.156 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 46.8406, \"unit\": \"g\"}", "dedupe_signature": "cd9d38850e5648a8f3f77a7e1adcab982ed8830b777b46638b80e57b9873ad23", "difficulty": "medium", "final_answer": {"answer": 46.8406, "unit": "g"}, "id": "stoich_mass_003103_glucose_0.26", "license": "Apache-2.0", "prompt": "A sample contains 0.26 mol of glucose. Using molar mass 180.156 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 0.26 mol * 180.156 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "glucose", "molar_mass": 180.156, "moles": 0.26}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 1120 mL to 1.12 L.\n3. Compute M = 4.82 / 1.12.\nFinal: {\"answer\": 4.3036, \"unit\": \"mol/L\"}", "dedupe_signature": "4c6a71c3f05530b19021eb361be73bcaa8e5b1b49d2290d5002f72351c188563", "difficulty": "medium", "final_answer": {"answer": 4.3036, "unit": "mol/L"}, "id": "molarity_003104_4.82_1120", "license": "Apache-2.0", "prompt": "A solution contains 4.82 mol of solute in 1120 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 1120 mL to 1.12 L.\nCompute M = 4.82 / 1.12.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 4.82, "volume_ml": 1120}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.7 y, so each step multiplies y by 1 - h*0.7.\n3. Apply that update for 5 steps and round the final state.\nFinal: {\"answer\": 0.0, \"unit\": \"state_units\"}", "dedupe_signature": "93219d93a72b6be6ddece703f73c86a0258330e504f9be5a5edf0ff7c03a6a33", "difficulty": "medium", "final_answer": {"answer": 0.0, "unit": "state_units"}, "id": "euler_decay_003105_55.5_0.7_1.4_5", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.7 y with y(0)=55.5, step size h=1.4, for 5 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.7 y, so each step multiplies y by 1 - h*0.7.\nApply that update for 5 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 55.5, "rate": 0.7, "step": 1.4, "steps": 5}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-8.8)=76.06 and f(1.1)=9.73.\n3. The interval width is 9.9.\nFinal: {\"answer\": 424.6605, \"unit\": \"area_units\"}", "dedupe_signature": "f6907b5e6dbe8e55faa8d73610bedfc2e98a013602a0140a3e636f882f202eed", "difficulty": "medium", "final_answer": {"answer": 424.6605, "unit": "area_units"}, "id": "trapz_linear_003106_-6.7_17.1_-8.8_1.1", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-6.7x+17.1 from x=-8.8 to x=1.1. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-8.8)=76.06 and f(1.1)=9.73.\nThe interval width is 9.9.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 17.1, "slope": -6.7, "x0": -8.8, "x1": 1.0999999999999996}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-1.6, 10.25], \"unit\": \"dimensionless\"}", "dedupe_signature": "1ffac314bf40ee9ea13a918a8c300b1fe99648d52f4e4ce3cd4bc2984a8ac3c0", "difficulty": "medium", "final_answer": {"answer": [-1.6, 10.25], "unit": "dimensionless"}, "id": "line_two_point_003110_-11.75_3_-1.6_10.25", "license": "Apache-2.0", "prompt": "A line passes through points (-11.75, 29.05) and (3, 5.45). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -11.75, "x2": 3.0, "y1": 29.05, "y2": 5.449999999999999}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. coulomb per second is ampere\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "6c0e3bdfae7affc533e5655cad373b51b5f02a025bdf2236d8fa320c474dca81", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_003111_consistent_8b38953d_262844", "license": "Apache-2.0", "prompt": "In sensor calibration case 262844, check dimensional consistency for I = Q / t. The left side has dimensions A and the right side has dimensions A. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\ncoulomb per second is ampere\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "I = Q / t"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef center_values_003112(values):\n    if not values:\n        raise ValueError('center_values requires at least one value')\n    mean = sum(values) / len(values)\n    return [value - mean for value in values]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"center_values_003112\"}", "dedupe_signature": "d6182c1a173665e05996d30e24f694c3e26aca642795e73a6cdf3e280edeb688", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "center_values_003112"}, "id": "code_003112_center_values_003112", "license": "Apache-2.0", "prompt": "Write a Python function center_values_003112(values) that subtracts the arithmetic mean from each value and returns a new list. Raise ValueError for an empty input. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "center_values_003112"}, "verifier": {"function": "center_values_003112", "tests": ["out = center_values_003112([1, 2, 3]); assert out == [-1, 0, 1]", "assert center_values_003112([5]) == [0]", "try:\n    center_values_003112([])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: rate_constant, number_of_steps.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"rate_constant\", \"number_of_steps\"]}", "dedupe_signature": "498fcb257114a21228f66fe0200386e4561fb122d366bbf70e26eab6cdd0b50e", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["rate_constant", "number_of_steps"]}, "id": "abstain_003113_rate_constant_number_of_steps", "license": "Apache-2.0", "prompt": "Use explicit Euler for dy/dt = -k y. The prompt gives y(0)=31 and h=1.95, but omits both k and the number of steps. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: rate_constant, number_of_steps.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["rate_constant", "number_of_steps"]}, "verifier": {"missing": ["rate_constant", "number_of_steps"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 1.05 kg and a = 14.95 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 15.6975, \"unit\": \"N\"}", "dedupe_signature": "18f665b930df29a758174ea7c1ebe97078e09e8c349f9777b419a5becb2ce23e", "difficulty": "easy", "final_answer": {"answer": 15.6975, "unit": "N"}, "id": "force_003114_1.05_14.95", "license": "Apache-2.0", "prompt": "A cart has mass 1.05 kg and measured acceleration 14.95 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 1.05 kg and a = 14.95 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 14.95, "mass": 1.05}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 18.75^2 and multiply by 0.5 * 21.35.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 3752.9297, \"unit\": \"J\"}", "dedupe_signature": "48432f83896e0f9a2d1ff17fe4dd51f281fb623b5c1cc13a46e68fe7bdf40602", "difficulty": "easy", "final_answer": {"answer": 3752.9297, "unit": "J"}, "id": "ke_003115_21.35_18.75", "license": "Apache-2.0", "prompt": "A body of mass 21.35 kg moves at 18.75 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 18.75^2 and multiply by 0.5 * 21.35.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 21.35, "velocity": 18.75}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=43 degrees through the sine of 2 theta.\n3. Substitute v=45.6 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 211.447, \"unit\": \"m\"}", "dedupe_signature": "33e92fb0cc8d3766d90dedcf6ee9fc13cd961bfa4d238acf85203ed0ccc51e7e", "difficulty": "medium", "final_answer": {"answer": 211.447, "unit": "m"}, "id": "projectile_range_003116_45.6_43", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 45.6 m/s and angle 43 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=43 degrees through the sine of 2 theta.\nSubstitute v=45.6 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 43, "gravity": 9.81, "speed": 45.6}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 50 * 2.89 * 82.\nFinal: {\"answer\": 11849.0, \"unit\": \"J\"}", "dedupe_signature": "b79c6f53d59868db746d78155678ffe19442788abbad03c45a3a7607232da44e", "difficulty": "easy", "final_answer": {"answer": 11849.0, "unit": "J"}, "id": "heat_q_003118_50_2.89_82", "license": "Apache-2.0", "prompt": "A 50 g sample has specific heat 2.89 J/(g*K). How much heat is needed to raise its temperature by 82 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 50 * 2.89 * 82.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 82, "heat_capacity": 2.89, "mass_g": 50}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=168.4 V and R=50.6 ohm.\nFinal: {\"answer\": 560.4458, \"unit\": \"W\"}", "dedupe_signature": "8f44b4bf8ab4f93502bac5c78e92a2e5af444220821136b3f1677f3f5f19e38a", "difficulty": "easy", "final_answer": {"answer": 560.4458, "unit": "W"}, "id": "ohm_power_003119_168.4_50.6", "license": "Apache-2.0", "prompt": "A resistor has resistance 50.6 ohm and voltage 168.4 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=168.4 V and R=50.6 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 50.6, "voltage": 168.4}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=783 mg, t=312.5 h, and T_half=63.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 25.8413, \"unit\": \"mg\"}", "dedupe_signature": "16d5e0b747b0662a4bf076713ea039a928e33acc9c524e83ef925a719d2300c8", "difficulty": "medium", "final_answer": {"answer": 25.8413, "unit": "mg"}, "id": "half_life_003120_783_63.5_312.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 783 mg. Its half-life is 63.5 hours. How many mg remain after 312.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=783 mg, t=312.5 h, and T_half=63.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 312.5, "half_life": 63.5, "initial_amount": 783.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 1155 mL to 1.155 L.\n3. Compute M = 2.36 / 1.155.\nFinal: {\"answer\": 2.0433, \"unit\": \"mol/L\"}", "dedupe_signature": "b893c4ca50a1cbad73d0c9b6126847205800614ae7c54e01da0c99e2085d9b86", "difficulty": "medium", "final_answer": {"answer": 2.0433, "unit": "mol/L"}, "id": "molarity_003122_2.36_1155", "license": "Apache-2.0", "prompt": "A solution contains 2.36 mol of solute in 1155 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 1155 mL to 1.155 L.\nCompute M = 2.36 / 1.155.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 2.36, "volume_ml": 1155}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.93 y, so each step multiplies y by 1 - h*0.93.\n3. Apply that update for 12 steps and round the final state.\nFinal: {\"answer\": 0.0001, \"unit\": \"state_units\"}", "dedupe_signature": "0652f877ef548ff5716901eab120e7c502afd8a95c13146e12dcabf3cb86718c", "difficulty": "medium", "final_answer": {"answer": 0.0001, "unit": "state_units"}, "id": "euler_decay_003123_17.5_0.93_1.45_12", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.93 y with y(0)=17.5, step size h=1.45, for 12 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.93 y, so each step multiplies y by 1 - h*0.93.\nApply that update for 12 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 17.5, "rate": 0.93, "step": 1.45, "steps": 12}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(0.7)=-2.72 and f(4)=-24.5.\n3. The interval width is 3.3.\nFinal: {\"answer\": -44.913, \"unit\": \"area_units\"}", "dedupe_signature": "fd4559c075c28e0076cc4db42d12086bfe9e3499f40493c0c9090331487b56c8", "difficulty": "medium", "final_answer": {"answer": -44.913, "unit": "area_units"}, "id": "trapz_linear_003124_-6.6_1.9_0.7_4", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-6.6x+1.9 from x=0.7 to x=4. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(0.7)=-2.72 and f(4)=-24.5.\nThe interval width is 3.3.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 1.9, "slope": -6.6, "x0": 0.7, "x1": 4.0}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.28 and add it to the current value.\nFinal: {\"answer\": [0.556, -0.352, 0.506], \"unit\": \"temperature_units\"}", "dedupe_signature": "b2f1c7d372ef19332c530f22db79482061e392329c34e04034c6d96c007c33ac", "difficulty": "hard", "final_answer": {"answer": [0.556, -0.352, 0.506], "unit": "temperature_units"}, "id": "heat_step_003125_0.28_2.5_0.85_-1.85_0.8_2.4", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=2.5, right=2.4; current interior values are [0.85, -1.85, 0.8]. Use r=0.28. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.28 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [0.85, -1.85, 0.8], "left": 2.5, "r": 0.28, "right": 2.4}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=306 degrees and keep the unit as newtons.\nFinal: {\"answer\": [165.4615, -227.7383], \"unit\": \"N\"}", "dedupe_signature": "f45c95f657c19644335c0e0319aea8270ac919092edde00717d3651605c6ab09", "difficulty": "medium", "final_answer": {"answer": [165.4615, -227.7383], "unit": "N"}, "id": "vector_components_003127_281.5_306", "license": "Apache-2.0", "prompt": "A vector has magnitude 281.5 N at 306 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=306 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 306, "magnitude": 281.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [0.35, 13.5], \"unit\": \"dimensionless\"}", "dedupe_signature": "5b7df501fb9bc559a103427b4214ed84624d3875e20280ae9554f8578eab2c3e", "difficulty": "medium", "final_answer": {"answer": [0.35, 13.5], "unit": "dimensionless"}, "id": "line_two_point_003128_12.25_22.25_0.35_13.5", "license": "Apache-2.0", "prompt": "A line passes through points (12.25, 17.7875) and (22.25, 21.2875). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 12.25, "x2": 22.25, "y1": 17.7875, "y2": 21.2875}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. speed squared over acceleration has units of meters\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "dd4a5a95194f3f03cf606c1402182800a88c2905b1bb1797533aa37944febd67", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_003129_consistent_741d4e34_3024", "license": "Apache-2.0", "prompt": "In instrument manual case 3024, check dimensional consistency for R = v^2 * sin(theta) / g. The left side has dimensions m and the right side has dimensions m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nspeed squared over acceleration has units of meters\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "R = v^2 * sin(theta) / g"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef normalize_003130(values):\n    total = sum(values)\n    if total == 0:\n        raise ValueError('cannot normalize zero-sum values')\n    return [v / total for v in values]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"normalize_003130\"}", "dedupe_signature": "ff8fe71908748dfb36d781bd34041768d3b61bf91dc1861f243260a58045e1bb", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "normalize_003130"}, "id": "code_003130_normalize_003130", "license": "Apache-2.0", "prompt": "Write a Python function normalize_003130(values) that returns a new list whose values sum to 1. Raise ValueError if the sum is zero. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "normalize_003130"}, "verifier": {"function": "normalize_003130", "tests": ["out = normalize_003130([2, 3, 5]); assert len(out) == 3", "assert abs(sum(normalize_003130([2, 3, 5])) - 1.0) < 1e-12", "assert normalize_003130([1, 1]) == [0.5, 0.5]", "try:\n    normalize_003130([1, -1])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 20.75 kg and a = 2.1 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 43.575, \"unit\": \"N\"}", "dedupe_signature": "5ce1bbffe6de240c8eb7f4769656633b95772db4cbb0b463e2bd83d5826319f8", "difficulty": "easy", "final_answer": {"answer": 43.575, "unit": "N"}, "id": "force_003132_20.75_2.1", "license": "Apache-2.0", "prompt": "A cart has mass 20.75 kg and measured acceleration 2.1 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 20.75 kg and a = 2.1 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 2.1, "mass": 20.75}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 3.2^2 and multiply by 0.5 * 22.85.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 116.992, \"unit\": \"J\"}", "dedupe_signature": "1e40ae373d292f38e90e3a70aa52c63ddc1fc326bb4a059a7ed382e7c8aec739", "difficulty": "easy", "final_answer": {"answer": 116.992, "unit": "J"}, "id": "ke_003133_22.85_3.2", "license": "Apache-2.0", "prompt": "A body of mass 22.85 kg moves at 3.2 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 3.2^2 and multiply by 0.5 * 22.85.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 22.85, "velocity": 3.2}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=28 degrees through the sine of 2 theta.\n3. Substitute v=37 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 115.6934, \"unit\": \"m\"}", "dedupe_signature": "a6a87d99c1e5e303d0b0e249661199fe8fbe6e07dbac527579329c790fd7ffd9", "difficulty": "medium", "final_answer": {"answer": 115.6934, "unit": "m"}, "id": "projectile_range_003134_37_28", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 37 m/s and angle 28 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=28 degrees through the sine of 2 theta.\nSubstitute v=37 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 28, "gravity": 9.81, "speed": 37.0}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 4.75 * 8.314 * 593 / 5.8.\nFinal: {\"answer\": 4037.6654, \"unit\": \"kPa\"}", "dedupe_signature": "e744177ed8d506cfa6ab53446c854896aa312f16beeb08eac23789c30da2839b", "difficulty": "medium", "final_answer": {"answer": 4037.6654, "unit": "kPa"}, "id": "ideal_gas_003135_4.75_593_5.8", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=4.75 mol, T=593 K, and V=5.8 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 4.75 * 8.314 * 593 / 5.8.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 4.75, "temp_k": 593, "volume_l": 5.8}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1000 * 2.65 * 10.\nFinal: {\"answer\": 26500.0, \"unit\": \"J\"}", "dedupe_signature": "2a913e0811c6ab44b255705b52760b9dc9ef7f33dff4d5712b9a3555f753f6d1", "difficulty": "easy", "final_answer": {"answer": 26500.0, "unit": "J"}, "id": "heat_q_003136_1000_2.65_10", "license": "Apache-2.0", "prompt": "A 1000 g sample has specific heat 2.65 J/(g*K). How much heat is needed to raise its temperature by 10 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1000 * 2.65 * 10.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 10, "heat_capacity": 2.65, "mass_g": 1000}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 3.35 mol * 180.156 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 603.5226, \"unit\": \"g\"}", "dedupe_signature": "3147cfd39728f7bc7825e67e97dbf36701cfc82245528a2e1549d094b02c928d", "difficulty": "medium", "final_answer": {"answer": 603.5226, "unit": "g"}, "id": "stoich_mass_003139_glucose_3.35", "license": "Apache-2.0", "prompt": "A sample contains 3.35 mol of glucose. Using molar mass 180.156 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 3.35 mol * 180.156 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "glucose", "molar_mass": 180.156, "moles": 3.35}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 940 mL to 0.94 L.\n3. Compute M = 3 / 0.94.\nFinal: {\"answer\": 3.1915, \"unit\": \"mol/L\"}", "dedupe_signature": "734c931dca0073268b642370f0bdaa469ca6992c608fd1f0a786f29379b7e739", "difficulty": "medium", "final_answer": {"answer": 3.1915, "unit": "mol/L"}, "id": "molarity_003140_3_940", "license": "Apache-2.0", "prompt": "A solution contains 3 mol of solute in 940 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 940 mL to 0.94 L.\nCompute M = 3 / 0.94.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 3.0, "volume_ml": 940}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.55 y, so each step multiplies y by 1 - h*0.55.\n3. Apply that update for 6 steps and round the final state.\nFinal: {\"answer\": 24.1036, \"unit\": \"state_units\"}", "dedupe_signature": "f16ddfa81dba64679996893f9f867aea41e81a73b7658373ff3b63edc11a061a", "difficulty": "medium", "final_answer": {"answer": 24.1036, "unit": "state_units"}, "id": "euler_decay_003141_48.5_0.55_0.2_6", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.55 y with y(0)=48.5, step size h=0.2, for 6 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.55 y, so each step multiplies y by 1 - h*0.55.\nApply that update for 6 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 48.5, "rate": 0.55, "step": 0.2, "steps": 6}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.36 and add it to the current value.\nFinal: {\"answer\": [0.996, 1.082, -0.438], \"unit\": \"temperature_units\"}", "dedupe_signature": "c6ba575bcd31b39795119105a9fa385a5e309625b14032a09a96846304b511a5", "difficulty": "hard", "final_answer": {"answer": [0.996, 1.082, -0.438], "unit": "temperature_units"}, "id": "heat_step_003143_0.36_-1.0_2.85_1.55_-1.05_-1.95", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-1, right=-1.95; current interior values are [2.85, 1.55, -1.05]. Use r=0.36. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.36 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [2.85, 1.55, -1.05], "left": -1.0, "r": 0.36, "right": -1.95}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 36999.0 / 1000.\nFinal: {\"answer\": 36.999, \"unit\": \"kg\"}", "dedupe_signature": "8d3f8fbff084d64d85f120d25b16512ce9ef11bf5baa408bf4f8dcfb89ae1202", "difficulty": "easy", "final_answer": {"answer": 36.999, "unit": "kg"}, "id": "unit_convert_003144_g_to_kg_36999", "license": "Apache-2.0", "prompt": "Convert 36999 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 36999.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 36999.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=198 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-389.9332, -126.697], \"unit\": \"N\"}", "dedupe_signature": "64848080843e21020db94c2ad6c84ecd8152bfe8bba10135dd8dfcba15f07c87", "difficulty": "medium", "final_answer": {"answer": [-389.9332, -126.697], "unit": "N"}, "id": "vector_components_003145_410_198", "license": "Apache-2.0", "prompt": "A vector has magnitude 410 N at 198 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=198 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 198, "magnitude": 410.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. density times acceleration times height gives kg/(m*s^2), or pascal\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "b499c54b9b6edda3e26804e45cb0a32be8897e7e746ba6662261e8ff95b27249", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_003147_consistent_b7d3eed1_120274", "license": "Apache-2.0", "prompt": "In lab notebook case 120274, check dimensional consistency for p = rho * g * h. The left side has dimensions Pa and the right side has dimensions Pa. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\ndensity times acceleration times height gives kg/(m*s^2), or pascal\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "p = rho * g * h"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef threshold_flags_003148(values, threshold):\n    return [value >= threshold for value in values]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"threshold_flags_003148\"}", "dedupe_signature": "ed184bae002028dd4906decc9b1261354bb1343dad6087c5225235e984ead36d", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "threshold_flags_003148"}, "id": "code_003148_threshold_flags_003148", "license": "Apache-2.0", "prompt": "Write a Python function threshold_flags_003148(values, threshold) that returns a list of booleans showing whether each value is greater than or equal to threshold. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "threshold_flags_003148"}, "verifier": {"function": "threshold_flags_003148", "tests": ["assert threshold_flags_003148([1, 2, 3], 2) == [False, True, True]", "assert threshold_flags_003148([], 5) == []", "assert threshold_flags_003148([-1, 0], 0) == [False, True]"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: launch_angle_or_vertical_velocity.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"launch_angle_or_vertical_velocity\"]}", "dedupe_signature": "0746bb41501ee2991cb75727d0d750566f52685fad0cc379cd93cb3db5e05e8a", "difficulty": "easy", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["launch_angle_or_vertical_velocity"]}, "id": "abstain_003149_launch_angle_or_vertical_velocity", "license": "Apache-2.0", "prompt": "Compute projectile range on level ground. The prompt gives initial speed 55.8 m/s but does not give launch angle or vertical velocity. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: launch_angle_or_vertical_velocity.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["launch_angle_or_vertical_velocity"]}, "verifier": {"missing": ["launch_angle_or_vertical_velocity"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 1.6 kg and a = 4.7 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 7.52, \"unit\": \"N\"}", "dedupe_signature": "01afeb8a90fbeb0fba52922b8e039614f7497583e72706bc9317c5fe0c1e237e", "difficulty": "easy", "final_answer": {"answer": 7.52, "unit": "N"}, "id": "force_003150_1.6_4.7", "license": "Apache-2.0", "prompt": "A cart has mass 1.6 kg and measured acceleration 4.7 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 1.6 kg and a = 4.7 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 4.7, "mass": 1.6}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 33.35^2 and multiply by 0.5 * 19.55.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 10871.9749, \"unit\": \"J\"}", "dedupe_signature": "459afa87b3bb10b8256ba82fca812a60c1236599a0af696ff74ca62693519a5e", "difficulty": "easy", "final_answer": {"answer": 10871.9749, "unit": "J"}, "id": "ke_003151_19.55_33.35", "license": "Apache-2.0", "prompt": "A body of mass 19.55 kg moves at 33.35 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 33.35^2 and multiply by 0.5 * 19.55.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 19.55, "velocity": 33.35}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=68 degrees through the sine of 2 theta.\n3. Substitute v=63.4 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 284.6301, \"unit\": \"m\"}", "dedupe_signature": "d46b75ed723701284e43de438ddbdeaf5a785a9afc8edcfaf6e71d9ab7d44a74", "difficulty": "medium", "final_answer": {"answer": 284.6301, "unit": "m"}, "id": "projectile_range_003152_63.4_68", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 63.4 m/s and angle 68 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=68 degrees through the sine of 2 theta.\nSubstitute v=63.4 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 68, "gravity": 9.81, "speed": 63.4}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 5.92 * 8.314 * 527 / 106.5.\nFinal: {\"answer\": 243.5526, \"unit\": \"kPa\"}", "dedupe_signature": "1b64ef7931a771fa1e370f5eba8ce4fc576fc8e59fa5ac1e7a87e3c962e46586", "difficulty": "medium", "final_answer": {"answer": 243.5526, "unit": "kPa"}, "id": "ideal_gas_003153_5.92_527_106.5", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=5.92 mol, T=527 K, and V=106.5 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 5.92 * 8.314 * 527 / 106.5.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 5.92, "temp_k": 527, "volume_l": 106.5}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1895 * 2.745 * 17.\nFinal: {\"answer\": 88430.175, \"unit\": \"J\"}", "dedupe_signature": "da0ae9b984df1d0dd99a78278e3e3ea193249d6522d69bdae826543fd668e3fb", "difficulty": "easy", "final_answer": {"answer": 88430.175, "unit": "J"}, "id": "heat_q_003154_1895_2.745_17", "license": "Apache-2.0", "prompt": "A 1895 g sample has specific heat 2.745 J/(g*K). How much heat is needed to raise its temperature by 17 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1895 * 2.745 * 17.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 17, "heat_capacity": 2.745, "mass_g": 1895}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=611 mg, t=170.5 h, and T_half=59.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 83.8351, \"unit\": \"mg\"}", "dedupe_signature": "a93fd2ada0a558ebb3432700370556e991a66b9b2fcf3933e1b9b3c5939bf4ff", "difficulty": "medium", "final_answer": {"answer": 83.8351, "unit": "mg"}, "id": "half_life_003156_611_59.5_170.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 611 mg. Its half-life is 59.5 hours. How many mg remain after 170.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=611 mg, t=170.5 h, and T_half=59.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 170.5, "half_life": 59.5, "initial_amount": 611.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 3.05 mol * 100.087 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 305.2654, \"unit\": \"g\"}", "dedupe_signature": "7326c3bccbb6fa1dc3065bf1e06fee2e1b6f61211b2ef1012f678123e2236f2e", "difficulty": "medium", "final_answer": {"answer": 305.2654, "unit": "g"}, "id": "stoich_mass_003157_calcium_carbonate_3.05", "license": "Apache-2.0", "prompt": "A sample contains 3.05 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 3.05 mol * 100.087 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "calcium carbonate", "molar_mass": 100.087, "moles": 3.05}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.93 y, so each step multiplies y by 1 - h*0.93.\n3. Apply that update for 7 steps and round the final state.\nFinal: {\"answer\": -26.4425, \"unit\": \"state_units\"}", "dedupe_signature": "137c3360f2ce18b0088807c0601722b1a50387a9d4843fcdf75f4bd34b63ff07", "difficulty": "medium", "final_answer": {"answer": -26.4425, "unit": "state_units"}, "id": "euler_decay_003159_76_0.93_2_7", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.93 y with y(0)=76, step size h=2, for 7 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.93 y, so each step multiplies y by 1 - h*0.93.\nApply that update for 7 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 76.0, "rate": 0.93, "step": 2.0, "steps": 7}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kelvin equals Celsius plus 273.15.\n2. Apply the conversion factor directly to the given value.\n3. Compute 18.0 + 273.15.\nFinal: {\"answer\": 291.15, \"unit\": \"K\"}", "dedupe_signature": "f0370b82e885fcd38052773c9736ab700b6766f1cbc41d52c90eb303d77b71b9", "difficulty": "easy", "final_answer": {"answer": 291.15, "unit": "K"}, "id": "unit_convert_003162_c_to_k_18", "license": "Apache-2.0", "prompt": "Convert 18 degC to K. Return the converted value with unit.", "reasoning_trace": "Kelvin equals Celsius plus 273.15.\nApply the conversion factor directly to the given value.\nCompute 18.0 + 273.15.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 18.0}, "verifier": {"formula": "value + 273.15", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=236 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-176.4254, -261.5614], \"unit\": \"N\"}", "dedupe_signature": "2f3c4bb2d3621ea10c85940eeed735125e90681d0492be6b7e3d8dde14546b22", "difficulty": "medium", "final_answer": {"answer": [-176.4254, -261.5614], "unit": "N"}, "id": "vector_components_003163_315.5_236", "license": "Apache-2.0", "prompt": "A vector has magnitude 315.5 N at 236 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=236 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 236, "magnitude": 315.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [8.45, 1.25], \"unit\": \"dimensionless\"}", "dedupe_signature": "0bb327b2cef419eafc71faa7f4637a09ef575c5c4d1b97a1b406fc07caf1b4a4", "difficulty": "medium", "final_answer": {"answer": [8.45, 1.25], "unit": "dimensionless"}, "id": "line_two_point_003164_13.5_22.25_8.45_1.25", "license": "Apache-2.0", "prompt": "A line passes through points (13.5, 115.325) and (22.25, 189.262). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 13.5, "x2": 22.25, "y1": 115.32499999999999, "y2": 189.2625}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef weighted_sum_003166(values, weights):\n    if len(values) != len(weights):\n        raise ValueError('length mismatch')\n    return sum(value * weight for value, weight in zip(values, weights))\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"weighted_sum_003166\"}", "dedupe_signature": "3c470d96a176a1ec8f9ff413390f16c3785fafbf637f9bce8b30305459099186", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "weighted_sum_003166"}, "id": "code_003166_weighted_sum_003166", "license": "Apache-2.0", "prompt": "Write a Python function weighted_sum_003166(values, weights) that returns sum(value*weight). Raise ValueError when the two inputs have different lengths. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "weighted_sum_003166"}, "verifier": {"function": "weighted_sum_003166", "tests": ["assert weighted_sum_003166([2, 3], [4, 5]) == 23", "assert weighted_sum_003166([], []) == 0", "try:\n    weighted_sum_003166([1], [1, 2])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: left_boundary, right_boundary.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"left_boundary\", \"right_boundary\"]}", "dedupe_signature": "81275aae356ba3000491c609e8ab6a400215299bd5bcf78c1d1880aa0bf45fd1", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["left_boundary", "right_boundary"]}, "id": "abstain_003167_left_boundary_right_boundary", "license": "Apache-2.0", "prompt": "Solve the 1D heat equation after one finite-difference step. The prompt gives r=0.28 and interior values [-1.45, 1.75, -0.6], but gives no boundary values. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: left_boundary, right_boundary.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["left_boundary", "right_boundary"]}, "verifier": {"missing": ["left_boundary", "right_boundary"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 8.95 kg and a = 10 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 89.5, \"unit\": \"N\"}", "dedupe_signature": "27b3621b01a9d6723fe43b14a727d30d0763d94dbbc54380a928318a7f5fc1cc", "difficulty": "easy", "final_answer": {"answer": 89.5, "unit": "N"}, "id": "force_003168_8.95_10", "license": "Apache-2.0", "prompt": "A cart has mass 8.95 kg and measured acceleration 10 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 8.95 kg and a = 10 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 10.0, "mass": 8.95}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=23 degrees through the sine of 2 theta.\n3. Substitute v=71.1 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 370.6844, \"unit\": \"m\"}", "dedupe_signature": "b60bb6f63db1d8129582e77e1b20656a373c22b3de0df2088fdeb0e6122c20f6", "difficulty": "medium", "final_answer": {"answer": 370.6844, "unit": "m"}, "id": "projectile_range_003170_71.1_23", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 71.1 m/s and angle 23 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=23 degrees through the sine of 2 theta.\nSubstitute v=71.1 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 23, "gravity": 9.81, "speed": 71.1}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1520 * 2.315 * 76.\nFinal: {\"answer\": 267428.8, \"unit\": \"J\"}", "dedupe_signature": "4632b0503123399379d956f14fda593575e42a883ff035a99ffb1b1853fbe490", "difficulty": "easy", "final_answer": {"answer": 267428.8, "unit": "J"}, "id": "heat_q_003172_1520_2.315_76", "license": "Apache-2.0", "prompt": "A 1520 g sample has specific heat 2.315 J/(g*K). How much heat is needed to raise its temperature by 76 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1520 * 2.315 * 76.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 76, "heat_capacity": 2.315, "mass_g": 1520}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=592.5 mg, t=306.5 h, and T_half=68 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 26.0519, \"unit\": \"mg\"}", "dedupe_signature": "8c983128b1dda5a94664ec8af56fdc8ef4c6b044cbd795b62d705de7875e9f17", "difficulty": "medium", "final_answer": {"answer": 26.0519, "unit": "mg"}, "id": "half_life_003174_592.5_68_306.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 592.5 mg. Its half-life is 68 hours. How many mg remain after 306.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=592.5 mg, t=306.5 h, and T_half=68 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 306.5, "half_life": 68.0, "initial_amount": 592.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 3.58 mol * 100.087 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 358.3115, \"unit\": \"g\"}", "dedupe_signature": "773f6fd980ec087b20e643e3ea2db0a1f69cdf1b2344c00dc9ffab64001611a6", "difficulty": "medium", "final_answer": {"answer": 358.3115, "unit": "g"}, "id": "stoich_mass_003175_calcium_carbonate_3.58", "license": "Apache-2.0", "prompt": "A sample contains 3.58 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 3.58 mol * 100.087 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "calcium carbonate", "molar_mass": 100.087, "moles": 3.58}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 4035 mL to 4.035 L.\n3. Compute M = 0.365 / 4.035.\nFinal: {\"answer\": 0.0905, \"unit\": \"mol/L\"}", "dedupe_signature": "357e58763364245d04a1d5049f0c4ba964db5db22e4db046989a81b41fec1521", "difficulty": "medium", "final_answer": {"answer": 0.0905, "unit": "mol/L"}, "id": "molarity_003176_0.365_4035", "license": "Apache-2.0", "prompt": "A solution contains 0.365 mol of solute in 4035 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 4035 mL to 4.035 L.\nCompute M = 0.365 / 4.035.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 0.365, "volume_ml": 4035}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.59 y, so each step multiplies y by 1 - h*0.59.\n3. Apply that update for 8 steps and round the final state.\nFinal: {\"answer\": 0.9154, \"unit\": \"state_units\"}", "dedupe_signature": "2dca38f44fd234e4817cd2cc172eb41b5de1a1a7292085f765b7d69bb6c69aa3", "difficulty": "medium", "final_answer": {"answer": 0.9154, "unit": "state_units"}, "id": "euler_decay_003177_15_0.59_0.5_8", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.59 y with y(0)=15, step size h=0.5, for 8 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.59 y, so each step multiplies y by 1 - h*0.59.\nApply that update for 8 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 15.0, "rate": 0.59, "step": 0.5, "steps": 8}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(3.9)=1.31 and f(5.4)=8.66.\n3. The interval width is 1.5.\nFinal: {\"answer\": 7.4775, \"unit\": \"area_units\"}", "dedupe_signature": "55bdaf22bab4aa0552a5e74091b15efe0a1bfbc478e45d0825e4294e72ee62d1", "difficulty": "medium", "final_answer": {"answer": 7.4775, "unit": "area_units"}, "id": "trapz_linear_003178_4.9_-17.8_3.9_5.4", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=4.9x+-17.8 from x=3.9 to x=5.4. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(3.9)=1.31 and f(5.4)=8.66.\nThe interval width is 1.5.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -17.8, "slope": 4.9, "x0": 3.9, "x1": 5.4}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.22 and add it to the current value.\nFinal: {\"answer\": [0.76, -0.055, 0.539], \"unit\": \"temperature_units\"}", "dedupe_signature": "14c81361f050ebd18300fb7c2b3f85e75b2eedf97583c747935440029acd1f20", "difficulty": "hard", "final_answer": {"answer": [0.76, -0.055, 0.539], "unit": "temperature_units"}, "id": "heat_step_003179_0.22_0.65_1.75_-1.65_2.2_-1.5", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=0.65, right=-1.5; current interior values are [1.75, -1.65, 2.2]. Use r=0.22. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.22 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [1.75, -1.65, 2.2], "left": 0.65, "r": 0.22, "right": -1.5}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=257 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-2.5869, -11.2053], \"unit\": \"N\"}", "dedupe_signature": "b63a9cd79a85ccb778cc253b227fc92bc50c320fd83c2879e2a328741e2d2ba5", "difficulty": "medium", "final_answer": {"answer": [-2.5869, -11.2053], "unit": "N"}, "id": "vector_components_003181_11.5_257", "license": "Apache-2.0", "prompt": "A vector has magnitude 11.5 N at 257 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=257 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 257, "magnitude": 11.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. coulomb per second is ampere\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "4f9d54375007221abb2244b1f83f776300749260e2b34a9a3f726ae996d0d8b5", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_003183_consistent_8b38953d_265775", "license": "Apache-2.0", "prompt": "In field worksheet case 265775, check dimensional consistency for I = Q / t. The left side has dimensions A and the right side has dimensions A. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\ncoulomb per second is ampere\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "I = Q / t"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef threshold_flags_003184(values, threshold):\n    return [value >= threshold for value in values]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"threshold_flags_003184\"}", "dedupe_signature": "53a3dc2eae64aa8a8c154bfa4e0c26e34ea716b92886433072493f70878e489c", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "threshold_flags_003184"}, "id": "code_003184_threshold_flags_003184", "license": "Apache-2.0", "prompt": "Write a Python function threshold_flags_003184(values, threshold) that returns a list of booleans showing whether each value is greater than or equal to threshold. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "threshold_flags_003184"}, "verifier": {"function": "threshold_flags_003184", "tests": ["assert threshold_flags_003184([1, 2, 3], 2) == [False, True, True]", "assert threshold_flags_003184([], 5) == []", "assert threshold_flags_003184([-1, 0], 0) == [False, True]"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: launch_angle_or_vertical_velocity.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"launch_angle_or_vertical_velocity\"]}", "dedupe_signature": "709ad23a7301894e01e4d4f6ec20c4125605b9dd80d062af3d55e0079e3e394a", "difficulty": "easy", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["launch_angle_or_vertical_velocity"]}, "id": "abstain_003185_launch_angle_or_vertical_velocity", "license": "Apache-2.0", "prompt": "Compute projectile range on level ground. The prompt gives initial speed 78.9 m/s but does not give launch angle or vertical velocity. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: launch_angle_or_vertical_velocity.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["launch_angle_or_vertical_velocity"]}, "verifier": {"missing": ["launch_angle_or_vertical_velocity"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 27.65^2 and multiply by 0.5 * 20.7.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 7912.8079, \"unit\": \"J\"}", "dedupe_signature": "629e0509f4d3eef2abf63217b5892739cea344d87a51323559753fea32cbb8ad", "difficulty": "easy", "final_answer": {"answer": 7912.8079, "unit": "J"}, "id": "ke_003187_20.7_27.65", "license": "Apache-2.0", "prompt": "A body of mass 20.7 kg moves at 27.65 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 27.65^2 and multiply by 0.5 * 20.7.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 20.7, "velocity": 27.65}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=51 degrees through the sine of 2 theta.\n3. Substitute v=9.6 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 9.1892, \"unit\": \"m\"}", "dedupe_signature": "23c402aee889c221e0a1399faa05bb88bef862b2fc05d35e27e2cba1674b7dcf", "difficulty": "medium", "final_answer": {"answer": 9.1892, "unit": "m"}, "id": "projectile_range_003188_9.6_51", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 9.6 m/s and angle 51 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=51 degrees through the sine of 2 theta.\nSubstitute v=9.6 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 51, "gravity": 9.81, "speed": 9.6}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 1.84 * 8.314 * 535 / 87.4.\nFinal: {\"answer\": 93.6419, \"unit\": \"kPa\"}", "dedupe_signature": "c29d545925ec453fbfdc612acfd6d6aeb563e9e18798becdf3f0960efc86cfa0", "difficulty": "medium", "final_answer": {"answer": 93.6419, "unit": "kPa"}, "id": "ideal_gas_003189_1.84_535_87.4", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=1.84 mol, T=535 K, and V=87.4 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 1.84 * 8.314 * 535 / 87.4.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 1.84, "temp_k": 535, "volume_l": 87.4}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1555 * 2.63 * 100.\nFinal: {\"answer\": 408965.0, \"unit\": \"J\"}", "dedupe_signature": "6b81fedbebd75d257f6d5f00b22b2126ab8836bef34a76fe78e63921417c4b93", "difficulty": "easy", "final_answer": {"answer": 408965.0, "unit": "J"}, "id": "heat_q_003190_1555_2.63_100", "license": "Apache-2.0", "prompt": "A 1555 g sample has specific heat 2.63 J/(g*K). How much heat is needed to raise its temperature by 100 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1555 * 2.63 * 100.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 100, "heat_capacity": 2.63, "mass_g": 1555}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=10.3 V and R=155.8 ohm.\nFinal: {\"answer\": 0.6809, \"unit\": \"W\"}", "dedupe_signature": "df50b10eee672eab614fa0c34dcf08f25649eeb0a76d70111f9128f858bb15df", "difficulty": "easy", "final_answer": {"answer": 0.6809, "unit": "W"}, "id": "ohm_power_003191_10.3_155.8", "license": "Apache-2.0", "prompt": "A resistor has resistance 155.8 ohm and voltage 10.3 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=10.3 V and R=155.8 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 155.8, "voltage": 10.3}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=83.5 mg, t=308 h, and T_half=23 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 0.0078, \"unit\": \"mg\"}", "dedupe_signature": "0553a3540964899dc4cb6eee2d4c5f62a92d7aa136893ea16247bfec8ed2a6f6", "difficulty": "medium", "final_answer": {"answer": 0.0078, "unit": "mg"}, "id": "half_life_003192_83.5_23_308", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 83.5 mg. Its half-life is 23 hours. How many mg remain after 308 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=83.5 mg, t=308 h, and T_half=23 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 308.0, "half_life": 23.0, "initial_amount": 83.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 0.92 mol * 18.015 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 16.5738, \"unit\": \"g\"}", "dedupe_signature": "8016c55c2a415d58df61bde521c31ca507879a450504202ad58c4b7a5c93924f", "difficulty": "medium", "final_answer": {"answer": 16.5738, "unit": "g"}, "id": "stoich_mass_003193_water_0.92", "license": "Apache-2.0", "prompt": "A sample contains 0.92 mol of water. Using molar mass 18.015 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 0.92 mol * 18.015 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "water", "molar_mass": 18.015, "moles": 0.92}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 1475 mL to 1.475 L.\n3. Compute M = 4.66 / 1.475.\nFinal: {\"answer\": 3.1593, \"unit\": \"mol/L\"}", "dedupe_signature": "22ecd2b7703a09672f67d4529c355ae7eee4dd4be8ad009c9e54cf26a1593d17", "difficulty": "medium", "final_answer": {"answer": 3.1593, "unit": "mol/L"}, "id": "molarity_003194_4.66_1475", "license": "Apache-2.0", "prompt": "A solution contains 4.66 mol of solute in 1475 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 1475 mL to 1.475 L.\nCompute M = 4.66 / 1.475.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 4.66, "volume_ml": 1475}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.48 and add it to the current value.\nFinal: {\"answer\": [0.456, -0.338, -0.292], \"unit\": \"temperature_units\"}", "dedupe_signature": "0428f80f84a855238e9e366927daffb42c4e54c4fd8eebedc1b2b1203e1e8e22", "difficulty": "hard", "final_answer": {"answer": [0.456, -0.338, -0.292], "unit": "temperature_units"}, "id": "heat_step_003197_0.48_1.05_-0.6_-0.05_-0.1_-0.55", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.05, right=-0.55; current interior values are [-0.6, -0.05, -0.1]. Use r=0.48. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.48 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-0.6, -0.05, -0.1], "left": 1.05, "r": 0.48, "right": -0.55}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 31118.0 / 1000.\nFinal: {\"answer\": 31.118, \"unit\": \"kg\"}", "dedupe_signature": "1a0e06e824ea1405fec65d44f46c569c8f0424d72641ec23e13ecf434b264f60", "difficulty": "easy", "final_answer": {"answer": 31.118, "unit": "kg"}, "id": "unit_convert_003198_g_to_kg_31118", "license": "Apache-2.0", "prompt": "Convert 31118 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 31118.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 31118.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-5.9, 2.0], \"unit\": \"dimensionless\"}", "dedupe_signature": "d22e7b9491fdfd5729b3d88febf89f80a1b61db1c9f56e4f94bb46ba355d7221", "difficulty": "medium", "final_answer": {"answer": [-5.9, 2.0], "unit": "dimensionless"}, "id": "line_two_point_003200_9.25_17_-5.9_2", "license": "Apache-2.0", "prompt": "A line passes through points (9.25, -52.575) and (17, -98.3). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 9.25, "x2": 17.0, "y1": -52.575, "y2": -98.30000000000001}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. amount times volume is not concentration\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "0d7c4d88d15f181ba84bdc5dd3dff1e431dace4ad31dcd85f319e14d806b1fb4", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_003201_inconsistent_74ac0b02_672739", "license": "Apache-2.0", "prompt": "In student derivation case 672739, check dimensional consistency for C = n * V. The left side has dimensions mol/L and the right side has dimensions mol*L. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\namount times volume is not concentration\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "C = n * V"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef center_values_003202(values):\n    if not values:\n        raise ValueError('center_values requires at least one value')\n    mean = sum(values) / len(values)\n    return [value - mean for value in values]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"center_values_003202\"}", "dedupe_signature": "97cee78bfd2a77ff47f57e72b81b473cbdb89f1a1e26dbecd4a79920534bdb13", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "center_values_003202"}, "id": "code_003202_center_values_003202", "license": "Apache-2.0", "prompt": "Write a Python function center_values_003202(values) that subtracts the arithmetic mean from each value and returns a new list. Raise ValueError for an empty input. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "center_values_003202"}, "verifier": {"function": "center_values_003202", "tests": ["out = center_values_003202([1, 2, 3]); assert out == [-1, 0, 1]", "assert center_values_003202([5]) == [0]", "try:\n    center_values_003202([])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: target_schema, valid_examples.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"target_schema\", \"valid_examples\"]}", "dedupe_signature": "462eb6da648a301871ffdb594e770143a3541f10ee33905546b6083a258d60af", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["target_schema", "valid_examples"]}, "id": "abstain_003203_target_schema_valid_examples", "license": "Apache-2.0", "prompt": "Write a parser that converts each mobile sensor record from batch 850165 into the correct schema, but the prompt does not include the target schema or examples. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: target_schema, valid_examples.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["target_schema", "valid_examples"]}, "verifier": {"missing": ["target_schema", "valid_examples"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 24.5 kg and a = 10.4 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 254.8, \"unit\": \"N\"}", "dedupe_signature": "24f129773774d6c1e72d03e0d76db41a26b45dadf64990bde5c4a14c5820a05e", "difficulty": "easy", "final_answer": {"answer": 254.8, "unit": "N"}, "id": "force_003204_24.5_10.4", "license": "Apache-2.0", "prompt": "A cart has mass 24.5 kg and measured acceleration 10.4 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 24.5 kg and a = 10.4 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 10.4, "mass": 24.5}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=42 degrees through the sine of 2 theta.\n3. Substitute v=62.9 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 401.0944, \"unit\": \"m\"}", "dedupe_signature": "8538909e4d30e640562b977bb10a74ab3eb1e6d4cc94cdb89dc6d52721dfee6d", "difficulty": "medium", "final_answer": {"answer": 401.0944, "unit": "m"}, "id": "projectile_range_003206_62.9_42", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 62.9 m/s and angle 42 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=42 degrees through the sine of 2 theta.\nSubstitute v=62.9 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 42, "gravity": 9.81, "speed": 62.9}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1170 * 0.605 * 75.\nFinal: {\"answer\": 53088.75, \"unit\": \"J\"}", "dedupe_signature": "e38d31f222672218f2071c791f7ff4582261823cecefc4f5406ea4d06067cc3d", "difficulty": "easy", "final_answer": {"answer": 53088.75, "unit": "J"}, "id": "heat_q_003208_1170_0.605_75", "license": "Apache-2.0", "prompt": "A 1170 g sample has specific heat 0.605 J/(g*K). How much heat is needed to raise its temperature by 75 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1170 * 0.605 * 75.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 75, "heat_capacity": 0.605, "mass_g": 1170}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=59.1 V and R=3.2 ohm.\nFinal: {\"answer\": 1091.5031, \"unit\": \"W\"}", "dedupe_signature": "bfd4029f36559886b4810963308a732cb9a30e917b2e672552ad10c7bb4510ad", "difficulty": "easy", "final_answer": {"answer": 1091.5031, "unit": "W"}, "id": "ohm_power_003209_59.1_3.2", "license": "Apache-2.0", "prompt": "A resistor has resistance 3.2 ohm and voltage 59.1 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=59.1 V and R=3.2 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 3.2, "voltage": 59.1}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=16 mg, t=126.5 h, and T_half=45 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 2.2798, \"unit\": \"mg\"}", "dedupe_signature": "500e4062b770c18f3b982be664969f7b51c6778be44c9a026ac2144ea326ec9f", "difficulty": "medium", "final_answer": {"answer": 2.2798, "unit": "mg"}, "id": "half_life_003210_16_45_126.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 16 mg. Its half-life is 45 hours. How many mg remain after 126.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=16 mg, t=126.5 h, and T_half=45 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 126.5, "half_life": 45.0, "initial_amount": 16.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 2290 mL to 2.29 L.\n3. Compute M = 0.485 / 2.29.\nFinal: {\"answer\": 0.2118, \"unit\": \"mol/L\"}", "dedupe_signature": "22f1a08f45278fd2acd826e0a99c1f43cf5ae1c74fa56b341abb7f213879062a", "difficulty": "medium", "final_answer": {"answer": 0.2118, "unit": "mol/L"}, "id": "molarity_003212_0.485_2290", "license": "Apache-2.0", "prompt": "A solution contains 0.485 mol of solute in 2290 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 2290 mL to 2.29 L.\nCompute M = 0.485 / 2.29.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 0.485, "volume_ml": 2290}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(9.3)=-53.81 and f(11.5)=-61.95.\n3. The interval width is 2.2.\nFinal: {\"answer\": -127.336, \"unit\": \"area_units\"}", "dedupe_signature": "9ce0a86ad0775d0abb6e63beaaf729b13b04a462efafe5da04e661a833e7883b", "difficulty": "medium", "final_answer": {"answer": -127.336, "unit": "area_units"}, "id": "trapz_linear_003214_-3.7_-19.4_9.3_11.5", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-3.7x+-19.4 from x=9.3 to x=11.5. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(9.3)=-53.81 and f(11.5)=-61.95.\nThe interval width is 2.2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -19.4, "slope": -3.7, "x0": 9.3, "x1": 11.5}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.28 and add it to the current value.\nFinal: {\"answer\": [1.336, 0.834, 0.448], \"unit\": \"temperature_units\"}", "dedupe_signature": "d7c968c92f4144b1d53132236bb46d00384f4bedaf680fb0b78319687f01cf8b", "difficulty": "hard", "final_answer": {"answer": [1.336, 0.834, 0.448], "unit": "temperature_units"}, "id": "heat_step_003215_0.28_2.15_0.3_2.15_-0.7_0.55", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=2.15, right=0.55; current interior values are [0.3, 2.15, -0.7]. Use r=0.28. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.28 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [0.3, 2.15, -0.7], "left": 2.15, "r": 0.28, "right": 0.55}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kelvin equals Celsius plus 273.15.\n2. Apply the conversion factor directly to the given value.\n3. Compute -36.5 + 273.15.\nFinal: {\"answer\": 236.65, \"unit\": \"K\"}", "dedupe_signature": "18433f99e49120f310bc15983c7d42e51b21b172c17ea75a71874d0efdd1142c", "difficulty": "easy", "final_answer": {"answer": 236.65, "unit": "K"}, "id": "unit_convert_003216_c_to_k_-36.5", "license": "Apache-2.0", "prompt": "Convert -36.5 degC to K. Return the converted value with unit.", "reasoning_trace": "Kelvin equals Celsius plus 273.15.\nApply the conversion factor directly to the given value.\nCompute -36.5 + 273.15.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": -36.5}, "verifier": {"formula": "value + 273.15", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=31 degrees and keep the unit as newtons.\nFinal: {\"answer\": [202.2915, 121.549], \"unit\": \"N\"}", "dedupe_signature": "8d7323a08cda1b59562c69ee08f1c08c341cae69ac28e06e246aa6cccf878313", "difficulty": "medium", "final_answer": {"answer": [202.2915, 121.549], "unit": "N"}, "id": "vector_components_003217_236_31", "license": "Apache-2.0", "prompt": "A vector has magnitude 236 N at 31 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=31 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 31, "magnitude": 236.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-1.2, 15.75], \"unit\": \"dimensionless\"}", "dedupe_signature": "ce72196ed52ff74aaa5142da8ba453938f1279e61c699cf1e924613bd893b784", "difficulty": "medium", "final_answer": {"answer": [-1.2, 15.75], "unit": "dimensionless"}, "id": "line_two_point_003218_12.5_15_-1.2_15.75", "license": "Apache-2.0", "prompt": "A line passes through points (12.5, 0.75) and (15, -2.25). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 12.5, "x2": 15.0, "y1": 0.75, "y2": -2.25}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. grams cancel with J/(g*K), and kelvin cancels, leaving joules\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "b80aa4840b2588032c3ec2db1403f685b36ff45c3e6b5bc15df475a3699333f8", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_003219_consistent_4153435f_824079", "license": "Apache-2.0", "prompt": "In instrument manual case 824079, check dimensional consistency for Q = m * c * DeltaT. The left side has dimensions J and the right side has dimensions J. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\ngrams cancel with J/(g*K), and kelvin cancels, leaving joules\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "Q = m * c * DeltaT"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef weighted_sum_003220(values, weights):\n    if len(values) != len(weights):\n        raise ValueError('length mismatch')\n    return sum(value * weight for value, weight in zip(values, weights))\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"weighted_sum_003220\"}", "dedupe_signature": "76e2ebec4a82cf973ad64a30623c33d3fa3b78946aeaabb797e6292b351fe194", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "weighted_sum_003220"}, "id": "code_003220_weighted_sum_003220", "license": "Apache-2.0", "prompt": "Write a Python function weighted_sum_003220(values, weights) that returns sum(value*weight). Raise ValueError when the two inputs have different lengths. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "weighted_sum_003220"}, "verifier": {"function": "weighted_sum_003220", "tests": ["assert weighted_sum_003220([2, 3], [4, 5]) == 23", "assert weighted_sum_003220([], []) == 0", "try:\n    weighted_sum_003220([1], [1, 2])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 17.95 kg and a = 2.45 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 43.9775, \"unit\": \"N\"}", "dedupe_signature": "aaf2131ee4697f0ed056514af8d6849932538fd061f08ca4c5543a297b540e12", "difficulty": "easy", "final_answer": {"answer": 43.9775, "unit": "N"}, "id": "force_003222_17.95_2.45", "license": "Apache-2.0", "prompt": "A cart has mass 17.95 kg and measured acceleration 2.45 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 17.95 kg and a = 2.45 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 2.45, "mass": 17.95}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 30.6^2 and multiply by 0.5 * 21.55.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 10089.279, \"unit\": \"J\"}", "dedupe_signature": "f8638dab6a78c6ce85346a3f9f789a40cc7b0d8cd405865bf4ed285122c9db3f", "difficulty": "easy", "final_answer": {"answer": 10089.279, "unit": "J"}, "id": "ke_003223_21.55_30.6", "license": "Apache-2.0", "prompt": "A body of mass 21.55 kg moves at 30.6 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 30.6^2 and multiply by 0.5 * 21.55.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 21.55, "velocity": 30.6}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 2000 * 0.83 * 119.\nFinal: {\"answer\": 197540.0, \"unit\": \"J\"}", "dedupe_signature": "58210ef17ba834579e735f6bd1be4f04770ee3601acfc54eef0edd8d2405ffd3", "difficulty": "easy", "final_answer": {"answer": 197540.0, "unit": "J"}, "id": "heat_q_003226_2000_0.83_119", "license": "Apache-2.0", "prompt": "A 2000 g sample has specific heat 0.83 J/(g*K). How much heat is needed to raise its temperature by 119 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 2000 * 0.83 * 119.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 119, "heat_capacity": 0.83, "mass_g": 2000}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=235.1 V and R=44.3 ohm.\nFinal: {\"answer\": 1247.6752, \"unit\": \"W\"}", "dedupe_signature": "5ad16ac0ab6ca6d0ecf044919976a089d1a48446a5ded97ca9bc73238d53da99", "difficulty": "easy", "final_answer": {"answer": 1247.6752, "unit": "W"}, "id": "ohm_power_003227_235.1_44.3", "license": "Apache-2.0", "prompt": "A resistor has resistance 44.3 ohm and voltage 235.1 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=235.1 V and R=44.3 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 44.3, "voltage": 235.1}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=394.5 mg, t=35 h, and T_half=109 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 315.781, \"unit\": \"mg\"}", "dedupe_signature": "172dca7f04a2fb0c2dfdf9dc7e42934f57b444503df276d4f29804ced6511cbc", "difficulty": "medium", "final_answer": {"answer": 315.781, "unit": "mg"}, "id": "half_life_003228_394.5_109_35", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 394.5 mg. Its half-life is 109 hours. How many mg remain after 35 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=394.5 mg, t=35 h, and T_half=109 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 35.0, "half_life": 109.0, "initial_amount": 394.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.48 y, so each step multiplies y by 1 - h*0.48.\n3. Apply that update for 11 steps and round the final state.\nFinal: {\"answer\": 0.0059, \"unit\": \"state_units\"}", "dedupe_signature": "57b02f59d88a96e9e4a998859a836386e117b1c516bed22373bd3ce60d87c3f1", "difficulty": "medium", "final_answer": {"answer": 0.0059, "unit": "state_units"}, "id": "euler_decay_003231_73.5_0.48_1.2_11", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.48 y with y(0)=73.5, step size h=1.2, for 11 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.48 y, so each step multiplies y by 1 - h*0.48.\nApply that update for 11 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 73.5, "rate": 0.48, "step": 1.2, "steps": 11}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 6354.0 / 1000.\nFinal: {\"answer\": 6.354, \"unit\": \"kg\"}", "dedupe_signature": "e782e85fe25dfca7ecdc949fcc5f3b94373f2cda04d7bd78911c3f1da24703c8", "difficulty": "easy", "final_answer": {"answer": 6.354, "unit": "kg"}, "id": "unit_convert_003234_g_to_kg_6354", "license": "Apache-2.0", "prompt": "Convert 6354 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 6354.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 6354.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. energy divided by length is force, not spring constant\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "91757b949abb6ce580f12a6bb4bb57b44f8d0f309caab5eda9ec4401e18c5e28", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_003237_inconsistent_56040f5d_438247", "license": "Apache-2.0", "prompt": "In quality-control check case 438247, check dimensional consistency for k = E / x. The left side has dimensions N/m and the right side has dimensions J/m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nenergy divided by length is force, not spring constant\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "k = E / x"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef threshold_flags_003238(values, threshold):\n    return [value >= threshold for value in values]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"threshold_flags_003238\"}", "dedupe_signature": "a16a48174f690b83469c7b781cf1cb40c5f1113ebd5c5aceaf8343aee3203ed6", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "threshold_flags_003238"}, "id": "code_003238_threshold_flags_003238", "license": "Apache-2.0", "prompt": "Write a Python function threshold_flags_003238(values, threshold) that returns a list of booleans showing whether each value is greater than or equal to threshold. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "threshold_flags_003238"}, "verifier": {"function": "threshold_flags_003238", "tests": ["assert threshold_flags_003238([1, 2, 3], 2) == [False, True, True]", "assert threshold_flags_003238([], 5) == []", "assert threshold_flags_003238([-1, 0], 0) == [False, True]"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: rate_constant, number_of_steps.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"rate_constant\", \"number_of_steps\"]}", "dedupe_signature": "84fd9e0dc827ff1596d2211a6f9ffd38f987d4ac85637faf737079dec63e58f4", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["rate_constant", "number_of_steps"]}, "id": "abstain_003239_rate_constant_number_of_steps", "license": "Apache-2.0", "prompt": "Use explicit Euler for dy/dt = -k y. The prompt gives y(0)=24 and h=1.2, but omits both k and the number of steps. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: rate_constant, number_of_steps.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["rate_constant", "number_of_steps"]}, "verifier": {"missing": ["rate_constant", "number_of_steps"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 9.15^2 and multiply by 0.5 * 20.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 837.225, \"unit\": \"J\"}", "dedupe_signature": "c75d868d6e7f64ce2e39b0b3f1ea0e08e195d35613e59ccd5771f250d319aa8d", "difficulty": "easy", "final_answer": {"answer": 837.225, "unit": "J"}, "id": "ke_003241_20_9.15", "license": "Apache-2.0", "prompt": "A body of mass 20 kg moves at 9.15 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 9.15^2 and multiply by 0.5 * 20.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 20.0, "velocity": 9.15}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=84 degrees through the sine of 2 theta.\n3. Substitute v=56.1 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 66.7015, \"unit\": \"m\"}", "dedupe_signature": "74adc7580c7bdbc3fbea8d8d5e55180c713b6ad64171a65de0bf92a69ed2296e", "difficulty": "medium", "final_answer": {"answer": 66.7015, "unit": "m"}, "id": "projectile_range_003242_56.1_84", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 56.1 m/s and angle 84 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=84 degrees through the sine of 2 theta.\nSubstitute v=56.1 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 84, "gravity": 9.81, "speed": 56.1}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 0.4 * 8.314 * 552 / 8.6.\nFinal: {\"answer\": 213.4571, \"unit\": \"kPa\"}", "dedupe_signature": "603d9e2dcd82740c8a191aebc1b80f5a2304c8f3767dae69341fa50f9dc78a58", "difficulty": "medium", "final_answer": {"answer": 213.4571, "unit": "kPa"}, "id": "ideal_gas_003243_0.4_552_8.6", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=0.4 mol, T=552 K, and V=8.6 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 0.4 * 8.314 * 552 / 8.6.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 0.4, "temp_k": 552, "volume_l": 8.6}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=471 mg, t=247 h, and T_half=42 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 7.9924, \"unit\": \"mg\"}", "dedupe_signature": "bdff0a3765feda32c3a34f71582ad5769c988b73437af5db056d7507bef78ae9", "difficulty": "medium", "final_answer": {"answer": 7.9924, "unit": "mg"}, "id": "half_life_003246_471_42_247", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 471 mg. Its half-life is 42 hours. How many mg remain after 247 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=471 mg, t=247 h, and T_half=42 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 247.0, "half_life": 42.0, "initial_amount": 471.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 1.06 mol * 44.01 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 46.6506, \"unit\": \"g\"}", "dedupe_signature": "fce808f0574017258ba1185f8048569cc582d4397bf528045bf3a68555ce4402", "difficulty": "medium", "final_answer": {"answer": 46.6506, "unit": "g"}, "id": "stoich_mass_003247_carbon_dioxide_1.06", "license": "Apache-2.0", "prompt": "A sample contains 1.06 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 1.06 mol * 44.01 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "carbon dioxide", "molar_mass": 44.01, "moles": 1.06}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 4925 mL to 4.925 L.\n3. Compute M = 2.485 / 4.925.\nFinal: {\"answer\": 0.5046, \"unit\": \"mol/L\"}", "dedupe_signature": "03057663188b205e330953b62c9c80ec11d026b7388e1c75fac57c87b93511e0", "difficulty": "medium", "final_answer": {"answer": 0.5046, "unit": "mol/L"}, "id": "molarity_003248_2.485_4925", "license": "Apache-2.0", "prompt": "A solution contains 2.485 mol of solute in 4925 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 4925 mL to 4.925 L.\nCompute M = 2.485 / 4.925.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 2.485, "volume_ml": 4925}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.41 y, so each step multiplies y by 1 - h*0.41.\n3. Apply that update for 3 steps and round the final state.\nFinal: {\"answer\": 29.3939, \"unit\": \"state_units\"}", "dedupe_signature": "31902c58bea84bf84fbd5b5380e4eedf2cffaa8b155bf6626c60fc119da447b0", "difficulty": "medium", "final_answer": {"answer": 29.3939, "unit": "state_units"}, "id": "euler_decay_003249_58.5_0.41_0.5_3", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.41 y with y(0)=58.5, step size h=0.5, for 3 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.41 y, so each step multiplies y by 1 - h*0.41.\nApply that update for 3 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 58.5, "rate": 0.41, "step": 0.5, "steps": 3}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(0.1)=-18.56 and f(8.9)=-23.84.\n3. The interval width is 8.8.\nFinal: {\"answer\": -186.56, \"unit\": \"area_units\"}", "dedupe_signature": "876477b5b08d5037b5b3337e3a5b91db5f4bcfb07e71e38d8c9940b581a88b45", "difficulty": "medium", "final_answer": {"answer": -186.56, "unit": "area_units"}, "id": "trapz_linear_003250_-0.6_-18.5_0.1_8.9", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-0.6x+-18.5 from x=0.1 to x=8.9. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(0.1)=-18.56 and f(8.9)=-23.84.\nThe interval width is 8.8.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -18.5, "slope": -0.6, "x0": 0.1, "x1": 8.9}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.28 and add it to the current value.\nFinal: {\"answer\": [-0.282, 0.28, 0.486], \"unit\": \"temperature_units\"}", "dedupe_signature": "f6e870d4aeaf353f352ea5194f163a21028ad6fe13c58b38771652564c0e5880", "difficulty": "hard", "final_answer": {"answer": [-0.282, 0.28, 0.486], "unit": "temperature_units"}, "id": "heat_step_003251_0.28_-1.65_1.3_-1.4_1.9_0.15", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-1.65, right=0.15; current interior values are [1.3, -1.4, 1.9]. Use r=0.28. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.28 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [1.3, -1.4, 1.9], "left": -1.65, "r": 0.28, "right": 0.15}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=126 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-187.2096, 257.6719], \"unit\": \"N\"}", "dedupe_signature": "900b84adb0f51734bcdef0bda58c525ce3b7f4b429b9f970c59cbd19ba1336aa", "difficulty": "medium", "final_answer": {"answer": [-187.2096, 257.6719], "unit": "N"}, "id": "vector_components_003253_318.5_126", "license": "Apache-2.0", "prompt": "A vector has magnitude 318.5 N at 126 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=126 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 126, "magnitude": 318.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. grams cancel with J/(g*K), and kelvin cancels, leaving joules\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "ce0aeeef09e788735c85a2070d82ac9377fc29c5e476906706645205f5f37f2c", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_003255_consistent_4153435f_685333", "license": "Apache-2.0", "prompt": "In sensor calibration case 685333, check dimensional consistency for Q = m * c * DeltaT. The left side has dimensions J and the right side has dimensions J. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\ngrams cancel with J/(g*K), and kelvin cancels, leaving joules\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "Q = m * c * DeltaT"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\nimport math\n\ndef unit_vector_003256(x, y):\n    norm = math.hypot(x, y)\n    if norm == 0:\n        raise ValueError('zero vector has no direction')\n    return (x / norm, y / norm)\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"unit_vector_003256\"}", "dedupe_signature": "1820f9708283abe8a9442dce1eca4b938eed72bbaf4a6718e118098eb460b1f9", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "unit_vector_003256"}, "id": "code_003256_unit_vector_003256", "license": "Apache-2.0", "prompt": "Write a Python function unit_vector_003256(x, y) that returns the 2D unit vector as a tuple. Raise ValueError for the zero vector. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "unit_vector_003256"}, "verifier": {"function": "unit_vector_003256", "tests": ["ux, uy = unit_vector_003256(3, 4); assert abs(ux - 0.6) < 1e-12 and abs(uy - 0.8) < 1e-12", "assert unit_vector_003256(0, 5) == (0, 1)", "try:\n    unit_vector_003256(0, 0)\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: recurrence, objective, tie_breaking_rule.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"recurrence\", \"objective\", \"tie_breaking_rule\"]}", "dedupe_signature": "d9c448fb512c573e559a0405affb96520a7661d19062e847fb1a51e458f10134", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["recurrence", "objective", "tie_breaking_rule"]}, "id": "abstain_003257_recurrence_objective_tie_breaking_rule", "license": "Apache-2.0", "prompt": "Write a dynamic-programming solver for a allocation scoring problem with 1101 items and budget 58785, but the recurrence, objective, and tie-breaking rule are all absent. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: recurrence, objective, tie_breaking_rule.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["recurrence", "objective", "tie_breaking_rule"]}, "verifier": {"missing": ["recurrence", "objective", "tie_breaking_rule"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 24 kg and a = 0.2 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 4.8, \"unit\": \"N\"}", "dedupe_signature": "8deef0e06795844fbc8ae10c1ffa7b91bcc0bdc84696d4d434be2cf635669bd6", "difficulty": "easy", "final_answer": {"answer": 4.8, "unit": "N"}, "id": "force_003258_24_0.2", "license": "Apache-2.0", "prompt": "A cart has mass 24 kg and measured acceleration 0.2 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 24 kg and a = 0.2 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 0.2, "mass": 24.0}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 5.1^2 and multiply by 0.5 * 10.95.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 142.4047, \"unit\": \"J\"}", "dedupe_signature": "3ee0044ea8e7d7af8fb833eb19a4913884d61ecdbca5402fbbc67802cacf8004", "difficulty": "easy", "final_answer": {"answer": 142.4047, "unit": "J"}, "id": "ke_003259_10.95_5.1", "license": "Apache-2.0", "prompt": "A body of mass 10.95 kg moves at 5.1 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 5.1^2 and multiply by 0.5 * 10.95.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 10.95, "velocity": 5.1}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=12 degrees through the sine of 2 theta.\n3. Substitute v=17.6 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 12.8431, \"unit\": \"m\"}", "dedupe_signature": "a081f88300a0f182c6d002d4ea019bae853138a348bdbf1ddfb6faacfda4149c", "difficulty": "medium", "final_answer": {"answer": 12.8431, "unit": "m"}, "id": "projectile_range_003260_17.6_12", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 17.6 m/s and angle 12 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=12 degrees through the sine of 2 theta.\nSubstitute v=17.6 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 12, "gravity": 9.81, "speed": 17.6}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 1.19 * 8.314 * 599 / 71.8.\nFinal: {\"answer\": 82.539, \"unit\": \"kPa\"}", "dedupe_signature": "c09ed6001a22dd51b2a4bec08dcc77d2c1076f78251a209f6dff19d25069c52d", "difficulty": "medium", "final_answer": {"answer": 82.539, "unit": "kPa"}, "id": "ideal_gas_003261_1.19_599_71.8", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=1.19 mol, T=599 K, and V=71.8 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 1.19 * 8.314 * 599 / 71.8.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 1.19, "temp_k": 599, "volume_l": 71.8}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 935 * 3.515 * 111.\nFinal: {\"answer\": 364804.275, \"unit\": \"J\"}", "dedupe_signature": "cc0d99e43ec6ab6880d88d614863368ebdefdebb3bc654c3a9a42d55cc37f51c", "difficulty": "easy", "final_answer": {"answer": 364804.275, "unit": "J"}, "id": "heat_q_003262_935_3.515_111", "license": "Apache-2.0", "prompt": "A 935 g sample has specific heat 3.515 J/(g*K). How much heat is needed to raise its temperature by 111 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 935 * 3.515 * 111.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 111, "heat_capacity": 3.515, "mass_g": 935}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=237.2 V and R=97.6 ohm.\nFinal: {\"answer\": 576.4738, \"unit\": \"W\"}", "dedupe_signature": "a1b947681e0abc339f61cd616ec55a1ac2feb53574df5fe14e837408df700511", "difficulty": "easy", "final_answer": {"answer": 576.4738, "unit": "W"}, "id": "ohm_power_003263_237.2_97.6", "license": "Apache-2.0", "prompt": "A resistor has resistance 97.6 ohm and voltage 237.2 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=237.2 V and R=97.6 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 97.6, "voltage": 237.2}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=149.5 mg, t=268.5 h, and T_half=108 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 26.6838, \"unit\": \"mg\"}", "dedupe_signature": "fb4e6463d5f1b0f945ae697be240528f82915ee019aa4ced3e44990142974173", "difficulty": "medium", "final_answer": {"answer": 26.6838, "unit": "mg"}, "id": "half_life_003264_149.5_108_268.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 149.5 mg. Its half-life is 108 hours. How many mg remain after 268.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=149.5 mg, t=268.5 h, and T_half=108 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 268.5, "half_life": 108.0, "initial_amount": 149.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 2.59 mol * 180.156 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 466.604, \"unit\": \"g\"}", "dedupe_signature": "1475de46cfb9fc7d5efeb6cc000d8ffa021731f8126e7afe86602970506dff43", "difficulty": "medium", "final_answer": {"answer": 466.604, "unit": "g"}, "id": "stoich_mass_003265_glucose_2.59", "license": "Apache-2.0", "prompt": "A sample contains 2.59 mol of glucose. Using molar mass 180.156 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 2.59 mol * 180.156 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "glucose", "molar_mass": 180.156, "moles": 2.59}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 4660 mL to 4.66 L.\n3. Compute M = 1.835 / 4.66.\nFinal: {\"answer\": 0.3938, \"unit\": \"mol/L\"}", "dedupe_signature": "a78d92b3e2b6b9f62045d6cc992f4630d7d904542f0505f239bd49ae6ee41a57", "difficulty": "medium", "final_answer": {"answer": 0.3938, "unit": "mol/L"}, "id": "molarity_003266_1.835_4660", "license": "Apache-2.0", "prompt": "A solution contains 1.835 mol of solute in 4660 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 4660 mL to 4.66 L.\nCompute M = 1.835 / 4.66.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 1.835, "volume_ml": 4660}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.24 y, so each step multiplies y by 1 - h*0.24.\n3. Apply that update for 10 steps and round the final state.\nFinal: {\"answer\": 37.1834, \"unit\": \"state_units\"}", "dedupe_signature": "45e2b7ec110f1e82613d2ab0e3208970fbbb3833b6494c9c9e8d9a15181318a1", "difficulty": "medium", "final_answer": {"answer": 37.1834, "unit": "state_units"}, "id": "euler_decay_003267_78.5_0.24_0.3_10", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.24 y with y(0)=78.5, step size h=0.3, for 10 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.24 y, so each step multiplies y by 1 - h*0.24.\nApply that update for 10 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 78.5, "rate": 0.24, "step": 0.3, "steps": 10}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(7.1)=-46.6 and f(10)=-58.2.\n3. The interval width is 2.9.\nFinal: {\"answer\": -151.96, \"unit\": \"area_units\"}", "dedupe_signature": "1c6d999c8d6d790eb067d456b2ed9e53a8dc577abe57c74fc622d5d68ed9d128", "difficulty": "medium", "final_answer": {"answer": -151.96, "unit": "area_units"}, "id": "trapz_linear_003268_-4_-18.2_7.1_10", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-4x+-18.2 from x=7.1 to x=10. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(7.1)=-46.6 and f(10)=-58.2.\nThe interval width is 2.9.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -18.2, "slope": -4.0, "x0": 7.1, "x1": 10.0}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.22 and add it to the current value.\nFinal: {\"answer\": [-0.112, 0.142, 1.067], \"unit\": \"temperature_units\"}", "dedupe_signature": "75faf15aeb30f95139756e4bc7c5749d56e90acecffd04df3b1f623a189d15ba", "difficulty": "hard", "final_answer": {"answer": [-0.112, 0.142, 1.067], "unit": "temperature_units"}, "id": "heat_step_003269_0.22_2.9_-1.3_-0.1_2.2_-0.65", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=2.9, right=-0.65; current interior values are [-1.3, -0.1, 2.2]. Use r=0.22. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.22 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-1.3, -0.1, 2.2], "left": 2.9, "r": 0.22, "right": -0.65}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 100 centimeters in one meter.\n2. Apply the conversion factor directly to the given value.\n3. Compute 2138.5 / 100.\nFinal: {\"answer\": 21.385, \"unit\": \"m\"}", "dedupe_signature": "5a7e3b3a90c7d17caa3d85f14c7d068b69b07d3696493f75a93939a106dce4d9", "difficulty": "easy", "final_answer": {"answer": 21.385, "unit": "m"}, "id": "unit_convert_003270_cm_to_m_2138.5", "license": "Apache-2.0", "prompt": "Convert 2138.5 cm to m. Return the converted value with unit.", "reasoning_trace": "There are 100 centimeters in one meter.\nApply the conversion factor directly to the given value.\nCompute 2138.5 / 100.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 2138.5}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=314 degrees and keep the unit as newtons.\nFinal: {\"answer\": [36.4696, -37.7653], \"unit\": \"N\"}", "dedupe_signature": "460d6e9889b50f32dc8159b8f6574ed9b190acd016769edc5ebaf21f2ab2fe75", "difficulty": "medium", "final_answer": {"answer": [36.4696, -37.7653], "unit": "N"}, "id": "vector_components_003271_52.5_314", "license": "Apache-2.0", "prompt": "A vector has magnitude 52.5 N at 314 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=314 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 314, "magnitude": 52.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-4.25, 30.0], \"unit\": \"dimensionless\"}", "dedupe_signature": "d35fa07f740e1c33ee50adad2feea61aabd24eedc7a36e9db2107d7c81fe4d94", "difficulty": "medium", "final_answer": {"answer": [-4.25, 30.0], "unit": "dimensionless"}, "id": "line_two_point_003272_9.25_9.75_-4.25_30", "license": "Apache-2.0", "prompt": "A line passes through points (9.25, -9.3125) and (9.75, -11.4375). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 9.25, "x2": 9.75, "y1": -9.3125, "y2": -11.4375}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. speed squared over acceleration has units of meters\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "30bc55f5597074dc52c6003b7f59359bda5a2ed02efbfea4b9dff91951b190fe", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_003273_consistent_741d4e34_783226", "license": "Apache-2.0", "prompt": "In instrument manual case 783226, check dimensional consistency for R = v^2 * sin(theta) / g. The left side has dimensions m and the right side has dimensions m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nspeed squared over acceleration has units of meters\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "R = v^2 * sin(theta) / g"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: rate_constant, number_of_steps.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"rate_constant\", \"number_of_steps\"]}", "dedupe_signature": "0bdbcc99b03180d40f0ae99ee7130fb78d49e3c81536abd6b32428dc5e60fcc3", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["rate_constant", "number_of_steps"]}, "id": "abstain_003275_rate_constant_number_of_steps", "license": "Apache-2.0", "prompt": "Use explicit Euler for dy/dt = -k y. The prompt gives y(0)=65 and h=1.9, but omits both k and the number of steps. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: rate_constant, number_of_steps.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["rate_constant", "number_of_steps"]}, "verifier": {"missing": ["rate_constant", "number_of_steps"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 18.8 kg and a = 0.25 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 4.7, \"unit\": \"N\"}", "dedupe_signature": "064f81446bf101e556d1d2b00d0bbc964ab8a6dff9d3826cf1685402ff0ecd01", "difficulty": "easy", "final_answer": {"answer": 4.7, "unit": "N"}, "id": "force_003276_18.8_0.25", "license": "Apache-2.0", "prompt": "A cart has mass 18.8 kg and measured acceleration 0.25 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 18.8 kg and a = 0.25 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 0.25, "mass": 18.8}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 15.35^2 and multiply by 0.5 * 26.95.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 3175.0132, \"unit\": \"J\"}", "dedupe_signature": "5ff065a565b7fe3096f4acbf97c02e359e2ece71d2dc8721fa25ec343d30171f", "difficulty": "easy", "final_answer": {"answer": 3175.0132, "unit": "J"}, "id": "ke_003277_26.95_15.35", "license": "Apache-2.0", "prompt": "A body of mass 26.95 kg moves at 15.35 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 15.35^2 and multiply by 0.5 * 26.95.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 26.95, "velocity": 15.35}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=61 degrees through the sine of 2 theta.\n3. Substitute v=30.2 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 78.8434, \"unit\": \"m\"}", "dedupe_signature": "302d613bc16a4f09e610b619bd28d49f3887e65d25684b598b53afce5c85a90c", "difficulty": "medium", "final_answer": {"answer": 78.8434, "unit": "m"}, "id": "projectile_range_003278_30.2_61", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 30.2 m/s and angle 61 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=61 degrees through the sine of 2 theta.\nSubstitute v=30.2 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 61, "gravity": 9.81, "speed": 30.2}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1905 * 2.815 * 49.\nFinal: {\"answer\": 262766.175, \"unit\": \"J\"}", "dedupe_signature": "5808f6bce7e7b92bbe889c93238b37832c1a73bf1aaaaec758c4c522fa251b36", "difficulty": "easy", "final_answer": {"answer": 262766.175, "unit": "J"}, "id": "heat_q_003280_1905_2.815_49", "license": "Apache-2.0", "prompt": "A 1905 g sample has specific heat 2.815 J/(g*K). How much heat is needed to raise its temperature by 49 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1905 * 2.815 * 49.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 49, "heat_capacity": 2.815, "mass_g": 1905}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=107.2 V and R=119.3 ohm.\nFinal: {\"answer\": 96.3272, \"unit\": \"W\"}", "dedupe_signature": "507444aefc4f39a111ab8a816043c5639901bc6eabff4c1ea0148c0e95cdfa1e", "difficulty": "easy", "final_answer": {"answer": 96.3272, "unit": "W"}, "id": "ohm_power_003281_107.2_119.3", "license": "Apache-2.0", "prompt": "A resistor has resistance 119.3 ohm and voltage 107.2 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=107.2 V and R=119.3 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 119.3, "voltage": 107.2}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=477 mg, t=200.5 h, and T_half=77.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 79.3825, \"unit\": \"mg\"}", "dedupe_signature": "aaccceeed9823953beae5ed55709d3e6d49a547217d96e26ccd3e1aa9d998975", "difficulty": "medium", "final_answer": {"answer": 79.3825, "unit": "mg"}, "id": "half_life_003282_477_77.5_200.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 477 mg. Its half-life is 77.5 hours. How many mg remain after 200.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=477 mg, t=200.5 h, and T_half=77.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 200.5, "half_life": 77.5, "initial_amount": 477.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 7.4 mol * 58.44 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 432.456, \"unit\": \"g\"}", "dedupe_signature": "aeb4bf751eef4ba341cc7cef9b95a16431c10040a30c86142b0061bf69fa40e9", "difficulty": "medium", "final_answer": {"answer": 432.456, "unit": "g"}, "id": "stoich_mass_003283_sodium_chloride_7.4", "license": "Apache-2.0", "prompt": "A sample contains 7.4 mol of sodium chloride. Using molar mass 58.44 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 7.4 mol * 58.44 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "sodium chloride", "molar_mass": 58.44, "moles": 7.4}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 975 mL to 0.975 L.\n3. Compute M = 1.31 / 0.975.\nFinal: {\"answer\": 1.3436, \"unit\": \"mol/L\"}", "dedupe_signature": "5f4e13f112763b4e3035dc996f00834f0437cb396eda351778363381c4a9d017", "difficulty": "medium", "final_answer": {"answer": 1.3436, "unit": "mol/L"}, "id": "molarity_003284_1.31_975", "license": "Apache-2.0", "prompt": "A solution contains 1.31 mol of solute in 975 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 975 mL to 0.975 L.\nCompute M = 1.31 / 0.975.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 1.31, "volume_ml": 975}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.9 y, so each step multiplies y by 1 - h*0.9.\n3. Apply that update for 5 steps and round the final state.\nFinal: {\"answer\": 1.3594, \"unit\": \"state_units\"}", "dedupe_signature": "97d967b353c6a8293b33050b559277fae0dc99290687d99be1c1aed4780974b8", "difficulty": "medium", "final_answer": {"answer": 1.3594, "unit": "state_units"}, "id": "euler_decay_003285_66_0.9_0.6_5", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.9 y with y(0)=66, step size h=0.6, for 5 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.9 y, so each step multiplies y by 1 - h*0.9.\nApply that update for 5 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 66.0, "rate": 0.9, "step": 0.6, "steps": 5}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.34 and add it to the current value.\nFinal: {\"answer\": [-0.864, -0.271, 0.913], \"unit\": \"temperature_units\"}", "dedupe_signature": "567170945ee09bdf835e19f0d5c608c7289aaf662e4d92b0b271429f773549ce", "difficulty": "hard", "final_answer": {"answer": [-0.864, -0.271, 0.913], "unit": "temperature_units"}, "id": "heat_step_003287_0.34_-0.75_-1.85_-0.05_1.1_1.7", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-0.75, right=1.7; current interior values are [-1.85, -0.05, 1.1]. Use r=0.34. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.34 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-1.85, -0.05, 1.1], "left": -0.75, "r": 0.34, "right": 1.7}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 100 centimeters in one meter.\n2. Apply the conversion factor directly to the given value.\n3. Compute 4049.5 / 100.\nFinal: {\"answer\": 40.495, \"unit\": \"m\"}", "dedupe_signature": "553db4e1731ba6aca2572e8699cfc7b35f16617493e6f731e499f6706321f653", "difficulty": "easy", "final_answer": {"answer": 40.495, "unit": "m"}, "id": "unit_convert_003288_cm_to_m_4049.5", "license": "Apache-2.0", "prompt": "Convert 4049.5 cm to m. Return the converted value with unit.", "reasoning_trace": "There are 100 centimeters in one meter.\nApply the conversion factor directly to the given value.\nCompute 4049.5 / 100.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 4049.5}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=120 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-101.75, 176.2362], \"unit\": \"N\"}", "dedupe_signature": "52e4394aac8c6db08e78010b12cd87ed33b2aa703f4f8df0fe63c54e41945085", "difficulty": "medium", "final_answer": {"answer": [-101.75, 176.2362], "unit": "N"}, "id": "vector_components_003289_203.5_120", "license": "Apache-2.0", "prompt": "A vector has magnitude 203.5 N at 120 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=120 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 120, "magnitude": 203.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. velocity divided by time is acceleration\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "5752136bfd604bca79fd1292fdde84d6431c042f5a97afc33aaa2061b69f6ebb", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_003291_inconsistent_c1271127_76001", "license": "Apache-2.0", "prompt": "In sensor calibration case 76001, check dimensional consistency for x = v / t. The left side has dimensions m and the right side has dimensions m/s^2. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nvelocity divided by time is acceleration\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "x = v / t"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef clamp_003292(x, lo, hi):\n    if lo > hi:\n        raise ValueError('lo must be <= hi')\n    return min(max(x, lo), hi)\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"clamp_003292\"}", "dedupe_signature": "ce95f37dc0e69c4a4f0338d90a032045ea3e9358598323a926de550b26d9df9e", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "clamp_003292"}, "id": "code_003292_clamp_003292", "license": "Apache-2.0", "prompt": "Write a Python function clamp_003292(x, lo, hi) that clips x into the inclusive interval [lo, hi]. It must raise ValueError if lo > hi. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "clamp_003292"}, "verifier": {"function": "clamp_003292", "tests": ["assert clamp_003292(5, 0, 10) == 5", "assert clamp_003292(-2, 0, 10) == 0", "assert clamp_003292(12, 0, 10) == 10", "try:\n    clamp_003292(1, 3, 2)\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 20.2 kg and a = 0.25 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 5.05, \"unit\": \"N\"}", "dedupe_signature": "d16ec594d508a161038b08ba96c5839858e4a8d74ede6a26a5da5115757ae284", "difficulty": "easy", "final_answer": {"answer": 5.05, "unit": "N"}, "id": "force_003294_20.2_0.25", "license": "Apache-2.0", "prompt": "A cart has mass 20.2 kg and measured acceleration 0.25 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 20.2 kg and a = 0.25 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 0.25, "mass": 20.2}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 34^2 and multiply by 0.5 * 1.35.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 780.3, \"unit\": \"J\"}", "dedupe_signature": "2d6590d1cb9d9d48409134bfe1b904f73c629f9ea049b86ecf68664b2b85e0a2", "difficulty": "easy", "final_answer": {"answer": 780.3, "unit": "J"}, "id": "ke_003295_1.35_34", "license": "Apache-2.0", "prompt": "A body of mass 1.35 kg moves at 34 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 34^2 and multiply by 0.5 * 1.35.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 1.35, "velocity": 34.0}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=34 degrees through the sine of 2 theta.\n3. Substitute v=8 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 6.0489, \"unit\": \"m\"}", "dedupe_signature": "c5628ba771ce370d0bfc3259edc28230eaf1d462bd00c5097cab483214f0c491", "difficulty": "medium", "final_answer": {"answer": 6.0489, "unit": "m"}, "id": "projectile_range_003296_8_34", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 8 m/s and angle 34 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=34 degrees through the sine of 2 theta.\nSubstitute v=8 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 34, "gravity": 9.81, "speed": 8.0}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 0.87 * 8.314 * 282 / 28.5.\nFinal: {\"answer\": 71.5704, \"unit\": \"kPa\"}", "dedupe_signature": "5dc7fda971ea80ea149f5a6e8d96a971611d31fc1b65956cba6e57fb2710c836", "difficulty": "medium", "final_answer": {"answer": 71.5704, "unit": "kPa"}, "id": "ideal_gas_003297_0.87_282_28.5", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=0.87 mol, T=282 K, and V=28.5 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 0.87 * 8.314 * 282 / 28.5.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 0.87, "temp_k": 282, "volume_l": 28.5}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 40 * 0.75 * 115.\nFinal: {\"answer\": 3450.0, \"unit\": \"J\"}", "dedupe_signature": "20c1a90c202cd5d31b7830b524a25069e5bb54f043ff87df6de0123d9a79a93c", "difficulty": "easy", "final_answer": {"answer": 3450.0, "unit": "J"}, "id": "heat_q_003298_40_0.75_115", "license": "Apache-2.0", "prompt": "A 40 g sample has specific heat 0.75 J/(g*K). How much heat is needed to raise its temperature by 115 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 40 * 0.75 * 115.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 115, "heat_capacity": 0.75, "mass_g": 40}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=238.9 V and R=36.2 ohm.\nFinal: {\"answer\": 1576.608, \"unit\": \"W\"}", "dedupe_signature": "1b311424c84e41afd19429d2e02d72d15165d315d420373935b8369615f1b3fc", "difficulty": "easy", "final_answer": {"answer": 1576.608, "unit": "W"}, "id": "ohm_power_003299_238.9_36.2", "license": "Apache-2.0", "prompt": "A resistor has resistance 36.2 ohm and voltage 238.9 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=238.9 V and R=36.2 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 36.2, "voltage": 238.9}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=814 mg, t=39.5 h, and T_half=51.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 478.3407, \"unit\": \"mg\"}", "dedupe_signature": "bd8ee23ceed281d1da46681d84ebb379cc3741471630baffa33f778553b2fb67", "difficulty": "medium", "final_answer": {"answer": 478.3407, "unit": "mg"}, "id": "half_life_003300_814_51.5_39.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 814 mg. Its half-life is 51.5 hours. How many mg remain after 39.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=814 mg, t=39.5 h, and T_half=51.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 39.5, "half_life": 51.5, "initial_amount": 814.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 3.98 mol * 44.01 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 175.1598, \"unit\": \"g\"}", "dedupe_signature": "48b85371862c345558d37037b617e6ee15f9bc543ae59f41211a19056b8b65c3", "difficulty": "medium", "final_answer": {"answer": 175.1598, "unit": "g"}, "id": "stoich_mass_003301_carbon_dioxide_3.98", "license": "Apache-2.0", "prompt": "A sample contains 3.98 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 3.98 mol * 44.01 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "carbon dioxide", "molar_mass": 44.01, "moles": 3.98}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 115 mL to 0.115 L.\n3. Compute M = 1.535 / 0.115.\nFinal: {\"answer\": 13.3478, \"unit\": \"mol/L\"}", "dedupe_signature": "da91f88e90c962ab1e2f6a3948ec3af1f697cf30a00e0a3cbc070d0eb1473c2a", "difficulty": "medium", "final_answer": {"answer": 13.3478, "unit": "mol/L"}, "id": "molarity_003302_1.535_115", "license": "Apache-2.0", "prompt": "A solution contains 1.535 mol of solute in 115 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 115 mL to 0.115 L.\nCompute M = 1.535 / 0.115.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 1.535, "volume_ml": 115}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.39 y, so each step multiplies y by 1 - h*0.39.\n3. Apply that update for 9 steps and round the final state.\nFinal: {\"answer\": 3.0955, \"unit\": \"state_units\"}", "dedupe_signature": "9cc900420a615953d6ecc824249e5b513650c3e0025535a740f64de1184cb2b3", "difficulty": "medium", "final_answer": {"answer": 3.0955, "unit": "state_units"}, "id": "euler_decay_003303_43_0.39_0.65_9", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.39 y with y(0)=43, step size h=0.65, for 9 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.39 y, so each step multiplies y by 1 - h*0.39.\nApply that update for 9 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 43.0, "rate": 0.39, "step": 0.65, "steps": 9}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.06 and add it to the current value.\nFinal: {\"answer\": [-0.096, -0.048, 1.157], \"unit\": \"temperature_units\"}", "dedupe_signature": "03b7809bb5943db6363c59c73256f5181aa0498506225cab46c959fb7c0be99c", "difficulty": "hard", "final_answer": {"answer": [-0.096, -0.048, 1.157], "unit": "temperature_units"}, "id": "heat_step_003305_0.06_-1.45_0.0_-0.15_1.4_-1.1", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-1.45, right=-1.1; current interior values are [0.0, -0.15, 1.4]. Use r=0.06. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.06 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [0.0, -0.15, 1.4], "left": -1.45, "r": 0.06, "right": -1.1}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 4675.0 / 1000.\nFinal: {\"answer\": 4.675, \"unit\": \"kg\"}", "dedupe_signature": "bc1b02192cd44f270425b845dc38f38c7e60d369bd771958851972410c4cba79", "difficulty": "easy", "final_answer": {"answer": 4.675, "unit": "kg"}, "id": "unit_convert_003306_g_to_kg_4675", "license": "Apache-2.0", "prompt": "Convert 4675 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 4675.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 4675.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=109 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-87.415, 253.8717], \"unit\": \"N\"}", "dedupe_signature": "a6f6b51b1a1bc0884fc31491d9bc528f3f4435b6975d26f727522c13c61e84e7", "difficulty": "medium", "final_answer": {"answer": [-87.415, 253.8717], "unit": "N"}, "id": "vector_components_003307_268.5_109", "license": "Apache-2.0", "prompt": "A vector has magnitude 268.5 N at 109 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=109 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 109, "magnitude": 268.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-3.65, -29.25], \"unit\": \"dimensionless\"}", "dedupe_signature": "4f81db00e67a81c5ec34faae12b208e00472c986722837731f0a52a23f96f28a", "difficulty": "medium", "final_answer": {"answer": [-3.65, -29.25], "unit": "dimensionless"}, "id": "line_two_point_003308_18.25_30.5_-3.65_-29.25", "license": "Apache-2.0", "prompt": "A line passes through points (18.25, -95.8625) and (30.5, -140.575). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 18.25, "x2": 30.5, "y1": -95.8625, "y2": -140.575}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: recurrence, objective, tie_breaking_rule.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"recurrence\", \"objective\", \"tie_breaking_rule\"]}", "dedupe_signature": "b01f358db91fce407a5110341b282b1972cf76be279be6d95738980d94eae1cd", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["recurrence", "objective", "tie_breaking_rule"]}, "id": "abstain_003311_recurrence_objective_tie_breaking_rule", "license": "Apache-2.0", "prompt": "Write a dynamic-programming solver for a alignment scoring problem with 4503 items and budget 8290, but the recurrence, objective, and tie-breaking rule are all absent. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: recurrence, objective, tie_breaking_rule.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["recurrence", "objective", "tie_breaking_rule"]}, "verifier": {"missing": ["recurrence", "objective", "tie_breaking_rule"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 22.1 kg and a = 1.75 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 38.675, \"unit\": \"N\"}", "dedupe_signature": "4c04789d2186c8123b3a2ea0dbbd1b1ba68f074342fe4fcf5d1733d2f31ee7e7", "difficulty": "easy", "final_answer": {"answer": 38.675, "unit": "N"}, "id": "force_003312_22.1_1.75", "license": "Apache-2.0", "prompt": "A cart has mass 22.1 kg and measured acceleration 1.75 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 22.1 kg and a = 1.75 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 1.75, "mass": 22.1}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 13.45^2 and multiply by 0.5 * 14.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 1266.3175, \"unit\": \"J\"}", "dedupe_signature": "8b264c6d62bfaeb7af117486b521f84093f7b6446316313839b5acbedf253f0f", "difficulty": "easy", "final_answer": {"answer": 1266.3175, "unit": "J"}, "id": "ke_003313_14_13.45", "license": "Apache-2.0", "prompt": "A body of mass 14 kg moves at 13.45 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 13.45^2 and multiply by 0.5 * 14.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 14.0, "velocity": 13.45}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=56 degrees through the sine of 2 theta.\n3. Substitute v=58.5 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 323.4511, \"unit\": \"m\"}", "dedupe_signature": "f021e9ad830f7f0e31652a0ed112adc9271e13a509bc9a31ff5ad4d0cd177eee", "difficulty": "medium", "final_answer": {"answer": 323.4511, "unit": "m"}, "id": "projectile_range_003314_58.5_56", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 58.5 m/s and angle 56 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=56 degrees through the sine of 2 theta.\nSubstitute v=58.5 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 56, "gravity": 9.81, "speed": 58.5}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 235 * 4.135 * 107.\nFinal: {\"answer\": 103974.575, \"unit\": \"J\"}", "dedupe_signature": "a139abbb43a4ab3518e63139098991b59533098972c457e5bbac3197261e7e8a", "difficulty": "easy", "final_answer": {"answer": 103974.575, "unit": "J"}, "id": "heat_q_003316_235_4.135_107", "license": "Apache-2.0", "prompt": "A 235 g sample has specific heat 4.135 J/(g*K). How much heat is needed to raise its temperature by 107 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 235 * 4.135 * 107.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 107, "heat_capacity": 4.135, "mass_g": 235}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=684 mg, t=34.5 h, and T_half=106.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 546.436, \"unit\": \"mg\"}", "dedupe_signature": "48ca15d1f5a844a04ecc1a58efd1b0465c649009ee25782e4c568c73c47f7573", "difficulty": "medium", "final_answer": {"answer": 546.436, "unit": "mg"}, "id": "half_life_003318_684_106.5_34.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 684 mg. Its half-life is 106.5 hours. How many mg remain after 34.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=684 mg, t=34.5 h, and T_half=106.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 34.5, "half_life": 106.5, "initial_amount": 684.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 1.6 mol * 100.087 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 160.1392, \"unit\": \"g\"}", "dedupe_signature": "20a2842e02601d158a7c0ee6701dca98eda9fd20f766b5c78cf4a2d1f8a9893f", "difficulty": "medium", "final_answer": {"answer": 160.1392, "unit": "g"}, "id": "stoich_mass_003319_calcium_carbonate_1.6", "license": "Apache-2.0", "prompt": "A sample contains 1.6 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 1.6 mol * 100.087 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "calcium carbonate", "molar_mass": 100.087, "moles": 1.6}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 2040 mL to 2.04 L.\n3. Compute M = 4.72 / 2.04.\nFinal: {\"answer\": 2.3137, \"unit\": \"mol/L\"}", "dedupe_signature": "0aa008ddc4075107aace5140fe09542865290c5dfbbea2967ebd9f892718bd2e", "difficulty": "medium", "final_answer": {"answer": 2.3137, "unit": "mol/L"}, "id": "molarity_003320_4.72_2040", "license": "Apache-2.0", "prompt": "A solution contains 4.72 mol of solute in 2040 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 2040 mL to 2.04 L.\nCompute M = 4.72 / 2.04.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 4.72, "volume_ml": 2040}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.21 y, so each step multiplies y by 1 - h*0.21.\n3. Apply that update for 5 steps and round the final state.\nFinal: {\"answer\": 13.6826, \"unit\": \"state_units\"}", "dedupe_signature": "dfa21ee28c1d87cb15f93332b4f5e6aa6a88aa0a704ac8e2983a7bbaee283f0b", "difficulty": "medium", "final_answer": {"answer": 13.6826, "unit": "state_units"}, "id": "euler_decay_003321_39_0.21_0.9_5", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.21 y with y(0)=39, step size h=0.9, for 5 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.21 y, so each step multiplies y by 1 - h*0.21.\nApply that update for 5 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 39.0, "rate": 0.21, "step": 0.9, "steps": 5}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.46 and add it to the current value.\nFinal: {\"answer\": [-0.379, 0.341, -0.389], \"unit\": \"temperature_units\"}", "dedupe_signature": "c1aaa5140864833851bc8d48c591cade99ccc2ee2d6466b275e1fac714641204", "difficulty": "hard", "final_answer": {"answer": [-0.379, 0.341, -0.389], "unit": "temperature_units"}, "id": "heat_step_003323_0.46_-1.0_1.3_-0.05_-0.55_-0.7", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-1, right=-0.7; current interior values are [1.3, -0.05, -0.55]. Use r=0.46. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.46 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [1.3, -0.05, -0.55], "left": -1.0, "r": 0.46, "right": -0.7}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kelvin equals Celsius plus 273.15.\n2. Apply the conversion factor directly to the given value.\n3. Compute 143.0 + 273.15.\nFinal: {\"answer\": 416.15, \"unit\": \"K\"}", "dedupe_signature": "b228dccf9bf8ee655fded896d874b5d5ce3db0d23cedc05882726cca724278db", "difficulty": "easy", "final_answer": {"answer": 416.15, "unit": "K"}, "id": "unit_convert_003324_c_to_k_143", "license": "Apache-2.0", "prompt": "Convert 143 degC to K. Return the converted value with unit.", "reasoning_trace": "Kelvin equals Celsius plus 273.15.\nApply the conversion factor directly to the given value.\nCompute 143.0 + 273.15.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 143.0}, "verifier": {"formula": "value + 273.15", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=297 degrees and keep the unit as newtons.\nFinal: {\"answer\": [147.7739, -290.0226], \"unit\": \"N\"}", "dedupe_signature": "7b98c06354963dd721d52a9180771c9b6af65d0bea1d709b7ece3c9f2c6373a3", "difficulty": "medium", "final_answer": {"answer": [147.7739, -290.0226], "unit": "N"}, "id": "vector_components_003325_325.5_297", "license": "Apache-2.0", "prompt": "A vector has magnitude 325.5 N at 297 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=297 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 297, "magnitude": 325.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [1.8, -5.75], \"unit\": \"dimensionless\"}", "dedupe_signature": "7990eac960ea7c5f31c37ea6044eee707e3398a2922cbae40c9af7c489e88428", "difficulty": "medium", "final_answer": {"answer": [1.8, -5.75], "unit": "dimensionless"}, "id": "line_two_point_003326_4.5_6.75_1.8_-5.75", "license": "Apache-2.0", "prompt": "A line passes through points (4.5, 2.35) and (6.75, 6.4). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 4.5, "x2": 6.75, "y1": 2.3499999999999996, "y2": 6.4}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. grams cancel with J/(g*K), and kelvin cancels, leaving joules\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "0a0c5b1923c58ffa10fb62ed6888f33747ac87d1a06e5c3bad9ff357f416e586", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_003327_consistent_4153435f_820179", "license": "Apache-2.0", "prompt": "In instrument manual case 820179, check dimensional consistency for Q = m * c * DeltaT. The left side has dimensions J and the right side has dimensions J. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\ngrams cancel with J/(g*K), and kelvin cancels, leaving joules\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "Q = m * c * DeltaT"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: volume.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"volume\"]}", "dedupe_signature": "5cc225ae2a6cffda48ac65da9e07a9302025d2bf57798e2afc6a2631b744d4ae", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["volume"]}, "id": "abstain_003329_volume", "license": "Apache-2.0", "prompt": "Compute pressure from the ideal gas law. The prompt gives n=1.28 mol and T=304 K, but does not give volume. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: volume.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["volume"]}, "verifier": {"missing": ["volume"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 12.2 kg and a = 14.9 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 181.78, \"unit\": \"N\"}", "dedupe_signature": "864b7adaa04d2f58ce76a71acb400bb8626079879116395f8c35f72d80ea6c02", "difficulty": "easy", "final_answer": {"answer": 181.78, "unit": "N"}, "id": "force_003330_12.2_14.9", "license": "Apache-2.0", "prompt": "A cart has mass 12.2 kg and measured acceleration 14.9 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 12.2 kg and a = 14.9 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 14.9, "mass": 12.2}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 4.82 * 8.314 * 550 / 68.9.\nFinal: {\"answer\": 319.8899, \"unit\": \"kPa\"}", "dedupe_signature": "83a516b85a7dfaeff179ce5176a65ff4cac8b8a6bfad75c4dec037da49c8c4d9", "difficulty": "medium", "final_answer": {"answer": 319.8899, "unit": "kPa"}, "id": "ideal_gas_003333_4.82_550_68.9", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=4.82 mol, T=550 K, and V=68.9 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 4.82 * 8.314 * 550 / 68.9.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 4.82, "temp_k": 550, "volume_l": 68.9}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 255 * 4.51 * 12.\nFinal: {\"answer\": 13800.6, \"unit\": \"J\"}", "dedupe_signature": "ca4879766decdd51144ef1abdd8801ed23cc775afd03c7b771c7105bb44e23c7", "difficulty": "easy", "final_answer": {"answer": 13800.6, "unit": "J"}, "id": "heat_q_003334_255_4.51_12", "license": "Apache-2.0", "prompt": "A 255 g sample has specific heat 4.51 J/(g*K). How much heat is needed to raise its temperature by 12 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 255 * 4.51 * 12.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 12, "heat_capacity": 4.51, "mass_g": 255}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=956 mg, t=303 h, and T_half=46 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 9.9446, \"unit\": \"mg\"}", "dedupe_signature": "09349be7f179a70cdfc16d378ac76eb2e68fe351664497ff9368fb2342dc24ee", "difficulty": "medium", "final_answer": {"answer": 9.9446, "unit": "mg"}, "id": "half_life_003336_956_46_303", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 956 mg. Its half-life is 46 hours. How many mg remain after 303 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=956 mg, t=303 h, and T_half=46 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 303.0, "half_life": 46.0, "initial_amount": 956.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 2.49 mol * 58.44 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 145.5156, \"unit\": \"g\"}", "dedupe_signature": "e44ba14714a5980adc9244484aac3bb9bc033ad841432e5c4216d6348c43a613", "difficulty": "medium", "final_answer": {"answer": 145.5156, "unit": "g"}, "id": "stoich_mass_003337_sodium_chloride_2.49", "license": "Apache-2.0", "prompt": "A sample contains 2.49 mol of sodium chloride. Using molar mass 58.44 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 2.49 mol * 58.44 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "sodium chloride", "molar_mass": 58.44, "moles": 2.49}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 675 mL to 0.675 L.\n3. Compute M = 2.795 / 0.675.\nFinal: {\"answer\": 4.1407, \"unit\": \"mol/L\"}", "dedupe_signature": "9adbe6c5f40977cd137d6e946296f294717d740664dcc7591faaa498b66bfc33", "difficulty": "medium", "final_answer": {"answer": 4.1407, "unit": "mol/L"}, "id": "molarity_003338_2.795_675", "license": "Apache-2.0", "prompt": "A solution contains 2.795 mol of solute in 675 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 675 mL to 0.675 L.\nCompute M = 2.795 / 0.675.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 2.795, "volume_ml": 675}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-0.7)=-13.01 and f(5.1)=29.33.\n3. The interval width is 5.8.\nFinal: {\"answer\": 47.328, \"unit\": \"area_units\"}", "dedupe_signature": "70d023d2ee00a12133e8cb1252acad876d54cc3f20ae22f1666bd5e098b43302", "difficulty": "medium", "final_answer": {"answer": 47.328, "unit": "area_units"}, "id": "trapz_linear_003340_7.3_-7.9_-0.7_5.1", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=7.3x+-7.9 from x=-0.7 to x=5.1. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-0.7)=-13.01 and f(5.1)=29.33.\nThe interval width is 5.8.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -7.9, "slope": 7.3, "x0": -0.7, "x1": 5.1}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 100 centimeters in one meter.\n2. Apply the conversion factor directly to the given value.\n3. Compute 494.0 / 100.\nFinal: {\"answer\": 4.94, \"unit\": \"m\"}", "dedupe_signature": "1b813bb9654f04d44fc4660057fb85105e2903aa4115e5571acf0be57e6db427", "difficulty": "easy", "final_answer": {"answer": 4.94, "unit": "m"}, "id": "unit_convert_003342_cm_to_m_494", "license": "Apache-2.0", "prompt": "Convert 494 cm to m. Return the converted value with unit.", "reasoning_trace": "There are 100 centimeters in one meter.\nApply the conversion factor directly to the given value.\nCompute 494.0 / 100.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 494.0}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=284 degrees and keep the unit as newtons.\nFinal: {\"answer\": [6.6529, -26.6831], \"unit\": \"N\"}", "dedupe_signature": "9650135e083344a6e4979b97d3ebb8fa54ab974c5f5af6c36efbd35ab7252051", "difficulty": "medium", "final_answer": {"answer": [6.6529, -26.6831], "unit": "N"}, "id": "vector_components_003343_27.5_284", "license": "Apache-2.0", "prompt": "A vector has magnitude 27.5 N at 284 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=284 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 284, "magnitude": 27.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-6.95, -4.0], \"unit\": \"dimensionless\"}", "dedupe_signature": "d9aaefa53921291ad2728a1c44a13403fe644c22bbb2a96fb20f9564596cdc25", "difficulty": "medium", "final_answer": {"answer": [-6.95, -4.0], "unit": "dimensionless"}, "id": "line_two_point_003344_11.25_22_-6.95_-4", "license": "Apache-2.0", "prompt": "A line passes through points (11.25, -82.1875) and (22, -156.9). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 11.25, "x2": 22.0, "y1": -82.1875, "y2": -156.9}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef threshold_flags_003346(values, threshold):\n    return [value >= threshold for value in values]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"threshold_flags_003346\"}", "dedupe_signature": "c4762518f850c93717edc06bd0ca82635fb7341ae4651fb8a08aa8f9ad94591c", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "threshold_flags_003346"}, "id": "code_003346_threshold_flags_003346", "license": "Apache-2.0", "prompt": "Write a Python function threshold_flags_003346(values, threshold) that returns a list of booleans showing whether each value is greater than or equal to threshold. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "threshold_flags_003346"}, "verifier": {"function": "threshold_flags_003346", "tests": ["assert threshold_flags_003346([1, 2, 3], 2) == [False, True, True]", "assert threshold_flags_003346([], 5) == []", "assert threshold_flags_003346([-1, 0], 0) == [False, True]"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: rate_constant, number_of_steps.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"rate_constant\", \"number_of_steps\"]}", "dedupe_signature": "e003c11d1096fee123e42faa1b04e9bf9a65dd0fd9fc6325fd044812e4ac842c", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["rate_constant", "number_of_steps"]}, "id": "abstain_003347_rate_constant_number_of_steps", "license": "Apache-2.0", "prompt": "Use explicit Euler for dy/dt = -k y. The prompt gives y(0)=49.5 and h=0.95, but omits both k and the number of steps. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: rate_constant, number_of_steps.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["rate_constant", "number_of_steps"]}, "verifier": {"missing": ["rate_constant", "number_of_steps"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 22.8 kg and a = 12 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 273.6, \"unit\": \"N\"}", "dedupe_signature": "d11c893308f3de95c173acf37f3f84ffabeeb48a96dbeb8277058a24688f5587", "difficulty": "easy", "final_answer": {"answer": 273.6, "unit": "N"}, "id": "force_003348_22.8_12", "license": "Apache-2.0", "prompt": "A cart has mass 22.8 kg and measured acceleration 12 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 22.8 kg and a = 12 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 12.0, "mass": 22.8}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 6.7^2 and multiply by 0.5 * 23.6.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 529.702, \"unit\": \"J\"}", "dedupe_signature": "445498627cd006120b6010d7af08db3123de247ec5cfdfe1decc12478e1e507e", "difficulty": "easy", "final_answer": {"answer": 529.702, "unit": "J"}, "id": "ke_003349_23.6_6.7", "license": "Apache-2.0", "prompt": "A body of mass 23.6 kg moves at 6.7 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 6.7^2 and multiply by 0.5 * 23.6.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 23.6, "velocity": 6.7}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=76 degrees through the sine of 2 theta.\n3. Substitute v=70 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 234.4965, \"unit\": \"m\"}", "dedupe_signature": "f7d05ff58d2eadce4461d994d12ecb912eff783f29a8c165ac1bdfe9507f8d72", "difficulty": "medium", "final_answer": {"answer": 234.4965, "unit": "m"}, "id": "projectile_range_003350_70_76", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 70 m/s and angle 76 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=76 degrees through the sine of 2 theta.\nSubstitute v=70 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 76, "gravity": 9.81, "speed": 70.0}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 4.51 * 8.314 * 506 / 56.4.\nFinal: {\"answer\": 336.4015, \"unit\": \"kPa\"}", "dedupe_signature": "4143cad0c76597bf4643d691ebd93f26045cc40b76c2f59b66ed1d39c3040b44", "difficulty": "medium", "final_answer": {"answer": 336.4015, "unit": "kPa"}, "id": "ideal_gas_003351_4.51_506_56.4", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=4.51 mol, T=506 K, and V=56.4 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 4.51 * 8.314 * 506 / 56.4.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 4.51, "temp_k": 506, "volume_l": 56.4}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1255 * 1.435 * 6.\nFinal: {\"answer\": 10805.55, \"unit\": \"J\"}", "dedupe_signature": "3ab11006465b4840490c8ce31003854b6fe9ec79e411f8fa7ff3ce4265871a4e", "difficulty": "easy", "final_answer": {"answer": 10805.55, "unit": "J"}, "id": "heat_q_003352_1255_1.435_6", "license": "Apache-2.0", "prompt": "A 1255 g sample has specific heat 1.435 J/(g*K). How much heat is needed to raise its temperature by 6 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1255 * 1.435 * 6.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 6, "heat_capacity": 1.435, "mass_g": 1255}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=204 V and R=89.9 ohm.\nFinal: {\"answer\": 462.9143, \"unit\": \"W\"}", "dedupe_signature": "f5d36ebd219f1a55efe2706010110f631b32eb37147e8b05694befc04dcb27ec", "difficulty": "easy", "final_answer": {"answer": 462.9143, "unit": "W"}, "id": "ohm_power_003353_204_89.9", "license": "Apache-2.0", "prompt": "A resistor has resistance 89.9 ohm and voltage 204 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=204 V and R=89.9 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 89.9, "voltage": 204.0}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=379.5 mg, t=1.5 h, and T_half=116 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 376.1137, \"unit\": \"mg\"}", "dedupe_signature": "0c86cf607490f2be468061244cb96974b64f92084d55845821d0b46a1ba9c25b", "difficulty": "medium", "final_answer": {"answer": 376.1137, "unit": "mg"}, "id": "half_life_003354_379.5_116_1.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 379.5 mg. Its half-life is 116 hours. How many mg remain after 1.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=379.5 mg, t=1.5 h, and T_half=116 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 1.5, "half_life": 116.0, "initial_amount": 379.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 5.04 mol * 44.01 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 221.8104, \"unit\": \"g\"}", "dedupe_signature": "863602cb53504099783192433207c8bf91e9ed0ee092acefb31b58ccc5dd0705", "difficulty": "medium", "final_answer": {"answer": 221.8104, "unit": "g"}, "id": "stoich_mass_003355_carbon_dioxide_5.04", "license": "Apache-2.0", "prompt": "A sample contains 5.04 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 5.04 mol * 44.01 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "carbon dioxide", "molar_mass": 44.01, "moles": 5.04}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 3585 mL to 3.585 L.\n3. Compute M = 0.225 / 3.585.\nFinal: {\"answer\": 0.0628, \"unit\": \"mol/L\"}", "dedupe_signature": "c184be2e42f26a16d4538a855c804c0339eadcf460ba2375d195da835dfb77de", "difficulty": "medium", "final_answer": {"answer": 0.0628, "unit": "mol/L"}, "id": "molarity_003356_0.225_3585", "license": "Apache-2.0", "prompt": "A solution contains 0.225 mol of solute in 3585 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 3585 mL to 3.585 L.\nCompute M = 0.225 / 3.585.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 0.225, "volume_ml": 3585}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.7 y, so each step multiplies y by 1 - h*0.7.\n3. Apply that update for 5 steps and round the final state.\nFinal: {\"answer\": 0.0, \"unit\": \"state_units\"}", "dedupe_signature": "60dd3631cff94e6df361114375ca5d3837218426baa07b5f01702dbab80c1f82", "difficulty": "medium", "final_answer": {"answer": 0.0, "unit": "state_units"}, "id": "euler_decay_003357_56_0.7_1.45_5", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.7 y with y(0)=56, step size h=1.45, for 5 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.7 y, so each step multiplies y by 1 - h*0.7.\nApply that update for 5 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 56.0, "rate": 0.7, "step": 1.45, "steps": 5}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-7.3)=5.61 and f(-1)=-5.1.\n3. The interval width is 6.3.\nFinal: {\"answer\": 1.6065, \"unit\": \"area_units\"}", "dedupe_signature": "4b0df6e7cdc0a2b7177dd602c779f928cf478951b26a521d982974a6cd2579eb", "difficulty": "medium", "final_answer": {"answer": 1.6065, "unit": "area_units"}, "id": "trapz_linear_003358_-1.7_-6.8_-7.3_-1", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-1.7x+-6.8 from x=-7.3 to x=-1. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-7.3)=5.61 and f(-1)=-5.1.\nThe interval width is 6.3.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -6.8, "slope": -1.7, "x0": -7.3, "x1": -1.0}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.12 and add it to the current value.\nFinal: {\"answer\": [2.114, 2.012, 1.728], \"unit\": \"temperature_units\"}", "dedupe_signature": "217811222e1d1d41d75c0ec9202214772c918627f095b900a15524adaa6d0131", "difficulty": "hard", "final_answer": {"answer": [2.114, 2.012, 1.728], "unit": "temperature_units"}, "id": "heat_step_003359_0.12_0.1_2.45_2.0_1.65_1.95", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=0.1, right=1.95; current interior values are [2.45, 2.0, 1.65]. Use r=0.12. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.12 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [2.45, 2.0, 1.65], "left": 0.1, "r": 0.12, "right": 1.95}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kelvin equals Celsius plus 273.15.\n2. Apply the conversion factor directly to the given value.\n3. Compute 246.0 + 273.15.\nFinal: {\"answer\": 519.15, \"unit\": \"K\"}", "dedupe_signature": "729c8a8ed911319a1c02dd5569f490e35cc2dedca93960eabfafaae7c8e53680", "difficulty": "easy", "final_answer": {"answer": 519.15, "unit": "K"}, "id": "unit_convert_003360_c_to_k_246", "license": "Apache-2.0", "prompt": "Convert 246 degC to K. Return the converted value with unit.", "reasoning_trace": "Kelvin equals Celsius plus 273.15.\nApply the conversion factor directly to the given value.\nCompute 246.0 + 273.15.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 246.0}, "verifier": {"formula": "value + 273.15", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-0.85, -15.25], \"unit\": \"dimensionless\"}", "dedupe_signature": "1ec88823a67f7aa194bc634c5e7b99b91c5da4eb507c413fa1d1c673e9fdc6f3", "difficulty": "medium", "final_answer": {"answer": [-0.85, -15.25], "unit": "dimensionless"}, "id": "line_two_point_003362_2.25_12.75_-0.85_-15.25", "license": "Apache-2.0", "prompt": "A line passes through points (2.25, -17.1625) and (12.75, -26.0875). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 2.25, "x2": 12.75, "y1": -17.1625, "y2": -26.0875}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. amount times volume is not concentration\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "0238fa9eaeaec480397815a5e1e85b894afa89adc57f65ae78c5719869c31051", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_003363_inconsistent_74ac0b02_620284", "license": "Apache-2.0", "prompt": "In instrument manual case 620284, check dimensional consistency for C = n * V. The left side has dimensions mol/L and the right side has dimensions mol*L. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\namount times volume is not concentration\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "C = n * V"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef running_total_003364(values):\n    total = 0\n    out = []\n    for value in values:\n        total += value\n        out.append(total)\n    return out\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"running_total_003364\"}", "dedupe_signature": "892ab25603086de42167aa9857121a0f30e009c3276f54e50263e843ce67e97e", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "running_total_003364"}, "id": "code_003364_running_total_003364", "license": "Apache-2.0", "prompt": "Write a Python function running_total_003364(values) that returns cumulative sums as a new list. It must not mutate the input list. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "running_total_003364"}, "verifier": {"function": "running_total_003364", "tests": ["assert running_total_003364([1, 2, 3]) == [1, 3, 6]", "xs = [4, -1, 2]; assert running_total_003364(xs) == [4, 3, 5] and xs == [4, -1, 2]", "assert running_total_003364([]) == []"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: volume.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"volume\"]}", "dedupe_signature": "6b07f8da123d3456563cea1f0af220eaaea662bf79526f48677c9b3402a0c8d2", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["volume"]}, "id": "abstain_003365_volume", "license": "Apache-2.0", "prompt": "Compute pressure from the ideal gas law. The prompt gives n=3.75 mol and T=527 K, but does not give volume. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: volume.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["volume"]}, "verifier": {"missing": ["volume"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 15.9 kg and a = 5.45 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 86.655, \"unit\": \"N\"}", "dedupe_signature": "91d0579bfab64b41e3888baca1e9c897948cb0b42063bc24d90b2a0078093f9e", "difficulty": "easy", "final_answer": {"answer": 86.655, "unit": "N"}, "id": "force_003366_15.9_5.45", "license": "Apache-2.0", "prompt": "A cart has mass 15.9 kg and measured acceleration 5.45 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 15.9 kg and a = 5.45 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 5.45, "mass": 15.9}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 1.45^2 and multiply by 0.5 * 6.35.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 6.6754, \"unit\": \"J\"}", "dedupe_signature": "03082127f1e8cb856cc49b962bd0c528baed58d2b7b1072a8bad4b6e7e1f2f36", "difficulty": "easy", "final_answer": {"answer": 6.6754, "unit": "J"}, "id": "ke_003367_6.35_1.45", "license": "Apache-2.0", "prompt": "A body of mass 6.35 kg moves at 1.45 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 1.45^2 and multiply by 0.5 * 6.35.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 6.35, "velocity": 1.45}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 0.74 * 8.314 * 508 / 119.5.\nFinal: {\"answer\": 26.154, \"unit\": \"kPa\"}", "dedupe_signature": "064337271f08cb6204f97022b702fd2741c1edee0e3fb20c6b466d59d5667003", "difficulty": "medium", "final_answer": {"answer": 26.154, "unit": "kPa"}, "id": "ideal_gas_003369_0.74_508_119.5", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=0.74 mol, T=508 K, and V=119.5 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 0.74 * 8.314 * 508 / 119.5.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 0.74, "temp_k": 508, "volume_l": 119.5}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=71.6 V and R=142 ohm.\nFinal: {\"answer\": 36.1025, \"unit\": \"W\"}", "dedupe_signature": "d9e4e884b823ea15ce168b8c89e85b93d9817039a711f0331339fc2d92d3a2e1", "difficulty": "easy", "final_answer": {"answer": 36.1025, "unit": "W"}, "id": "ohm_power_003371_71.6_142", "license": "Apache-2.0", "prompt": "A resistor has resistance 142 ohm and voltage 71.6 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=71.6 V and R=142 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 142.0, "voltage": 71.6}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=117 mg, t=51.5 h, and T_half=2 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 0.0, \"unit\": \"mg\"}", "dedupe_signature": "cd3cb9f75cb98d57e5ed8773e68459925f419844f896f7855ef5b96ad081ed1a", "difficulty": "medium", "final_answer": {"answer": 0.0, "unit": "mg"}, "id": "half_life_003372_117_2_51.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 117 mg. Its half-life is 2 hours. How many mg remain after 51.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=117 mg, t=51.5 h, and T_half=2 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 51.5, "half_life": 2.0, "initial_amount": 117.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 4.26 mol * 18.015 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 76.7439, \"unit\": \"g\"}", "dedupe_signature": "ecd302d6ed6b9dbf991cfdb79817c3a8fc96639e682a167f8de278dd4ae3581a", "difficulty": "medium", "final_answer": {"answer": 76.7439, "unit": "g"}, "id": "stoich_mass_003373_water_4.26", "license": "Apache-2.0", "prompt": "A sample contains 4.26 mol of water. Using molar mass 18.015 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 4.26 mol * 18.015 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "water", "molar_mass": 18.015, "moles": 4.26}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(6.9)=31.19 and f(14.2)=83.02.\n3. The interval width is 7.3.\nFinal: {\"answer\": 416.8665, \"unit\": \"area_units\"}", "dedupe_signature": "d4f930864551d7a5f840a398ccf4a8dbb54f158087dbbc225f5ea4585d78a273", "difficulty": "medium", "final_answer": {"answer": 416.8665, "unit": "area_units"}, "id": "trapz_linear_003376_7.1_-17.8_6.9_14.2", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=7.1x+-17.8 from x=6.9 to x=14.2. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(6.9)=31.19 and f(14.2)=83.02.\nThe interval width is 7.3.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -17.8, "slope": 7.1, "x0": 6.9, "x1": 14.2}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.46 and add it to the current value.\nFinal: {\"answer\": [-0.669, 1.729, 0.709], \"unit\": \"temperature_units\"}", "dedupe_signature": "f64d5118362840e80f0dd00fc56e2c1692ebc6a67f380a8c1055ba27e6713595", "difficulty": "hard", "final_answer": {"answer": [-0.669, 1.729, 0.709], "unit": "temperature_units"}, "id": "heat_step_003377_0.46_-0.85_2.85_-1.1_1.1_2.45", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-0.85, right=2.45; current interior values are [2.85, -1.1, 1.1]. Use r=0.46. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.46 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [2.85, -1.1, 1.1], "left": -0.85, "r": 0.46, "right": 2.45}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 100 centimeters in one meter.\n2. Apply the conversion factor directly to the given value.\n3. Compute 482.0 / 100.\nFinal: {\"answer\": 4.82, \"unit\": \"m\"}", "dedupe_signature": "a2f1edbb035c26636bda3da00eba64ec6340e9f0b3e17c3c06365ae7cdf8d152", "difficulty": "easy", "final_answer": {"answer": 4.82, "unit": "m"}, "id": "unit_convert_003378_cm_to_m_482", "license": "Apache-2.0", "prompt": "Convert 482 cm to m. Return the converted value with unit.", "reasoning_trace": "There are 100 centimeters in one meter.\nApply the conversion factor directly to the given value.\nCompute 482.0 / 100.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 482.0}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=156 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-335.728, 149.4757], \"unit\": \"N\"}", "dedupe_signature": "8651e7afd7c8b46f2fc5e46b51cbab286fead8cd9ac81b5db4ab2f2cce0a9ec3", "difficulty": "medium", "final_answer": {"answer": [-335.728, 149.4757], "unit": "N"}, "id": "vector_components_003379_367.5_156", "license": "Apache-2.0", "prompt": "A vector has magnitude 367.5 N at 156 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=156 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 156, "magnitude": 367.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-7.35, 8.75], \"unit\": \"dimensionless\"}", "dedupe_signature": "0c2bcb694065bf86f71da9ce5cf02221f0ff02923d0dd306e772215f662d87cf", "difficulty": "medium", "final_answer": {"answer": [-7.35, 8.75], "unit": "dimensionless"}, "id": "line_two_point_003380_15_29.5_-7.35_8.75", "license": "Apache-2.0", "prompt": "A line passes through points (15, -101.5) and (29.5, -208.075). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 15.0, "x2": 29.5, "y1": -101.5, "y2": -208.075}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. velocity times time gives distance, not acceleration\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "5dd53e91f7d81ecb2048e2946e3aa90eae966edf7862c7c2ec370e398b780ece", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_003381_inconsistent_7481c798_461347", "license": "Apache-2.0", "prompt": "In field worksheet case 461347, check dimensional consistency for a = v * t. The left side has dimensions m/s^2 and the right side has dimensions m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nvelocity times time gives distance, not acceleration\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "a = v * t"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef clamp_003382(x, lo, hi):\n    if lo > hi:\n        raise ValueError('lo must be <= hi')\n    return min(max(x, lo), hi)\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"clamp_003382\"}", "dedupe_signature": "fe00d014f558b9ffc817d69b0445b400d7fefb3dcfc16697efed9f8bcf40904f", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "clamp_003382"}, "id": "code_003382_clamp_003382", "license": "Apache-2.0", "prompt": "Write a Python function clamp_003382(x, lo, hi) that clips x into the inclusive interval [lo, hi]. It must raise ValueError if lo > hi. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "clamp_003382"}, "verifier": {"function": "clamp_003382", "tests": ["assert clamp_003382(5, 0, 10) == 5", "assert clamp_003382(-2, 0, 10) == 0", "assert clamp_003382(12, 0, 10) == 10", "try:\n    clamp_003382(1, 3, 2)\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: launch_angle_or_vertical_velocity.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"launch_angle_or_vertical_velocity\"]}", "dedupe_signature": "5792daefa802cf15a3ea83c264883030186db8bfd577e7ac7fe18c7af779ef1d", "difficulty": "easy", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["launch_angle_or_vertical_velocity"]}, "id": "abstain_003383_launch_angle_or_vertical_velocity", "license": "Apache-2.0", "prompt": "Compute projectile range on level ground. The prompt gives initial speed 30.7 m/s but does not give launch angle or vertical velocity. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: launch_angle_or_vertical_velocity.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["launch_angle_or_vertical_velocity"]}, "verifier": {"missing": ["launch_angle_or_vertical_velocity"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 9.3 kg and a = 11.75 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 109.275, \"unit\": \"N\"}", "dedupe_signature": "ea0a852d8c51950c32da2460cd06174934a8cea5b00ca27f0a04e378b8f9ccd0", "difficulty": "easy", "final_answer": {"answer": 109.275, "unit": "N"}, "id": "force_003384_9.3_11.75", "license": "Apache-2.0", "prompt": "A cart has mass 9.3 kg and measured acceleration 11.75 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 9.3 kg and a = 11.75 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 11.75, "mass": 9.3}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 31.6^2 and multiply by 0.5 * 7.5.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 3744.6, \"unit\": \"J\"}", "dedupe_signature": "814da3fae17aa59c2e0c0f9e6ce0ec34db75165ec2e1eedb20ae7b48b51eee11", "difficulty": "easy", "final_answer": {"answer": 3744.6, "unit": "J"}, "id": "ke_003385_7.5_31.6", "license": "Apache-2.0", "prompt": "A body of mass 7.5 kg moves at 31.6 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 31.6^2 and multiply by 0.5 * 7.5.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 7.5, "velocity": 31.6}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=29 degrees through the sine of 2 theta.\n3. Substitute v=34.1 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 100.5218, \"unit\": \"m\"}", "dedupe_signature": "75beca95504a581fc19a2f7998f24dcbefd10a5769193e477e5e0194ac350315", "difficulty": "medium", "final_answer": {"answer": 100.5218, "unit": "m"}, "id": "projectile_range_003386_34.1_29", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 34.1 m/s and angle 29 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=29 degrees through the sine of 2 theta.\nSubstitute v=34.1 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 29, "gravity": 9.81, "speed": 34.1}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 2.15 * 8.314 * 526 / 110.0.\nFinal: {\"answer\": 85.4755, \"unit\": \"kPa\"}", "dedupe_signature": "bc89d9505bde5000a62d22092adb84117ad67527f032397bb827373f091f6116", "difficulty": "medium", "final_answer": {"answer": 85.4755, "unit": "kPa"}, "id": "ideal_gas_003387_2.15_526_110.0", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=2.15 mol, T=526 K, and V=110.0 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 2.15 * 8.314 * 526 / 110.0.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 2.15, "temp_k": 526, "volume_l": 110.0}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 360 * 2.365 * 79.\nFinal: {\"answer\": 67260.6, \"unit\": \"J\"}", "dedupe_signature": "c40de8c2705895f6a44677c5c789f74cbe1ce97de9a78cbd582b324a6c2ab48a", "difficulty": "easy", "final_answer": {"answer": 67260.6, "unit": "J"}, "id": "heat_q_003388_360_2.365_79", "license": "Apache-2.0", "prompt": "A 360 g sample has specific heat 2.365 J/(g*K). How much heat is needed to raise its temperature by 79 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 360 * 2.365 * 79.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 79, "heat_capacity": 2.365, "mass_g": 360}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=175.2 V and R=131.1 ohm.\nFinal: {\"answer\": 234.1346, \"unit\": \"W\"}", "dedupe_signature": "093640eda4c8c9bc6acd1ba7fac4ab24eee2b71165c1b01b8ac2a272e0e4ce11", "difficulty": "easy", "final_answer": {"answer": 234.1346, "unit": "W"}, "id": "ohm_power_003389_175.2_131.1", "license": "Apache-2.0", "prompt": "A resistor has resistance 131.1 ohm and voltage 175.2 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=175.2 V and R=131.1 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 131.1, "voltage": 175.2}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=470 mg, t=92.5 h, and T_half=31 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 59.4105, \"unit\": \"mg\"}", "dedupe_signature": "471a0ac13fbe2457ad761d8875e9178d6dc13e323fde86c3c14193982a99fe58", "difficulty": "medium", "final_answer": {"answer": 59.4105, "unit": "mg"}, "id": "half_life_003390_470_31_92.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 470 mg. Its half-life is 31 hours. How many mg remain after 92.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=470 mg, t=92.5 h, and T_half=31 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 92.5, "half_life": 31.0, "initial_amount": 470.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 2.99 mol * 44.01 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 131.5899, \"unit\": \"g\"}", "dedupe_signature": "53cf1b0b96508d89fe20907d6cb88b4dd1498dfdf8625263df8ef88f463113c1", "difficulty": "medium", "final_answer": {"answer": 131.5899, "unit": "g"}, "id": "stoich_mass_003391_carbon_dioxide_2.99", "license": "Apache-2.0", "prompt": "A sample contains 2.99 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 2.99 mol * 44.01 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "carbon dioxide", "molar_mass": 44.01, "moles": 2.99}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 2590 mL to 2.59 L.\n3. Compute M = 1.915 / 2.59.\nFinal: {\"answer\": 0.7394, \"unit\": \"mol/L\"}", "dedupe_signature": "556c5572738dd0473cd181c474cbce60de8ab0898776370563e750a7fc155b16", "difficulty": "medium", "final_answer": {"answer": 0.7394, "unit": "mol/L"}, "id": "molarity_003392_1.915_2590", "license": "Apache-2.0", "prompt": "A solution contains 1.915 mol of solute in 2590 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 2590 mL to 2.59 L.\nCompute M = 1.915 / 2.59.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 1.915, "volume_ml": 2590}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.8 y, so each step multiplies y by 1 - h*0.8.\n3. Apply that update for 2 steps and round the final state.\nFinal: {\"answer\": 6.5448, \"unit\": \"state_units\"}", "dedupe_signature": "60ec6a04e16d058e51c9f1d2c45df480f5f942e1be26bc7ceae8311adfb269a2", "difficulty": "medium", "final_answer": {"answer": 6.5448, "unit": "state_units"}, "id": "euler_decay_003393_50.5_0.8_1.7_2", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.8 y with y(0)=50.5, step size h=1.7, for 2 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.8 y, so each step multiplies y by 1 - h*0.8.\nApply that update for 2 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 50.5, "rate": 0.8, "step": 1.7, "steps": 2}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.02 and add it to the current value.\nFinal: {\"answer\": [-1.642, 2.233, 0.659], \"unit\": \"temperature_units\"}", "dedupe_signature": "51201a70024e95da4eb83350f087db58f5fdb75128ab179135ab28b6a19b6b03", "difficulty": "hard", "final_answer": {"answer": [-1.642, 2.233, 0.659], "unit": "temperature_units"}, "id": "heat_step_003395_0.02_1.95_-1.8_2.35_0.65_-0.6", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.95, right=-0.6; current interior values are [-1.8, 2.35, 0.65]. Use r=0.02. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.02 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-1.8, 2.35, 0.65], "left": 1.95, "r": 0.02, "right": -0.6}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kelvin equals Celsius plus 273.15.\n2. Apply the conversion factor directly to the given value.\n3. Compute 38.5 + 273.15.\nFinal: {\"answer\": 311.65, \"unit\": \"K\"}", "dedupe_signature": "826acd78b2fd7a560a2280829543c88a55092934b8c748074def0bebbe909793", "difficulty": "easy", "final_answer": {"answer": 311.65, "unit": "K"}, "id": "unit_convert_003396_c_to_k_38.5", "license": "Apache-2.0", "prompt": "Convert 38.5 degC to K. Return the converted value with unit.", "reasoning_trace": "Kelvin equals Celsius plus 273.15.\nApply the conversion factor directly to the given value.\nCompute 38.5 + 273.15.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 38.5}, "verifier": {"formula": "value + 273.15", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=251 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-109.3909, -317.6942], \"unit\": \"N\"}", "dedupe_signature": "127450356c25097420a7b5d097b4def65c53b3204c22ad27efcc9b6d7cd85a3d", "difficulty": "medium", "final_answer": {"answer": [-109.3909, -317.6942], "unit": "N"}, "id": "vector_components_003397_336_251", "license": "Apache-2.0", "prompt": "A vector has magnitude 336 N at 251 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=251 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 251, "magnitude": 336.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-2.5, -9.25], \"unit\": \"dimensionless\"}", "dedupe_signature": "145085db189433cb0f3d64990e667a5144124e1b3fccd86f0a40f9d919f12ba9", "difficulty": "medium", "final_answer": {"answer": [-2.5, -9.25], "unit": "dimensionless"}, "id": "line_two_point_003398_10.75_24.75_-2.5_-9.25", "license": "Apache-2.0", "prompt": "A line passes through points (10.75, -36.125) and (24.75, -71.125). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 10.75, "x2": 24.75, "y1": -36.125, "y2": -71.125}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef safe_mean_003400(values):\n    if not values:\n        raise ValueError('safe_mean requires at least one value')\n    return sum(values) / len(values)\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"safe_mean_003400\"}", "dedupe_signature": "65c36b4902661b021f4a43ffb01f0332d1a689d50c437faadbec1d7951dddbe0", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "safe_mean_003400"}, "id": "code_003400_safe_mean_003400", "license": "Apache-2.0", "prompt": "Write a Python function safe_mean_003400(values) that returns the arithmetic mean. It must raise ValueError for an empty input and must not mutate the input list. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "safe_mean_003400"}, "verifier": {"function": "safe_mean_003400", "tests": ["assert safe_mean_003400([2, 4, 6]) == 4", "xs = [1, 2, 3]; assert safe_mean_003400(xs) == 2 and xs == [1, 2, 3]", "try:\n    safe_mean_003400([])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: launch_angle_or_vertical_velocity.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"launch_angle_or_vertical_velocity\"]}", "dedupe_signature": "f18bd9bec56fc71191d04a01a740038eaa3317672533231fb97ff431e8a9b12a", "difficulty": "easy", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["launch_angle_or_vertical_velocity"]}, "id": "abstain_003401_launch_angle_or_vertical_velocity", "license": "Apache-2.0", "prompt": "Compute projectile range on level ground. The prompt gives initial speed 13 m/s but does not give launch angle or vertical velocity. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: launch_angle_or_vertical_velocity.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["launch_angle_or_vertical_velocity"]}, "verifier": {"missing": ["launch_angle_or_vertical_velocity"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=26 degrees through the sine of 2 theta.\n3. Substitute v=59.3 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 282.4701, \"unit\": \"m\"}", "dedupe_signature": "61547d9cc65827464a148a88f048304388a9c0a9a3a19a18fb3afed5453f449f", "difficulty": "medium", "final_answer": {"answer": 282.4701, "unit": "m"}, "id": "projectile_range_003404_59.3_26", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 59.3 m/s and angle 26 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=26 degrees through the sine of 2 theta.\nSubstitute v=59.3 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 26, "gravity": 9.81, "speed": 59.3}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1815 * 3.125 * 44.\nFinal: {\"answer\": 249562.5, \"unit\": \"J\"}", "dedupe_signature": "e5a9969e7b8bcb5bd1252a2e774b7bb025ecfcee036fffcc839b4883c0a46ed1", "difficulty": "easy", "final_answer": {"answer": 249562.5, "unit": "J"}, "id": "heat_q_003406_1815_3.125_44", "license": "Apache-2.0", "prompt": "A 1815 g sample has specific heat 3.125 J/(g*K). How much heat is needed to raise its temperature by 44 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1815 * 3.125 * 44.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 44, "heat_capacity": 3.125, "mass_g": 1815}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=10.9 V and R=41 ohm.\nFinal: {\"answer\": 2.8978, \"unit\": \"W\"}", "dedupe_signature": "c8286445433378845aeec7b53231437a9d182fd45c084bfa5326cd40721e29b9", "difficulty": "easy", "final_answer": {"answer": 2.8978, "unit": "W"}, "id": "ohm_power_003407_10.9_41", "license": "Apache-2.0", "prompt": "A resistor has resistance 41 ohm and voltage 10.9 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=10.9 V and R=41 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 41.0, "voltage": 10.9}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=946 mg, t=319 h, and T_half=119.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 148.6979, \"unit\": \"mg\"}", "dedupe_signature": "d32dab1476c614960612e8ec3545d90b7d3ed37d476a1c39a319280cd65639b2", "difficulty": "medium", "final_answer": {"answer": 148.6979, "unit": "mg"}, "id": "half_life_003408_946_119.5_319", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 946 mg. Its half-life is 119.5 hours. How many mg remain after 319 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=946 mg, t=319 h, and T_half=119.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 319.0, "half_life": 119.5, "initial_amount": 946.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 6.34 mol * 58.44 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 370.5096, \"unit\": \"g\"}", "dedupe_signature": "7092578ce643d818e5d299f6c0f432ad8496cb1bce4acc51c271ba0b1bd240a1", "difficulty": "medium", "final_answer": {"answer": 370.5096, "unit": "g"}, "id": "stoich_mass_003409_sodium_chloride_6.34", "license": "Apache-2.0", "prompt": "A sample contains 6.34 mol of sodium chloride. Using molar mass 58.44 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 6.34 mol * 58.44 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "sodium chloride", "molar_mass": 58.44, "moles": 6.34}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 310 mL to 0.31 L.\n3. Compute M = 2.71 / 0.31.\nFinal: {\"answer\": 8.7419, \"unit\": \"mol/L\"}", "dedupe_signature": "6dd6fee97d86b0919db698f92fa2599a2b28bf7c6a873f929d08866253ef7e18", "difficulty": "medium", "final_answer": {"answer": 8.7419, "unit": "mol/L"}, "id": "molarity_003410_2.71_310", "license": "Apache-2.0", "prompt": "A solution contains 2.71 mol of solute in 310 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 310 mL to 0.31 L.\nCompute M = 2.71 / 0.31.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 2.71, "volume_ml": 310}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.36 y, so each step multiplies y by 1 - h*0.36.\n3. Apply that update for 10 steps and round the final state.\nFinal: {\"answer\": 0.0003, \"unit\": \"state_units\"}", "dedupe_signature": "037edb6ae6954a087904e703cd5d3b68ac26f61a4a2cd58e72ea234fd7804b11", "difficulty": "medium", "final_answer": {"answer": 0.0003, "unit": "state_units"}, "id": "euler_decay_003411_50.5_0.36_1.95_10", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.36 y with y(0)=50.5, step size h=1.95, for 10 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.36 y, so each step multiplies y by 1 - h*0.36.\nApply that update for 10 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 50.5, "rate": 0.36, "step": 1.95, "steps": 10}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.3 and add it to the current value.\nFinal: {\"answer\": [-0.26, -0.23, 0.055], \"unit\": \"temperature_units\"}", "dedupe_signature": "fd85962f2af9486ab7619ed62ddf71e59595da090a7a77ba1779578c7bfcef5d", "difficulty": "hard", "final_answer": {"answer": [-0.26, -0.23, 0.055], "unit": "temperature_units"}, "id": "heat_step_003413_0.3_1.15_-0.8_-0.95_1.3_-0.6", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.15, right=-0.6; current interior values are [-0.8, -0.95, 1.3]. Use r=0.3. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.3 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-0.8, -0.95, 1.3], "left": 1.15, "r": 0.3, "right": -0.6}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 45026.0 / 1000.\nFinal: {\"answer\": 45.026, \"unit\": \"kg\"}", "dedupe_signature": "2c8bd5711286466aa4ee3206dfee6bef18d3fc00b63ebc8e1c73a7f138300858", "difficulty": "easy", "final_answer": {"answer": 45.026, "unit": "kg"}, "id": "unit_convert_003414_g_to_kg_45026", "license": "Apache-2.0", "prompt": "Convert 45026 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 45026.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 45026.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=228 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-81.6339, -90.6637], \"unit\": \"N\"}", "dedupe_signature": "582e6e520714507ca77c05e8e4fa80b604e9e91c40ddb1c0dd71d8a32f3eb353", "difficulty": "medium", "final_answer": {"answer": [-81.6339, -90.6637], "unit": "N"}, "id": "vector_components_003415_122_228", "license": "Apache-2.0", "prompt": "A vector has magnitude 122 N at 228 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=228 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 228, "magnitude": 122.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-5.4, 6.75], \"unit\": \"dimensionless\"}", "dedupe_signature": "42567c249d753de137f9c928d8b3c673b679b02ac5355de5e3b39c0efceb4160", "difficulty": "medium", "final_answer": {"answer": [-5.4, 6.75], "unit": "dimensionless"}, "id": "line_two_point_003416_-15.5_-12.25_-5.4_6.75", "license": "Apache-2.0", "prompt": "A line passes through points (-15.5, 90.45) and (-12.25, 72.9). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -15.5, "x2": -12.25, "y1": 90.45, "y2": 72.9}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. m*v is momentum, not energy\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "829c8d3a4acdb061b467a424e55990bfe7d08869dfd33001b4ebd41e98be4f3f", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_003417_inconsistent_1e14b074_160666", "license": "Apache-2.0", "prompt": "In quality-control check case 160666, check dimensional consistency for E = m * v. The left side has dimensions kg*m^2/s^2 and the right side has dimensions kg*m/s. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nm*v is momentum, not energy\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "E = m * v"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef pairwise_ratios_003418(numerators, denominators):\n    if len(numerators) != len(denominators):\n        raise ValueError('length mismatch')\n    out = []\n    for numerator, denominator in zip(numerators, denominators):\n        if denominator == 0:\n            raise ValueError('zero denominator')\n        out.append(numerator / denominator)\n    return out\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"pairwise_ratios_003418\"}", "dedupe_signature": "ffdc8c7d0cc14b6cb8debe2d593512d9cee14d5b964c9d94be0dfb4c022f6bb5", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "pairwise_ratios_003418"}, "id": "code_003418_pairwise_ratios_003418", "license": "Apache-2.0", "prompt": "Write a Python function pairwise_ratios_003418(numerators, denominators) that returns a list of n/d values. Raise ValueError if lengths differ or any denominator is zero. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "pairwise_ratios_003418"}, "verifier": {"function": "pairwise_ratios_003418", "tests": ["assert pairwise_ratios_003418([2, 9], [4, 3]) == [0.5, 3.0]", "try:\n    pairwise_ratios_003418([1], [0])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass", "try:\n    pairwise_ratios_003418([1, 2], [1])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: recurrence, objective, tie_breaking_rule.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"recurrence\", \"objective\", \"tie_breaking_rule\"]}", "dedupe_signature": "e875a6d3a4050531b837c0046e86560b3bf272139a7cf665b63d34a8821c5faf", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["recurrence", "objective", "tie_breaking_rule"]}, "id": "abstain_003419_recurrence_objective_tie_breaking_rule", "license": "Apache-2.0", "prompt": "Write a dynamic-programming solver for a scheduler scoring problem with 3832 items and budget 8000, but the recurrence, objective, and tie-breaking rule are all absent. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: recurrence, objective, tie_breaking_rule.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["recurrence", "objective", "tie_breaking_rule"]}, "verifier": {"missing": ["recurrence", "objective", "tie_breaking_rule"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 4.15 kg and a = 4.3 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 17.845, \"unit\": \"N\"}", "dedupe_signature": "083eaa51720c6ca94d67ed49d30fc3946f63a642ef8eeb90f594765a664a32a5", "difficulty": "easy", "final_answer": {"answer": 17.845, "unit": "N"}, "id": "force_003420_4.15_4.3", "license": "Apache-2.0", "prompt": "A cart has mass 4.15 kg and measured acceleration 4.3 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 4.15 kg and a = 4.3 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 4.3, "mass": 4.15}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 42.15^2 and multiply by 0.5 * 25.7.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 22829.5991, \"unit\": \"J\"}", "dedupe_signature": "6bffec7958f447befd6fb7839b949fd7df8db66ce86cb374db6bc2b0dcf74acd", "difficulty": "easy", "final_answer": {"answer": 22829.5991, "unit": "J"}, "id": "ke_003421_25.7_42.15", "license": "Apache-2.0", "prompt": "A body of mass 25.7 kg moves at 42.15 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 42.15^2 and multiply by 0.5 * 25.7.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 25.7, "velocity": 42.15}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=44 degrees through the sine of 2 theta.\n3. Substitute v=70.9 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 512.1048, \"unit\": \"m\"}", "dedupe_signature": "fe145358f97efaa4a9bb4d2c727ae1d5f4997df0a556842eb10ad7e423c63ceb", "difficulty": "medium", "final_answer": {"answer": 512.1048, "unit": "m"}, "id": "projectile_range_003422_70.9_44", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 70.9 m/s and angle 44 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=44 degrees through the sine of 2 theta.\nSubstitute v=70.9 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 44, "gravity": 9.81, "speed": 70.9}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1980 * 3.51 * 33.\nFinal: {\"answer\": 229343.4, \"unit\": \"J\"}", "dedupe_signature": "b67fff7fb462add1fa35d81261d72b719d202b4e624966d76a9e915a5d94a0b3", "difficulty": "easy", "final_answer": {"answer": 229343.4, "unit": "J"}, "id": "heat_q_003424_1980_3.51_33", "license": "Apache-2.0", "prompt": "A 1980 g sample has specific heat 3.51 J/(g*K). How much heat is needed to raise its temperature by 33 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1980 * 3.51 * 33.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 33, "heat_capacity": 3.51, "mass_g": 1980}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=133.5 V and R=3.8 ohm.\nFinal: {\"answer\": 4690.0658, \"unit\": \"W\"}", "dedupe_signature": "8416c72e7e9d4dcc96066abc6f64704bfb7ef1fc6426e7c4573b6030e355a9a5", "difficulty": "easy", "final_answer": {"answer": 4690.0658, "unit": "W"}, "id": "ohm_power_003425_133.5_3.8", "license": "Apache-2.0", "prompt": "A resistor has resistance 3.8 ohm and voltage 133.5 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=133.5 V and R=3.8 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 3.8, "voltage": 133.5}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=292 mg, t=61.5 h, and T_half=87 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 178.8899, \"unit\": \"mg\"}", "dedupe_signature": "22cff65b36756ccf10443dacee742f58400dcd0a33575280da618c23b1ad6b7b", "difficulty": "medium", "final_answer": {"answer": 178.8899, "unit": "mg"}, "id": "half_life_003426_292_87_61.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 292 mg. Its half-life is 87 hours. How many mg remain after 61.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=292 mg, t=61.5 h, and T_half=87 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 61.5, "half_life": 87.0, "initial_amount": 292.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 4.98 mol * 100.087 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 498.4333, \"unit\": \"g\"}", "dedupe_signature": "35f268efb36d6f503273024987b712d82d0c7f1395d022b6b82167ac204ccc72", "difficulty": "medium", "final_answer": {"answer": 498.4333, "unit": "g"}, "id": "stoich_mass_003427_calcium_carbonate_4.98", "license": "Apache-2.0", "prompt": "A sample contains 4.98 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 4.98 mol * 100.087 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "calcium carbonate", "molar_mass": 100.087, "moles": 4.98}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.05 y, so each step multiplies y by 1 - h*0.05.\n3. Apply that update for 6 steps and round the final state.\nFinal: {\"answer\": 60.2783, \"unit\": \"state_units\"}", "dedupe_signature": "b58bce3460084741f024a3e34c6c24b71e414cd5543836d20d59e610bc7dd583", "difficulty": "medium", "final_answer": {"answer": 60.2783, "unit": "state_units"}, "id": "euler_decay_003429_66_0.05_0.3_6", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.05 y with y(0)=66, step size h=0.3, for 6 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.05 y, so each step multiplies y by 1 - h*0.05.\nApply that update for 6 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 66.0, "rate": 0.05, "step": 0.3, "steps": 6}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(9.7)=40.44 and f(18.4)=85.68.\n3. The interval width is 8.7.\nFinal: {\"answer\": 548.622, \"unit\": \"area_units\"}", "dedupe_signature": "db94d78d16392c8566b316a412f758b72abafda4985cbe8d62959477d2e13502", "difficulty": "medium", "final_answer": {"answer": 548.622, "unit": "area_units"}, "id": "trapz_linear_003430_5.2_-10_9.7_18.4", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=5.2x+-10 from x=9.7 to x=18.4. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(9.7)=40.44 and f(18.4)=85.68.\nThe interval width is 8.7.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -10.0, "slope": 5.2, "x0": 9.7, "x1": 18.4}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.14 and add it to the current value.\nFinal: {\"answer\": [0.316, 2.287, 2.47], \"unit\": \"temperature_units\"}", "dedupe_signature": "1aa4741c2c090a4b57341341805aafb232ff321e1833b9f4d5e5c406122f61c9", "difficulty": "hard", "final_answer": {"answer": [0.316, 2.287, 2.47], "unit": "temperature_units"}, "id": "heat_step_003431_0.14_-0.7_0.05_2.7_2.4_2.6", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-0.7, right=2.6; current interior values are [0.05, 2.7, 2.4]. Use r=0.14. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.14 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [0.05, 2.7, 2.4], "left": -0.7, "r": 0.14, "right": 2.6}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 100 centimeters in one meter.\n2. Apply the conversion factor directly to the given value.\n3. Compute 3410.5 / 100.\nFinal: {\"answer\": 34.105, \"unit\": \"m\"}", "dedupe_signature": "f3fbc267334fb7ea4921d3b114b080db71e1c3c3478963ecc62312ec0fa59f6e", "difficulty": "easy", "final_answer": {"answer": 34.105, "unit": "m"}, "id": "unit_convert_003432_cm_to_m_3410.5", "license": "Apache-2.0", "prompt": "Convert 3410.5 cm to m. Return the converted value with unit.", "reasoning_trace": "There are 100 centimeters in one meter.\nApply the conversion factor directly to the given value.\nCompute 3410.5 / 100.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 3410.5}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=156 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-309.2351, 137.6804], \"unit\": \"N\"}", "dedupe_signature": "7c795b71e4403ce44412b71bc972a6b16ccf322032c06d64d43df67e59255f2d", "difficulty": "medium", "final_answer": {"answer": [-309.2351, 137.6804], "unit": "N"}, "id": "vector_components_003433_338.5_156", "license": "Apache-2.0", "prompt": "A vector has magnitude 338.5 N at 156 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=156 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 156, "magnitude": 338.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [7.9, -17.5], \"unit\": \"dimensionless\"}", "dedupe_signature": "aad1f3958da552edaecef04473904f15cb49dc652002cf355b897fed1d660fc2", "difficulty": "medium", "final_answer": {"answer": [7.9, -17.5], "unit": "dimensionless"}, "id": "line_two_point_003434_3.5_13.25_7.9_-17.5", "license": "Apache-2.0", "prompt": "A line passes through points (3.5, 10.15) and (13.25, 87.175). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 3.5, "x2": 13.25, "y1": 10.150000000000002, "y2": 87.17500000000001}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. velocity times time gives distance, not acceleration\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "8e1dddb0bc7d52bd33d0432630131ef70b4bea398073f685bb22e97b60a240a9", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_003435_inconsistent_7481c798_921558", "license": "Apache-2.0", "prompt": "In simulation spec case 921558, check dimensional consistency for a = v * t. The left side has dimensions m/s^2 and the right side has dimensions m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nvelocity times time gives distance, not acceleration\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "a = v * t"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef center_values_003436(values):\n    if not values:\n        raise ValueError('center_values requires at least one value')\n    mean = sum(values) / len(values)\n    return [value - mean for value in values]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"center_values_003436\"}", "dedupe_signature": "7eb238880a95b126e84e6f672a52a86c6a98d96b5bb06794b906e0b90e3eb071", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "center_values_003436"}, "id": "code_003436_center_values_003436", "license": "Apache-2.0", "prompt": "Write a Python function center_values_003436(values) that subtracts the arithmetic mean from each value and returns a new list. Raise ValueError for an empty input. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "center_values_003436"}, "verifier": {"function": "center_values_003436", "tests": ["out = center_values_003436([1, 2, 3]); assert out == [-1, 0, 1]", "assert center_values_003436([5]) == [0]", "try:\n    center_values_003436([])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: required_fields, allowed_transformations.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"required_fields\", \"allowed_transformations\"]}", "dedupe_signature": "704eb257a89ac5f56ef1c30bbe6a6dd6c5fe3a7b30117b2c98ec5f34def3a15e", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["required_fields", "allowed_transformations"]}, "id": "abstain_003437_required_fields_allowed_transformations", "license": "Apache-2.0", "prompt": "Write a sanitizer for valid billing clinical records in release 303562, but the prompt does not state which fields are required or which transformations are allowed. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: required_fields, allowed_transformations.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["required_fields", "allowed_transformations"]}, "verifier": {"missing": ["required_fields", "allowed_transformations"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 3.95 kg and a = 5.55 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 21.9225, \"unit\": \"N\"}", "dedupe_signature": "79f968f1ea7c25a7d312aa838e7389707ba3fb75ad7aff5d13fb5008a45931c7", "difficulty": "easy", "final_answer": {"answer": 21.9225, "unit": "N"}, "id": "force_003438_3.95_5.55", "license": "Apache-2.0", "prompt": "A cart has mass 3.95 kg and measured acceleration 5.55 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 3.95 kg and a = 5.55 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 5.55, "mass": 3.95}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 41.1^2 and multiply by 0.5 * 4.05.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 3420.6503, \"unit\": \"J\"}", "dedupe_signature": "f647d925aa7577e136e06b4b4f9f38bacb54ebcdabd3fd3ad4f35c51d1bc504b", "difficulty": "easy", "final_answer": {"answer": 3420.6503, "unit": "J"}, "id": "ke_003439_4.05_41.1", "license": "Apache-2.0", "prompt": "A body of mass 4.05 kg moves at 41.1 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 41.1^2 and multiply by 0.5 * 4.05.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 4.05, "velocity": 41.1}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=24 degrees through the sine of 2 theta.\n3. Substitute v=5.5 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 2.2916, \"unit\": \"m\"}", "dedupe_signature": "774badf1ff1eab95784fb7962250f1407c1a8c89701d4531ba0f457428810eb5", "difficulty": "medium", "final_answer": {"answer": 2.2916, "unit": "m"}, "id": "projectile_range_003440_5.5_24", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 5.5 m/s and angle 24 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=24 degrees through the sine of 2 theta.\nSubstitute v=5.5 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 24, "gravity": 9.81, "speed": 5.5}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 0.46 * 8.314 * 396 / 9.1.\nFinal: {\"answer\": 166.4262, \"unit\": \"kPa\"}", "dedupe_signature": "ce3ef85c78305c0415a90543ab235418f0b05ca32dbcc1868a2534acb2f71dcc", "difficulty": "medium", "final_answer": {"answer": 166.4262, "unit": "kPa"}, "id": "ideal_gas_003441_0.46_396_9.1", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=0.46 mol, T=396 K, and V=9.1 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 0.46 * 8.314 * 396 / 9.1.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 0.46, "temp_k": 396, "volume_l": 9.1}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1925 * 4.925 * 80.\nFinal: {\"answer\": 758450.0, \"unit\": \"J\"}", "dedupe_signature": "17c8e0aef772234b766142ad7b5bc5a65a017ae2c8faa2940d70dd5f694eae99", "difficulty": "easy", "final_answer": {"answer": 758450.0, "unit": "J"}, "id": "heat_q_003442_1925_4.925_80", "license": "Apache-2.0", "prompt": "A 1925 g sample has specific heat 4.925 J/(g*K). How much heat is needed to raise its temperature by 80 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1925 * 4.925 * 80.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 80, "heat_capacity": 4.925, "mass_g": 1925}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=152.3 V and R=97.2 ohm.\nFinal: {\"answer\": 238.6347, \"unit\": \"W\"}", "dedupe_signature": "fe370c95a45c55d8035931c98cb75af730f469fe247fdcfcc1dad4abde74764a", "difficulty": "easy", "final_answer": {"answer": 238.6347, "unit": "W"}, "id": "ohm_power_003443_152.3_97.2", "license": "Apache-2.0", "prompt": "A resistor has resistance 97.2 ohm and voltage 152.3 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=152.3 V and R=97.2 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 97.2, "voltage": 152.3}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=322.5 mg, t=228.5 h, and T_half=55.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 18.5846, \"unit\": \"mg\"}", "dedupe_signature": "c33bcd6d00c62b59e662d2f3b517de8a12a8382ee8406f3b30cbbad4149c0a96", "difficulty": "medium", "final_answer": {"answer": 18.5846, "unit": "mg"}, "id": "half_life_003444_322.5_55.5_228.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 322.5 mg. Its half-life is 55.5 hours. How many mg remain after 228.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=322.5 mg, t=228.5 h, and T_half=55.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 228.5, "half_life": 55.5, "initial_amount": 322.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 1960 mL to 1.96 L.\n3. Compute M = 1.875 / 1.96.\nFinal: {\"answer\": 0.9566, \"unit\": \"mol/L\"}", "dedupe_signature": "2d12d4435d514ca2a82f388b7f55312a23917e10189e57a01050205490ef7974", "difficulty": "medium", "final_answer": {"answer": 0.9566, "unit": "mol/L"}, "id": "molarity_003446_1.875_1960", "license": "Apache-2.0", "prompt": "A solution contains 1.875 mol of solute in 1960 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 1960 mL to 1.96 L.\nCompute M = 1.875 / 1.96.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 1.875, "volume_ml": 1960}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.41 y, so each step multiplies y by 1 - h*0.41.\n3. Apply that update for 3 steps and round the final state.\nFinal: {\"answer\": 3.2476, \"unit\": \"state_units\"}", "dedupe_signature": "545e328258dc15f3effc703a9764a603877eee94c6187de55812d1fae6c3d1ce", "difficulty": "medium", "final_answer": {"answer": 3.2476, "unit": "state_units"}, "id": "euler_decay_003447_22_0.41_1.15_3", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.41 y with y(0)=22, step size h=1.15, for 3 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.41 y, so each step multiplies y by 1 - h*0.41.\nApply that update for 3 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 22.0, "rate": 0.41, "step": 1.15, "steps": 3}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(7.6)=30.6 and f(12.8)=56.6.\n3. The interval width is 5.2.\nFinal: {\"answer\": 226.72, \"unit\": \"area_units\"}", "dedupe_signature": "2f41d093c8d7e930aa4a2be0775b02d094bd841fafa7db0366e387d6686f3493", "difficulty": "medium", "final_answer": {"answer": 226.72, "unit": "area_units"}, "id": "trapz_linear_003448_5_-7.4_7.6_12.8", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=5x+-7.4 from x=7.6 to x=12.8. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(7.6)=30.6 and f(12.8)=56.6.\nThe interval width is 5.2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -7.4, "slope": 5.0, "x0": 7.6, "x1": 12.8}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=274 degrees and keep the unit as newtons.\nFinal: {\"answer\": [24.6938, -353.1377], \"unit\": \"N\"}", "dedupe_signature": "fbffd2d4cfb45d3b1b2c29b5cb85e1d955667fa20a18c4edb4ba0c1058bae762", "difficulty": "medium", "final_answer": {"answer": [24.6938, -353.1377], "unit": "N"}, "id": "vector_components_003451_354_274", "license": "Apache-2.0", "prompt": "A vector has magnitude 354 N at 274 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=274 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 274, "magnitude": 354.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-5.95, -2.0], \"unit\": \"dimensionless\"}", "dedupe_signature": "eaed1cfa1fb5bf8f3b89787c6f0468f8259f9d0e7e0af187d8184e58cacd9fea", "difficulty": "medium", "final_answer": {"answer": [-5.95, -2.0], "unit": "dimensionless"}, "id": "line_two_point_003452_-19_-15.5_-5.95_-2", "license": "Apache-2.0", "prompt": "A line passes through points (-19, 111.05) and (-15.5, 90.225). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -19.0, "x2": -15.5, "y1": 111.05, "y2": 90.22500000000001}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. velocity times time gives distance, not acceleration\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "35cb7508e3cc55e24b8282eea4246671b36542c21f7ba73e2935159cd51af592", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_003453_inconsistent_7481c798_764834", "license": "Apache-2.0", "prompt": "In field worksheet case 764834, check dimensional consistency for a = v * t. The left side has dimensions m/s^2 and the right side has dimensions m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nvelocity times time gives distance, not acceleration\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "a = v * t"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef safe_mean_003454(values):\n    if not values:\n        raise ValueError('safe_mean requires at least one value')\n    return sum(values) / len(values)\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"safe_mean_003454\"}", "dedupe_signature": "2a978a8ba82f91b9e03b3c601595c6582006c24e7015ab33a77c2f694ba5d1ff", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "safe_mean_003454"}, "id": "code_003454_safe_mean_003454", "license": "Apache-2.0", "prompt": "Write a Python function safe_mean_003454(values) that returns the arithmetic mean. It must raise ValueError for an empty input and must not mutate the input list. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "safe_mean_003454"}, "verifier": {"function": "safe_mean_003454", "tests": ["assert safe_mean_003454([2, 4, 6]) == 4", "xs = [1, 2, 3]; assert safe_mean_003454(xs) == 2 and xs == [1, 2, 3]", "try:\n    safe_mean_003454([])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: left_boundary, right_boundary.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"left_boundary\", \"right_boundary\"]}", "dedupe_signature": "37aacf879071632e4773b8a53896a74d9bcc19cfc1f00d1a87c307d5b658c4b2", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["left_boundary", "right_boundary"]}, "id": "abstain_003455_left_boundary_right_boundary", "license": "Apache-2.0", "prompt": "Solve the 1D heat equation after one finite-difference step. The prompt gives r=0.3 and interior values [-1.65, 1.5, 1.2], but gives no boundary values. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: left_boundary, right_boundary.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["left_boundary", "right_boundary"]}, "verifier": {"missing": ["left_boundary", "right_boundary"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 36.9^2 and multiply by 0.5 * 28.4.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 19334.862, \"unit\": \"J\"}", "dedupe_signature": "feb960384ada0730de4a8c9165ea2e2832d6f9cef593435480bf55a4b74cb626", "difficulty": "easy", "final_answer": {"answer": 19334.862, "unit": "J"}, "id": "ke_003457_28.4_36.9", "license": "Apache-2.0", "prompt": "A body of mass 28.4 kg moves at 36.9 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 36.9^2 and multiply by 0.5 * 28.4.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 28.4, "velocity": 36.9}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=54 degrees through the sine of 2 theta.\n3. Substitute v=78.6 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 598.9387, \"unit\": \"m\"}", "dedupe_signature": "a8480a46578f6fc9c307e623114c03bb1e85710398cc1276f3180c18ee6307bc", "difficulty": "medium", "final_answer": {"answer": 598.9387, "unit": "m"}, "id": "projectile_range_003458_78.6_54", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 78.6 m/s and angle 54 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=54 degrees through the sine of 2 theta.\nSubstitute v=78.6 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 54, "gravity": 9.81, "speed": 78.6}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 4.37 * 8.314 * 447 / 27.6.\nFinal: {\"answer\": 588.4233, \"unit\": \"kPa\"}", "dedupe_signature": "ef99d50d3acd8b96f7a6b79c44c9d1aa84a5d30c223244555dc94576a564a92f", "difficulty": "medium", "final_answer": {"answer": 588.4233, "unit": "kPa"}, "id": "ideal_gas_003459_4.37_447_27.6", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=4.37 mol, T=447 K, and V=27.6 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 4.37 * 8.314 * 447 / 27.6.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 4.37, "temp_k": 447, "volume_l": 27.6}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 835 * 2.875 * 113.\nFinal: {\"answer\": 271270.625, \"unit\": \"J\"}", "dedupe_signature": "53cf661d10e7c2a64858eae783cdf112a9bede23e10bc9edd6dd6c0876ae7cdc", "difficulty": "easy", "final_answer": {"answer": 271270.625, "unit": "J"}, "id": "heat_q_003460_835_2.875_113", "license": "Apache-2.0", "prompt": "A 835 g sample has specific heat 2.875 J/(g*K). How much heat is needed to raise its temperature by 113 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 835 * 2.875 * 113.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 113, "heat_capacity": 2.875, "mass_g": 835}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=631.5 mg, t=162.5 h, and T_half=86 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 170.4381, \"unit\": \"mg\"}", "dedupe_signature": "f1339244e35f839d56e8be128c1b948f14c48693f5685fdc419790e751784807", "difficulty": "medium", "final_answer": {"answer": 170.4381, "unit": "mg"}, "id": "half_life_003462_631.5_86_162.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 631.5 mg. Its half-life is 86 hours. How many mg remain after 162.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=631.5 mg, t=162.5 h, and T_half=86 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 162.5, "half_life": 86.0, "initial_amount": 631.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 3.77 mol * 100.087 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 377.328, \"unit\": \"g\"}", "dedupe_signature": "f875d39e076e6bef0f033bcd0a66b47c63d6da56a8d5b0c7533c6efa4f42b915", "difficulty": "medium", "final_answer": {"answer": 377.328, "unit": "g"}, "id": "stoich_mass_003463_calcium_carbonate_3.77", "license": "Apache-2.0", "prompt": "A sample contains 3.77 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 3.77 mol * 100.087 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "calcium carbonate", "molar_mass": 100.087, "moles": 3.77}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 1680 mL to 1.68 L.\n3. Compute M = 3.445 / 1.68.\nFinal: {\"answer\": 2.0506, \"unit\": \"mol/L\"}", "dedupe_signature": "f6f8add52b6a88da81b7871da653a376250d3889e9a89937961c391e0ac5208f", "difficulty": "medium", "final_answer": {"answer": 2.0506, "unit": "mol/L"}, "id": "molarity_003464_3.445_1680", "license": "Apache-2.0", "prompt": "A solution contains 3.445 mol of solute in 1680 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 1680 mL to 1.68 L.\nCompute M = 3.445 / 1.68.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 3.445, "volume_ml": 1680}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.43 y, so each step multiplies y by 1 - h*0.43.\n3. Apply that update for 11 steps and round the final state.\nFinal: {\"answer\": 0.0011, \"unit\": \"state_units\"}", "dedupe_signature": "2581b7eb88ff56334146ec44aabea938c8899574725d878f2addb1136283a017", "difficulty": "medium", "final_answer": {"answer": 0.0011, "unit": "state_units"}, "id": "euler_decay_003465_5.5_0.43_1.25_11", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.43 y with y(0)=5.5, step size h=1.25, for 11 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.43 y, so each step multiplies y by 1 - h*0.43.\nApply that update for 11 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 5.5, "rate": 0.43, "step": 1.25, "steps": 11}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.06 and add it to the current value.\nFinal: {\"answer\": [1.801, -1.55, 1.237], \"unit\": \"temperature_units\"}", "dedupe_signature": "a9eb53ee4b91d193c97c9a22e3aade2a4f4529d4acac466d09b720b93ae2b72d", "difficulty": "hard", "final_answer": {"answer": [1.801, -1.55, 1.237], "unit": "temperature_units"}, "id": "heat_step_003467_0.06_1.95_2.05_-2.0_1.45_1.35", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.95, right=1.35; current interior values are [2.05, -2.0, 1.45]. Use r=0.06. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.06 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [2.05, -2.0, 1.45], "left": 1.95, "r": 0.06, "right": 1.35}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=35 degrees and keep the unit as newtons.\nFinal: {\"answer\": [208.0646, 145.6884], \"unit\": \"N\"}", "dedupe_signature": "43771c82bc760b6018bd8e16532b54ca147155973d1a98e3a52c52d024cc543b", "difficulty": "medium", "final_answer": {"answer": [208.0646, 145.6884], "unit": "N"}, "id": "vector_components_003469_254_35", "license": "Apache-2.0", "prompt": "A vector has magnitude 254 N at 35 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=35 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 35, "magnitude": 254.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: required_fields, allowed_transformations.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"required_fields\", \"allowed_transformations\"]}", "dedupe_signature": "abb2137e29cee86b4f1ae75408160fab2dd2697084bfcd75f12efef534e512bc", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["required_fields", "allowed_transformations"]}, "id": "abstain_003473_required_fields_allowed_transformations", "license": "Apache-2.0", "prompt": "Write a sanitizer for valid registry invoice records in release 993551, but the prompt does not state which fields are required or which transformations are allowed. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: required_fields, allowed_transformations.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["required_fields", "allowed_transformations"]}, "verifier": {"missing": ["required_fields", "allowed_transformations"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 15.4 kg and a = 5.85 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 90.09, \"unit\": \"N\"}", "dedupe_signature": "e9b6a50b3eb5d500c35d5b3955a40357b94e2175dcf0b6c2ce8345543f9fb86f", "difficulty": "easy", "final_answer": {"answer": 90.09, "unit": "N"}, "id": "force_003474_15.4_5.85", "license": "Apache-2.0", "prompt": "A cart has mass 15.4 kg and measured acceleration 5.85 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 15.4 kg and a = 5.85 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 5.85, "mass": 15.4}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 1.95^2 and multiply by 0.5 * 12.9.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 24.5261, \"unit\": \"J\"}", "dedupe_signature": "0d84bd045eb0f9f7018eb1cc4e2a980bbbaaaf32d61a0d8eb43b2d3782a892dd", "difficulty": "easy", "final_answer": {"answer": 24.5261, "unit": "J"}, "id": "ke_003475_12.9_1.95", "license": "Apache-2.0", "prompt": "A body of mass 12.9 kg moves at 1.95 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 1.95^2 and multiply by 0.5 * 12.9.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 12.9, "velocity": 1.95}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=69 degrees through the sine of 2 theta.\n3. Substitute v=30.5 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 63.4515, \"unit\": \"m\"}", "dedupe_signature": "8b03aba2b17d899f6d9f9d0a18f6d08b7a05c0d55ca7f9309069f92f7100ad55", "difficulty": "medium", "final_answer": {"answer": 63.4515, "unit": "m"}, "id": "projectile_range_003476_30.5_69", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 30.5 m/s and angle 69 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=69 degrees through the sine of 2 theta.\nSubstitute v=30.5 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 69, "gravity": 9.81, "speed": 30.5}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 3.71 * 8.314 * 507 / 22.9.\nFinal: {\"answer\": 682.8989, \"unit\": \"kPa\"}", "dedupe_signature": "c0a3c36125c9fcbbdbddd3e867a39c906f99efd6f5e17be23c6bc68c3f7d6a94", "difficulty": "medium", "final_answer": {"answer": 682.8989, "unit": "kPa"}, "id": "ideal_gas_003477_3.71_507_22.9", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=3.71 mol, T=507 K, and V=22.9 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 3.71 * 8.314 * 507 / 22.9.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 3.71, "temp_k": 507, "volume_l": 22.9}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 755 * 4.66 * 4.\nFinal: {\"answer\": 14073.2, \"unit\": \"J\"}", "dedupe_signature": "05bd0379e9a69ecd28bc4d931b34e8b59d51ecd501137f43625f0fe715d2d9b3", "difficulty": "easy", "final_answer": {"answer": 14073.2, "unit": "J"}, "id": "heat_q_003478_755_4.66_4", "license": "Apache-2.0", "prompt": "A 755 g sample has specific heat 4.66 J/(g*K). How much heat is needed to raise its temperature by 4 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 755 * 4.66 * 4.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 4, "heat_capacity": 4.66, "mass_g": 755}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=220.4 V and R=74.5 ohm.\nFinal: {\"answer\": 652.029, \"unit\": \"W\"}", "dedupe_signature": "f187558d8f0614d963888aa6054bf126d0fb24188dba2c4a4659bd361536b2f0", "difficulty": "easy", "final_answer": {"answer": 652.029, "unit": "W"}, "id": "ohm_power_003479_220.4_74.5", "license": "Apache-2.0", "prompt": "A resistor has resistance 74.5 ohm and voltage 220.4 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=220.4 V and R=74.5 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 74.5, "voltage": 220.4}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 0.22 mol * 18.015 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 3.9633, \"unit\": \"g\"}", "dedupe_signature": "5191d2e741077e0142ea274be6cd5cf8e7e790c7aae33b4d055124715af4bc70", "difficulty": "medium", "final_answer": {"answer": 3.9633, "unit": "g"}, "id": "stoich_mass_003481_water_0.22", "license": "Apache-2.0", "prompt": "A sample contains 0.22 mol of water. Using molar mass 18.015 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 0.22 mol * 18.015 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "water", "molar_mass": 18.015, "moles": 0.22}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(9.9)=-19.12 and f(15.5)=-40.4.\n3. The interval width is 5.6.\nFinal: {\"answer\": -166.656, \"unit\": \"area_units\"}", "dedupe_signature": "ecddf7a44301793c5a6fd2094a041e5f0208e19860a778cb9a75c28aba7699f8", "difficulty": "medium", "final_answer": {"answer": -166.656, "unit": "area_units"}, "id": "trapz_linear_003484_-3.8_18.5_9.9_15.5", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-3.8x+18.5 from x=9.9 to x=15.5. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(9.9)=-19.12 and f(15.5)=-40.4.\nThe interval width is 5.6.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 18.5, "slope": -3.8, "x0": 9.9, "x1": 15.5}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.42 and add it to the current value.\nFinal: {\"answer\": [0.76, 0.366, -0.815], \"unit\": \"temperature_units\"}", "dedupe_signature": "8f4efff28b87a2e220345dc0f40485c92acfc8b38193cf060953a644f4dfa1a8", "difficulty": "hard", "final_answer": {"answer": [0.76, 0.366, -0.815], "unit": "temperature_units"}, "id": "heat_step_003485_0.42_2.6_-0.5_-0.6_1.6_-1.95", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=2.6, right=-1.95; current interior values are [-0.5, -0.6, 1.6]. Use r=0.42. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.42 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-0.5, -0.6, 1.6], "left": 2.6, "r": 0.42, "right": -1.95}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 100 centimeters in one meter.\n2. Apply the conversion factor directly to the given value.\n3. Compute 3408.0 / 100.\nFinal: {\"answer\": 34.08, \"unit\": \"m\"}", "dedupe_signature": "fd0ed0bcc5d2f788a748e0becfcf7e6fd0c53052ce994be022948d1346888ce7", "difficulty": "easy", "final_answer": {"answer": 34.08, "unit": "m"}, "id": "unit_convert_003486_cm_to_m_3408", "license": "Apache-2.0", "prompt": "Convert 3408 cm to m. Return the converted value with unit.", "reasoning_trace": "There are 100 centimeters in one meter.\nApply the conversion factor directly to the given value.\nCompute 3408.0 / 100.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 3408.0}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=12 degrees and keep the unit as newtons.\nFinal: {\"answer\": [211.769, 45.0129], \"unit\": \"N\"}", "dedupe_signature": "2da7e67d99db0ede5d135886d8c3cde872a17934a2f3146fe6865f6d533ac52d", "difficulty": "medium", "final_answer": {"answer": [211.769, 45.0129], "unit": "N"}, "id": "vector_components_003487_216.5_12", "license": "Apache-2.0", "prompt": "A vector has magnitude 216.5 N at 12 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=12 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 12, "magnitude": 216.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [5.25, 18.25], \"unit\": \"dimensionless\"}", "dedupe_signature": "334f4e8bb8cc6da46db90e70aa2505167606b53bc0db4a576d5d429355552519", "difficulty": "medium", "final_answer": {"answer": [5.25, 18.25], "unit": "dimensionless"}, "id": "line_two_point_003488_-3_2.75_5.25_18.25", "license": "Apache-2.0", "prompt": "A line passes through points (-3, 2.5) and (2.75, 32.6875). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -3.0, "x2": 2.75, "y1": 2.5, "y2": 32.6875}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef threshold_flags_003490(values, threshold):\n    return [value >= threshold for value in values]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"threshold_flags_003490\"}", "dedupe_signature": "8f55d122608f7eedbb63c2b014fdeb8834ecb022ee040f7a66ac0dc580e842f0", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "threshold_flags_003490"}, "id": "code_003490_threshold_flags_003490", "license": "Apache-2.0", "prompt": "Write a Python function threshold_flags_003490(values, threshold) that returns a list of booleans showing whether each value is greater than or equal to threshold. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "threshold_flags_003490"}, "verifier": {"function": "threshold_flags_003490", "tests": ["assert threshold_flags_003490([1, 2, 3], 2) == [False, True, True]", "assert threshold_flags_003490([], 5) == []", "assert threshold_flags_003490([-1, 0], 0) == [False, True]"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: left_boundary, right_boundary.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"left_boundary\", \"right_boundary\"]}", "dedupe_signature": "6aec5e40d354cd37ce94785a9b9f09b832d59add025135656eb10de3896aae16", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["left_boundary", "right_boundary"]}, "id": "abstain_003491_left_boundary_right_boundary", "license": "Apache-2.0", "prompt": "Solve the 1D heat equation after one finite-difference step. The prompt gives r=0.16 and interior values [0.7, 0.65, 2.8], but gives no boundary values. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: left_boundary, right_boundary.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["left_boundary", "right_boundary"]}, "verifier": {"missing": ["left_boundary", "right_boundary"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 1.1 kg and a = 15.95 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 17.545, \"unit\": \"N\"}", "dedupe_signature": "18b667c710cd36cd8a17376d2087492e93dc52fd3c4bf315edc1fce80e96ea3e", "difficulty": "easy", "final_answer": {"answer": 17.545, "unit": "N"}, "id": "force_003492_1.1_15.95", "license": "Apache-2.0", "prompt": "A cart has mass 1.1 kg and measured acceleration 15.95 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 1.1 kg and a = 15.95 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 15.95, "mass": 1.1}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=45 degrees through the sine of 2 theta.\n3. Substitute v=78.7 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 631.3649, \"unit\": \"m\"}", "dedupe_signature": "14093e458ddfde44d4542b1a19f4f7c02620b7fb0179def349326e91d6a5db29", "difficulty": "medium", "final_answer": {"answer": 631.3649, "unit": "m"}, "id": "projectile_range_003494_78.7_45", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 78.7 m/s and angle 45 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=45 degrees through the sine of 2 theta.\nSubstitute v=78.7 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 45, "gravity": 9.81, "speed": 78.7}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 2.81 * 8.314 * 497 / 47.3.\nFinal: {\"answer\": 245.4774, \"unit\": \"kPa\"}", "dedupe_signature": "bc858a60c28858cf8048de8824aaf052d95c70cadbe7e39911cf1d382f228284", "difficulty": "medium", "final_answer": {"answer": 245.4774, "unit": "kPa"}, "id": "ideal_gas_003495_2.81_497_47.3", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=2.81 mol, T=497 K, and V=47.3 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 2.81 * 8.314 * 497 / 47.3.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 2.81, "temp_k": 497, "volume_l": 47.3}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 240 * 4.335 * 98.\nFinal: {\"answer\": 101959.2, \"unit\": \"J\"}", "dedupe_signature": "a6d756cd1b8ab6c9ae6807484abc28eb30003d1e4283aa8c9ede760c816825d2", "difficulty": "easy", "final_answer": {"answer": 101959.2, "unit": "J"}, "id": "heat_q_003496_240_4.335_98", "license": "Apache-2.0", "prompt": "A 240 g sample has specific heat 4.335 J/(g*K). How much heat is needed to raise its temperature by 98 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 240 * 4.335 * 98.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 98, "heat_capacity": 4.335, "mass_g": 240}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=188 V and R=2.5 ohm.\nFinal: {\"answer\": 14137.6, \"unit\": \"W\"}", "dedupe_signature": "91e236cf24c5df49ee65c8cb4b22655b4843a1251a15dbd727a9fe4a5c287987", "difficulty": "easy", "final_answer": {"answer": 14137.6, "unit": "W"}, "id": "ohm_power_003497_188_2.5", "license": "Apache-2.0", "prompt": "A resistor has resistance 2.5 ohm and voltage 188 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=188 V and R=2.5 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 2.5, "voltage": 188.0}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=148.5 mg, t=289.5 h, and T_half=41 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 1.1121, \"unit\": \"mg\"}", "dedupe_signature": "7f63755711e7d1ac757a78cc08eab333a664d44439288d55b6e77c50d9e03750", "difficulty": "medium", "final_answer": {"answer": 1.1121, "unit": "mg"}, "id": "half_life_003498_148.5_41_289.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 148.5 mg. Its half-life is 41 hours. How many mg remain after 289.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=148.5 mg, t=289.5 h, and T_half=41 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 289.5, "half_life": 41.0, "initial_amount": 148.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 4.77 mol * 180.156 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 859.3441, \"unit\": \"g\"}", "dedupe_signature": "c45f70b335d57ea0596fd835b7b3c5c52ff66110874f2e71545107dfbe244b03", "difficulty": "medium", "final_answer": {"answer": 859.3441, "unit": "g"}, "id": "stoich_mass_003499_glucose_4.77", "license": "Apache-2.0", "prompt": "A sample contains 4.77 mol of glucose. Using molar mass 180.156 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 4.77 mol * 180.156 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "glucose", "molar_mass": 180.156, "moles": 4.77}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 2500 mL to 2.5 L.\n3. Compute M = 4.54 / 2.5.\nFinal: {\"answer\": 1.816, \"unit\": \"mol/L\"}", "dedupe_signature": "5d058f23bb830e5344b6dd472a335f2ab60161b65434b27c4f264364cdb97bb6", "difficulty": "medium", "final_answer": {"answer": 1.816, "unit": "mol/L"}, "id": "molarity_003500_4.54_2500", "license": "Apache-2.0", "prompt": "A solution contains 4.54 mol of solute in 2500 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 2500 mL to 2.5 L.\nCompute M = 4.54 / 2.5.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 4.54, "volume_ml": 2500}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(10)=11.6 and f(20)=34.6.\n3. The interval width is 10.\nFinal: {\"answer\": 231.0, \"unit\": \"area_units\"}", "dedupe_signature": "36ef9026dbbca0b58477c8594821f7b97d35a5d80ec58c2427ad9e76865abe0f", "difficulty": "medium", "final_answer": {"answer": 231.0, "unit": "area_units"}, "id": "trapz_linear_003502_2.3_-11.4_10_20", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=2.3x+-11.4 from x=10 to x=20. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(10)=11.6 and f(20)=34.6.\nThe interval width is 10.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -11.4, "slope": 2.3, "x0": 10.0, "x1": 20.0}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kelvin equals Celsius plus 273.15.\n2. Apply the conversion factor directly to the given value.\n3. Compute -47.5 + 273.15.\nFinal: {\"answer\": 225.65, \"unit\": \"K\"}", "dedupe_signature": "a1a5bd5062b484998d778377413d7f740bc1e92704f68882c91ce5ae5c1b0793", "difficulty": "easy", "final_answer": {"answer": 225.65, "unit": "K"}, "id": "unit_convert_003504_c_to_k_-47.5", "license": "Apache-2.0", "prompt": "Convert -47.5 degC to K. Return the converted value with unit.", "reasoning_trace": "Kelvin equals Celsius plus 273.15.\nApply the conversion factor directly to the given value.\nCompute -47.5 + 273.15.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": -47.5}, "verifier": {"formula": "value + 273.15", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-2.9, -3.75], \"unit\": \"dimensionless\"}", "dedupe_signature": "855ffedf32e435f8a524fd54725a58a9aa9d44f639a82e575389a391b9232639", "difficulty": "medium", "final_answer": {"answer": [-2.9, -3.75], "unit": "dimensionless"}, "id": "line_two_point_003506_-6.5_-2.25_-2.9_-3.75", "license": "Apache-2.0", "prompt": "A line passes through points (-6.5, 15.1) and (-2.25, 2.775). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -6.5, "x2": -2.25, "y1": 15.099999999999998, "y2": 2.7749999999999995}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. energy divided by length is force, not spring constant\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "cc2aff8750b779c883a2b1d26578413b1453ebc99deab79512040a3fe6bf6f4d", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_003507_inconsistent_56040f5d_299417", "license": "Apache-2.0", "prompt": "In student derivation case 299417, check dimensional consistency for k = E / x. The left side has dimensions N/m and the right side has dimensions J/m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nenergy divided by length is force, not spring constant\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "k = E / x"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef running_total_003508(values):\n    total = 0\n    out = []\n    for value in values:\n        total += value\n        out.append(total)\n    return out\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"running_total_003508\"}", "dedupe_signature": "1505b2515d096d96d92635eac87f7e950a2455191db4bda1cc5bbd3d6e06705f", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "running_total_003508"}, "id": "code_003508_running_total_003508", "license": "Apache-2.0", "prompt": "Write a Python function running_total_003508(values) that returns cumulative sums as a new list. It must not mutate the input list. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "running_total_003508"}, "verifier": {"function": "running_total_003508", "tests": ["assert running_total_003508([1, 2, 3]) == [1, 3, 6]", "xs = [4, -1, 2]; assert running_total_003508(xs) == [4, 3, 5] and xs == [4, -1, 2]", "assert running_total_003508([]) == []"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: left_boundary, right_boundary.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"left_boundary\", \"right_boundary\"]}", "dedupe_signature": "6a8064631e5dfdd305e9558ec0a35bdfeeccdf4e429e1f20178c459446009fed", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["left_boundary", "right_boundary"]}, "id": "abstain_003509_left_boundary_right_boundary", "license": "Apache-2.0", "prompt": "Solve the 1D heat equation after one finite-difference step. The prompt gives r=0.26 and interior values [1.7, -1.5, -0.1], but gives no boundary values. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: left_boundary, right_boundary.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["left_boundary", "right_boundary"]}, "verifier": {"missing": ["left_boundary", "right_boundary"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 1.2^2 and multiply by 0.5 * 17.6.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 12.672, \"unit\": \"J\"}", "dedupe_signature": "0af12def9f01c287d3a2123d08fc9d9acba41ae2443e7c9439d4784888a10160", "difficulty": "easy", "final_answer": {"answer": 12.672, "unit": "J"}, "id": "ke_003511_17.6_1.2", "license": "Apache-2.0", "prompt": "A body of mass 17.6 kg moves at 1.2 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 1.2^2 and multiply by 0.5 * 17.6.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 17.6, "velocity": 1.2}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=81 degrees through the sine of 2 theta.\n3. Substitute v=60.9 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 116.8283, \"unit\": \"m\"}", "dedupe_signature": "f4e7c204f134ae285c414dd96fe9cc1e78d987602b3fece5a72af1bb246fc6d4", "difficulty": "medium", "final_answer": {"answer": 116.8283, "unit": "m"}, "id": "projectile_range_003512_60.9_81", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 60.9 m/s and angle 81 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=81 degrees through the sine of 2 theta.\nSubstitute v=60.9 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 81, "gravity": 9.81, "speed": 60.9}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 2.94 * 8.314 * 427 / 35.5.\nFinal: {\"answer\": 294.0065, \"unit\": \"kPa\"}", "dedupe_signature": "8773ebbf6eea0a7ff0e8133c2f893a074dcd8e118c5f3172c11fe1689e7834e1", "difficulty": "medium", "final_answer": {"answer": 294.0065, "unit": "kPa"}, "id": "ideal_gas_003513_2.94_427_35.5", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=2.94 mol, T=427 K, and V=35.5 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 2.94 * 8.314 * 427 / 35.5.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 2.94, "temp_k": 427, "volume_l": 35.5}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=169 V and R=43.7 ohm.\nFinal: {\"answer\": 653.5698, \"unit\": \"W\"}", "dedupe_signature": "36c96d991b373b5131bfc329003df4234c849b00eb737c62257a249032ae1f70", "difficulty": "easy", "final_answer": {"answer": 653.5698, "unit": "W"}, "id": "ohm_power_003515_169_43.7", "license": "Apache-2.0", "prompt": "A resistor has resistance 43.7 ohm and voltage 169 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=169 V and R=43.7 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 43.7, "voltage": 169.0}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=171.5 mg, t=12.5 h, and T_half=96 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 156.6995, \"unit\": \"mg\"}", "dedupe_signature": "d8a1a614b33e7ee5431491c954246534b935810027b7840b1df9f82b11494293", "difficulty": "medium", "final_answer": {"answer": 156.6995, "unit": "mg"}, "id": "half_life_003516_171.5_96_12.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 171.5 mg. Its half-life is 96 hours. How many mg remain after 12.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=171.5 mg, t=12.5 h, and T_half=96 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 12.5, "half_life": 96.0, "initial_amount": 171.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -1 y, so each step multiplies y by 1 - h*1.\n3. Apply that update for 3 steps and round the final state.\nFinal: {\"answer\": -0.033, \"unit\": \"state_units\"}", "dedupe_signature": "01131273f1a1196ae76264442589fe8eaf67cf0b55edb7eb0f25050d1903ceb8", "difficulty": "medium", "final_answer": {"answer": -0.033, "unit": "state_units"}, "id": "euler_decay_003519_33_1_1.1_3", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -1 y with y(0)=33, step size h=1.1, for 3 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -1 y, so each step multiplies y by 1 - h*1.\nApply that update for 3 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 33.0, "rate": 1.0, "step": 1.1, "steps": 3}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-7.5)=-36.05 and f(2.3)=2.17.\n3. The interval width is 9.8.\nFinal: {\"answer\": -166.012, \"unit\": \"area_units\"}", "dedupe_signature": "ff586b6b732b7fbfe8aa28ef6128346ca558a9101dee74164b77630068de4572", "difficulty": "medium", "final_answer": {"answer": -166.012, "unit": "area_units"}, "id": "trapz_linear_003520_3.9_-6.8_-7.5_2.3", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=3.9x+-6.8 from x=-7.5 to x=2.3. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-7.5)=-36.05 and f(2.3)=2.17.\nThe interval width is 9.8.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -6.8, "slope": 3.9, "x0": -7.5, "x1": 2.3000000000000007}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.18 and add it to the current value.\nFinal: {\"answer\": [1.536, 1.198, 1.976], \"unit\": \"temperature_units\"}", "dedupe_signature": "5d6f00703e9ef6e5cfab4c0302219e4f1706e15613b609632c6289f266a3a6d9", "difficulty": "hard", "final_answer": {"answer": [1.536, 1.198, 1.976], "unit": "temperature_units"}, "id": "heat_step_003521_0.18_-0.55_2.4_0.55_2.3_2.25", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-0.55, right=2.25; current interior values are [2.4, 0.55, 2.3]. Use r=0.18. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.18 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [2.4, 0.55, 2.3], "left": -0.55, "r": 0.18, "right": 2.25}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 47522.0 / 1000.\nFinal: {\"answer\": 47.522, \"unit\": \"kg\"}", "dedupe_signature": "a6951fad17e05a107c4bd30fabfbafe56b53c2df4b29a64ef11061cbe70b4466", "difficulty": "easy", "final_answer": {"answer": 47.522, "unit": "kg"}, "id": "unit_convert_003522_g_to_kg_47522", "license": "Apache-2.0", "prompt": "Convert 47522 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 47522.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 47522.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=121 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-194.1694, 323.1521], \"unit\": \"N\"}", "dedupe_signature": "1283d5918d809a3100e7e14cb6f39a87a9ef40c66be9c6faf2252ae9b15931c5", "difficulty": "medium", "final_answer": {"answer": [-194.1694, 323.1521], "unit": "N"}, "id": "vector_components_003523_377_121", "license": "Apache-2.0", "prompt": "A vector has magnitude 377 N at 121 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=121 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 121, "magnitude": 377.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. energy divided by length is force, not spring constant\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "e5ea3b7d793512e41e1c5c1e60e67ccf56a285afc065102924f67f2d752325d0", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_003525_inconsistent_56040f5d_920586", "license": "Apache-2.0", "prompt": "In student derivation case 920586, check dimensional consistency for k = E / x. The left side has dimensions N/m and the right side has dimensions J/m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nenergy divided by length is force, not spring constant\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "k = E / x"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef threshold_flags_003526(values, threshold):\n    return [value >= threshold for value in values]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"threshold_flags_003526\"}", "dedupe_signature": "6a5a48f9dca305a0d58b9765df9d8cd520365baccd7e035a5136e38fa35dad9a", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "threshold_flags_003526"}, "id": "code_003526_threshold_flags_003526", "license": "Apache-2.0", "prompt": "Write a Python function threshold_flags_003526(values, threshold) that returns a list of booleans showing whether each value is greater than or equal to threshold. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "threshold_flags_003526"}, "verifier": {"function": "threshold_flags_003526", "tests": ["assert threshold_flags_003526([1, 2, 3], 2) == [False, True, True]", "assert threshold_flags_003526([], 5) == []", "assert threshold_flags_003526([-1, 0], 0) == [False, True]"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: launch_angle_or_vertical_velocity.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"launch_angle_or_vertical_velocity\"]}", "dedupe_signature": "2efe688de7e769b30911ac7046f4c6a908e243fe2ce853b6ccc748962322a68e", "difficulty": "easy", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["launch_angle_or_vertical_velocity"]}, "id": "abstain_003527_launch_angle_or_vertical_velocity", "license": "Apache-2.0", "prompt": "Compute projectile range on level ground. The prompt gives initial speed 34.7 m/s but does not give launch angle or vertical velocity. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: launch_angle_or_vertical_velocity.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["launch_angle_or_vertical_velocity"]}, "verifier": {"missing": ["launch_angle_or_vertical_velocity"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 2.85 kg and a = 14.2 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 40.47, \"unit\": \"N\"}", "dedupe_signature": "5e041eac373aade6ce8edfd21f7069be87618634f78388da7abac8dd0dbdb773", "difficulty": "easy", "final_answer": {"answer": 40.47, "unit": "N"}, "id": "force_003528_2.85_14.2", "license": "Apache-2.0", "prompt": "A cart has mass 2.85 kg and measured acceleration 14.2 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 2.85 kg and a = 14.2 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 14.2, "mass": 2.85}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=656 mg, t=142.5 h, and T_half=106 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 258.3552, \"unit\": \"mg\"}", "dedupe_signature": "235e8b19ab1f2f5ad4c65afc7d11e717aaf11d8dafd50a8d058c9071c2ad63cb", "difficulty": "medium", "final_answer": {"answer": 258.3552, "unit": "mg"}, "id": "half_life_003534_656_106_142.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 656 mg. Its half-life is 106 hours. How many mg remain after 142.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=656 mg, t=142.5 h, and T_half=106 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 142.5, "half_life": 106.0, "initial_amount": 656.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 1540 mL to 1.54 L.\n3. Compute M = 4.925 / 1.54.\nFinal: {\"answer\": 3.1981, \"unit\": \"mol/L\"}", "dedupe_signature": "c4f232b49ff5cddef4362264e06ebf5aaedc8e34f05eb4cf58571bffad3e0717", "difficulty": "medium", "final_answer": {"answer": 3.1981, "unit": "mol/L"}, "id": "molarity_003536_4.925_1540", "license": "Apache-2.0", "prompt": "A solution contains 4.925 mol of solute in 1540 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 1540 mL to 1.54 L.\nCompute M = 4.925 / 1.54.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 4.925, "volume_ml": 1540}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.47 y, so each step multiplies y by 1 - h*0.47.\n3. Apply that update for 10 steps and round the final state.\nFinal: {\"answer\": 20.3426, \"unit\": \"state_units\"}", "dedupe_signature": "1d01b2cf179e9139ce224cd05a745e2744c78bff3088be3f15f995b0ec96451a", "difficulty": "medium", "final_answer": {"answer": 20.3426, "unit": "state_units"}, "id": "euler_decay_003537_71_0.47_0.25_10", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.47 y with y(0)=71, step size h=0.25, for 10 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.47 y, so each step multiplies y by 1 - h*0.47.\nApply that update for 10 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 71.0, "rate": 0.47, "step": 0.25, "steps": 10}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-7.7)=-49.71 and f(-5.2)=-36.46.\n3. The interval width is 2.5.\nFinal: {\"answer\": -107.7125, \"unit\": \"area_units\"}", "dedupe_signature": "1f4122739226987b329e09ad353344b3b6f8c93085002c1dae55f2cfd4620376", "difficulty": "medium", "final_answer": {"answer": -107.7125, "unit": "area_units"}, "id": "trapz_linear_003538_5.3_-8.9_-7.7_-5.2", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=5.3x+-8.9 from x=-7.7 to x=-5.2. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-7.7)=-49.71 and f(-5.2)=-36.46.\nThe interval width is 2.5.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -8.9, "slope": 5.3, "x0": -7.7, "x1": -5.2}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.2 and add it to the current value.\nFinal: {\"answer\": [0.33, 1.1, 0.39], \"unit\": \"temperature_units\"}", "dedupe_signature": "4fa1e1d2ecd1b619a40e988c051e707b16ef1ce0795f0823999f9e90f05ebe27", "difficulty": "hard", "final_answer": {"answer": [0.33, 1.1, 0.39], "unit": "temperature_units"}, "id": "heat_step_003539_0.2_2.9_-1.25_2.5_-0.75_1.7", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=2.9, right=1.7; current interior values are [-1.25, 2.5, -0.75]. Use r=0.2. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.2 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-1.25, 2.5, -0.75], "left": 2.9, "r": 0.2, "right": 1.7}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kelvin equals Celsius plus 273.15.\n2. Apply the conversion factor directly to the given value.\n3. Compute -38.5 + 273.15.\nFinal: {\"answer\": 234.65, \"unit\": \"K\"}", "dedupe_signature": "e0ada45d4b24255fef582602af5dce3d75efee82a2f837e7cd23a6b4c277c3ba", "difficulty": "easy", "final_answer": {"answer": 234.65, "unit": "K"}, "id": "unit_convert_003540_c_to_k_-38.5", "license": "Apache-2.0", "prompt": "Convert -38.5 degC to K. Return the converted value with unit.", "reasoning_trace": "Kelvin equals Celsius plus 273.15.\nApply the conversion factor directly to the given value.\nCompute -38.5 + 273.15.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": -38.5}, "verifier": {"formula": "value + 273.15", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=137 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-315.5791, 294.2823], \"unit\": \"N\"}", "dedupe_signature": "f233238c65442ac426613ca55b6585de3315428cfdbc7be17f8b7b6e9fa55e0e", "difficulty": "medium", "final_answer": {"answer": [-315.5791, 294.2823], "unit": "N"}, "id": "vector_components_003541_431.5_137", "license": "Apache-2.0", "prompt": "A vector has magnitude 431.5 N at 137 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=137 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 137, "magnitude": 431.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [7.15, 24.25], \"unit\": \"dimensionless\"}", "dedupe_signature": "c3959653649e9148a1877704cf82627054280930eee45989cfadffcf3bf672af", "difficulty": "medium", "final_answer": {"answer": [7.15, 24.25], "unit": "dimensionless"}, "id": "line_two_point_003542_-9.25_-4.75_7.15_24.25", "license": "Apache-2.0", "prompt": "A line passes through points (-9.25, -41.8875) and (-4.75, -9.7125). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -9.25, "x2": -4.75, "y1": -41.8875, "y2": -9.712499999999999}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. lever arm times force has torque dimensions\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "d9effe789a92e7255f85eb48d862820963cf3644c4817ed6ff42ef49994bf0e8", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_003543_consistent_5ca82cb9_447898", "license": "Apache-2.0", "prompt": "In quality-control check case 447898, check dimensional consistency for tau = r * F. The left side has dimensions N*m and the right side has dimensions N*m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nlever arm times force has torque dimensions\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "tau = r * F"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\nimport math\n\ndef unit_vector_003544(x, y):\n    norm = math.hypot(x, y)\n    if norm == 0:\n        raise ValueError('zero vector has no direction')\n    return (x / norm, y / norm)\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"unit_vector_003544\"}", "dedupe_signature": "1e96831d192dc2411ba774192c6d8d42b4d9a3b053b372b5d2e4c77284869a30", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "unit_vector_003544"}, "id": "code_003544_unit_vector_003544", "license": "Apache-2.0", "prompt": "Write a Python function unit_vector_003544(x, y) that returns the 2D unit vector as a tuple. Raise ValueError for the zero vector. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "unit_vector_003544"}, "verifier": {"function": "unit_vector_003544", "tests": ["ux, uy = unit_vector_003544(3, 4); assert abs(ux - 0.6) < 1e-12 and abs(uy - 0.8) < 1e-12", "assert unit_vector_003544(0, 5) == (0, 1)", "try:\n    unit_vector_003544(0, 0)\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: rate_constant, number_of_steps.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"rate_constant\", \"number_of_steps\"]}", "dedupe_signature": "1b36d88a12dfe9096d29115c9047930492988600f2b9f4eb75217106fed0a427", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["rate_constant", "number_of_steps"]}, "id": "abstain_003545_rate_constant_number_of_steps", "license": "Apache-2.0", "prompt": "Use explicit Euler for dy/dt = -k y. The prompt gives y(0)=11.5 and h=0.15, but omits both k and the number of steps. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: rate_constant, number_of_steps.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["rate_constant", "number_of_steps"]}, "verifier": {"missing": ["rate_constant", "number_of_steps"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 9.5 kg and a = 13.95 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 132.525, \"unit\": \"N\"}", "dedupe_signature": "c787709768869624cde07ddb99165aa7edb1b52c0894d72c39c2bcd1bf9e409a", "difficulty": "easy", "final_answer": {"answer": 132.525, "unit": "N"}, "id": "force_003546_9.5_13.95", "license": "Apache-2.0", "prompt": "A cart has mass 9.5 kg and measured acceleration 13.95 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 9.5 kg and a = 13.95 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 13.95, "mass": 9.5}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 31.05^2 and multiply by 0.5 * 9.95.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 4796.4099, \"unit\": \"J\"}", "dedupe_signature": "b4b32234363ebe0754d4860ea3ec9a4f5803d139ba90de0789da331ec670a14d", "difficulty": "easy", "final_answer": {"answer": 4796.4099, "unit": "J"}, "id": "ke_003547_9.95_31.05", "license": "Apache-2.0", "prompt": "A body of mass 9.95 kg moves at 31.05 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 31.05^2 and multiply by 0.5 * 9.95.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 9.95, "velocity": 31.05}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=55 degrees through the sine of 2 theta.\n3. Substitute v=26.2 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 65.7536, \"unit\": \"m\"}", "dedupe_signature": "77848b6b7e95447ef45fb8f5f76901ad82a24a7ff6bd8aa6b78e4fb990ff5153", "difficulty": "medium", "final_answer": {"answer": 65.7536, "unit": "m"}, "id": "projectile_range_003548_26.2_55", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 26.2 m/s and angle 55 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=55 degrees through the sine of 2 theta.\nSubstitute v=26.2 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 55, "gravity": 9.81, "speed": 26.2}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 2.88 * 8.314 * 497 / 57.3.\nFinal: {\"answer\": 207.6846, \"unit\": \"kPa\"}", "dedupe_signature": "c5dc2d2f26b937fca95dc33388ea0bf48cd119567047d4259b8c1f81abb28d16", "difficulty": "medium", "final_answer": {"answer": 207.6846, "unit": "kPa"}, "id": "ideal_gas_003549_2.88_497_57.3", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=2.88 mol, T=497 K, and V=57.3 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 2.88 * 8.314 * 497 / 57.3.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 2.88, "temp_k": 497, "volume_l": 57.3}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 235 * 1.115 * 51.\nFinal: {\"answer\": 13363.275, \"unit\": \"J\"}", "dedupe_signature": "0be3db9e11921e5d22c6919169c140e8c926a03c80b6eb9b68510e36cb60cfc8", "difficulty": "easy", "final_answer": {"answer": 13363.275, "unit": "J"}, "id": "heat_q_003550_235_1.115_51", "license": "Apache-2.0", "prompt": "A 235 g sample has specific heat 1.115 J/(g*K). How much heat is needed to raise its temperature by 51 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 235 * 1.115 * 51.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 51, "heat_capacity": 1.115, "mass_g": 235}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=197.6 V and R=3 ohm.\nFinal: {\"answer\": 13015.2533, \"unit\": \"W\"}", "dedupe_signature": "b2a7b3cc68a75d8767e702629e7615a618351722f28be89b5be6064b675d9522", "difficulty": "easy", "final_answer": {"answer": 13015.2533, "unit": "W"}, "id": "ohm_power_003551_197.6_3", "license": "Apache-2.0", "prompt": "A resistor has resistance 3 ohm and voltage 197.6 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=197.6 V and R=3 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 3.0, "voltage": 197.6}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=124.5 mg, t=225.5 h, and T_half=11 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 0.0001, \"unit\": \"mg\"}", "dedupe_signature": "b338eafd3b17c4e7640d6ea89551750872bc312a3f4642d00c4d189cde1ba14f", "difficulty": "medium", "final_answer": {"answer": 0.0001, "unit": "mg"}, "id": "half_life_003552_124.5_11_225.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 124.5 mg. Its half-life is 11 hours. How many mg remain after 225.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=124.5 mg, t=225.5 h, and T_half=11 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 225.5, "half_life": 11.0, "initial_amount": 124.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 0.37 mol * 44.01 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 16.2837, \"unit\": \"g\"}", "dedupe_signature": "568c280dbc08ec4823ddb42efbf421498f0cba7004a321e79b5bb03be60863a2", "difficulty": "medium", "final_answer": {"answer": 16.2837, "unit": "g"}, "id": "stoich_mass_003553_carbon_dioxide_0.37", "license": "Apache-2.0", "prompt": "A sample contains 0.37 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 0.37 mol * 44.01 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "carbon dioxide", "molar_mass": 44.01, "moles": 0.37}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.12 y, so each step multiplies y by 1 - h*0.12.\n3. Apply that update for 9 steps and round the final state.\nFinal: {\"answer\": 12.0262, \"unit\": \"state_units\"}", "dedupe_signature": "a5a0a0f2887a16ef798cef7995e6a198dea9a249482836fda8059a07e8e01f32", "difficulty": "medium", "final_answer": {"answer": 12.0262, "unit": "state_units"}, "id": "euler_decay_003555_38_0.12_1_9", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.12 y with y(0)=38, step size h=1, for 9 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.12 y, so each step multiplies y by 1 - h*0.12.\nApply that update for 9 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 38.0, "rate": 0.12, "step": 1.0, "steps": 9}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-1.4)=7.42 and f(-0.5)=13.45.\n3. The interval width is 0.9.\nFinal: {\"answer\": 9.3915, \"unit\": \"area_units\"}", "dedupe_signature": "c3e5dd6462df9a67ddda2f945b44a79fdd53ac470db56d4e4838599220025903", "difficulty": "medium", "final_answer": {"answer": 9.3915, "unit": "area_units"}, "id": "trapz_linear_003556_6.7_16.8_-1.4_-0.5", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=6.7x+16.8 from x=-1.4 to x=-0.5. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-1.4)=7.42 and f(-0.5)=13.45.\nThe interval width is 0.9.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 16.8, "slope": 6.7, "x0": -1.4, "x1": -0.4999999999999999}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.46 and add it to the current value.\nFinal: {\"answer\": [2.083, 0.245, 0.091], \"unit\": \"temperature_units\"}", "dedupe_signature": "fb05ee0c03551744dd2291b6cdf829c2ef2b077524b1b80af869828da46927ec", "difficulty": "hard", "final_answer": {"answer": [2.083, 0.245, 0.091], "unit": "temperature_units"}, "id": "heat_step_003557_0.46_2.05_1.6_2.2_-1.45_-1.75", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=2.05, right=-1.75; current interior values are [1.6, 2.2, -1.45]. Use r=0.46. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.46 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [1.6, 2.2, -1.45], "left": 2.05, "r": 0.46, "right": -1.75}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 9145.0 / 1000.\nFinal: {\"answer\": 9.145, \"unit\": \"kg\"}", "dedupe_signature": "8eda585afa54616f464500cf0fbd7b106a7d62e15690a0a044717a384b166ab4", "difficulty": "easy", "final_answer": {"answer": 9.145, "unit": "kg"}, "id": "unit_convert_003558_g_to_kg_9145", "license": "Apache-2.0", "prompt": "Convert 9145 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 9145.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 9145.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=267 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-4.9457, -94.3705], \"unit\": \"N\"}", "dedupe_signature": "c90ef3f263c02d766468f533fa5a62df4c1aa2d40ed342de19e0d3ce38645f62", "difficulty": "medium", "final_answer": {"answer": [-4.9457, -94.3705], "unit": "N"}, "id": "vector_components_003559_94.5_267", "license": "Apache-2.0", "prompt": "A vector has magnitude 94.5 N at 267 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=267 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 267, "magnitude": 94.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-5.8, -3.5], \"unit\": \"dimensionless\"}", "dedupe_signature": "02ed4d454dd923679b544b6fe1bbe5c69d572a2f5f5a863353553dbbb91d1e01", "difficulty": "medium", "final_answer": {"answer": [-5.8, -3.5], "unit": "dimensionless"}, "id": "line_two_point_003560_-4.75_0_-5.8_-3.5", "license": "Apache-2.0", "prompt": "A line passes through points (-4.75, 24.05) and (0, -3.5). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -4.75, "x2": 0.0, "y1": 24.05, "y2": -3.5}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. lever arm times force has torque dimensions\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "f71598e8666175c9cb3123ae27d1dd35a97fe54ff400d6bb0548531036810ab2", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_003561_consistent_5ca82cb9_200786", "license": "Apache-2.0", "prompt": "In simulation spec case 200786, check dimensional consistency for tau = r * F. The left side has dimensions N*m and the right side has dimensions N*m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nlever arm times force has torque dimensions\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "tau = r * F"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef pairwise_ratios_003562(numerators, denominators):\n    if len(numerators) != len(denominators):\n        raise ValueError('length mismatch')\n    out = []\n    for numerator, denominator in zip(numerators, denominators):\n        if denominator == 0:\n            raise ValueError('zero denominator')\n        out.append(numerator / denominator)\n    return out\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"pairwise_ratios_003562\"}", "dedupe_signature": "fa57d5206506eb5e5aac5d413aa94ff00d42056e62d7195e7cc8efb3075e51b8", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "pairwise_ratios_003562"}, "id": "code_003562_pairwise_ratios_003562", "license": "Apache-2.0", "prompt": "Write a Python function pairwise_ratios_003562(numerators, denominators) that returns a list of n/d values. Raise ValueError if lengths differ or any denominator is zero. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "pairwise_ratios_003562"}, "verifier": {"function": "pairwise_ratios_003562", "tests": ["assert pairwise_ratios_003562([2, 9], [4, 3]) == [0.5, 3.0]", "try:\n    pairwise_ratios_003562([1], [0])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass", "try:\n    pairwise_ratios_003562([1, 2], [1])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: recurrence, objective, tie_breaking_rule.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"recurrence\", \"objective\", \"tie_breaking_rule\"]}", "dedupe_signature": "63d1dd9f3db28af85ec19a27d58c252560ce40abb590e8ae9fdfc8bc9ba1a1b8", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["recurrence", "objective", "tie_breaking_rule"]}, "id": "abstain_003563_recurrence_objective_tie_breaking_rule", "license": "Apache-2.0", "prompt": "Write a dynamic-programming solver for a allocation scoring problem with 1505 items and budget 89045, but the recurrence, objective, and tie-breaking rule are all absent. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: recurrence, objective, tie_breaking_rule.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["recurrence", "objective", "tie_breaking_rule"]}, "verifier": {"missing": ["recurrence", "objective", "tie_breaking_rule"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 21.4 kg and a = 5.95 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 127.33, \"unit\": \"N\"}", "dedupe_signature": "448148dded42dc039c5d4a142ab81badb9f2ac79347948b9e18385cd653c3698", "difficulty": "easy", "final_answer": {"answer": 127.33, "unit": "N"}, "id": "force_003564_21.4_5.95", "license": "Apache-2.0", "prompt": "A cart has mass 21.4 kg and measured acceleration 5.95 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 21.4 kg and a = 5.95 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 5.95, "mass": 21.4}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 5.24 * 8.314 * 392 / 33.7.\nFinal: {\"answer\": 506.7543, \"unit\": \"kPa\"}", "dedupe_signature": "8780042b2f7104c98d2ea82ca3ad314e8dcd595e70da1da3cc3af9c51c9b6d10", "difficulty": "medium", "final_answer": {"answer": 506.7543, "unit": "kPa"}, "id": "ideal_gas_003567_5.24_392_33.7", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=5.24 mol, T=392 K, and V=33.7 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 5.24 * 8.314 * 392 / 33.7.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 5.24, "temp_k": 392, "volume_l": 33.7}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1825 * 3.455 * 110.\nFinal: {\"answer\": 693591.25, \"unit\": \"J\"}", "dedupe_signature": "2b8068f70fcdb1ece75d1a55048abeda808ccb459dd911dbc7e08af51d3d609b", "difficulty": "easy", "final_answer": {"answer": 693591.25, "unit": "J"}, "id": "heat_q_003568_1825_3.455_110", "license": "Apache-2.0", "prompt": "A 1825 g sample has specific heat 3.455 J/(g*K). How much heat is needed to raise its temperature by 110 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1825 * 3.455 * 110.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 110, "heat_capacity": 3.455, "mass_g": 1825}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=190.9 V and R=198.3 ohm.\nFinal: {\"answer\": 183.7761, \"unit\": \"W\"}", "dedupe_signature": "d337c9ac7abfc04dac6fd4b32fb7942de9ed3282f7c62e8ba5d1a14f1aeb87a8", "difficulty": "easy", "final_answer": {"answer": 183.7761, "unit": "W"}, "id": "ohm_power_003569_190.9_198.3", "license": "Apache-2.0", "prompt": "A resistor has resistance 198.3 ohm and voltage 190.9 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=190.9 V and R=198.3 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 198.3, "voltage": 190.9}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=101.5 mg, t=239 h, and T_half=15.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 0.0023, \"unit\": \"mg\"}", "dedupe_signature": "ce27d7d5ae8424191b3a99e0b4f206a90a6b78cfd5ca56a29404b4c5fbfb15e4", "difficulty": "medium", "final_answer": {"answer": 0.0023, "unit": "mg"}, "id": "half_life_003570_101.5_15.5_239", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 101.5 mg. Its half-life is 15.5 hours. How many mg remain after 239 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=101.5 mg, t=239 h, and T_half=15.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 239.0, "half_life": 15.5, "initial_amount": 101.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 410 mL to 0.41 L.\n3. Compute M = 2.785 / 0.41.\nFinal: {\"answer\": 6.7927, \"unit\": \"mol/L\"}", "dedupe_signature": "afd16512984cdbf24a96524ec3f3198f6a9b7e7d5c61dde033b81df28978fdd4", "difficulty": "medium", "final_answer": {"answer": 6.7927, "unit": "mol/L"}, "id": "molarity_003572_2.785_410", "license": "Apache-2.0", "prompt": "A solution contains 2.785 mol of solute in 410 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 410 mL to 0.41 L.\nCompute M = 2.785 / 0.41.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 2.785, "volume_ml": 410}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.46 y, so each step multiplies y by 1 - h*0.46.\n3. Apply that update for 6 steps and round the final state.\nFinal: {\"answer\": 0.001, \"unit\": \"state_units\"}", "dedupe_signature": "1063f877f286a6d0fd7847338febf0f5917c67e635b663c0c2f5f08afcdbafb0", "difficulty": "medium", "final_answer": {"answer": 0.001, "unit": "state_units"}, "id": "euler_decay_003573_40.5_0.46_1.8_6", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.46 y with y(0)=40.5, step size h=1.8, for 6 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.46 y, so each step multiplies y by 1 - h*0.46.\nApply that update for 6 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 40.5, "rate": 0.46, "step": 1.8, "steps": 6}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-6.3)=-38.47 and f(-2)=-17.4.\n3. The interval width is 4.3.\nFinal: {\"answer\": -120.1205, \"unit\": \"area_units\"}", "dedupe_signature": "07ddce4b08634eb781a8e5fae87396a305b674c09b34e44dffdb2a528e0532b4", "difficulty": "medium", "final_answer": {"answer": -120.1205, "unit": "area_units"}, "id": "trapz_linear_003574_4.9_-7.6_-6.3_-2", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=4.9x+-7.6 from x=-6.3 to x=-2. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-6.3)=-38.47 and f(-2)=-17.4.\nThe interval width is 4.3.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -7.6, "slope": 4.9, "x0": -6.3, "x1": -2.0}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-0.35, 29.5], \"unit\": \"dimensionless\"}", "dedupe_signature": "954bc8bacb1f8a6a2636c5a9e09bdb48ceaa9e1bce6e25f93f807fbe76d73d79", "difficulty": "medium", "final_answer": {"answer": [-0.35, 29.5], "unit": "dimensionless"}, "id": "line_two_point_003578_-12.75_-8.5_-0.35_29.5", "license": "Apache-2.0", "prompt": "A line passes through points (-12.75, 33.9625) and (-8.5, 32.475). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -12.75, "x2": -8.5, "y1": 33.9625, "y2": 32.475}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. coulomb per second is ampere\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "c90e7095dbb030461f73180359fec4475be609227a54a65a07b4724c4601f16d", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_003579_consistent_8b38953d_284724", "license": "Apache-2.0", "prompt": "In model card equation case 284724, check dimensional consistency for I = Q / t. The left side has dimensions A and the right side has dimensions A. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\ncoulomb per second is ampere\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "I = Q / t"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef threshold_flags_003580(values, threshold):\n    return [value >= threshold for value in values]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"threshold_flags_003580\"}", "dedupe_signature": "c205f7fbafae4ce1fa267677ff41866b1f21a6cf872e219919761c3b4d27924f", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "threshold_flags_003580"}, "id": "code_003580_threshold_flags_003580", "license": "Apache-2.0", "prompt": "Write a Python function threshold_flags_003580(values, threshold) that returns a list of booleans showing whether each value is greater than or equal to threshold. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "threshold_flags_003580"}, "verifier": {"function": "threshold_flags_003580", "tests": ["assert threshold_flags_003580([1, 2, 3], 2) == [False, True, True]", "assert threshold_flags_003580([], 5) == []", "assert threshold_flags_003580([-1, 0], 0) == [False, True]"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: rate_constant, number_of_steps.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"rate_constant\", \"number_of_steps\"]}", "dedupe_signature": "02c4fbeb64ceca88c0f506c1ca6b3248ae5884a0c9dea83f7331e9bb53ee2a20", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["rate_constant", "number_of_steps"]}, "id": "abstain_003581_rate_constant_number_of_steps", "license": "Apache-2.0", "prompt": "Use explicit Euler for dy/dt = -k y. The prompt gives y(0)=74.5 and h=1.85, but omits both k and the number of steps. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: rate_constant, number_of_steps.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["rate_constant", "number_of_steps"]}, "verifier": {"missing": ["rate_constant", "number_of_steps"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 23 kg and a = 12.7 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 292.1, \"unit\": \"N\"}", "dedupe_signature": "ce4f272f0ea695a7c7ae668d464a94b3081638e51cdab739fbca605ae574b03c", "difficulty": "easy", "final_answer": {"answer": 292.1, "unit": "N"}, "id": "force_003582_23_12.7", "license": "Apache-2.0", "prompt": "A cart has mass 23 kg and measured acceleration 12.7 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 23 kg and a = 12.7 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 12.7, "mass": 23.0}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=24 degrees through the sine of 2 theta.\n3. Substitute v=13.5 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 13.8061, \"unit\": \"m\"}", "dedupe_signature": "2e99616a60539835e776e2da7cf22614d763353b582035e8522364b5bac3aa91", "difficulty": "medium", "final_answer": {"answer": 13.8061, "unit": "m"}, "id": "projectile_range_003584_13.5_24", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 13.5 m/s and angle 24 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=24 degrees through the sine of 2 theta.\nSubstitute v=13.5 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 24, "gravity": 9.81, "speed": 13.5}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 1.85 * 8.314 * 602 / 80.3.\nFinal: {\"answer\": 115.3089, \"unit\": \"kPa\"}", "dedupe_signature": "fbe68fb380ac1bdf6e6197ea8bbcce97845579c756a9dc56daba7d2a6d8d1e7c", "difficulty": "medium", "final_answer": {"answer": 115.3089, "unit": "kPa"}, "id": "ideal_gas_003585_1.85_602_80.3", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=1.85 mol, T=602 K, and V=80.3 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 1.85 * 8.314 * 602 / 80.3.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 1.85, "temp_k": 602, "volume_l": 80.3}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1500 * 1.9 * 20.\nFinal: {\"answer\": 57000.0, \"unit\": \"J\"}", "dedupe_signature": "a28a06e987dce929953608ce17be28befd03bc71de678d296b03206fcd36bb9b", "difficulty": "easy", "final_answer": {"answer": 57000.0, "unit": "J"}, "id": "heat_q_003586_1500_1.9_20", "license": "Apache-2.0", "prompt": "A 1500 g sample has specific heat 1.9 J/(g*K). How much heat is needed to raise its temperature by 20 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1500 * 1.9 * 20.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 20, "heat_capacity": 1.9, "mass_g": 1500}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=122.9 V and R=52.9 ohm.\nFinal: {\"answer\": 285.5276, \"unit\": \"W\"}", "dedupe_signature": "73b4ba83bc939780652a10c669d4dcc1ff5e2da1c61a31b8fc452f2119bf0966", "difficulty": "easy", "final_answer": {"answer": 285.5276, "unit": "W"}, "id": "ohm_power_003587_122.9_52.9", "license": "Apache-2.0", "prompt": "A resistor has resistance 52.9 ohm and voltage 122.9 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=122.9 V and R=52.9 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 52.9, "voltage": 122.9}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 2185 mL to 2.185 L.\n3. Compute M = 0.465 / 2.185.\nFinal: {\"answer\": 0.2128, \"unit\": \"mol/L\"}", "dedupe_signature": "887299df89738cada285dee6a001fa2c41c54908409f053c5fd1862c11a6ef51", "difficulty": "medium", "final_answer": {"answer": 0.2128, "unit": "mol/L"}, "id": "molarity_003590_0.465_2185", "license": "Apache-2.0", "prompt": "A solution contains 0.465 mol of solute in 2185 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 2185 mL to 2.185 L.\nCompute M = 0.465 / 2.185.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 0.465, "volume_ml": 2185}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.63 y, so each step multiplies y by 1 - h*0.63.\n3. Apply that update for 8 steps and round the final state.\nFinal: {\"answer\": 0.0, \"unit\": \"state_units\"}", "dedupe_signature": "c31c0c84b01378caaade598655fef164318bc0cb75a09754e12ef96b78ef397f", "difficulty": "medium", "final_answer": {"answer": 0.0, "unit": "state_units"}, "id": "euler_decay_003591_2_0.63_1.85_8", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.63 y with y(0)=2, step size h=1.85, for 8 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.63 y, so each step multiplies y by 1 - h*0.63.\nApply that update for 8 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 2.0, "rate": 0.63, "step": 1.85, "steps": 8}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-9.3)=30.47 and f(0)=-15.1.\n3. The interval width is 9.3.\nFinal: {\"answer\": 71.4705, \"unit\": \"area_units\"}", "dedupe_signature": "c63d1a657bd4325f47b327082bc705b260c0c8673417fd4103e103dff1d868d1", "difficulty": "medium", "final_answer": {"answer": 71.4705, "unit": "area_units"}, "id": "trapz_linear_003592_-4.9_-15.1_-9.3_0", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-4.9x+-15.1 from x=-9.3 to x=0. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-9.3)=30.47 and f(0)=-15.1.\nThe interval width is 9.3.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -15.1, "slope": -4.9, "x0": -9.3, "x1": 0.0}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.24 and add it to the current value.\nFinal: {\"answer\": [2.47, 1.75, 1.044], \"unit\": \"temperature_units\"}", "dedupe_signature": "8ba6ea5f177cdedfad67de7bee780bfcb9af98541d301451439cc800eb60c3f0", "difficulty": "hard", "final_answer": {"answer": [2.47, 1.75, 1.044], "unit": "temperature_units"}, "id": "heat_step_003593_0.24_2.45_2.95_1.45_1.2_0.3", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=2.45, right=0.3; current interior values are [2.95, 1.45, 1.2]. Use r=0.24. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.24 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [2.95, 1.45, 1.2], "left": 2.45, "r": 0.24, "right": 0.3}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 100 centimeters in one meter.\n2. Apply the conversion factor directly to the given value.\n3. Compute 3361.0 / 100.\nFinal: {\"answer\": 33.61, \"unit\": \"m\"}", "dedupe_signature": "deb272c2bb81ec7fa4259707b2496a434258734d09d679588a2bbff4ed7a99ae", "difficulty": "easy", "final_answer": {"answer": 33.61, "unit": "m"}, "id": "unit_convert_003594_cm_to_m_3361", "license": "Apache-2.0", "prompt": "Convert 3361 cm to m. Return the converted value with unit.", "reasoning_trace": "There are 100 centimeters in one meter.\nApply the conversion factor directly to the given value.\nCompute 3361.0 / 100.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 3361.0}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-2.15, -22.75], \"unit\": \"dimensionless\"}", "dedupe_signature": "f9d80fb660347b20b5bb778212d02342c4f5623523e743ded533869f3753785b", "difficulty": "medium", "final_answer": {"answer": [-2.15, -22.75], "unit": "dimensionless"}, "id": "line_two_point_003596_-2.5_1.25_-2.15_-22.75", "license": "Apache-2.0", "prompt": "A line passes through points (-2.5, -17.375) and (1.25, -25.4375). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -2.5, "x2": 1.25, "y1": -17.375, "y2": -25.4375}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef pairwise_ratios_003598(numerators, denominators):\n    if len(numerators) != len(denominators):\n        raise ValueError('length mismatch')\n    out = []\n    for numerator, denominator in zip(numerators, denominators):\n        if denominator == 0:\n            raise ValueError('zero denominator')\n        out.append(numerator / denominator)\n    return out\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"pairwise_ratios_003598\"}", "dedupe_signature": "917e880bed16a2ec15935994c45b1e60626d7eaa7a5e9725f81e6f0c0410aa44", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "pairwise_ratios_003598"}, "id": "code_003598_pairwise_ratios_003598", "license": "Apache-2.0", "prompt": "Write a Python function pairwise_ratios_003598(numerators, denominators) that returns a list of n/d values. Raise ValueError if lengths differ or any denominator is zero. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "pairwise_ratios_003598"}, "verifier": {"function": "pairwise_ratios_003598", "tests": ["assert pairwise_ratios_003598([2, 9], [4, 3]) == [0.5, 3.0]", "try:\n    pairwise_ratios_003598([1], [0])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass", "try:\n    pairwise_ratios_003598([1, 2], [1])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: left_boundary, right_boundary.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"left_boundary\", \"right_boundary\"]}", "dedupe_signature": "8b8ce71d7c348ac7a92ef555eb98b26de47c7196ddec22d96eb4be897d3d3249", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["left_boundary", "right_boundary"]}, "id": "abstain_003599_left_boundary_right_boundary", "license": "Apache-2.0", "prompt": "Solve the 1D heat equation after one finite-difference step. The prompt gives r=0.3 and interior values [2.6, 0.35, 0.95], but gives no boundary values. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: left_boundary, right_boundary.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["left_boundary", "right_boundary"]}, "verifier": {"missing": ["left_boundary", "right_boundary"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 5.45 kg and a = 7.55 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 41.1475, \"unit\": \"N\"}", "dedupe_signature": "49338cfb26df9d99c5715ee1ee611eab0fc5bc91dd5436de8497216f81a52f54", "difficulty": "easy", "final_answer": {"answer": 41.1475, "unit": "N"}, "id": "force_003600_5.45_7.55", "license": "Apache-2.0", "prompt": "A cart has mass 5.45 kg and measured acceleration 7.55 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 5.45 kg and a = 7.55 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 7.55, "mass": 5.45}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 16.9^2 and multiply by 0.5 * 0.5.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 71.4025, \"unit\": \"J\"}", "dedupe_signature": "79b3afdc194d38b2b602b62589eb16c518f4ee30a6f6a2e718c2ef226fa0b1ad", "difficulty": "easy", "final_answer": {"answer": 71.4025, "unit": "J"}, "id": "ke_003601_0.5_16.9", "license": "Apache-2.0", "prompt": "A body of mass 0.5 kg moves at 16.9 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 16.9^2 and multiply by 0.5 * 0.5.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 0.5, "velocity": 16.9}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 0.62 * 8.314 * 399 / 90.4.\nFinal: {\"answer\": 22.7513, \"unit\": \"kPa\"}", "dedupe_signature": "bd2650a1ef1ad0c39d94459dbab4ec46ddfcb3d53154b0d08fdc1c5935624b56", "difficulty": "medium", "final_answer": {"answer": 22.7513, "unit": "kPa"}, "id": "ideal_gas_003603_0.62_399_90.4", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=0.62 mol, T=399 K, and V=90.4 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 0.62 * 8.314 * 399 / 90.4.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 0.62, "temp_k": 399, "volume_l": 90.4}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 365 * 3.565 * 36.\nFinal: {\"answer\": 46844.1, \"unit\": \"J\"}", "dedupe_signature": "7d5639c871dc2d4b7b3118c6a7dacebffa2551f8c6bab8e5bade2fa0c95f24c9", "difficulty": "easy", "final_answer": {"answer": 46844.1, "unit": "J"}, "id": "heat_q_003604_365_3.565_36", "license": "Apache-2.0", "prompt": "A 365 g sample has specific heat 3.565 J/(g*K). How much heat is needed to raise its temperature by 36 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 365 * 3.565 * 36.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 36, "heat_capacity": 3.565, "mass_g": 365}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=134 mg, t=292 h, and T_half=92 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 14.8478, \"unit\": \"mg\"}", "dedupe_signature": "d94c6d713a2b081b41694445eadc111abd85bf66807d3d239648ee6e757fa4d8", "difficulty": "medium", "final_answer": {"answer": 14.8478, "unit": "mg"}, "id": "half_life_003606_134_92_292", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 134 mg. Its half-life is 92 hours. How many mg remain after 292 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=134 mg, t=292 h, and T_half=92 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 292.0, "half_life": 92.0, "initial_amount": 134.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(7.3)=-48 and f(10.9)=-66.\n3. The interval width is 3.6.\nFinal: {\"answer\": -205.2, \"unit\": \"area_units\"}", "dedupe_signature": "8e450a96136fed548b7068b3a7df02e214e23f12c22a3bbe06e95785ba334db8", "difficulty": "medium", "final_answer": {"answer": -205.2, "unit": "area_units"}, "id": "trapz_linear_003610_-5_-11.5_7.3_10.9", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-5x+-11.5 from x=7.3 to x=10.9. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(7.3)=-48 and f(10.9)=-66.\nThe interval width is 3.6.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -11.5, "slope": -5.0, "x0": 7.3, "x1": 10.9}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 100 centimeters in one meter.\n2. Apply the conversion factor directly to the given value.\n3. Compute 1440.0 / 100.\nFinal: {\"answer\": 14.4, \"unit\": \"m\"}", "dedupe_signature": "cdf7d86524fe98f34c5e91e23d745ff842e75880fe5f31485508f76f4684c2ac", "difficulty": "easy", "final_answer": {"answer": 14.4, "unit": "m"}, "id": "unit_convert_003612_cm_to_m_1440", "license": "Apache-2.0", "prompt": "Convert 1440 cm to m. Return the converted value with unit.", "reasoning_trace": "There are 100 centimeters in one meter.\nApply the conversion factor directly to the given value.\nCompute 1440.0 / 100.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 1440.0}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. velocity times time gives distance, not acceleration\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "aa663f0adb575ce0d32a0acab4fb6b557d8de091b1eab3669e7801c73e2ff6f3", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_003615_inconsistent_7481c798_990126", "license": "Apache-2.0", "prompt": "In instrument manual case 990126, check dimensional consistency for a = v * t. The left side has dimensions m/s^2 and the right side has dimensions m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nvelocity times time gives distance, not acceleration\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "a = v * t"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef safe_mean_003616(values):\n    if not values:\n        raise ValueError('safe_mean requires at least one value')\n    return sum(values) / len(values)\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"safe_mean_003616\"}", "dedupe_signature": "f74b2a389d7ad0c064423b66f95980bd7f1f76b84abcab56e73d591e4bc7a4a0", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "safe_mean_003616"}, "id": "code_003616_safe_mean_003616", "license": "Apache-2.0", "prompt": "Write a Python function safe_mean_003616(values) that returns the arithmetic mean. It must raise ValueError for an empty input and must not mutate the input list. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "safe_mean_003616"}, "verifier": {"function": "safe_mean_003616", "tests": ["assert safe_mean_003616([2, 4, 6]) == 4", "xs = [1, 2, 3]; assert safe_mean_003616(xs) == 2 and xs == [1, 2, 3]", "try:\n    safe_mean_003616([])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: rate_constant, number_of_steps.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"rate_constant\", \"number_of_steps\"]}", "dedupe_signature": "a9fde311cc6bfb3d92cdbb3935ae9a1687d1743aadc50b49e3ba1d9031860bc3", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["rate_constant", "number_of_steps"]}, "id": "abstain_003617_rate_constant_number_of_steps", "license": "Apache-2.0", "prompt": "Use explicit Euler for dy/dt = -k y. The prompt gives y(0)=32.5 and h=1.7, but omits both k and the number of steps. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: rate_constant, number_of_steps.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["rate_constant", "number_of_steps"]}, "verifier": {"missing": ["rate_constant", "number_of_steps"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 18.7 kg and a = 14.25 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 266.475, \"unit\": \"N\"}", "dedupe_signature": "5f270ff89c1fd253bdaf0c51949252b7ebe7002731b4f4155a9accda41d4c52f", "difficulty": "easy", "final_answer": {"answer": 266.475, "unit": "N"}, "id": "force_003618_18.7_14.25", "license": "Apache-2.0", "prompt": "A cart has mass 18.7 kg and measured acceleration 14.25 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 18.7 kg and a = 14.25 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 14.25, "mass": 18.7}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 18.7^2 and multiply by 0.5 * 21.5.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 3759.1675, \"unit\": \"J\"}", "dedupe_signature": "3e1e5b7d2e98a3f2c14d602181f275e8373b1a924939d9d25a88a0db7181b15e", "difficulty": "easy", "final_answer": {"answer": 3759.1675, "unit": "J"}, "id": "ke_003619_21.5_18.7", "license": "Apache-2.0", "prompt": "A body of mass 21.5 kg moves at 18.7 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 18.7^2 and multiply by 0.5 * 21.5.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 21.5, "velocity": 18.7}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=72 degrees through the sine of 2 theta.\n3. Substitute v=11.2 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 7.516, \"unit\": \"m\"}", "dedupe_signature": "5ddfd7ee38586fce435d2d165d27f7c3f10a333620a785bff2923d0eafa0a59d", "difficulty": "medium", "final_answer": {"answer": 7.516, "unit": "m"}, "id": "projectile_range_003620_11.2_72", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 11.2 m/s and angle 72 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=72 degrees through the sine of 2 theta.\nSubstitute v=11.2 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 72, "gravity": 9.81, "speed": 11.2}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 2.92 * 8.314 * 517 / 25.4.\nFinal: {\"answer\": 494.1396, \"unit\": \"kPa\"}", "dedupe_signature": "9a5dd42e3393e2f2845931d17206ec5dc3b6e1d3ea4b76dd368ba6ee2e1b5e82", "difficulty": "medium", "final_answer": {"answer": 494.1396, "unit": "kPa"}, "id": "ideal_gas_003621_2.92_517_25.4", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=2.92 mol, T=517 K, and V=25.4 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 2.92 * 8.314 * 517 / 25.4.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 2.92, "temp_k": 517, "volume_l": 25.4}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1705 * 2.905 * 40.\nFinal: {\"answer\": 198121.0, \"unit\": \"J\"}", "dedupe_signature": "66b8185f0aba0c7f0c711e38f581e8578bdb2edda988866e1ce48c28db539813", "difficulty": "easy", "final_answer": {"answer": 198121.0, "unit": "J"}, "id": "heat_q_003622_1705_2.905_40", "license": "Apache-2.0", "prompt": "A 1705 g sample has specific heat 2.905 J/(g*K). How much heat is needed to raise its temperature by 40 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1705 * 2.905 * 40.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 40, "heat_capacity": 2.905, "mass_g": 1705}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=200.2 V and R=187.9 ohm.\nFinal: {\"answer\": 213.3052, \"unit\": \"W\"}", "dedupe_signature": "51d2aaf1066db28f1b6c21619e3ee9ab76454321e6d2e326c4830e015dbb63e3", "difficulty": "easy", "final_answer": {"answer": 213.3052, "unit": "W"}, "id": "ohm_power_003623_200.2_187.9", "license": "Apache-2.0", "prompt": "A resistor has resistance 187.9 ohm and voltage 200.2 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=200.2 V and R=187.9 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 187.9, "voltage": 200.2}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=281 mg, t=141.5 h, and T_half=80 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 82.4631, \"unit\": \"mg\"}", "dedupe_signature": "2dad3318b8cd1749eae123934faf8af72c0eea031babe2df35e02663cf4f166c", "difficulty": "medium", "final_answer": {"answer": 82.4631, "unit": "mg"}, "id": "half_life_003624_281_80_141.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 281 mg. Its half-life is 80 hours. How many mg remain after 141.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=281 mg, t=141.5 h, and T_half=80 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 141.5, "half_life": 80.0, "initial_amount": 281.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 2665 mL to 2.665 L.\n3. Compute M = 4.855 / 2.665.\nFinal: {\"answer\": 1.8218, \"unit\": \"mol/L\"}", "dedupe_signature": "1c510b3216f2e7c31f52dd925f46f889ae439be962f60a16036d6c3736136a66", "difficulty": "medium", "final_answer": {"answer": 1.8218, "unit": "mol/L"}, "id": "molarity_003626_4.855_2665", "license": "Apache-2.0", "prompt": "A solution contains 4.855 mol of solute in 2665 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 2665 mL to 2.665 L.\nCompute M = 4.855 / 2.665.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 4.855, "volume_ml": 2665}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.18 y, so each step multiplies y by 1 - h*0.18.\n3. Apply that update for 2 steps and round the final state.\nFinal: {\"answer\": 13.6875, \"unit\": \"state_units\"}", "dedupe_signature": "2f4a3dc6028e73405f8132aeffe27127a40c76660d5e2b3aee4c864b32791ba4", "difficulty": "medium", "final_answer": {"answer": 13.6875, "unit": "state_units"}, "id": "euler_decay_003627_27_0.18_1.6_2", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.18 y with y(0)=27, step size h=1.6, for 2 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.18 y, so each step multiplies y by 1 - h*0.18.\nApply that update for 2 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 27.0, "rate": 0.18, "step": 1.6, "steps": 2}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.48 and add it to the current value.\nFinal: {\"answer\": [1.03, 0.756, 0.93], \"unit\": \"temperature_units\"}", "dedupe_signature": "caa3a3c87f3c8cc325330b76c4e0fdce870780c8daf1e4b0ba0c9dc27c008367", "difficulty": "hard", "final_answer": {"answer": [1.03, 0.756, 0.93], "unit": "temperature_units"}, "id": "heat_step_003629_0.48_2.2_2.95_-0.3_-1.35_2.35", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=2.2, right=2.35; current interior values are [2.95, -0.3, -1.35]. Use r=0.48. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.48 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [2.95, -0.3, -1.35], "left": 2.2, "r": 0.48, "right": 2.35}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 21359.0 / 1000.\nFinal: {\"answer\": 21.359, \"unit\": \"kg\"}", "dedupe_signature": "eb0d3efef74dcc9d0f1a1527245b6d02de7fd4d4b51912a6514668220471badc", "difficulty": "easy", "final_answer": {"answer": 21.359, "unit": "kg"}, "id": "unit_convert_003630_g_to_kg_21359", "license": "Apache-2.0", "prompt": "Convert 21359 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 21359.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 21359.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=136 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-241.6982, 233.4052], \"unit\": \"N\"}", "dedupe_signature": "06ac83ac1c0b5a8417f36530a0f73ef3eeae9aa6c7a4376c12ea063c48fbd685", "difficulty": "medium", "final_answer": {"answer": [-241.6982, 233.4052], "unit": "N"}, "id": "vector_components_003631_336_136", "license": "Apache-2.0", "prompt": "A vector has magnitude 336 N at 136 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=136 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 136, "magnitude": 336.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. velocity divided by time is acceleration\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "03e328d8c176886c0cb7e75e47a22f153cecb121158489ca4651eb7ae08be7d2", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_003633_inconsistent_c1271127_511262", "license": "Apache-2.0", "prompt": "In field worksheet case 511262, check dimensional consistency for x = v / t. The left side has dimensions m and the right side has dimensions m/s^2. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nvelocity divided by time is acceleration\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "x = v / t"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: rate_constant, number_of_steps.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"rate_constant\", \"number_of_steps\"]}", "dedupe_signature": "f99c319d4b2beb04015148e62897e27b06f4b85073b1035afa77b964ffb636fb", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["rate_constant", "number_of_steps"]}, "id": "abstain_003635_rate_constant_number_of_steps", "license": "Apache-2.0", "prompt": "Use explicit Euler for dy/dt = -k y. The prompt gives y(0)=70 and h=1.8, but omits both k and the number of steps. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: rate_constant, number_of_steps.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["rate_constant", "number_of_steps"]}, "verifier": {"missing": ["rate_constant", "number_of_steps"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 21.15^2 and multiply by 0.5 * 28.3.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 6329.6134, \"unit\": \"J\"}", "dedupe_signature": "94cc25646ff65f2c0cd4b318f09cde3c696b8592b821a4c460f71ded8b3d563e", "difficulty": "easy", "final_answer": {"answer": 6329.6134, "unit": "J"}, "id": "ke_003637_28.3_21.15", "license": "Apache-2.0", "prompt": "A body of mass 28.3 kg moves at 21.15 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 21.15^2 and multiply by 0.5 * 28.3.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 28.3, "velocity": 21.15}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=29 degrees through the sine of 2 theta.\n3. Substitute v=18.4 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 29.2676, \"unit\": \"m\"}", "dedupe_signature": "17980baa6d5fa344b105bf5ad235dec60ceefb9021db7ce228e31b94475b35dc", "difficulty": "medium", "final_answer": {"answer": 29.2676, "unit": "m"}, "id": "projectile_range_003638_18.4_29", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 18.4 m/s and angle 29 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=29 degrees through the sine of 2 theta.\nSubstitute v=18.4 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 29, "gravity": 9.81, "speed": 18.4}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 0.72 * 8.314 * 432 / 99.6.\nFinal: {\"answer\": 25.9637, \"unit\": \"kPa\"}", "dedupe_signature": "b9afa7fc8d87c25e709ee042f9406f7796392a321bab65ce615f873cac372816", "difficulty": "medium", "final_answer": {"answer": 25.9637, "unit": "kPa"}, "id": "ideal_gas_003639_0.72_432_99.6", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=0.72 mol, T=432 K, and V=99.6 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 0.72 * 8.314 * 432 / 99.6.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 0.72, "temp_k": 432, "volume_l": 99.6}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1415 * 2.64 * 55.\nFinal: {\"answer\": 205458.0, \"unit\": \"J\"}", "dedupe_signature": "de052255c602872ee88f48191ecb72b03bac128b112770200b5f46d219ba8a5e", "difficulty": "easy", "final_answer": {"answer": 205458.0, "unit": "J"}, "id": "heat_q_003640_1415_2.64_55", "license": "Apache-2.0", "prompt": "A 1415 g sample has specific heat 2.64 J/(g*K). How much heat is needed to raise its temperature by 55 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1415 * 2.64 * 55.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 55, "heat_capacity": 2.64, "mass_g": 1415}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=145.6 V and R=91.7 ohm.\nFinal: {\"answer\": 231.1817, \"unit\": \"W\"}", "dedupe_signature": "21e0f085ea2e99a260527426b1d06ec6e44238840048fc9314176e7e5788a57f", "difficulty": "easy", "final_answer": {"answer": 231.1817, "unit": "W"}, "id": "ohm_power_003641_145.6_91.7", "license": "Apache-2.0", "prompt": "A resistor has resistance 91.7 ohm and voltage 145.6 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=145.6 V and R=91.7 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 91.7, "voltage": 145.6}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=394.5 mg, t=294 h, and T_half=8 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 0.0, \"unit\": \"mg\"}", "dedupe_signature": "a2e7dba7179399865746fe6cb3951d1588de1d5172519f6974de57386883e80f", "difficulty": "medium", "final_answer": {"answer": 0.0, "unit": "mg"}, "id": "half_life_003642_394.5_8_294", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 394.5 mg. Its half-life is 8 hours. How many mg remain after 294 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=394.5 mg, t=294 h, and T_half=8 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 294.0, "half_life": 8.0, "initial_amount": 394.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 4535 mL to 4.535 L.\n3. Compute M = 4.36 / 4.535.\nFinal: {\"answer\": 0.9614, \"unit\": \"mol/L\"}", "dedupe_signature": "1f2e427f61b026a7e4929210e661bcd1bc641296ea78f2050232a68bb9e5a525", "difficulty": "medium", "final_answer": {"answer": 0.9614, "unit": "mol/L"}, "id": "molarity_003644_4.36_4535", "license": "Apache-2.0", "prompt": "A solution contains 4.36 mol of solute in 4535 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 4535 mL to 4.535 L.\nCompute M = 4.36 / 4.535.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 4.36, "volume_ml": 4535}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.63 y, so each step multiplies y by 1 - h*0.63.\n3. Apply that update for 10 steps and round the final state.\nFinal: {\"answer\": 0.3969, \"unit\": \"state_units\"}", "dedupe_signature": "a1dfef3b2d920f8e19dab9ac6f4929afbca4375d148a5821ad1ff37ae3c6a96c", "difficulty": "medium", "final_answer": {"answer": 0.3969, "unit": "state_units"}, "id": "euler_decay_003645_77_0.63_0.65_10", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.63 y with y(0)=77, step size h=0.65, for 10 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.63 y, so each step multiplies y by 1 - h*0.63.\nApply that update for 10 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 77.0, "rate": 0.63, "step": 0.65, "steps": 10}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(2.5)=0.45 and f(11.9)=-36.21.\n3. The interval width is 9.4.\nFinal: {\"answer\": -168.072, \"unit\": \"area_units\"}", "dedupe_signature": "9fe80a8056dbb7c52b538e89622d075461c40b4640eeb9b10e01edf48a783cde", "difficulty": "medium", "final_answer": {"answer": -168.072, "unit": "area_units"}, "id": "trapz_linear_003646_-3.9_10.2_2.5_11.9", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-3.9x+10.2 from x=2.5 to x=11.9. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(2.5)=0.45 and f(11.9)=-36.21.\nThe interval width is 9.4.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 10.2, "slope": -3.9, "x0": 2.5, "x1": 11.9}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 100 centimeters in one meter.\n2. Apply the conversion factor directly to the given value.\n3. Compute 415.0 / 100.\nFinal: {\"answer\": 4.15, \"unit\": \"m\"}", "dedupe_signature": "0631bcb1f08740f1a820fa6962f979df73c8cb08bed703c111eebd9889f5fef2", "difficulty": "easy", "final_answer": {"answer": 4.15, "unit": "m"}, "id": "unit_convert_003648_cm_to_m_415", "license": "Apache-2.0", "prompt": "Convert 415 cm to m. Return the converted value with unit.", "reasoning_trace": "There are 100 centimeters in one meter.\nApply the conversion factor directly to the given value.\nCompute 415.0 / 100.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 415.0}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=152 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-221.6198, 117.8374], \"unit\": \"N\"}", "dedupe_signature": "ec432d960f4cf6b26b0a0978f7487f464a515a5236d4d3d3aa912489d883d53a", "difficulty": "medium", "final_answer": {"answer": [-221.6198, 117.8374], "unit": "N"}, "id": "vector_components_003649_251_152", "license": "Apache-2.0", "prompt": "A vector has magnitude 251 N at 152 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=152 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 152, "magnitude": 251.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [1.6, -27.25], \"unit\": \"dimensionless\"}", "dedupe_signature": "5790a6d8e01f333726b63ab034b2267bc43f3b5c959613bf2d7cd360cb8091f2", "difficulty": "medium", "final_answer": {"answer": [1.6, -27.25], "unit": "dimensionless"}, "id": "line_two_point_003650_5.75_9.25_1.6_-27.25", "license": "Apache-2.0", "prompt": "A line passes through points (5.75, -18.05) and (9.25, -12.45). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 5.75, "x2": 9.25, "y1": -18.049999999999997, "y2": -12.45}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. volt squared divided by ohm is watt\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "2ae96ecbca556bb01fe10e024c61f1fde6cea58771bc882b8dd966e78493fd7e", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_003651_consistent_82e93f3d_127393", "license": "Apache-2.0", "prompt": "In quality-control check case 127393, check dimensional consistency for P = V^2 / R. The left side has dimensions W and the right side has dimensions W. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nvolt squared divided by ohm is watt\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "P = V^2 / R"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef running_total_003652(values):\n    total = 0\n    out = []\n    for value in values:\n        total += value\n        out.append(total)\n    return out\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"running_total_003652\"}", "dedupe_signature": "3628ddeaf311cc90753b421ad1c061e7da4d8fcc24930455ba75ee24935f77e0", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "running_total_003652"}, "id": "code_003652_running_total_003652", "license": "Apache-2.0", "prompt": "Write a Python function running_total_003652(values) that returns cumulative sums as a new list. It must not mutate the input list. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "running_total_003652"}, "verifier": {"function": "running_total_003652", "tests": ["assert running_total_003652([1, 2, 3]) == [1, 3, 6]", "xs = [4, -1, 2]; assert running_total_003652(xs) == [4, 3, 5] and xs == [4, -1, 2]", "assert running_total_003652([]) == []"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: launch_angle_or_vertical_velocity.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"launch_angle_or_vertical_velocity\"]}", "dedupe_signature": "3bd8aa76eac48f409ddcdf3d4bb8faa36bf24204bdd2b0b659e1ab60efcdca50", "difficulty": "easy", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["launch_angle_or_vertical_velocity"]}, "id": "abstain_003653_launch_angle_or_vertical_velocity", "license": "Apache-2.0", "prompt": "Compute projectile range on level ground. The prompt gives initial speed 58.3 m/s but does not give launch angle or vertical velocity. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: launch_angle_or_vertical_velocity.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["launch_angle_or_vertical_velocity"]}, "verifier": {"missing": ["launch_angle_or_vertical_velocity"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 24.05 kg and a = 14.35 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 345.1175, \"unit\": \"N\"}", "dedupe_signature": "a6b376915961bba7d11b34ed2df9131673578a7c8bde1b608776e1e0ce8f39ab", "difficulty": "easy", "final_answer": {"answer": 345.1175, "unit": "N"}, "id": "force_003654_24.05_14.35", "license": "Apache-2.0", "prompt": "A cart has mass 24.05 kg and measured acceleration 14.35 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 24.05 kg and a = 14.35 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 14.35, "mass": 24.05}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=55 degrees through the sine of 2 theta.\n3. Substitute v=22.6 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 48.9253, \"unit\": \"m\"}", "dedupe_signature": "03532bb126641e15ab6a13902e9b06915c761535cf2f8b87ad42b46c302b8a91", "difficulty": "medium", "final_answer": {"answer": 48.9253, "unit": "m"}, "id": "projectile_range_003656_22.6_55", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 22.6 m/s and angle 55 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=55 degrees through the sine of 2 theta.\nSubstitute v=22.6 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 55, "gravity": 9.81, "speed": 22.6}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 5.58 * 8.314 * 614 / 4.4.\nFinal: {\"answer\": 6473.8095, \"unit\": \"kPa\"}", "dedupe_signature": "c111b4ce4be3d1190d62af7eb169a687b2fe8e92fd7606e3a21518b705679a8a", "difficulty": "medium", "final_answer": {"answer": 6473.8095, "unit": "kPa"}, "id": "ideal_gas_003657_5.58_614_4.4", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=5.58 mol, T=614 K, and V=4.4 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 5.58 * 8.314 * 614 / 4.4.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 5.58, "temp_k": 614, "volume_l": 4.4}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1610 * 2.555 * 69.\nFinal: {\"answer\": 283834.95, \"unit\": \"J\"}", "dedupe_signature": "194c68cff267275fa5720867a818e0cca2557b7fd0fb5f4573a98152311f9562", "difficulty": "easy", "final_answer": {"answer": 283834.95, "unit": "J"}, "id": "heat_q_003658_1610_2.555_69", "license": "Apache-2.0", "prompt": "A 1610 g sample has specific heat 2.555 J/(g*K). How much heat is needed to raise its temperature by 69 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1610 * 2.555 * 69.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 69, "heat_capacity": 2.555, "mass_g": 1610}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=170.2 V and R=36 ohm.\nFinal: {\"answer\": 804.6678, \"unit\": \"W\"}", "dedupe_signature": "e6fc4f9e45dc2701777be6432ee0a0c271ed86dc3dc2db3bc55250ad5aa18dd8", "difficulty": "easy", "final_answer": {"answer": 804.6678, "unit": "W"}, "id": "ohm_power_003659_170.2_36", "license": "Apache-2.0", "prompt": "A resistor has resistance 36 ohm and voltage 170.2 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=170.2 V and R=36 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 36.0, "voltage": 170.2}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=449.5 mg, t=12.5 h, and T_half=8 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 152.1845, \"unit\": \"mg\"}", "dedupe_signature": "b7f37656c0a20cc6d3035809135b44fe30794ddd7c3388c52cc86e90f3a26559", "difficulty": "medium", "final_answer": {"answer": 152.1845, "unit": "mg"}, "id": "half_life_003660_449.5_8_12.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 449.5 mg. Its half-life is 8 hours. How many mg remain after 12.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=449.5 mg, t=12.5 h, and T_half=8 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 12.5, "half_life": 8.0, "initial_amount": 449.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.42 y, so each step multiplies y by 1 - h*0.42.\n3. Apply that update for 9 steps and round the final state.\nFinal: {\"answer\": 0.0564, \"unit\": \"state_units\"}", "dedupe_signature": "2c9d0f095dff7e3a72151277bed80c2acd3410e094604ed5c4f273a3091258e6", "difficulty": "medium", "final_answer": {"answer": 0.0564, "unit": "state_units"}, "id": "euler_decay_003663_3_0.42_0.85_9", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.42 y with y(0)=3, step size h=0.85, for 9 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.42 y, so each step multiplies y by 1 - h*0.42.\nApply that update for 9 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 3.0, "rate": 0.42, "step": 0.85, "steps": 9}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(0.2)=-16.24 and f(1)=-18.4.\n3. The interval width is 0.8.\nFinal: {\"answer\": -13.856, \"unit\": \"area_units\"}", "dedupe_signature": "07382c75f458ba65c93e7cc6fd02a8bc05322f1f31b9eed8a34466b9617e627b", "difficulty": "medium", "final_answer": {"answer": -13.856, "unit": "area_units"}, "id": "trapz_linear_003664_-2.7_-15.7_0.2_1", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-2.7x+-15.7 from x=0.2 to x=1. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(0.2)=-16.24 and f(1)=-18.4.\nThe interval width is 0.8.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -15.7, "slope": -2.7, "x0": 0.2, "x1": 1.0}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.02 and add it to the current value.\nFinal: {\"answer\": [2.525, 0.752, -0.897], \"unit\": \"temperature_units\"}", "dedupe_signature": "067bc83ff01da7fd8ac8e70a9926b659a546531b5b9d185b6483891e43dbe79c", "difficulty": "hard", "final_answer": {"answer": [2.525, 0.752, -0.897], "unit": "temperature_units"}, "id": "heat_step_003665_0.02_0.7_2.6_0.75_-1.0_2.4", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=0.7, right=2.4; current interior values are [2.6, 0.75, -1.0]. Use r=0.02. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.02 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [2.6, 0.75, -1.0], "left": 0.7, "r": 0.02, "right": 2.4}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 36735.0 / 1000.\nFinal: {\"answer\": 36.735, \"unit\": \"kg\"}", "dedupe_signature": "9dab265a4b843a970658ff42e4b9aebb88674973078125d05aeb1c443e38a1c7", "difficulty": "easy", "final_answer": {"answer": 36.735, "unit": "kg"}, "id": "unit_convert_003666_g_to_kg_36735", "license": "Apache-2.0", "prompt": "Convert 36735 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 36735.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 36735.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=9 degrees and keep the unit as newtons.\nFinal: {\"answer\": [484.4611, 76.7311], \"unit\": \"N\"}", "dedupe_signature": "235a12c762211593d04cbb73cc71953f0529cebe82ffc9183f11722adf6d349c", "difficulty": "medium", "final_answer": {"answer": [484.4611, 76.7311], "unit": "N"}, "id": "vector_components_003667_490.5_9", "license": "Apache-2.0", "prompt": "A vector has magnitude 490.5 N at 9 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=9 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 9, "magnitude": 490.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [0.2, 9.75], \"unit\": \"dimensionless\"}", "dedupe_signature": "dd96e91b5cc91a1bbe5193a4d850cd2dab196b5e33167f667bc020df8baf439f", "difficulty": "medium", "final_answer": {"answer": [0.2, 9.75], "unit": "dimensionless"}, "id": "line_two_point_003668_-4.5_8_0.2_9.75", "license": "Apache-2.0", "prompt": "A line passes through points (-4.5, 8.85) and (8, 11.35). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -4.5, "x2": 8.0, "y1": 8.85, "y2": 11.35}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. m*v is momentum, not energy\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "4ec8447b3fedd9bc01869e3d04d35766795b0821797a9a77ca2d58de67fbde1c", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_003669_inconsistent_1e14b074_614084", "license": "Apache-2.0", "prompt": "In sensor calibration case 614084, check dimensional consistency for E = m * v. The left side has dimensions kg*m^2/s^2 and the right side has dimensions kg*m/s. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nm*v is momentum, not energy\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "E = m * v"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: rate_constant, number_of_steps.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"rate_constant\", \"number_of_steps\"]}", "dedupe_signature": "bba60bf5eb2ba02beeed1f480934bccf97470a36fd327549d67931320707719f", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["rate_constant", "number_of_steps"]}, "id": "abstain_003671_rate_constant_number_of_steps", "license": "Apache-2.0", "prompt": "Use explicit Euler for dy/dt = -k y. The prompt gives y(0)=77 and h=1.05, but omits both k and the number of steps. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: rate_constant, number_of_steps.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["rate_constant", "number_of_steps"]}, "verifier": {"missing": ["rate_constant", "number_of_steps"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 8.1^2 and multiply by 0.5 * 29.35.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 962.8268, \"unit\": \"J\"}", "dedupe_signature": "1e341dfe59f358846feca4f45337d8ab1876eead4b4c87794cab734cc92e06d8", "difficulty": "easy", "final_answer": {"answer": 962.8268, "unit": "J"}, "id": "ke_003673_29.35_8.1", "license": "Apache-2.0", "prompt": "A body of mass 29.35 kg moves at 8.1 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 8.1^2 and multiply by 0.5 * 29.35.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 29.35, "velocity": 8.1}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=82 degrees through the sine of 2 theta.\n3. Substitute v=19.6 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 10.794, \"unit\": \"m\"}", "dedupe_signature": "4c112c3d108eb4dc61a1b2f1618cbd4a86a66e2fe45537a4cfffe6c6a1d9c4fe", "difficulty": "medium", "final_answer": {"answer": 10.794, "unit": "m"}, "id": "projectile_range_003674_19.6_82", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 19.6 m/s and angle 82 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=82 degrees through the sine of 2 theta.\nSubstitute v=19.6 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 82, "gravity": 9.81, "speed": 19.6}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 4.51 * 8.314 * 414 / 4.8.\nFinal: {\"answer\": 3234.0421, \"unit\": \"kPa\"}", "dedupe_signature": "ef0fdbf64ab74529c8d1382cd0552b6a7666b7edcc3d3599abdaa2870c1b432d", "difficulty": "medium", "final_answer": {"answer": 3234.0421, "unit": "kPa"}, "id": "ideal_gas_003675_4.51_414_4.8", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=4.51 mol, T=414 K, and V=4.8 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 4.51 * 8.314 * 414 / 4.8.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 4.51, "temp_k": 414, "volume_l": 4.8}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1250 * 4.635 * 31.\nFinal: {\"answer\": 179606.25, \"unit\": \"J\"}", "dedupe_signature": "a9e3847c61e88928e107aa0af6ebbec74418adfafa71ce3571da13a6c6158e5f", "difficulty": "easy", "final_answer": {"answer": 179606.25, "unit": "J"}, "id": "heat_q_003676_1250_4.635_31", "license": "Apache-2.0", "prompt": "A 1250 g sample has specific heat 4.635 J/(g*K). How much heat is needed to raise its temperature by 31 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1250 * 4.635 * 31.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 31, "heat_capacity": 4.635, "mass_g": 1250}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=162.1 V and R=55 ohm.\nFinal: {\"answer\": 477.7529, \"unit\": \"W\"}", "dedupe_signature": "d21af9b51ccfd007db57572c6a72b877ae0871d2adf2d4cc8c87fae9ba40c62f", "difficulty": "easy", "final_answer": {"answer": 477.7529, "unit": "W"}, "id": "ohm_power_003677_162.1_55", "license": "Apache-2.0", "prompt": "A resistor has resistance 55 ohm and voltage 162.1 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=162.1 V and R=55 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 55.0, "voltage": 162.1}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=417.5 mg, t=227 h, and T_half=112.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 103.0967, \"unit\": \"mg\"}", "dedupe_signature": "89750f074b42a61ad1f5bf0b039403f526c1c80aae10f147e41d5782e90004aa", "difficulty": "medium", "final_answer": {"answer": 103.0967, "unit": "mg"}, "id": "half_life_003678_417.5_112.5_227", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 417.5 mg. Its half-life is 112.5 hours. How many mg remain after 227 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=417.5 mg, t=227 h, and T_half=112.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 227.0, "half_life": 112.5, "initial_amount": 417.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.34 y, so each step multiplies y by 1 - h*0.34.\n3. Apply that update for 10 steps and round the final state.\nFinal: {\"answer\": 0.8641, \"unit\": \"state_units\"}", "dedupe_signature": "2b4e5272f6f6c77496a42f49bfd72a35d02d39464824f4b0b77910c98f8c3a0d", "difficulty": "medium", "final_answer": {"answer": 0.8641, "unit": "state_units"}, "id": "euler_decay_003681_10.5_0.34_0.65_10", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.34 y with y(0)=10.5, step size h=0.65, for 10 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.34 y, so each step multiplies y by 1 - h*0.34.\nApply that update for 10 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 10.5, "rate": 0.34, "step": 0.65, "steps": 10}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(1.1)=8.46 and f(10.8)=-34.22.\n3. The interval width is 9.7.\nFinal: {\"answer\": -124.936, \"unit\": \"area_units\"}", "dedupe_signature": "656bda6681b0696f6918089df42d1c6da8e7484f46125663e486c73567fcafb1", "difficulty": "medium", "final_answer": {"answer": -124.936, "unit": "area_units"}, "id": "trapz_linear_003682_-4.4_13.3_1.1_10.8", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-4.4x+13.3 from x=1.1 to x=10.8. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(1.1)=8.46 and f(10.8)=-34.22.\nThe interval width is 9.7.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 13.3, "slope": -4.4, "x0": 1.1, "x1": 10.799999999999999}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.4 and add it to the current value.\nFinal: {\"answer\": [1.04, 1.05, 0.11], \"unit\": \"temperature_units\"}", "dedupe_signature": "6532bf72e7a8360dbdba83b13c1172f316bb329f54e7ff63e1b9d667b1d9e0bc", "difficulty": "hard", "final_answer": {"answer": [1.04, 1.05, 0.11], "unit": "temperature_units"}, "id": "heat_step_003683_0.4_2.8_2.9_-1.65_0.55_1.65", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=2.8, right=1.65; current interior values are [2.9, -1.65, 0.55]. Use r=0.4. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.4 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [2.9, -1.65, 0.55], "left": 2.8, "r": 0.4, "right": 1.65}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 100 centimeters in one meter.\n2. Apply the conversion factor directly to the given value.\n3. Compute 2176.5 / 100.\nFinal: {\"answer\": 21.765, \"unit\": \"m\"}", "dedupe_signature": "cfaac8f88ef0cf6a952ef58448e12567aa4083293b116901c74d6b059550dec1", "difficulty": "easy", "final_answer": {"answer": 21.765, "unit": "m"}, "id": "unit_convert_003684_cm_to_m_2176.5", "license": "Apache-2.0", "prompt": "Convert 2176.5 cm to m. Return the converted value with unit.", "reasoning_trace": "There are 100 centimeters in one meter.\nApply the conversion factor directly to the given value.\nCompute 2176.5 / 100.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 2176.5}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=277 degrees and keep the unit as newtons.\nFinal: {\"answer\": [5.2404, -42.6795], \"unit\": \"N\"}", "dedupe_signature": "96a7c0044d143bedd72977abba5921cdc7d6c7cb12cf67decc2c7e775defa7ec", "difficulty": "medium", "final_answer": {"answer": [5.2404, -42.6795], "unit": "N"}, "id": "vector_components_003685_43_277", "license": "Apache-2.0", "prompt": "A vector has magnitude 43 N at 277 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=277 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 277, "magnitude": 43.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-0.4, -24.5], \"unit\": \"dimensionless\"}", "dedupe_signature": "4b8208a204b38f0813389c1fd5820e4e32a9b6df9719fe3a4a8c70c3bd541310", "difficulty": "medium", "final_answer": {"answer": [-0.4, -24.5], "unit": "dimensionless"}, "id": "line_two_point_003686_13_13.75_-0.4_-24.5", "license": "Apache-2.0", "prompt": "A line passes through points (13, -29.7) and (13.75, -30). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 13.0, "x2": 13.75, "y1": -29.7, "y2": -30.0}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. speed squared over acceleration has units of meters\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "e031edab40782c3163d5d42745d9357d9711a8159bf561767ab9f659706eb461", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_003687_consistent_741d4e34_45238", "license": "Apache-2.0", "prompt": "In field worksheet case 45238, check dimensional consistency for R = v^2 * sin(theta) / g. The left side has dimensions m and the right side has dimensions m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nspeed squared over acceleration has units of meters\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "R = v^2 * sin(theta) / g"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef clamp_003688(x, lo, hi):\n    if lo > hi:\n        raise ValueError('lo must be <= hi')\n    return min(max(x, lo), hi)\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"clamp_003688\"}", "dedupe_signature": "296bbace078a7a4606e0e1298547dcad22a8f0546d25f768c177b90069b44caa", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "clamp_003688"}, "id": "code_003688_clamp_003688", "license": "Apache-2.0", "prompt": "Write a Python function clamp_003688(x, lo, hi) that clips x into the inclusive interval [lo, hi]. It must raise ValueError if lo > hi. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "clamp_003688"}, "verifier": {"function": "clamp_003688", "tests": ["assert clamp_003688(5, 0, 10) == 5", "assert clamp_003688(-2, 0, 10) == 0", "assert clamp_003688(12, 0, 10) == 10", "try:\n    clamp_003688(1, 3, 2)\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: launch_angle_or_vertical_velocity.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"launch_angle_or_vertical_velocity\"]}", "dedupe_signature": "34caf0fc8d937bb9bb11603f6a0f8892cdac4fef7b4f755103be6199c0205e49", "difficulty": "easy", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["launch_angle_or_vertical_velocity"]}, "id": "abstain_003689_launch_angle_or_vertical_velocity", "license": "Apache-2.0", "prompt": "Compute projectile range on level ground. The prompt gives initial speed 14.8 m/s but does not give launch angle or vertical velocity. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: launch_angle_or_vertical_velocity.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["launch_angle_or_vertical_velocity"]}, "verifier": {"missing": ["launch_angle_or_vertical_velocity"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 1.9 kg and a = 8.6 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 16.34, \"unit\": \"N\"}", "dedupe_signature": "e5d01993188d02de07e5da7c840e253e3ac92b036cc9a17dbacdcc14948a9225", "difficulty": "easy", "final_answer": {"answer": 16.34, "unit": "N"}, "id": "force_003690_1.9_8.6", "license": "Apache-2.0", "prompt": "A cart has mass 1.9 kg and measured acceleration 8.6 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 1.9 kg and a = 8.6 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 8.6, "mass": 1.9}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 24.75^2 and multiply by 0.5 * 9.6.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 2940.3, \"unit\": \"J\"}", "dedupe_signature": "3873a9bcc1ab58e4d4ced10ef7ae35dc2e4e348c0a35e66e8454d3614677c897", "difficulty": "easy", "final_answer": {"answer": 2940.3, "unit": "J"}, "id": "ke_003691_9.6_24.75", "license": "Apache-2.0", "prompt": "A body of mass 9.6 kg moves at 24.75 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 24.75^2 and multiply by 0.5 * 9.6.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 9.6, "velocity": 24.75}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=33 degrees through the sine of 2 theta.\n3. Substitute v=83.8 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 653.957, \"unit\": \"m\"}", "dedupe_signature": "84aecc60e3aca81b88fb176881a36ef76109b92c0d8799d97f63758908817fcc", "difficulty": "medium", "final_answer": {"answer": 653.957, "unit": "m"}, "id": "projectile_range_003692_83.8_33", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 83.8 m/s and angle 33 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=33 degrees through the sine of 2 theta.\nSubstitute v=83.8 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 33, "gravity": 9.81, "speed": 83.8}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1350 * 2.16 * 97.\nFinal: {\"answer\": 282852.0, \"unit\": \"J\"}", "dedupe_signature": "45ada1894f21fb2d4428a420cb50666862e80d979a8b8f964856ac425c21d349", "difficulty": "easy", "final_answer": {"answer": 282852.0, "unit": "J"}, "id": "heat_q_003694_1350_2.16_97", "license": "Apache-2.0", "prompt": "A 1350 g sample has specific heat 2.16 J/(g*K). How much heat is needed to raise its temperature by 97 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1350 * 2.16 * 97.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 97, "heat_capacity": 2.16, "mass_g": 1350}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=10.1 V and R=144.7 ohm.\nFinal: {\"answer\": 0.705, \"unit\": \"W\"}", "dedupe_signature": "cb811eda7f9a27280884fd558676e9d597bc4324871582993b9c456b81d2a14c", "difficulty": "easy", "final_answer": {"answer": 0.705, "unit": "W"}, "id": "ohm_power_003695_10.1_144.7", "license": "Apache-2.0", "prompt": "A resistor has resistance 144.7 ohm and voltage 10.1 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=10.1 V and R=144.7 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 144.7, "voltage": 10.1}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=313 mg, t=215 h, and T_half=3.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 0.0, \"unit\": \"mg\"}", "dedupe_signature": "e5806c66eea2f762a5e698648b8845c183da54ee70d3f5e25b134205f06e8e31", "difficulty": "medium", "final_answer": {"answer": 0.0, "unit": "mg"}, "id": "half_life_003696_313_3.5_215", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 313 mg. Its half-life is 3.5 hours. How many mg remain after 215 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=313 mg, t=215 h, and T_half=3.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 215.0, "half_life": 3.5, "initial_amount": 313.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 7.27 mol * 18.015 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 130.9691, \"unit\": \"g\"}", "dedupe_signature": "1b79bada7858f7b9966ea844d45731a29c92f007de7039584958c7c30ae5c82d", "difficulty": "medium", "final_answer": {"answer": 130.9691, "unit": "g"}, "id": "stoich_mass_003697_water_7.27", "license": "Apache-2.0", "prompt": "A sample contains 7.27 mol of water. Using molar mass 18.015 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 7.27 mol * 18.015 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "water", "molar_mass": 18.015, "moles": 7.27}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 4285 mL to 4.285 L.\n3. Compute M = 2.155 / 4.285.\nFinal: {\"answer\": 0.5029, \"unit\": \"mol/L\"}", "dedupe_signature": "1ac45ec082b61faf1099d9fb7b4030e4d01f2d12bbaa4223c2998ec82b0c2384", "difficulty": "medium", "final_answer": {"answer": 0.5029, "unit": "mol/L"}, "id": "molarity_003698_2.155_4285", "license": "Apache-2.0", "prompt": "A solution contains 2.155 mol of solute in 4285 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 4285 mL to 4.285 L.\nCompute M = 2.155 / 4.285.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 2.155, "volume_ml": 4285}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.63 y, so each step multiplies y by 1 - h*0.63.\n3. Apply that update for 9 steps and round the final state.\nFinal: {\"answer\": 2.2644, \"unit\": \"state_units\"}", "dedupe_signature": "e3bb171f9b57c8ce6080f46445c95ba9cedb5a5067cf99013c858ef1f1feb60d", "difficulty": "medium", "final_answer": {"answer": 2.2644, "unit": "state_units"}, "id": "euler_decay_003699_45.5_0.63_0.45_9", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.63 y with y(0)=45.5, step size h=0.45, for 9 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.63 y, so each step multiplies y by 1 - h*0.63.\nApply that update for 9 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 45.5, "rate": 0.63, "step": 0.45, "steps": 9}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(7.7)=45.71 and f(12.6)=66.78.\n3. The interval width is 4.9.\nFinal: {\"answer\": 275.6005, \"unit\": \"area_units\"}", "dedupe_signature": "540664547e2cceccec03ed3b179520a692f58e40ccadba813cfe38cb1ac40762", "difficulty": "medium", "final_answer": {"answer": 275.6005, "unit": "area_units"}, "id": "trapz_linear_003700_4.3_12.6_7.7_12.6", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=4.3x+12.6 from x=7.7 to x=12.6. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(7.7)=45.71 and f(12.6)=66.78.\nThe interval width is 4.9.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 12.6, "slope": 4.3, "x0": 7.7, "x1": 12.600000000000001}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.42 and add it to the current value.\nFinal: {\"answer\": [1.872, -1.148, 1.426], \"unit\": \"temperature_units\"}", "dedupe_signature": "63c5a2baf247a0a58d13a540a3d5a9707466b238a5376990ab388fdcef7eef47", "difficulty": "hard", "final_answer": {"answer": [1.872, -1.148, 1.426], "unit": "temperature_units"}, "id": "heat_step_003701_0.42_2.4_-1.95_2.8_-1.85_1.3", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=2.4, right=1.3; current interior values are [-1.95, 2.8, -1.85]. Use r=0.42. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.42 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-1.95, 2.8, -1.85], "left": 2.4, "r": 0.42, "right": 1.3}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=298 degrees and keep the unit as newtons.\nFinal: {\"answer\": [73.9418, -139.0642], \"unit\": \"N\"}", "dedupe_signature": "3f4d0b68aacf7d89aa4007d6e8536da4f8ecc9a44d2bd3f52c68c9ce33a9620f", "difficulty": "medium", "final_answer": {"answer": [73.9418, -139.0642], "unit": "N"}, "id": "vector_components_003703_157.5_298", "license": "Apache-2.0", "prompt": "A vector has magnitude 157.5 N at 298 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=298 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 298, "magnitude": 157.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-5.55, 16.5], \"unit\": \"dimensionless\"}", "dedupe_signature": "3dc57c766cc4ef08475c0203f1d6cd780b1e9526c10ada41cd0479289925984e", "difficulty": "medium", "final_answer": {"answer": [-5.55, 16.5], "unit": "dimensionless"}, "id": "line_two_point_003704_6.5_17.5_-5.55_16.5", "license": "Apache-2.0", "prompt": "A line passes through points (6.5, -19.575) and (17.5, -80.625). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 6.5, "x2": 17.5, "y1": -19.574999999999996, "y2": -80.625}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. energy divided by length is force, not spring constant\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "b1e49b1733438bc2a2bd57b836e8f8df3dae45f5e86fe2af8728d6db23bb2e93", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_003705_inconsistent_56040f5d_362388", "license": "Apache-2.0", "prompt": "In instrument manual case 362388, check dimensional consistency for k = E / x. The left side has dimensions N/m and the right side has dimensions J/m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nenergy divided by length is force, not spring constant\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "k = E / x"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef weighted_sum_003706(values, weights):\n    if len(values) != len(weights):\n        raise ValueError('length mismatch')\n    return sum(value * weight for value, weight in zip(values, weights))\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"weighted_sum_003706\"}", "dedupe_signature": "dd290ae4e07fcba7ed195ad7cad6457051265eaa058828bed0c1d7712b5a8a15", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "weighted_sum_003706"}, "id": "code_003706_weighted_sum_003706", "license": "Apache-2.0", "prompt": "Write a Python function weighted_sum_003706(values, weights) that returns sum(value*weight). Raise ValueError when the two inputs have different lengths. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "weighted_sum_003706"}, "verifier": {"function": "weighted_sum_003706", "tests": ["assert weighted_sum_003706([2, 3], [4, 5]) == 23", "assert weighted_sum_003706([], []) == 0", "try:\n    weighted_sum_003706([1], [1, 2])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 2.8 kg and a = 8.1 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 22.68, \"unit\": \"N\"}", "dedupe_signature": "419145dbcfb5a5e0c0949c2976c2de01b1c9f76d98797b2e56e6f7bdf22ef774", "difficulty": "easy", "final_answer": {"answer": 22.68, "unit": "N"}, "id": "force_003708_2.8_8.1", "license": "Apache-2.0", "prompt": "A cart has mass 2.8 kg and measured acceleration 8.1 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 2.8 kg and a = 8.1 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 8.1, "mass": 2.8}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 37.1^2 and multiply by 0.5 * 27.85.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 19166.5093, \"unit\": \"J\"}", "dedupe_signature": "047c035830d7271d0be591a7718e1f43d7a38f9d9967a8656bc491855f30cf6c", "difficulty": "easy", "final_answer": {"answer": 19166.5093, "unit": "J"}, "id": "ke_003709_27.85_37.1", "license": "Apache-2.0", "prompt": "A body of mass 27.85 kg moves at 37.1 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 37.1^2 and multiply by 0.5 * 27.85.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 27.85, "velocity": 37.1}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 580 * 0.745 * 77.\nFinal: {\"answer\": 33271.7, \"unit\": \"J\"}", "dedupe_signature": "a4ab6f3b7c97f8ef6062af27660f26ab2c392904d662aeefd908057a456bd54d", "difficulty": "easy", "final_answer": {"answer": 33271.7, "unit": "J"}, "id": "heat_q_003712_580_0.745_77", "license": "Apache-2.0", "prompt": "A 580 g sample has specific heat 0.745 J/(g*K). How much heat is needed to raise its temperature by 77 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 580 * 0.745 * 77.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 77, "heat_capacity": 0.745, "mass_g": 580}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=180.8 V and R=186.8 ohm.\nFinal: {\"answer\": 174.9927, \"unit\": \"W\"}", "dedupe_signature": "d0fca77357b7d2f4b8735415ff6d48a89fb8c5d2c42c0743539fdb9989e04369", "difficulty": "easy", "final_answer": {"answer": 174.9927, "unit": "W"}, "id": "ohm_power_003713_180.8_186.8", "license": "Apache-2.0", "prompt": "A resistor has resistance 186.8 ohm and voltage 180.8 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=180.8 V and R=186.8 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 186.8, "voltage": 180.8}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=845.5 mg, t=199.5 h, and T_half=33 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 12.8012, \"unit\": \"mg\"}", "dedupe_signature": "166fa983cb0c627b0dddfd7865cda0e324a0a70e059d93a23e158df8f04e9a47", "difficulty": "medium", "final_answer": {"answer": 12.8012, "unit": "mg"}, "id": "half_life_003714_845.5_33_199.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 845.5 mg. Its half-life is 33 hours. How many mg remain after 199.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=845.5 mg, t=199.5 h, and T_half=33 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 199.5, "half_life": 33.0, "initial_amount": 845.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 1000 mL to 1 L.\n3. Compute M = 3.06 / 1.\nFinal: {\"answer\": 3.06, \"unit\": \"mol/L\"}", "dedupe_signature": "89c6a9168d287cb046df09fbf39c4acc31ca290c45a7f582afbda9af2d1468fa", "difficulty": "medium", "final_answer": {"answer": 3.06, "unit": "mol/L"}, "id": "molarity_003716_3.06_1000", "license": "Apache-2.0", "prompt": "A solution contains 3.06 mol of solute in 1000 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 1000 mL to 1 L.\nCompute M = 3.06 / 1.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 3.06, "volume_ml": 1000}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.53 y, so each step multiplies y by 1 - h*0.53.\n3. Apply that update for 2 steps and round the final state.\nFinal: {\"answer\": 21.9619, \"unit\": \"state_units\"}", "dedupe_signature": "3379ccccf116894ec2ad6bce050988069123203722be0b9799f648a619ad391c", "difficulty": "medium", "final_answer": {"answer": 21.9619, "unit": "state_units"}, "id": "euler_decay_003717_60.5_0.53_0.75_2", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.53 y with y(0)=60.5, step size h=0.75, for 2 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.53 y, so each step multiplies y by 1 - h*0.53.\nApply that update for 2 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 60.5, "rate": 0.53, "step": 0.75, "steps": 2}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.18 and add it to the current value.\nFinal: {\"answer\": [-0.649, 1.428, 1.91], \"unit\": \"temperature_units\"}", "dedupe_signature": "96e794a83843df38905b203c2de89ff82b608981291936704ad0ea9b4005afb4", "difficulty": "hard", "final_answer": {"answer": [-0.649, 1.428, 1.91], "unit": "temperature_units"}, "id": "heat_step_003719_0.18_1.2_-1.9_1.95_2.9_-1.65", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.2, right=-1.65; current interior values are [-1.9, 1.95, 2.9]. Use r=0.18. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.18 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-1.9, 1.95, 2.9], "left": 1.2, "r": 0.18, "right": -1.65}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=136 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-205.0118, 197.9776], \"unit\": \"N\"}", "dedupe_signature": "d327605ae57ce7e93d9935679f94cd3b1d79b8a64b61c86fe3d505abca518e4f", "difficulty": "medium", "final_answer": {"answer": [-205.0118, 197.9776], "unit": "N"}, "id": "vector_components_003721_285_136", "license": "Apache-2.0", "prompt": "A vector has magnitude 285 N at 136 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=136 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 136, "magnitude": 285.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [9.15, 12.5], \"unit\": \"dimensionless\"}", "dedupe_signature": "4ffcc28e861b59b5386212bedcc97284e1b1354f48e11a2e6c36c389b3e8cc42", "difficulty": "medium", "final_answer": {"answer": [9.15, 12.5], "unit": "dimensionless"}, "id": "line_two_point_003722_4_4.75_9.15_12.5", "license": "Apache-2.0", "prompt": "A line passes through points (4, 49.1) and (4.75, 55.9625). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 4.0, "x2": 4.75, "y1": 49.1, "y2": 55.9625}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. grams cancel with J/(g*K), and kelvin cancels, leaving joules\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "e7f8b23534084c408505a4a871251da76376c93d09ca5ca65ad42c010452657c", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_003723_consistent_4153435f_71420", "license": "Apache-2.0", "prompt": "In sensor calibration case 71420, check dimensional consistency for Q = m * c * DeltaT. The left side has dimensions J and the right side has dimensions J. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\ngrams cancel with J/(g*K), and kelvin cancels, leaving joules\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "Q = m * c * DeltaT"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef finite_differences_003724(values):\n    return [values[i + 1] - values[i] for i in range(len(values) - 1)]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"finite_differences_003724\"}", "dedupe_signature": "1cb221eb1b6f6991df1c5218ecb5670d521ec76ad898e9eb9c683def9f24e0a9", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "finite_differences_003724"}, "id": "code_003724_finite_differences_003724", "license": "Apache-2.0", "prompt": "Write a Python function finite_differences_003724(values) that returns the list of successive differences values[i+1] - values[i]. It must return [] for fewer than two values. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "finite_differences_003724"}, "verifier": {"function": "finite_differences_003724", "tests": ["assert finite_differences_003724([1, 4, 9, 16]) == [3, 5, 7]", "assert finite_differences_003724([5]) == []", "assert finite_differences_003724([]) == []"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: recurrence, objective, tie_breaking_rule.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"recurrence\", \"objective\", \"tie_breaking_rule\"]}", "dedupe_signature": "079fcbcd6dcb3189cbbd4aac104555417ee524f19f3d1be1b88e30e01250e6e3", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["recurrence", "objective", "tie_breaking_rule"]}, "id": "abstain_003725_recurrence_objective_tie_breaking_rule", "license": "Apache-2.0", "prompt": "Write a dynamic-programming solver for a segmentation scoring problem with 4806 items and budget 8920, but the recurrence, objective, and tie-breaking rule are all absent. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: recurrence, objective, tie_breaking_rule.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["recurrence", "objective", "tie_breaking_rule"]}, "verifier": {"missing": ["recurrence", "objective", "tie_breaking_rule"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 12.95 kg and a = 4.3 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 55.685, \"unit\": \"N\"}", "dedupe_signature": "cf3bbd80eeca2e93900281ea35c0d1a798736f827ac10ac08a69cdac2a088ce7", "difficulty": "easy", "final_answer": {"answer": 55.685, "unit": "N"}, "id": "force_003726_12.95_4.3", "license": "Apache-2.0", "prompt": "A cart has mass 12.95 kg and measured acceleration 4.3 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 12.95 kg and a = 4.3 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 4.3, "mass": 12.95}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 2.45^2 and multiply by 0.5 * 26.25.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 78.7828, \"unit\": \"J\"}", "dedupe_signature": "a51b1b53babc89df3e38ada6349637deaedd2881655e89640a1827fedaf7b496", "difficulty": "easy", "final_answer": {"answer": 78.7828, "unit": "J"}, "id": "ke_003727_26.25_2.45", "license": "Apache-2.0", "prompt": "A body of mass 26.25 kg moves at 2.45 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 2.45^2 and multiply by 0.5 * 26.25.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 26.25, "velocity": 2.45}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=71 degrees through the sine of 2 theta.\n3. Substitute v=35.5 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 79.0915, \"unit\": \"m\"}", "dedupe_signature": "785e88b9d931c4236ee57ec5cdb62902947b798dab507ea4f614e31d8577f113", "difficulty": "medium", "final_answer": {"answer": 79.0915, "unit": "m"}, "id": "projectile_range_003728_35.5_71", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 35.5 m/s and angle 71 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=71 degrees through the sine of 2 theta.\nSubstitute v=35.5 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 71, "gravity": 9.81, "speed": 35.5}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 3.67 * 8.314 * 612 / 79.2.\nFinal: {\"answer\": 235.7775, \"unit\": \"kPa\"}", "dedupe_signature": "d2249a34c1894a0b53c48fa7f0a7079945d889806745a1cac0b2c77f9803f5f3", "difficulty": "medium", "final_answer": {"answer": 235.7775, "unit": "kPa"}, "id": "ideal_gas_003729_3.67_612_79.2", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=3.67 mol, T=612 K, and V=79.2 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 3.67 * 8.314 * 612 / 79.2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 3.67, "temp_k": 612, "volume_l": 79.2}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1550 * 4.2 * 52.\nFinal: {\"answer\": 338520.0, \"unit\": \"J\"}", "dedupe_signature": "8c93fa579c8312674894fe78cb6ab0a7f303f29fa9f77fe4dc57d6ab0d63f6c5", "difficulty": "easy", "final_answer": {"answer": 338520.0, "unit": "J"}, "id": "heat_q_003730_1550_4.2_52", "license": "Apache-2.0", "prompt": "A 1550 g sample has specific heat 4.2 J/(g*K). How much heat is needed to raise its temperature by 52 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1550 * 4.2 * 52.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 52, "heat_capacity": 4.2, "mass_g": 1550}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=134.3 V and R=22.6 ohm.\nFinal: {\"answer\": 798.0748, \"unit\": \"W\"}", "dedupe_signature": "4d37035be6bc6e387cf4ff7606dcc9f869b1eafe021086f3c7047c87abc630de", "difficulty": "easy", "final_answer": {"answer": 798.0748, "unit": "W"}, "id": "ohm_power_003731_134.3_22.6", "license": "Apache-2.0", "prompt": "A resistor has resistance 22.6 ohm and voltage 134.3 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=134.3 V and R=22.6 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 22.6, "voltage": 134.3}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=214 mg, t=234 h, and T_half=117.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 53.8165, \"unit\": \"mg\"}", "dedupe_signature": "3e47ba298da904ce9a92b4168249352808a93ba9ae917acc4ae53c8d473f8ed4", "difficulty": "medium", "final_answer": {"answer": 53.8165, "unit": "mg"}, "id": "half_life_003732_214_117.5_234", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 214 mg. Its half-life is 117.5 hours. How many mg remain after 234 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=214 mg, t=234 h, and T_half=117.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 234.0, "half_life": 117.5, "initial_amount": 214.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 7.52 mol * 44.01 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 330.9552, \"unit\": \"g\"}", "dedupe_signature": "f25e4ae96774ff9ceea13259e50deee9381a5d7faba0910388860ec72382fa2c", "difficulty": "medium", "final_answer": {"answer": 330.9552, "unit": "g"}, "id": "stoich_mass_003733_carbon_dioxide_7.52", "license": "Apache-2.0", "prompt": "A sample contains 7.52 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 7.52 mol * 44.01 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "carbon dioxide", "molar_mass": 44.01, "moles": 7.52}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 3345 mL to 3.345 L.\n3. Compute M = 3.165 / 3.345.\nFinal: {\"answer\": 0.9462, \"unit\": \"mol/L\"}", "dedupe_signature": "ee1e06b23cf8b7c73ae415bf40c2506df0efe2592bad364525591a2de3233299", "difficulty": "medium", "final_answer": {"answer": 0.9462, "unit": "mol/L"}, "id": "molarity_003734_3.165_3345", "license": "Apache-2.0", "prompt": "A solution contains 3.165 mol of solute in 3345 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 3345 mL to 3.345 L.\nCompute M = 3.165 / 3.345.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 3.165, "volume_ml": 3345}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.51 y, so each step multiplies y by 1 - h*0.51.\n3. Apply that update for 8 steps and round the final state.\nFinal: {\"answer\": 0.1072, \"unit\": \"state_units\"}", "dedupe_signature": "e629fe3179212b0f11c1664144e36502bf909599ac7cb87685d83c0f80044fe1", "difficulty": "medium", "final_answer": {"answer": 0.1072, "unit": "state_units"}, "id": "euler_decay_003735_21.5_0.51_0.95_8", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.51 y with y(0)=21.5, step size h=0.95, for 8 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.51 y, so each step multiplies y by 1 - h*0.51.\nApply that update for 8 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 21.5, "rate": 0.51, "step": 0.95, "steps": 8}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(3.1)=2.36 and f(4)=-2.5.\n3. The interval width is 0.9.\nFinal: {\"answer\": -0.063, \"unit\": \"area_units\"}", "dedupe_signature": "b5d6029bb1e187517502914eed409712027303ec0331f44273d3e3856555e974", "difficulty": "medium", "final_answer": {"answer": -0.063, "unit": "area_units"}, "id": "trapz_linear_003736_-5.4_19.1_3.1_4", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-5.4x+19.1 from x=3.1 to x=4. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(3.1)=2.36 and f(4)=-2.5.\nThe interval width is 0.9.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 19.1, "slope": -5.4, "x0": 3.1, "x1": 4.0}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.14 and add it to the current value.\nFinal: {\"answer\": [-1.689, -0.521, 1.415], \"unit\": \"temperature_units\"}", "dedupe_signature": "92fd61bb84bdb11f43afd36929567b3fe27518e8d93c4bebf8762bdc835239d8", "difficulty": "hard", "final_answer": {"answer": [-1.689, -0.521, 1.415], "unit": "temperature_units"}, "id": "heat_step_003737_0.14_-1.7_-1.85_-0.85_2.5_-1.9", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-1.7, right=-1.9; current interior values are [-1.85, -0.85, 2.5]. Use r=0.14. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.14 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-1.85, -0.85, 2.5], "left": -1.7, "r": 0.14, "right": -1.9}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=43 degrees and keep the unit as newtons.\nFinal: {\"answer\": [297.2953, 277.2323], \"unit\": \"N\"}", "dedupe_signature": "62f548221af81c41eef8cfbca222092b908dd379bdb49d972caae9c295957ffe", "difficulty": "medium", "final_answer": {"answer": [297.2953, 277.2323], "unit": "N"}, "id": "vector_components_003739_406.5_43", "license": "Apache-2.0", "prompt": "A vector has magnitude 406.5 N at 43 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=43 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 43, "magnitude": 406.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. velocity divided by time is acceleration\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "d7403984f22e0d4c13b2a310c3ccda50f9000f34142984e71b726bf5e0407df2", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_003741_inconsistent_c1271127_338794", "license": "Apache-2.0", "prompt": "In simulation spec case 338794, check dimensional consistency for x = v / t. The left side has dimensions m and the right side has dimensions m/s^2. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nvelocity divided by time is acceleration\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "x = v / t"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef weighted_sum_003742(values, weights):\n    if len(values) != len(weights):\n        raise ValueError('length mismatch')\n    return sum(value * weight for value, weight in zip(values, weights))\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"weighted_sum_003742\"}", "dedupe_signature": "f6cccaac977d1aab7b2649189fd48697acb8f35de046e778d0a2b5a745c65559", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "weighted_sum_003742"}, "id": "code_003742_weighted_sum_003742", "license": "Apache-2.0", "prompt": "Write a Python function weighted_sum_003742(values, weights) that returns sum(value*weight). Raise ValueError when the two inputs have different lengths. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "weighted_sum_003742"}, "verifier": {"function": "weighted_sum_003742", "tests": ["assert weighted_sum_003742([2, 3], [4, 5]) == 23", "assert weighted_sum_003742([], []) == 0", "try:\n    weighted_sum_003742([1], [1, 2])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: launch_angle_or_vertical_velocity.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"launch_angle_or_vertical_velocity\"]}", "dedupe_signature": "cf2d16720a58aa161e799b08dc3f369d47a17a753fd08d722a19002bd092daf1", "difficulty": "easy", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["launch_angle_or_vertical_velocity"]}, "id": "abstain_003743_launch_angle_or_vertical_velocity", "license": "Apache-2.0", "prompt": "Compute projectile range on level ground. The prompt gives initial speed 59.5 m/s but does not give launch angle or vertical velocity. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: launch_angle_or_vertical_velocity.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["launch_angle_or_vertical_velocity"]}, "verifier": {"missing": ["launch_angle_or_vertical_velocity"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 22.25 kg and a = 6.85 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 152.4125, \"unit\": \"N\"}", "dedupe_signature": "37f41c2318c4a5366ca5563aea1c76e05a2a0ce63d7a70aa382d3bdca2126507", "difficulty": "easy", "final_answer": {"answer": 152.4125, "unit": "N"}, "id": "force_003744_22.25_6.85", "license": "Apache-2.0", "prompt": "A cart has mass 22.25 kg and measured acceleration 6.85 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 22.25 kg and a = 6.85 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 6.85, "mass": 22.25}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 29.2^2 and multiply by 0.5 * 8.25.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 3517.14, \"unit\": \"J\"}", "dedupe_signature": "a57d1290a17a1bf9240cd7204b15e42a686be0b2af3d627bf178a4f8812f50b8", "difficulty": "easy", "final_answer": {"answer": 3517.14, "unit": "J"}, "id": "ke_003745_8.25_29.2", "license": "Apache-2.0", "prompt": "A body of mass 8.25 kg moves at 29.2 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 29.2^2 and multiply by 0.5 * 8.25.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 8.25, "velocity": 29.2}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=19 degrees through the sine of 2 theta.\n3. Substitute v=82.3 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 425.0819, \"unit\": \"m\"}", "dedupe_signature": "ea05772bb752de421e94104443b096d6e12ba0919a7efdf59da59ab53a436493", "difficulty": "medium", "final_answer": {"answer": 425.0819, "unit": "m"}, "id": "projectile_range_003746_82.3_19", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 82.3 m/s and angle 19 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=19 degrees through the sine of 2 theta.\nSubstitute v=82.3 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 19, "gravity": 9.81, "speed": 82.3}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 6 * 8.314 * 296 / 37.0.\nFinal: {\"answer\": 399.072, \"unit\": \"kPa\"}", "dedupe_signature": "8f5e2ca33a108a97ac627ddca14bf6391a33c740dd1b293ef75b6e952695226b", "difficulty": "medium", "final_answer": {"answer": 399.072, "unit": "kPa"}, "id": "ideal_gas_003747_6_296_37.0", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=6 mol, T=296 K, and V=37.0 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 6 * 8.314 * 296 / 37.0.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 6.0, "temp_k": 296, "volume_l": 37.0}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1720 * 0.555 * 53.\nFinal: {\"answer\": 50593.8, \"unit\": \"J\"}", "dedupe_signature": "3c55e4a496a6f164645d348362722dbc3bce31b7faa8de1a580e6cc668fe80ea", "difficulty": "easy", "final_answer": {"answer": 50593.8, "unit": "J"}, "id": "heat_q_003748_1720_0.555_53", "license": "Apache-2.0", "prompt": "A 1720 g sample has specific heat 0.555 J/(g*K). How much heat is needed to raise its temperature by 53 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1720 * 0.555 * 53.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 53, "heat_capacity": 0.555, "mass_g": 1720}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=187.6 V and R=92.7 ohm.\nFinal: {\"answer\": 379.6522, \"unit\": \"W\"}", "dedupe_signature": "8a201d9f80599b04c79e7cff1c878a0957c2807968e6713740da36fb752a9498", "difficulty": "easy", "final_answer": {"answer": 379.6522, "unit": "W"}, "id": "ohm_power_003749_187.6_92.7", "license": "Apache-2.0", "prompt": "A resistor has resistance 92.7 ohm and voltage 187.6 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=187.6 V and R=92.7 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 92.7, "voltage": 187.6}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=168.5 mg, t=289 h, and T_half=77 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 12.4957, \"unit\": \"mg\"}", "dedupe_signature": "9262cd353f4987c5963c4f124664a6dd74a59446d164dc8dddc209363f53f2a6", "difficulty": "medium", "final_answer": {"answer": 12.4957, "unit": "mg"}, "id": "half_life_003750_168.5_77_289", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 168.5 mg. Its half-life is 77 hours. How many mg remain after 289 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=168.5 mg, t=289 h, and T_half=77 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 289.0, "half_life": 77.0, "initial_amount": 168.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 7.77 mol * 180.156 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 1399.8121, \"unit\": \"g\"}", "dedupe_signature": "84263d598a21223d92d542681a480ad6599290b844d7f025017e09eec5e55ee1", "difficulty": "medium", "final_answer": {"answer": 1399.8121, "unit": "g"}, "id": "stoich_mass_003751_glucose_7.77", "license": "Apache-2.0", "prompt": "A sample contains 7.77 mol of glucose. Using molar mass 180.156 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 7.77 mol * 180.156 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "glucose", "molar_mass": 180.156, "moles": 7.77}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 4005 mL to 4.005 L.\n3. Compute M = 1.02 / 4.005.\nFinal: {\"answer\": 0.2547, \"unit\": \"mol/L\"}", "dedupe_signature": "efe15b9891daeff8c15e4189ca9d63af0a4b2d9597d6c29b7ba464c575308f0d", "difficulty": "medium", "final_answer": {"answer": 0.2547, "unit": "mol/L"}, "id": "molarity_003752_1.02_4005", "license": "Apache-2.0", "prompt": "A solution contains 1.02 mol of solute in 4005 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 4005 mL to 4.005 L.\nCompute M = 1.02 / 4.005.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 1.02, "volume_ml": 4005}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.43 y, so each step multiplies y by 1 - h*0.43.\n3. Apply that update for 10 steps and round the final state.\nFinal: {\"answer\": 0.1426, \"unit\": \"state_units\"}", "dedupe_signature": "78944fac7e0340e8d98e7e0b40ab540018839f2f10f29a1debf880c3a8e24b26", "difficulty": "medium", "final_answer": {"answer": 0.1426, "unit": "state_units"}, "id": "euler_decay_003753_7_0.43_0.75_10", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.43 y with y(0)=7, step size h=0.75, for 10 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.43 y, so each step multiplies y by 1 - h*0.43.\nApply that update for 10 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 7.0, "rate": 0.43, "step": 0.75, "steps": 10}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(2.6)=14.3 and f(4.7)=16.4.\n3. The interval width is 2.1.\nFinal: {\"answer\": 32.235, \"unit\": \"area_units\"}", "dedupe_signature": "f956bdd0388081bb61e9cca21a8d40cc296e7091ad293cfd3d7236b5e53efb26", "difficulty": "medium", "final_answer": {"answer": 32.235, "unit": "area_units"}, "id": "trapz_linear_003754_1_11.7_2.6_4.7", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=1x+11.7 from x=2.6 to x=4.7. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(2.6)=14.3 and f(4.7)=16.4.\nThe interval width is 2.1.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 11.7, "slope": 1.0, "x0": 2.6, "x1": 4.7}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.16 and add it to the current value.\nFinal: {\"answer\": [-0.194, -0.398, 0.718], \"unit\": \"temperature_units\"}", "dedupe_signature": "3954bc18250c4279f2635a09e7f2c1b6ce323faf13be6504d5ac76ea6b9682f0", "difficulty": "hard", "final_answer": {"answer": [-0.194, -0.398, 0.718], "unit": "temperature_units"}, "id": "heat_step_003755_0.16_0.6_-0.25_-0.75_0.95_1.2", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=0.6, right=1.2; current interior values are [-0.25, -0.75, 0.95]. Use r=0.16. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.16 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-0.25, -0.75, 0.95], "left": 0.6, "r": 0.16, "right": 1.2}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 22084.0 / 1000.\nFinal: {\"answer\": 22.084, \"unit\": \"kg\"}", "dedupe_signature": "cd83d7bce11be40a6b3ec45fc5ace715ddd7e763ec2bbbf95d1ad725d098c0ae", "difficulty": "easy", "final_answer": {"answer": 22.084, "unit": "kg"}, "id": "unit_convert_003756_g_to_kg_22084", "license": "Apache-2.0", "prompt": "Convert 22084 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 22084.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 22084.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=229 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-243.0699, -279.6199], \"unit\": \"N\"}", "dedupe_signature": "5925b35f2da5a3bd48b8dd7872c46aa4e3110e83e37a9610c83fcfb2aefd0c5a", "difficulty": "medium", "final_answer": {"answer": [-243.0699, -279.6199], "unit": "N"}, "id": "vector_components_003757_370.5_229", "license": "Apache-2.0", "prompt": "A vector has magnitude 370.5 N at 229 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=229 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 229, "magnitude": 370.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. velocity times time gives distance, not acceleration\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "13870318225330691f18e89d7dc45ae952afbd5dcf95cab7b9977c91c260b3bd", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_003759_inconsistent_7481c798_50574", "license": "Apache-2.0", "prompt": "In student derivation case 50574, check dimensional consistency for a = v * t. The left side has dimensions m/s^2 and the right side has dimensions m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nvelocity times time gives distance, not acceleration\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "a = v * t"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef finite_differences_003760(values):\n    return [values[i + 1] - values[i] for i in range(len(values) - 1)]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"finite_differences_003760\"}", "dedupe_signature": "be64a446bc337bb89da18c09d5e3fc63a3af6e4f81fab9aedb3d9e541a267a13", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "finite_differences_003760"}, "id": "code_003760_finite_differences_003760", "license": "Apache-2.0", "prompt": "Write a Python function finite_differences_003760(values) that returns the list of successive differences values[i+1] - values[i]. It must return [] for fewer than two values. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "finite_differences_003760"}, "verifier": {"function": "finite_differences_003760", "tests": ["assert finite_differences_003760([1, 4, 9, 16]) == [3, 5, 7]", "assert finite_differences_003760([5]) == []", "assert finite_differences_003760([]) == []"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: volume.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"volume\"]}", "dedupe_signature": "c60c5c3c1a074004e9ce8a1cd068ca377b0d96a8394bea4bdb4d29ddbe4a8c7b", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["volume"]}, "id": "abstain_003761_volume", "license": "Apache-2.0", "prompt": "Compute pressure from the ideal gas law. The prompt gives n=0.29 mol and T=605 K, but does not give volume. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: volume.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["volume"]}, "verifier": {"missing": ["volume"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 24.8 kg and a = 13.35 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 331.08, \"unit\": \"N\"}", "dedupe_signature": "e724f41cd7b688e22d0e83fc3b173c87a0dd67415bae0c91b1142ea51d3678a0", "difficulty": "easy", "final_answer": {"answer": 331.08, "unit": "N"}, "id": "force_003762_24.8_13.35", "license": "Apache-2.0", "prompt": "A cart has mass 24.8 kg and measured acceleration 13.35 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 24.8 kg and a = 13.35 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 13.35, "mass": 24.8}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 44.7^2 and multiply by 0.5 * 13.8.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 13786.821, \"unit\": \"J\"}", "dedupe_signature": "c24c1b9b60d5273a5c9c53c6be871456353c924cc60151fb438a4aec65da9f38", "difficulty": "easy", "final_answer": {"answer": 13786.821, "unit": "J"}, "id": "ke_003763_13.8_44.7", "license": "Apache-2.0", "prompt": "A body of mass 13.8 kg moves at 44.7 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 44.7^2 and multiply by 0.5 * 13.8.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 13.8, "velocity": 44.7}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=62 degrees through the sine of 2 theta.\n3. Substitute v=74.2 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 465.2785, \"unit\": \"m\"}", "dedupe_signature": "218217d35284d3e159d5d11cfd1bf657e3d5d3a58a7f5318e9fa4e0b755f5a3b", "difficulty": "medium", "final_answer": {"answer": 465.2785, "unit": "m"}, "id": "projectile_range_003764_74.2_62", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 74.2 m/s and angle 62 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=62 degrees through the sine of 2 theta.\nSubstitute v=74.2 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 62, "gravity": 9.81, "speed": 74.2}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 5.31 * 8.314 * 362 / 32.7.\nFinal: {\"answer\": 488.7259, \"unit\": \"kPa\"}", "dedupe_signature": "92caa4eae915eedd3b1e830bdbab6a757f8edcfc3879858b1f421703b465f8ea", "difficulty": "medium", "final_answer": {"answer": 488.7259, "unit": "kPa"}, "id": "ideal_gas_003765_5.31_362_32.7", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=5.31 mol, T=362 K, and V=32.7 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 5.31 * 8.314 * 362 / 32.7.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 5.31, "temp_k": 362, "volume_l": 32.7}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1460 * 3.615 * 13.\nFinal: {\"answer\": 68612.7, \"unit\": \"J\"}", "dedupe_signature": "248b7aaba7324546e3251edcf95b47ed6951ed068decdbdb438a7a27097114dd", "difficulty": "easy", "final_answer": {"answer": 68612.7, "unit": "J"}, "id": "heat_q_003766_1460_3.615_13", "license": "Apache-2.0", "prompt": "A 1460 g sample has specific heat 3.615 J/(g*K). How much heat is needed to raise its temperature by 13 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1460 * 3.615 * 13.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 13, "heat_capacity": 3.615, "mass_g": 1460}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=29.5 V and R=164 ohm.\nFinal: {\"answer\": 5.3064, \"unit\": \"W\"}", "dedupe_signature": "1f8ba18b18584b284220fb2e6ef10ca8f2bd4af2f3b97e6d3f71b197c4f73247", "difficulty": "easy", "final_answer": {"answer": 5.3064, "unit": "W"}, "id": "ohm_power_003767_29.5_164", "license": "Apache-2.0", "prompt": "A resistor has resistance 164 ohm and voltage 29.5 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=29.5 V and R=164 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 164.0, "voltage": 29.5}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=957 mg, t=322 h, and T_half=72 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 43.116, \"unit\": \"mg\"}", "dedupe_signature": "d82f89a2dca75a5c35949c15caa29a009549a19dc8d7b9f8c9e247733710cdad", "difficulty": "medium", "final_answer": {"answer": 43.116, "unit": "mg"}, "id": "half_life_003768_957_72_322", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 957 mg. Its half-life is 72 hours. How many mg remain after 322 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=957 mg, t=322 h, and T_half=72 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 322.0, "half_life": 72.0, "initial_amount": 957.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 3650 mL to 3.65 L.\n3. Compute M = 4.02 / 3.65.\nFinal: {\"answer\": 1.1014, \"unit\": \"mol/L\"}", "dedupe_signature": "ca5f7b17ae497c83e644633f788569062ae3a9ec01b4318f6d09313202d96bd7", "difficulty": "medium", "final_answer": {"answer": 1.1014, "unit": "mol/L"}, "id": "molarity_003770_4.02_3650", "license": "Apache-2.0", "prompt": "A solution contains 4.02 mol of solute in 3650 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 3650 mL to 3.65 L.\nCompute M = 4.02 / 3.65.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 4.02, "volume_ml": 3650}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.77 y, so each step multiplies y by 1 - h*0.77.\n3. Apply that update for 6 steps and round the final state.\nFinal: {\"answer\": 0.002, \"unit\": \"state_units\"}", "dedupe_signature": "ba4943d034857ddb034d10baefc7e004e4c87e826afeec2822fe8c1e0f54d07e", "difficulty": "medium", "final_answer": {"answer": 0.002, "unit": "state_units"}, "id": "euler_decay_003771_13_0.77_1.6_6", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.77 y with y(0)=13, step size h=1.6, for 6 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.77 y, so each step multiplies y by 1 - h*0.77.\nApply that update for 6 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 13.0, "rate": 0.77, "step": 1.6, "steps": 6}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-3.7)=5.15 and f(-2.7)=7.65.\n3. The interval width is 1.\nFinal: {\"answer\": 6.4, \"unit\": \"area_units\"}", "dedupe_signature": "8b1e4a04d47c574703e83ef00db09a6f160f6958bfd16e7707d1d46b71c68f03", "difficulty": "medium", "final_answer": {"answer": 6.4, "unit": "area_units"}, "id": "trapz_linear_003772_2.5_14.4_-3.7_-2.7", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=2.5x+14.4 from x=-3.7 to x=-2.7. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-3.7)=5.15 and f(-2.7)=7.65.\nThe interval width is 1.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 14.4, "slope": 2.5, "x0": -3.7, "x1": -2.7}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.18 and add it to the current value.\nFinal: {\"answer\": [1.012, -0.074, 0.195], \"unit\": \"temperature_units\"}", "dedupe_signature": "adb3891b50b717bcb8d099a693f6a7738ecf45f696809d58bf79fa7efa6043bd", "difficulty": "hard", "final_answer": {"answer": [1.012, -0.074, 0.195], "unit": "temperature_units"}, "id": "heat_step_003773_0.18_0.05_1.75_-0.65_0.15_1.2", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=0.05, right=1.2; current interior values are [1.75, -0.65, 0.15]. Use r=0.18. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.18 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [1.75, -0.65, 0.15], "left": 0.05, "r": 0.18, "right": 1.2}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 13762.0 / 1000.\nFinal: {\"answer\": 13.762, \"unit\": \"kg\"}", "dedupe_signature": "b85891ef7896ed7523e8048b7e87bf3467a9b5914484b77772879e7393324bee", "difficulty": "easy", "final_answer": {"answer": 13.762, "unit": "kg"}, "id": "unit_convert_003774_g_to_kg_13762", "license": "Apache-2.0", "prompt": "Convert 13762 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 13762.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 13762.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. volt squared divided by ohm is watt\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "b350f05e812c1397613f084baf874cb560f9d5eccc3432ff56b2f4e8a410752c", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_003777_consistent_82e93f3d_997084", "license": "Apache-2.0", "prompt": "In instrument manual case 997084, check dimensional consistency for P = V^2 / R. The left side has dimensions W and the right side has dimensions W. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nvolt squared divided by ohm is watt\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "P = V^2 / R"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: launch_angle_or_vertical_velocity.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"launch_angle_or_vertical_velocity\"]}", "dedupe_signature": "f94dbeb6b65874f5b956446c1faab35df7c7158779f4b94e2f82cbad5e39873e", "difficulty": "easy", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["launch_angle_or_vertical_velocity"]}, "id": "abstain_003779_launch_angle_or_vertical_velocity", "license": "Apache-2.0", "prompt": "Compute projectile range on level ground. The prompt gives initial speed 55.6 m/s but does not give launch angle or vertical velocity. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: launch_angle_or_vertical_velocity.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["launch_angle_or_vertical_velocity"]}, "verifier": {"missing": ["launch_angle_or_vertical_velocity"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 5.75 kg and a = 10.25 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 58.9375, \"unit\": \"N\"}", "dedupe_signature": "00b320eed1092884cf1df5172bd38ed14952a1e7e07ffb70662bcfa998d00357", "difficulty": "easy", "final_answer": {"answer": 58.9375, "unit": "N"}, "id": "force_003780_5.75_10.25", "license": "Apache-2.0", "prompt": "A cart has mass 5.75 kg and measured acceleration 10.25 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 5.75 kg and a = 10.25 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 10.25, "mass": 5.75}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 17.3^2 and multiply by 0.5 * 10.2.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 1526.379, \"unit\": \"J\"}", "dedupe_signature": "724c5961ff4683e39f518914d32451a088edd4b6b3c97ad3be55f6310a7f4aa1", "difficulty": "easy", "final_answer": {"answer": 1526.379, "unit": "J"}, "id": "ke_003781_10.2_17.3", "license": "Apache-2.0", "prompt": "A body of mass 10.2 kg moves at 17.3 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 17.3^2 and multiply by 0.5 * 10.2.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 10.2, "velocity": 17.3}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=37 degrees through the sine of 2 theta.\n3. Substitute v=33.1 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 107.3566, \"unit\": \"m\"}", "dedupe_signature": "ff2bfe36408e1fdd3dad6ac5085e2927900a285780197ca00507f9c474c02bfe", "difficulty": "medium", "final_answer": {"answer": 107.3566, "unit": "m"}, "id": "projectile_range_003782_33.1_37", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 33.1 m/s and angle 37 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=37 degrees through the sine of 2 theta.\nSubstitute v=33.1 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 37, "gravity": 9.81, "speed": 33.1}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 1.93 * 8.314 * 483 / 106.6.\nFinal: {\"answer\": 72.7038, \"unit\": \"kPa\"}", "dedupe_signature": "cc00ddb224af55bf7d5c9062e11dbeb186c74eefbe80f15b636d9a2fa4996fd1", "difficulty": "medium", "final_answer": {"answer": 72.7038, "unit": "kPa"}, "id": "ideal_gas_003783_1.93_483_106.6", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=1.93 mol, T=483 K, and V=106.6 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 1.93 * 8.314 * 483 / 106.6.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 1.93, "temp_k": 483, "volume_l": 106.6}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 605 * 2.93 * 100.\nFinal: {\"answer\": 177265.0, \"unit\": \"J\"}", "dedupe_signature": "cf2ef7ec9dcbacb75d3261598f63ac13163662ebb83d7e1cbcf117f90bf5087a", "difficulty": "easy", "final_answer": {"answer": 177265.0, "unit": "J"}, "id": "heat_q_003784_605_2.93_100", "license": "Apache-2.0", "prompt": "A 605 g sample has specific heat 2.93 J/(g*K). How much heat is needed to raise its temperature by 100 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 605 * 2.93 * 100.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 100, "heat_capacity": 2.93, "mass_g": 605}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=23.1 V and R=59.3 ohm.\nFinal: {\"answer\": 8.9985, \"unit\": \"W\"}", "dedupe_signature": "aeb429973bdc272f4bda553ecfb6bd73bb23e5c15cd26c7757ba35b5fee5ac3c", "difficulty": "easy", "final_answer": {"answer": 8.9985, "unit": "W"}, "id": "ohm_power_003785_23.1_59.3", "license": "Apache-2.0", "prompt": "A resistor has resistance 59.3 ohm and voltage 23.1 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=23.1 V and R=59.3 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 59.3, "voltage": 23.1}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 0.51 mol * 100.087 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 51.0444, \"unit\": \"g\"}", "dedupe_signature": "2bce15b851b6140d2de29d8d7171da64545f5f67c3840ea9585ef172fd88a2f1", "difficulty": "medium", "final_answer": {"answer": 51.0444, "unit": "g"}, "id": "stoich_mass_003787_calcium_carbonate_0.51", "license": "Apache-2.0", "prompt": "A sample contains 0.51 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 0.51 mol * 100.087 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "calcium carbonate", "molar_mass": 100.087, "moles": 0.51}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 295 mL to 0.295 L.\n3. Compute M = 4.915 / 0.295.\nFinal: {\"answer\": 16.661, \"unit\": \"mol/L\"}", "dedupe_signature": "6f66fc843f7de92ced1628f48c81b08e9eec12bea9718bd5d39cacf401747d1e", "difficulty": "medium", "final_answer": {"answer": 16.661, "unit": "mol/L"}, "id": "molarity_003788_4.915_295", "license": "Apache-2.0", "prompt": "A solution contains 4.915 mol of solute in 295 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 295 mL to 0.295 L.\nCompute M = 4.915 / 0.295.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 4.915, "volume_ml": 295}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.03 y, so each step multiplies y by 1 - h*0.03.\n3. Apply that update for 4 steps and round the final state.\nFinal: {\"answer\": 28.8275, \"unit\": \"state_units\"}", "dedupe_signature": "028d1ac5763c58f608696405c1342da160dffe368fa61ce673cc0c5c3366f430", "difficulty": "medium", "final_answer": {"answer": 28.8275, "unit": "state_units"}, "id": "euler_decay_003789_31_0.03_0.6_4", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.03 y with y(0)=31, step size h=0.6, for 4 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.03 y, so each step multiplies y by 1 - h*0.03.\nApply that update for 4 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 31.0, "rate": 0.03, "step": 0.6, "steps": 4}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-5.1)=-7.11 and f(2.1)=-20.79.\n3. The interval width is 7.2.\nFinal: {\"answer\": -100.44, \"unit\": \"area_units\"}", "dedupe_signature": "0758fb9be0f3f2e2c32eaae4af282ffd174f72dad99af1e37673c9d969e17fe3", "difficulty": "medium", "final_answer": {"answer": -100.44, "unit": "area_units"}, "id": "trapz_linear_003790_-1.9_-16.8_-5.1_2.1", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-1.9x+-16.8 from x=-5.1 to x=2.1. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-5.1)=-7.11 and f(2.1)=-20.79.\nThe interval width is 7.2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -16.8, "slope": -1.9, "x0": -5.1, "x1": 2.1000000000000005}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.3 and add it to the current value.\nFinal: {\"answer\": [0.695, 0.285, 0.78], \"unit\": \"temperature_units\"}", "dedupe_signature": "1084bed6f3b0dc62eae4a6e25f66489b1d162ed093c39d2fc831ffa44c4c7e4d", "difficulty": "hard", "final_answer": {"answer": [0.695, 0.285, 0.78], "unit": "temperature_units"}, "id": "heat_step_003791_0.3_0.4_-0.25_2.25_-1.8_2.75", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=0.4, right=2.75; current interior values are [-0.25, 2.25, -1.8]. Use r=0.3. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.3 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-0.25, 2.25, -1.8], "left": 0.4, "r": 0.3, "right": 2.75}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 100 centimeters in one meter.\n2. Apply the conversion factor directly to the given value.\n3. Compute 2201.5 / 100.\nFinal: {\"answer\": 22.015, \"unit\": \"m\"}", "dedupe_signature": "2ff37bad253f3ec24edf86e93701395bdbc8a8fc0408c15c0e799575f7191a0e", "difficulty": "easy", "final_answer": {"answer": 22.015, "unit": "m"}, "id": "unit_convert_003792_cm_to_m_2201.5", "license": "Apache-2.0", "prompt": "Convert 2201.5 cm to m. Return the converted value with unit.", "reasoning_trace": "There are 100 centimeters in one meter.\nApply the conversion factor directly to the given value.\nCompute 2201.5 / 100.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 2201.5}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=201 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-268.4044, -103.0308], \"unit\": \"N\"}", "dedupe_signature": "074fd97bac3f4a460d790318274a8c26248e334275b58f5b48e9c3c231cd4634", "difficulty": "medium", "final_answer": {"answer": [-268.4044, -103.0308], "unit": "N"}, "id": "vector_components_003793_287.5_201", "license": "Apache-2.0", "prompt": "A vector has magnitude 287.5 N at 201 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=201 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 201, "magnitude": 287.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. velocity times time gives distance, not acceleration\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "c243ecb22bc6017dc13b3327f41584f7197c3810903458e805d304c19ece8e03", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_003795_inconsistent_7481c798_716812", "license": "Apache-2.0", "prompt": "In model card equation case 716812, check dimensional consistency for a = v * t. The left side has dimensions m/s^2 and the right side has dimensions m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nvelocity times time gives distance, not acceleration\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "a = v * t"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef center_values_003796(values):\n    if not values:\n        raise ValueError('center_values requires at least one value')\n    mean = sum(values) / len(values)\n    return [value - mean for value in values]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"center_values_003796\"}", "dedupe_signature": "36c8a97f7794142f17d37886594ec975052fbd69b2906b26eac707404bcb3429", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "center_values_003796"}, "id": "code_003796_center_values_003796", "license": "Apache-2.0", "prompt": "Write a Python function center_values_003796(values) that subtracts the arithmetic mean from each value and returns a new list. Raise ValueError for an empty input. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "center_values_003796"}, "verifier": {"function": "center_values_003796", "tests": ["out = center_values_003796([1, 2, 3]); assert out == [-1, 0, 1]", "assert center_values_003796([5]) == [0]", "try:\n    center_values_003796([])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: rate_constant, number_of_steps.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"rate_constant\", \"number_of_steps\"]}", "dedupe_signature": "aa7a1060438544d3c897c81547db5e84299f055ba02808d1e7882fe933bc828a", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["rate_constant", "number_of_steps"]}, "id": "abstain_003797_rate_constant_number_of_steps", "license": "Apache-2.0", "prompt": "Use explicit Euler for dy/dt = -k y. The prompt gives y(0)=6 and h=0.85, but omits both k and the number of steps. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: rate_constant, number_of_steps.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["rate_constant", "number_of_steps"]}, "verifier": {"missing": ["rate_constant", "number_of_steps"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 2.75 kg and a = 8.2 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 22.55, \"unit\": \"N\"}", "dedupe_signature": "7f9dd55d640c9d4da92a637220c90c145b8d8b51109cbb0213fc2e7c7cb1273c", "difficulty": "easy", "final_answer": {"answer": 22.55, "unit": "N"}, "id": "force_003798_2.75_8.2", "license": "Apache-2.0", "prompt": "A cart has mass 2.75 kg and measured acceleration 8.2 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 2.75 kg and a = 8.2 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 8.2, "mass": 2.75}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 19.6^2 and multiply by 0.5 * 5.85.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 1123.668, \"unit\": \"J\"}", "dedupe_signature": "5a16897dddfc77b68b07a9703bfa8d3d736a457d5a4193ac87a79ab55b459064", "difficulty": "easy", "final_answer": {"answer": 1123.668, "unit": "J"}, "id": "ke_003799_5.85_19.6", "license": "Apache-2.0", "prompt": "A body of mass 5.85 kg moves at 19.6 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 19.6^2 and multiply by 0.5 * 5.85.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 5.85, "velocity": 19.6}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=43 degrees through the sine of 2 theta.\n3. Substitute v=64.1 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 417.8187, \"unit\": \"m\"}", "dedupe_signature": "bf102e8b719ed8ea80474d90fef1abf472c434fb21d983f80d8d455d86154e38", "difficulty": "medium", "final_answer": {"answer": 417.8187, "unit": "m"}, "id": "projectile_range_003800_64.1_43", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 64.1 m/s and angle 43 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=43 degrees through the sine of 2 theta.\nSubstitute v=64.1 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 43, "gravity": 9.81, "speed": 64.1}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1415 * 1.395 * 98.\nFinal: {\"answer\": 193444.65, \"unit\": \"J\"}", "dedupe_signature": "3dafc19a294ba586355deb166ba525bb1faea9972f7e37ef5bb93e1dcc6b3e7d", "difficulty": "easy", "final_answer": {"answer": 193444.65, "unit": "J"}, "id": "heat_q_003802_1415_1.395_98", "license": "Apache-2.0", "prompt": "A 1415 g sample has specific heat 1.395 J/(g*K). How much heat is needed to raise its temperature by 98 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1415 * 1.395 * 98.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 98, "heat_capacity": 1.395, "mass_g": 1415}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 3540 mL to 3.54 L.\n3. Compute M = 4.37 / 3.54.\nFinal: {\"answer\": 1.2345, \"unit\": \"mol/L\"}", "dedupe_signature": "0c68287b18e26f17fa1d8a1203dbb1fcf6596f7921937bf7c3560b38f0378b57", "difficulty": "medium", "final_answer": {"answer": 1.2345, "unit": "mol/L"}, "id": "molarity_003806_4.37_3540", "license": "Apache-2.0", "prompt": "A solution contains 4.37 mol of solute in 3540 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 3540 mL to 3.54 L.\nCompute M = 4.37 / 3.54.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 4.37, "volume_ml": 3540}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.23 y, so each step multiplies y by 1 - h*0.23.\n3. Apply that update for 6 steps and round the final state.\nFinal: {\"answer\": 51.4384, \"unit\": \"state_units\"}", "dedupe_signature": "5e7fafa4de662628d15e0f685ddea811cae1de565f4586861f50ea83030affbf", "difficulty": "medium", "final_answer": {"answer": 51.4384, "unit": "state_units"}, "id": "euler_decay_003807_63.5_0.23_0.15_6", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.23 y with y(0)=63.5, step size h=0.15, for 6 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.23 y, so each step multiplies y by 1 - h*0.23.\nApply that update for 6 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 63.5, "rate": 0.23, "step": 0.15, "steps": 6}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.44 and add it to the current value.\nFinal: {\"answer\": [1.954, 0.054, 1.618], \"unit\": \"temperature_units\"}", "dedupe_signature": "e78a2150d19c23fac4f82f784ea574554ea4f61a481b8fbd72557d6e1307ffc0", "difficulty": "hard", "final_answer": {"answer": [1.954, 0.054, 1.618], "unit": "temperature_units"}, "id": "heat_step_003809_0.44_2.85_0.15_1.55_-0.45_2.25", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=2.85, right=2.25; current interior values are [0.15, 1.55, -0.45]. Use r=0.44. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.44 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [0.15, 1.55, -0.45], "left": 2.85, "r": 0.44, "right": 2.25}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 100 centimeters in one meter.\n2. Apply the conversion factor directly to the given value.\n3. Compute 1559.0 / 100.\nFinal: {\"answer\": 15.59, \"unit\": \"m\"}", "dedupe_signature": "e5a62ad5ffdf198cc532d3f22f7bbb2c40870210dcd52277e63acd7231a7f819", "difficulty": "easy", "final_answer": {"answer": 15.59, "unit": "m"}, "id": "unit_convert_003810_cm_to_m_1559", "license": "Apache-2.0", "prompt": "Convert 1559 cm to m. Return the converted value with unit.", "reasoning_trace": "There are 100 centimeters in one meter.\nApply the conversion factor directly to the given value.\nCompute 1559.0 / 100.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 1559.0}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. velocity times time gives distance, not acceleration\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "6ba006391a46c4190971e0ff890ac295b1954a74fe0edf0114e4251723a37e02", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_003813_inconsistent_7481c798_555071", "license": "Apache-2.0", "prompt": "In quality-control check case 555071, check dimensional consistency for a = v * t. The left side has dimensions m/s^2 and the right side has dimensions m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nvelocity times time gives distance, not acceleration\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "a = v * t"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef safe_mean_003814(values):\n    if not values:\n        raise ValueError('safe_mean requires at least one value')\n    return sum(values) / len(values)\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"safe_mean_003814\"}", "dedupe_signature": "6591d40cf5f28e9c34f50dfd61d4a2cbee9522c5e237ddf16eac29454c22d13c", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "safe_mean_003814"}, "id": "code_003814_safe_mean_003814", "license": "Apache-2.0", "prompt": "Write a Python function safe_mean_003814(values) that returns the arithmetic mean. It must raise ValueError for an empty input and must not mutate the input list. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "safe_mean_003814"}, "verifier": {"function": "safe_mean_003814", "tests": ["assert safe_mean_003814([2, 4, 6]) == 4", "xs = [1, 2, 3]; assert safe_mean_003814(xs) == 2 and xs == [1, 2, 3]", "try:\n    safe_mean_003814([])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: target_schema, valid_examples.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"target_schema\", \"valid_examples\"]}", "dedupe_signature": "bd09a53aa572f8269cf0b03798cdbab61998cc32986e07bcda50aa843dcbf656", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["target_schema", "valid_examples"]}, "id": "abstain_003815_target_schema_valid_examples", "license": "Apache-2.0", "prompt": "Write a parser that converts each laboratory invoice record from batch 895369 into the correct schema, but the prompt does not include the target schema or examples. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: target_schema, valid_examples.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["target_schema", "valid_examples"]}, "verifier": {"missing": ["target_schema", "valid_examples"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 18.75 kg and a = 10.45 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 195.9375, \"unit\": \"N\"}", "dedupe_signature": "1b6f5193abea303a428048a7ea249fd2268386c4e7ad92d364568d28b48a7fd6", "difficulty": "easy", "final_answer": {"answer": 195.9375, "unit": "N"}, "id": "force_003816_18.75_10.45", "license": "Apache-2.0", "prompt": "A cart has mass 18.75 kg and measured acceleration 10.45 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 18.75 kg and a = 10.45 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 10.45, "mass": 18.75}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 34.35^2 and multiply by 0.5 * 7.55.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 4454.2074, \"unit\": \"J\"}", "dedupe_signature": "3262d8fdf43ce5d6a84ff4f464e5b99586e974c64987e5a2831ee6ac9339f72f", "difficulty": "easy", "final_answer": {"answer": 4454.2074, "unit": "J"}, "id": "ke_003817_7.55_34.35", "license": "Apache-2.0", "prompt": "A body of mass 7.55 kg moves at 34.35 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 34.35^2 and multiply by 0.5 * 7.55.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 7.55, "velocity": 34.35}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=20 degrees through the sine of 2 theta.\n3. Substitute v=20.6 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 27.8056, \"unit\": \"m\"}", "dedupe_signature": "f65013ed6b464f5073937037a0305f14c9f6106f44001e443da091cdcbf1c890", "difficulty": "medium", "final_answer": {"answer": 27.8056, "unit": "m"}, "id": "projectile_range_003818_20.6_20", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 20.6 m/s and angle 20 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=20 degrees through the sine of 2 theta.\nSubstitute v=20.6 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 20, "gravity": 9.81, "speed": 20.6}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 1.31 * 8.314 * 248 / 119.5.\nFinal: {\"answer\": 22.6029, \"unit\": \"kPa\"}", "dedupe_signature": "d849734e8ba94f66e4525e924f4ca3717b263d3f7fa6b30871745cdbbd7ee6c8", "difficulty": "medium", "final_answer": {"answer": 22.6029, "unit": "kPa"}, "id": "ideal_gas_003819_1.31_248_119.5", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=1.31 mol, T=248 K, and V=119.5 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 1.31 * 8.314 * 248 / 119.5.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 1.31, "temp_k": 248, "volume_l": 119.5}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 440 * 1.995 * 24.\nFinal: {\"answer\": 21067.2, \"unit\": \"J\"}", "dedupe_signature": "9cfd3cd51862135a87cbca9640771cc77633f24a701caa500aa94664eaa227f7", "difficulty": "easy", "final_answer": {"answer": 21067.2, "unit": "J"}, "id": "heat_q_003820_440_1.995_24", "license": "Apache-2.0", "prompt": "A 440 g sample has specific heat 1.995 J/(g*K). How much heat is needed to raise its temperature by 24 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 440 * 1.995 * 24.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 24, "heat_capacity": 1.995, "mass_g": 440}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=221.1 V and R=137.5 ohm.\nFinal: {\"answer\": 355.5288, \"unit\": \"W\"}", "dedupe_signature": "f38af3d172dcb5f3a8cf76ac8c41568f0f97c0a7ef4128007a930af0965120fb", "difficulty": "easy", "final_answer": {"answer": 355.5288, "unit": "W"}, "id": "ohm_power_003821_221.1_137.5", "license": "Apache-2.0", "prompt": "A resistor has resistance 137.5 ohm and voltage 221.1 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=221.1 V and R=137.5 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 137.5, "voltage": 221.1}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=426.5 mg, t=260 h, and T_half=78 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 42.3142, \"unit\": \"mg\"}", "dedupe_signature": "7f1fc0845ecd081b77aededec1d8418dc8fa27f84dc5dfb753fa444abd80cc2f", "difficulty": "medium", "final_answer": {"answer": 42.3142, "unit": "mg"}, "id": "half_life_003822_426.5_78_260", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 426.5 mg. Its half-life is 78 hours. How many mg remain after 260 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=426.5 mg, t=260 h, and T_half=78 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 260.0, "half_life": 78.0, "initial_amount": 426.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 6.18 mol * 100.087 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 618.5377, \"unit\": \"g\"}", "dedupe_signature": "4c546bd8dc9b16734befe82ae29034feba7cd4065455d8ae7809b3f574c8197c", "difficulty": "medium", "final_answer": {"answer": 618.5377, "unit": "g"}, "id": "stoich_mass_003823_calcium_carbonate_6.18", "license": "Apache-2.0", "prompt": "A sample contains 6.18 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 6.18 mol * 100.087 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "calcium carbonate", "molar_mass": 100.087, "moles": 6.18}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.01 y, so each step multiplies y by 1 - h*0.01.\n3. Apply that update for 7 steps and round the final state.\nFinal: {\"answer\": 9.7177, \"unit\": \"state_units\"}", "dedupe_signature": "5ca74a91b4dbb3c25c2a1b6e319722deac9ca86d5d97ab58e601e4216074933d", "difficulty": "medium", "final_answer": {"answer": 9.7177, "unit": "state_units"}, "id": "euler_decay_003825_10.5_0.01_1.1_7", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.01 y with y(0)=10.5, step size h=1.1, for 7 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.01 y, so each step multiplies y by 1 - h*0.01.\nApply that update for 7 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 10.5, "rate": 0.01, "step": 1.1, "steps": 7}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(5.6)=-30.52 and f(6.1)=-31.62.\n3. The interval width is 0.5.\nFinal: {\"answer\": -15.535, \"unit\": \"area_units\"}", "dedupe_signature": "d26c12c91831106ff6f625e259485fd7a01d2d7bb735b1c09ff0ef421514359c", "difficulty": "medium", "final_answer": {"answer": -15.535, "unit": "area_units"}, "id": "trapz_linear_003826_-2.2_-18.2_5.6_6.1", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-2.2x+-18.2 from x=5.6 to x=6.1. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(5.6)=-30.52 and f(6.1)=-31.62.\nThe interval width is 0.5.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -18.2, "slope": -2.2, "x0": 5.6, "x1": 6.1}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.46 and add it to the current value.\nFinal: {\"answer\": [-0.758, 1.036, -1.564], \"unit\": \"temperature_units\"}", "dedupe_signature": "24d7bece746d4d976668a22f90b1c4958246ef290dc6086704c9e564e4b0929a", "difficulty": "hard", "final_answer": {"answer": [-0.758, 1.036, -1.564], "unit": "temperature_units"}, "id": "heat_step_003827_0.46_0.1_1.45_-2.0_1.15_-1.6", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=0.1, right=-1.6; current interior values are [1.45, -2.0, 1.15]. Use r=0.46. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.46 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [1.45, -2.0, 1.15], "left": 0.1, "r": 0.46, "right": -1.6}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 35110.0 / 1000.\nFinal: {\"answer\": 35.11, \"unit\": \"kg\"}", "dedupe_signature": "e6f50eabe443d0697fd3078f61388be80b42c510c9ddea44e36ef62074a0eb52", "difficulty": "easy", "final_answer": {"answer": 35.11, "unit": "kg"}, "id": "unit_convert_003828_g_to_kg_35110", "license": "Apache-2.0", "prompt": "Convert 35110 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 35110.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 35110.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=318 degrees and keep the unit as newtons.\nFinal: {\"answer\": [282.0235, -253.9351], \"unit\": \"N\"}", "dedupe_signature": "3b694e6817d9860c7b562742fad6052dfc52509cca732ac7f6695a1ef157e611", "difficulty": "medium", "final_answer": {"answer": [282.0235, -253.9351], "unit": "N"}, "id": "vector_components_003829_379.5_318", "license": "Apache-2.0", "prompt": "A vector has magnitude 379.5 N at 318 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=318 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 318, "magnitude": 379.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-6.05, -3.0], \"unit\": \"dimensionless\"}", "dedupe_signature": "4bc2e5de0510955aaa137532ac6b7ce7311f2a2b5f8ca1938f5e604aef606675", "difficulty": "medium", "final_answer": {"answer": [-6.05, -3.0], "unit": "dimensionless"}, "id": "line_two_point_003830_-9.5_0.5_-6.05_-3", "license": "Apache-2.0", "prompt": "A line passes through points (-9.5, 54.475) and (0.5, -6.025). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -9.5, "x2": 0.5, "y1": 54.475, "y2": -6.025}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. energy divided by length is force, not spring constant\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "5ccb091e7e12923288f4f89e54faa34c872c8a55345d9496890ab9c38c8f5923", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_003831_inconsistent_56040f5d_813950", "license": "Apache-2.0", "prompt": "In quality-control check case 813950, check dimensional consistency for k = E / x. The left side has dimensions N/m and the right side has dimensions J/m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nenergy divided by length is force, not spring constant\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "k = E / x"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef clamp_003832(x, lo, hi):\n    if lo > hi:\n        raise ValueError('lo must be <= hi')\n    return min(max(x, lo), hi)\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"clamp_003832\"}", "dedupe_signature": "50a7c436e07d8eb6551af3a3fa0dcacf46fffc8818663db3fc8432a060883f7a", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "clamp_003832"}, "id": "code_003832_clamp_003832", "license": "Apache-2.0", "prompt": "Write a Python function clamp_003832(x, lo, hi) that clips x into the inclusive interval [lo, hi]. It must raise ValueError if lo > hi. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "clamp_003832"}, "verifier": {"function": "clamp_003832", "tests": ["assert clamp_003832(5, 0, 10) == 5", "assert clamp_003832(-2, 0, 10) == 0", "assert clamp_003832(12, 0, 10) == 10", "try:\n    clamp_003832(1, 3, 2)\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 7.9 kg and a = 9.05 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 71.495, \"unit\": \"N\"}", "dedupe_signature": "48f7ad4fef7d5a67d6876a3a3d7680c0acec9d0ff95519fba5741ded45577042", "difficulty": "easy", "final_answer": {"answer": 71.495, "unit": "N"}, "id": "force_003834_7.9_9.05", "license": "Apache-2.0", "prompt": "A cart has mass 7.9 kg and measured acceleration 9.05 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 7.9 kg and a = 9.05 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 9.05, "mass": 7.9}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 13^2 and multiply by 0.5 * 25.4.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 2146.3, \"unit\": \"J\"}", "dedupe_signature": "040eb50b8ec70ce7d071a30b83dd59ce42dde0018f5cc2dae6c7654fba0aef37", "difficulty": "easy", "final_answer": {"answer": 2146.3, "unit": "J"}, "id": "ke_003835_25.4_13", "license": "Apache-2.0", "prompt": "A body of mass 25.4 kg moves at 13 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 13^2 and multiply by 0.5 * 25.4.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 25.4, "velocity": 13.0}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=36 degrees through the sine of 2 theta.\n3. Substitute v=70.8 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 485.9637, \"unit\": \"m\"}", "dedupe_signature": "692d88cc1eec44fea2a209bd2f583de2bbdc73856dd8fdc8b892e952ca2aad89", "difficulty": "medium", "final_answer": {"answer": 485.9637, "unit": "m"}, "id": "projectile_range_003836_70.8_36", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 70.8 m/s and angle 36 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=36 degrees through the sine of 2 theta.\nSubstitute v=70.8 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 36, "gravity": 9.81, "speed": 70.8}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 4.22 * 8.314 * 286 / 34.4.\nFinal: {\"answer\": 291.6957, \"unit\": \"kPa\"}", "dedupe_signature": "6d2f362b96f9f29e09611f0b20d8801ed68eb3f336fa8b5a0f501ee43fbd0651", "difficulty": "medium", "final_answer": {"answer": 291.6957, "unit": "kPa"}, "id": "ideal_gas_003837_4.22_286_34.4", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=4.22 mol, T=286 K, and V=34.4 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 4.22 * 8.314 * 286 / 34.4.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 4.22, "temp_k": 286, "volume_l": 34.4}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 330 * 3.025 * 77.\nFinal: {\"answer\": 76865.25, \"unit\": \"J\"}", "dedupe_signature": "7d8d2e928a3e62b62f7bad4b6b348bf38693ead415a2145eeba93144daf294db", "difficulty": "easy", "final_answer": {"answer": 76865.25, "unit": "J"}, "id": "heat_q_003838_330_3.025_77", "license": "Apache-2.0", "prompt": "A 330 g sample has specific heat 3.025 J/(g*K). How much heat is needed to raise its temperature by 77 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 330 * 3.025 * 77.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 77, "heat_capacity": 3.025, "mass_g": 330}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=103.5 V and R=53.2 ohm.\nFinal: {\"answer\": 201.3581, \"unit\": \"W\"}", "dedupe_signature": "5406148c0250234ff8f7a42e9e200cd7085fe27fe27a42475b14cf0582db7225", "difficulty": "easy", "final_answer": {"answer": 201.3581, "unit": "W"}, "id": "ohm_power_003839_103.5_53.2", "license": "Apache-2.0", "prompt": "A resistor has resistance 53.2 ohm and voltage 103.5 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=103.5 V and R=53.2 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 53.2, "voltage": 103.5}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=747 mg, t=149 h, and T_half=58 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 125.8882, \"unit\": \"mg\"}", "dedupe_signature": "5d1894b07b32ea8c7ec1dc00c1e1029420208eb2ec668c05d2bb1d252f26daf7", "difficulty": "medium", "final_answer": {"answer": 125.8882, "unit": "mg"}, "id": "half_life_003840_747_58_149", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 747 mg. Its half-life is 58 hours. How many mg remain after 149 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=747 mg, t=149 h, and T_half=58 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 149.0, "half_life": 58.0, "initial_amount": 747.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 4.82 mol * 18.015 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 86.8323, \"unit\": \"g\"}", "dedupe_signature": "f3ad4d9d3d968d6a3a41856f4002cc2f520f5d753c2b0d8bf3265e860e5955b1", "difficulty": "medium", "final_answer": {"answer": 86.8323, "unit": "g"}, "id": "stoich_mass_003841_water_4.82", "license": "Apache-2.0", "prompt": "A sample contains 4.82 mol of water. Using molar mass 18.015 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 4.82 mol * 18.015 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "water", "molar_mass": 18.015, "moles": 4.82}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 4385 mL to 4.385 L.\n3. Compute M = 3.345 / 4.385.\nFinal: {\"answer\": 0.7628, \"unit\": \"mol/L\"}", "dedupe_signature": "f2d463fc5cd8d4d534a89f703281f018c34e4682fba1bba5dddc6fee2daf0361", "difficulty": "medium", "final_answer": {"answer": 0.7628, "unit": "mol/L"}, "id": "molarity_003842_3.345_4385", "license": "Apache-2.0", "prompt": "A solution contains 3.345 mol of solute in 4385 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 4385 mL to 4.385 L.\nCompute M = 3.345 / 4.385.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 3.345, "volume_ml": 4385}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.08 y, so each step multiplies y by 1 - h*0.08.\n3. Apply that update for 10 steps and round the final state.\nFinal: {\"answer\": 8.0037, \"unit\": \"state_units\"}", "dedupe_signature": "ea3d72be38c270dda290a6508ba11b485f63e0bd4ee7e05ff7e52a7c52ffeedd", "difficulty": "medium", "final_answer": {"answer": 8.0037, "unit": "state_units"}, "id": "euler_decay_003843_24_0.08_1.3_10", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.08 y with y(0)=24, step size h=1.3, for 10 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.08 y, so each step multiplies y by 1 - h*0.08.\nApply that update for 10 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 24.0, "rate": 0.08, "step": 1.3, "steps": 10}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(6.3)=48.71 and f(8.2)=63.34.\n3. The interval width is 1.9.\nFinal: {\"answer\": 106.4475, \"unit\": \"area_units\"}", "dedupe_signature": "216ad0b4ea513a3f5bc295d048ecc9afeb6c6e103b39231ba819931cfb2635fd", "difficulty": "medium", "final_answer": {"answer": 106.4475, "unit": "area_units"}, "id": "trapz_linear_003844_7.7_0.2_6.3_8.2", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=7.7x+0.2 from x=6.3 to x=8.2. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(6.3)=48.71 and f(8.2)=63.34.\nThe interval width is 1.9.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 0.2, "slope": 7.7, "x0": 6.3, "x1": 8.2}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.22 and add it to the current value.\nFinal: {\"answer\": [1.162, 0.054, 0.722], \"unit\": \"temperature_units\"}", "dedupe_signature": "b1adb97633c7b6032a22860ef4784d4177c5cb5d4253b10f2b54cf9000489ff2", "difficulty": "hard", "final_answer": {"answer": [1.162, 0.054, 0.722], "unit": "temperature_units"}, "id": "heat_step_003845_0.22_-0.35_2.9_-1.75_1.8_0.45", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-0.35, right=0.45; current interior values are [2.9, -1.75, 1.8]. Use r=0.22. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.22 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [2.9, -1.75, 1.8], "left": -0.35, "r": 0.22, "right": 0.45}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 31482.0 / 1000.\nFinal: {\"answer\": 31.482, \"unit\": \"kg\"}", "dedupe_signature": "e0065b9b2ead842b48e5313e380cb1027d808bda0ab7c32a9ce20022f44b2f5a", "difficulty": "easy", "final_answer": {"answer": 31.482, "unit": "kg"}, "id": "unit_convert_003846_g_to_kg_31482", "license": "Apache-2.0", "prompt": "Convert 31482 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 31482.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 31482.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=0 degrees and keep the unit as newtons.\nFinal: {\"answer\": [422.0, 0.0], \"unit\": \"N\"}", "dedupe_signature": "31e57d931e0dadba3650fa78c1bb8464ddd0f31cef04bbc179a26761d2188425", "difficulty": "medium", "final_answer": {"answer": [422.0, 0.0], "unit": "N"}, "id": "vector_components_003847_422_0", "license": "Apache-2.0", "prompt": "A vector has magnitude 422 N at 0 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=0 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 0, "magnitude": 422.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef finite_differences_003850(values):\n    return [values[i + 1] - values[i] for i in range(len(values) - 1)]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"finite_differences_003850\"}", "dedupe_signature": "578d643097fd83c089b7f7de3717a2c0bd7ed2963813d57743bcd665349bd361", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "finite_differences_003850"}, "id": "code_003850_finite_differences_003850", "license": "Apache-2.0", "prompt": "Write a Python function finite_differences_003850(values) that returns the list of successive differences values[i+1] - values[i]. It must return [] for fewer than two values. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "finite_differences_003850"}, "verifier": {"function": "finite_differences_003850", "tests": ["assert finite_differences_003850([1, 4, 9, 16]) == [3, 5, 7]", "assert finite_differences_003850([5]) == []", "assert finite_differences_003850([]) == []"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: launch_angle_or_vertical_velocity.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"launch_angle_or_vertical_velocity\"]}", "dedupe_signature": "171b7d7ad87473d579ff9b293bfd1073afd577fb83b5108e7127f9d23b0ef79a", "difficulty": "easy", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["launch_angle_or_vertical_velocity"]}, "id": "abstain_003851_launch_angle_or_vertical_velocity", "license": "Apache-2.0", "prompt": "Compute projectile range on level ground. The prompt gives initial speed 56.3 m/s but does not give launch angle or vertical velocity. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: launch_angle_or_vertical_velocity.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["launch_angle_or_vertical_velocity"]}, "verifier": {"missing": ["launch_angle_or_vertical_velocity"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 24.35 kg and a = 8 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 194.8, \"unit\": \"N\"}", "dedupe_signature": "8fc43ff05a2dda4a02a43e35f21c231fd40ed7895c6b690f5b91837b7f021b78", "difficulty": "easy", "final_answer": {"answer": 194.8, "unit": "N"}, "id": "force_003852_24.35_8", "license": "Apache-2.0", "prompt": "A cart has mass 24.35 kg and measured acceleration 8 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 24.35 kg and a = 8 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 8.0, "mass": 24.35}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 2.65^2 and multiply by 0.5 * 22.25.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 78.1253, \"unit\": \"J\"}", "dedupe_signature": "9a43d610d475747712cd2bed2b6d95a8263c77b908ad0ca59f6bab8a9edddb57", "difficulty": "easy", "final_answer": {"answer": 78.1253, "unit": "J"}, "id": "ke_003853_22.25_2.65", "license": "Apache-2.0", "prompt": "A body of mass 22.25 kg moves at 2.65 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 2.65^2 and multiply by 0.5 * 22.25.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 22.25, "velocity": 2.65}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=56 degrees through the sine of 2 theta.\n3. Substitute v=83.9 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 665.305, \"unit\": \"m\"}", "dedupe_signature": "00a427669fe28669e1a5b6aa0d311bbe932d1039262b7a3a2fb64559fade8847", "difficulty": "medium", "final_answer": {"answer": 665.305, "unit": "m"}, "id": "projectile_range_003854_83.9_56", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 83.9 m/s and angle 56 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=56 degrees through the sine of 2 theta.\nSubstitute v=83.9 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 56, "gravity": 9.81, "speed": 83.9}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 4.11 * 8.314 * 324 / 46.1.\nFinal: {\"answer\": 240.1574, \"unit\": \"kPa\"}", "dedupe_signature": "b9c5ae5a21f50ab347f981703c81c106f7b329021b4c079f95bdcced02b152ca", "difficulty": "medium", "final_answer": {"answer": 240.1574, "unit": "kPa"}, "id": "ideal_gas_003855_4.11_324_46.1", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=4.11 mol, T=324 K, and V=46.1 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 4.11 * 8.314 * 324 / 46.1.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 4.11, "temp_k": 324, "volume_l": 46.1}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 35 * 3.005 * 97.\nFinal: {\"answer\": 10201.975, \"unit\": \"J\"}", "dedupe_signature": "8d5179c63f3d55fd36a8f548b2102c420e5b8e9c1272b022b62bfe88b9a8e1f4", "difficulty": "easy", "final_answer": {"answer": 10201.975, "unit": "J"}, "id": "heat_q_003856_35_3.005_97", "license": "Apache-2.0", "prompt": "A 35 g sample has specific heat 3.005 J/(g*K). How much heat is needed to raise its temperature by 97 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 35 * 3.005 * 97.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 97, "heat_capacity": 3.005, "mass_g": 35}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=18.2 V and R=157 ohm.\nFinal: {\"answer\": 2.1098, \"unit\": \"W\"}", "dedupe_signature": "1aea8f0b4ed293008818b3698bf40596f6dc13e422cb3aa8241d35d4ff8adef9", "difficulty": "easy", "final_answer": {"answer": 2.1098, "unit": "W"}, "id": "ohm_power_003857_18.2_157", "license": "Apache-2.0", "prompt": "A resistor has resistance 157 ohm and voltage 18.2 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=18.2 V and R=157 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 157.0, "voltage": 18.2}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=138 mg, t=117.5 h, and T_half=20.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 2.5969, \"unit\": \"mg\"}", "dedupe_signature": "cc9ee1ede7e25e8edbfa01b0b4d189b5fd323d970c8d412416f88ed965f22621", "difficulty": "medium", "final_answer": {"answer": 2.5969, "unit": "mg"}, "id": "half_life_003858_138_20.5_117.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 138 mg. Its half-life is 20.5 hours. How many mg remain after 117.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=138 mg, t=117.5 h, and T_half=20.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 117.5, "half_life": 20.5, "initial_amount": 138.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 2.1 mol * 180.156 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 378.3276, \"unit\": \"g\"}", "dedupe_signature": "27e27acb2aa971215f8e6bb540f54977eef502601164f02f9b4a14b6e4954713", "difficulty": "medium", "final_answer": {"answer": 378.3276, "unit": "g"}, "id": "stoich_mass_003859_glucose_2.1", "license": "Apache-2.0", "prompt": "A sample contains 2.1 mol of glucose. Using molar mass 180.156 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 2.1 mol * 180.156 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "glucose", "molar_mass": 180.156, "moles": 2.1}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 3865 mL to 3.865 L.\n3. Compute M = 2.21 / 3.865.\nFinal: {\"answer\": 0.5718, \"unit\": \"mol/L\"}", "dedupe_signature": "f7f0cb271dc98c282d8c957f285b0d42704cb618d01f49e317c7b25d542fa84d", "difficulty": "medium", "final_answer": {"answer": 0.5718, "unit": "mol/L"}, "id": "molarity_003860_2.21_3865", "license": "Apache-2.0", "prompt": "A solution contains 2.21 mol of solute in 3865 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 3865 mL to 3.865 L.\nCompute M = 2.21 / 3.865.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 2.21, "volume_ml": 3865}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-9)=-40.2 and f(-7.5)=-33.15.\n3. The interval width is 1.5.\nFinal: {\"answer\": -55.0125, \"unit\": \"area_units\"}", "dedupe_signature": "1b9144649edcd59df451c7b56f807f8227c3bda49dd221e01a45f223cca8f6d8", "difficulty": "medium", "final_answer": {"answer": -55.0125, "unit": "area_units"}, "id": "trapz_linear_003862_4.7_2.1_-9_-7.5", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=4.7x+2.1 from x=-9 to x=-7.5. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-9)=-40.2 and f(-7.5)=-33.15.\nThe interval width is 1.5.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 2.1, "slope": 4.7, "x0": -9.0, "x1": -7.5}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.06 and add it to the current value.\nFinal: {\"answer\": [0.356, 1.959, 1.503], \"unit\": \"temperature_units\"}", "dedupe_signature": "1d797b5a257f4b76c60df741356035e14bac9479db7502ca9087701e58da982b", "difficulty": "hard", "final_answer": {"answer": [0.356, 1.959, 1.503], "unit": "temperature_units"}, "id": "heat_step_003863_0.06_0.9_0.2_2.1_1.65_-1.25", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=0.9, right=-1.25; current interior values are [0.2, 2.1, 1.65]. Use r=0.06. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.06 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [0.2, 2.1, 1.65], "left": 0.9, "r": 0.06, "right": -1.25}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kelvin equals Celsius plus 273.15.\n2. Apply the conversion factor directly to the given value.\n3. Compute 23.0 + 273.15.\nFinal: {\"answer\": 296.15, \"unit\": \"K\"}", "dedupe_signature": "b124e126071cd4d678f77981f1ac239a19c54300890cdc36013ed4379d530d1a", "difficulty": "easy", "final_answer": {"answer": 296.15, "unit": "K"}, "id": "unit_convert_003864_c_to_k_23", "license": "Apache-2.0", "prompt": "Convert 23 degC to K. Return the converted value with unit.", "reasoning_trace": "Kelvin equals Celsius plus 273.15.\nApply the conversion factor directly to the given value.\nCompute 23.0 + 273.15.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 23.0}, "verifier": {"formula": "value + 273.15", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=81 degrees and keep the unit as newtons.\nFinal: {\"answer\": [30.1919, 190.6238], \"unit\": \"N\"}", "dedupe_signature": "b631f4bebee6d29ae983c729ceaa8582e060379bf19e7b0084ee7416862bdbfa", "difficulty": "medium", "final_answer": {"answer": [30.1919, 190.6238], "unit": "N"}, "id": "vector_components_003865_193_81", "license": "Apache-2.0", "prompt": "A vector has magnitude 193 N at 81 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=81 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 81, "magnitude": 193.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-1.0, -27.0], \"unit\": \"dimensionless\"}", "dedupe_signature": "de7708b251c560e9d9b6b18599e63036f4d895b9816bf434c9dda771c3dc1ce4", "difficulty": "medium", "final_answer": {"answer": [-1.0, -27.0], "unit": "dimensionless"}, "id": "line_two_point_003866_-17_-13.5_-1_-27", "license": "Apache-2.0", "prompt": "A line passes through points (-17, -10) and (-13.5, -13.5). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -17.0, "x2": -13.5, "y1": -10.0, "y2": -13.5}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef finite_differences_003868(values):\n    return [values[i + 1] - values[i] for i in range(len(values) - 1)]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"finite_differences_003868\"}", "dedupe_signature": "c1e6d3fdeb682531642165d02b777e34bb0e387e69afb0e29267a4539a1adfa7", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "finite_differences_003868"}, "id": "code_003868_finite_differences_003868", "license": "Apache-2.0", "prompt": "Write a Python function finite_differences_003868(values) that returns the list of successive differences values[i+1] - values[i]. It must return [] for fewer than two values. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "finite_differences_003868"}, "verifier": {"function": "finite_differences_003868", "tests": ["assert finite_differences_003868([1, 4, 9, 16]) == [3, 5, 7]", "assert finite_differences_003868([5]) == []", "assert finite_differences_003868([]) == []"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: required_fields, allowed_transformations.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"required_fields\", \"allowed_transformations\"]}", "dedupe_signature": "60b86f2c6ef1b01392582db8186d582e9a7ed85a89e0c3c6744efbc8c1633099", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["required_fields", "allowed_transformations"]}, "id": "abstain_003869_required_fields_allowed_transformations", "license": "Apache-2.0", "prompt": "Write a sanitizer for valid mobile crop records in release 448901, but the prompt does not state which fields are required or which transformations are allowed. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: required_fields, allowed_transformations.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["required_fields", "allowed_transformations"]}, "verifier": {"missing": ["required_fields", "allowed_transformations"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 17.25 kg and a = 11.05 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 190.6125, \"unit\": \"N\"}", "dedupe_signature": "f20b2e383f6dc6cde1c4614ae772189f043ed71de2e32b63a69ed0020f650e85", "difficulty": "easy", "final_answer": {"answer": 190.6125, "unit": "N"}, "id": "force_003870_17.25_11.05", "license": "Apache-2.0", "prompt": "A cart has mass 17.25 kg and measured acceleration 11.05 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 17.25 kg and a = 11.05 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 11.05, "mass": 17.25}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=10 degrees through the sine of 2 theta.\n3. Substitute v=34.8 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 42.2222, \"unit\": \"m\"}", "dedupe_signature": "470fc51b45dc514dd23bba4e090736a57750de94cf2bf59d16c956cda4927116", "difficulty": "medium", "final_answer": {"answer": 42.2222, "unit": "m"}, "id": "projectile_range_003872_34.8_10", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 34.8 m/s and angle 10 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=10 degrees through the sine of 2 theta.\nSubstitute v=34.8 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 10, "gravity": 9.81, "speed": 34.8}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 0.13 * 8.314 * 382 / 12.7.\nFinal: {\"answer\": 32.5097, \"unit\": \"kPa\"}", "dedupe_signature": "8ef9037f22f3a23dbba31ce475262991c66a5f5708a78c63466ee50e348f9537", "difficulty": "medium", "final_answer": {"answer": 32.5097, "unit": "kPa"}, "id": "ideal_gas_003873_0.13_382_12.7", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=0.13 mol, T=382 K, and V=12.7 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 0.13 * 8.314 * 382 / 12.7.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 0.13, "temp_k": 382, "volume_l": 12.7}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=135 mg, t=1.5 h, and T_half=40 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 131.5362, \"unit\": \"mg\"}", "dedupe_signature": "58f8a6bd3c21d5c09b00813e2041fb728f7b19f12e0d9bc91ce430cf8a1bcbc1", "difficulty": "medium", "final_answer": {"answer": 131.5362, "unit": "mg"}, "id": "half_life_003876_135_40_1.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 135 mg. Its half-life is 40 hours. How many mg remain after 1.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=135 mg, t=1.5 h, and T_half=40 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 1.5, "half_life": 40.0, "initial_amount": 135.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 7.58 mol * 100.087 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 758.6595, \"unit\": \"g\"}", "dedupe_signature": "b0a9dbc968089d37d66c5a66b702d434a898dd9fbb7c4860785f900af1469a72", "difficulty": "medium", "final_answer": {"answer": 758.6595, "unit": "g"}, "id": "stoich_mass_003877_calcium_carbonate_7.58", "license": "Apache-2.0", "prompt": "A sample contains 7.58 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 7.58 mol * 100.087 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "calcium carbonate", "molar_mass": 100.087, "moles": 7.58}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 500 mL to 0.5 L.\n3. Compute M = 0.64 / 0.5.\nFinal: {\"answer\": 1.28, \"unit\": \"mol/L\"}", "dedupe_signature": "e66ea1e91e06bc4ba2d5f12071476556d1ecb639a3b5d907f0b1d44c753a7fc3", "difficulty": "medium", "final_answer": {"answer": 1.28, "unit": "mol/L"}, "id": "molarity_003878_0.64_500", "license": "Apache-2.0", "prompt": "A solution contains 0.64 mol of solute in 500 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 500 mL to 0.5 L.\nCompute M = 0.64 / 0.5.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 0.64, "volume_ml": 500}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.52 y, so each step multiplies y by 1 - h*0.52.\n3. Apply that update for 10 steps and round the final state.\nFinal: {\"answer\": 0.0, \"unit\": \"state_units\"}", "dedupe_signature": "dd2403820e8f9a717e2a1ffc15f712e36a27b01c6eff0bff2318abdbab4f2f48", "difficulty": "medium", "final_answer": {"answer": 0.0, "unit": "state_units"}, "id": "euler_decay_003879_55_0.52_1.95_10", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.52 y with y(0)=55, step size h=1.95, for 10 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.52 y, so each step multiplies y by 1 - h*0.52.\nApply that update for 10 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 55.0, "rate": 0.52, "step": 1.95, "steps": 10}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(7)=-31.3 and f(13)=-47.5.\n3. The interval width is 6.\nFinal: {\"answer\": -236.4, \"unit\": \"area_units\"}", "dedupe_signature": "e39d69404c3ea6a37bb9f0fb8e54f11f604f8fdbc55cc1f2b9f0b087a34ad6a3", "difficulty": "medium", "final_answer": {"answer": -236.4, "unit": "area_units"}, "id": "trapz_linear_003880_-2.7_-12.4_7_13", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-2.7x+-12.4 from x=7 to x=13. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(7)=-31.3 and f(13)=-47.5.\nThe interval width is 6.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -12.4, "slope": -2.7, "x0": 7.0, "x1": 13.0}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.04 and add it to the current value.\nFinal: {\"answer\": [0.134, 2.002, 2.804], \"unit\": \"temperature_units\"}", "dedupe_signature": "910b482341c4508deda51dbc92792ecae6641a75550558e293e24e419b63fd5c", "difficulty": "hard", "final_answer": {"answer": [0.134, 2.002, 2.804], "unit": "temperature_units"}, "id": "heat_step_003881_0.04_1.3_0.0_2.05_2.9_1.35", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.3, right=1.35; current interior values are [0.0, 2.05, 2.9]. Use r=0.04. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.04 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [0.0, 2.05, 2.9], "left": 1.3, "r": 0.04, "right": 1.35}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kelvin equals Celsius plus 273.15.\n2. Apply the conversion factor directly to the given value.\n3. Compute 56.5 + 273.15.\nFinal: {\"answer\": 329.65, \"unit\": \"K\"}", "dedupe_signature": "a1146de304f8549e9bbd683507fa41ed53b20dfc83867a78ffed1fac692e1ceb", "difficulty": "easy", "final_answer": {"answer": 329.65, "unit": "K"}, "id": "unit_convert_003882_c_to_k_56.5", "license": "Apache-2.0", "prompt": "Convert 56.5 degC to K. Return the converted value with unit.", "reasoning_trace": "Kelvin equals Celsius plus 273.15.\nApply the conversion factor directly to the given value.\nCompute 56.5 + 273.15.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 56.5}, "verifier": {"formula": "value + 273.15", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=319 degrees and keep the unit as newtons.\nFinal: {\"answer\": [342.2608, -297.5228], \"unit\": \"N\"}", "dedupe_signature": "8c36f2b15fdb8cced25a546b1e8f6b578b766c81063ff31121981ff54699ebaf", "difficulty": "medium", "final_answer": {"answer": [342.2608, -297.5228], "unit": "N"}, "id": "vector_components_003883_453.5_319", "license": "Apache-2.0", "prompt": "A vector has magnitude 453.5 N at 319 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=319 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 319, "magnitude": 453.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-1.75, 5.0], \"unit\": \"dimensionless\"}", "dedupe_signature": "b739c85f2d2546b856326ca86941a5ca6c79d6124810fdf0a4c6fad27b2b44ef", "difficulty": "medium", "final_answer": {"answer": [-1.75, 5.0], "unit": "dimensionless"}, "id": "line_two_point_003884_-4.5_-1_-1.75_5", "license": "Apache-2.0", "prompt": "A line passes through points (-4.5, 12.875) and (-1, 6.75). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -4.5, "x2": -1.0, "y1": 12.875, "y2": 6.75}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. volt squared divided by ohm is watt\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "b71407f9930db5cae8804be617fc337bdbd92f077282f1f6ecd71eec1faa4547", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_003885_consistent_82e93f3d_616650", "license": "Apache-2.0", "prompt": "In student derivation case 616650, check dimensional consistency for P = V^2 / R. The left side has dimensions W and the right side has dimensions W. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nvolt squared divided by ohm is watt\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "P = V^2 / R"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef pairwise_ratios_003886(numerators, denominators):\n    if len(numerators) != len(denominators):\n        raise ValueError('length mismatch')\n    out = []\n    for numerator, denominator in zip(numerators, denominators):\n        if denominator == 0:\n            raise ValueError('zero denominator')\n        out.append(numerator / denominator)\n    return out\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"pairwise_ratios_003886\"}", "dedupe_signature": "7473492b0a5f92020f4f7ba2f6e1f4c5fe816d4525525fb8002ec1a8eeefd121", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "pairwise_ratios_003886"}, "id": "code_003886_pairwise_ratios_003886", "license": "Apache-2.0", "prompt": "Write a Python function pairwise_ratios_003886(numerators, denominators) that returns a list of n/d values. Raise ValueError if lengths differ or any denominator is zero. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "pairwise_ratios_003886"}, "verifier": {"function": "pairwise_ratios_003886", "tests": ["assert pairwise_ratios_003886([2, 9], [4, 3]) == [0.5, 3.0]", "try:\n    pairwise_ratios_003886([1], [0])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass", "try:\n    pairwise_ratios_003886([1, 2], [1])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: recurrence, objective, tie_breaking_rule.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"recurrence\", \"objective\", \"tie_breaking_rule\"]}", "dedupe_signature": "3373746b6a9b3df0b48d5cf5b93eddf790592c0c6efb21b95c0c441678a13017", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["recurrence", "objective", "tie_breaking_rule"]}, "id": "abstain_003887_recurrence_objective_tie_breaking_rule", "license": "Apache-2.0", "prompt": "Write a dynamic-programming solver for a allocation scoring problem with 599 items and budget 44210, but the recurrence, objective, and tie-breaking rule are all absent. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: recurrence, objective, tie_breaking_rule.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["recurrence", "objective", "tie_breaking_rule"]}, "verifier": {"missing": ["recurrence", "objective", "tie_breaking_rule"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 15.4^2 and multiply by 0.5 * 25.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 2964.5, \"unit\": \"J\"}", "dedupe_signature": "788af849ed614ea7a8cd5745d84ac1e57ff1ce5616f14ae00e2077434f8f4f2b", "difficulty": "easy", "final_answer": {"answer": 2964.5, "unit": "J"}, "id": "ke_003889_25_15.4", "license": "Apache-2.0", "prompt": "A body of mass 25 kg moves at 15.4 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 15.4^2 and multiply by 0.5 * 25.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 25.0, "velocity": 15.4}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 5.16 * 8.314 * 550 / 46.6.\nFinal: {\"answer\": 506.3333, \"unit\": \"kPa\"}", "dedupe_signature": "8ee168fcd6578998373fa79ab360250bfeed807fb098b7cc02a4ce5eefbe9d4b", "difficulty": "medium", "final_answer": {"answer": 506.3333, "unit": "kPa"}, "id": "ideal_gas_003891_5.16_550_46.6", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=5.16 mol, T=550 K, and V=46.6 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 5.16 * 8.314 * 550 / 46.6.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 5.16, "temp_k": 550, "volume_l": 46.6}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1315 * 2.825 * 100.\nFinal: {\"answer\": 371487.5, \"unit\": \"J\"}", "dedupe_signature": "0d4bc3469bcbdd1d587848b82efddb5c4bdabd587331de9d72a38472e3979a94", "difficulty": "easy", "final_answer": {"answer": 371487.5, "unit": "J"}, "id": "heat_q_003892_1315_2.825_100", "license": "Apache-2.0", "prompt": "A 1315 g sample has specific heat 2.825 J/(g*K). How much heat is needed to raise its temperature by 100 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1315 * 2.825 * 100.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 100, "heat_capacity": 2.825, "mass_g": 1315}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=216.9 V and R=125.1 ohm.\nFinal: {\"answer\": 376.064, \"unit\": \"W\"}", "dedupe_signature": "24c9e5e2838ad1fa0ac1454a5b180fb71d3ff5be050960871bebb0a6ad27bf3a", "difficulty": "easy", "final_answer": {"answer": 376.064, "unit": "W"}, "id": "ohm_power_003893_216.9_125.1", "license": "Apache-2.0", "prompt": "A resistor has resistance 125.1 ohm and voltage 216.9 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=216.9 V and R=125.1 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 125.1, "voltage": 216.9}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=347 mg, t=103 h, and T_half=54.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 93.629, \"unit\": \"mg\"}", "dedupe_signature": "c57794f08e7fa61f6c5ea6fb7336b4a50570cc947bc6b2d9e489ab3002fdfac6", "difficulty": "medium", "final_answer": {"answer": 93.629, "unit": "mg"}, "id": "half_life_003894_347_54.5_103", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 347 mg. Its half-life is 54.5 hours. How many mg remain after 103 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=347 mg, t=103 h, and T_half=54.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 103.0, "half_life": 54.5, "initial_amount": 347.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 1.01 mol * 44.01 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 44.4501, \"unit\": \"g\"}", "dedupe_signature": "8586c50e46bdd4c065fd20d609c5b8e4718e8b3124030722cfdb837e3f702edc", "difficulty": "medium", "final_answer": {"answer": 44.4501, "unit": "g"}, "id": "stoich_mass_003895_carbon_dioxide_1.01", "license": "Apache-2.0", "prompt": "A sample contains 1.01 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 1.01 mol * 44.01 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "carbon dioxide", "molar_mass": 44.01, "moles": 1.01}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 2005 mL to 2.005 L.\n3. Compute M = 1.225 / 2.005.\nFinal: {\"answer\": 0.611, \"unit\": \"mol/L\"}", "dedupe_signature": "e8bc908d0784f1c4c42494fbbc7aafad29cde15d4c128fe6f90cbfb79349da1a", "difficulty": "medium", "final_answer": {"answer": 0.611, "unit": "mol/L"}, "id": "molarity_003896_1.225_2005", "license": "Apache-2.0", "prompt": "A solution contains 1.225 mol of solute in 2005 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 2005 mL to 2.005 L.\nCompute M = 1.225 / 2.005.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 1.225, "volume_ml": 2005}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.83 y, so each step multiplies y by 1 - h*0.83.\n3. Apply that update for 4 steps and round the final state.\nFinal: {\"answer\": 0.3241, \"unit\": \"state_units\"}", "dedupe_signature": "1ff4aa81ef782be968b03b96477097515b9576dab49df1ae37bd913b30f95c85", "difficulty": "medium", "final_answer": {"answer": 0.3241, "unit": "state_units"}, "id": "euler_decay_003897_28_0.83_1.6_4", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.83 y with y(0)=28, step size h=1.6, for 4 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.83 y, so each step multiplies y by 1 - h*0.83.\nApply that update for 4 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 28.0, "rate": 0.83, "step": 1.6, "steps": 4}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(3)=-20.3 and f(12.3)=-74.24.\n3. The interval width is 9.3.\nFinal: {\"answer\": -439.611, \"unit\": \"area_units\"}", "dedupe_signature": "210cdf75bdff5ea769850d46be22054241399c2305bcaa4d5173722b1437ec8a", "difficulty": "medium", "final_answer": {"answer": -439.611, "unit": "area_units"}, "id": "trapz_linear_003898_-5.8_-2.9_3_12.3", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-5.8x+-2.9 from x=3 to x=12.3. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(3)=-20.3 and f(12.3)=-74.24.\nThe interval width is 9.3.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -2.9, "slope": -5.8, "x0": 3.0, "x1": 12.3}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.28 and add it to the current value.\nFinal: {\"answer\": [0.808, 1.886, 2.314], \"unit\": \"temperature_units\"}", "dedupe_signature": "35bffe5f34ee2307d5c46aec6f8797bfb507b78724848dc9e45392ac3544a392", "difficulty": "hard", "final_answer": {"answer": [0.808, 1.886, 2.314], "unit": "temperature_units"}, "id": "heat_step_003899_0.28_-0.85_0.5_2.95_1.6_2.8", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-0.85, right=2.8; current interior values are [0.5, 2.95, 1.6]. Use r=0.28. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.28 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [0.5, 2.95, 1.6], "left": -0.85, "r": 0.28, "right": 2.8}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kelvin equals Celsius plus 273.15.\n2. Apply the conversion factor directly to the given value.\n3. Compute 8.0 + 273.15.\nFinal: {\"answer\": 281.15, \"unit\": \"K\"}", "dedupe_signature": "55e09c32a34f9594626facff9af427063669f4a7d7626268a1943a22b67cbbf6", "difficulty": "easy", "final_answer": {"answer": 281.15, "unit": "K"}, "id": "unit_convert_003900_c_to_k_8", "license": "Apache-2.0", "prompt": "Convert 8 degC to K. Return the converted value with unit.", "reasoning_trace": "Kelvin equals Celsius plus 273.15.\nApply the conversion factor directly to the given value.\nCompute 8.0 + 273.15.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 8.0}, "verifier": {"formula": "value + 273.15", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=64 degrees and keep the unit as newtons.\nFinal: {\"answer\": [0.8767, 1.7976], \"unit\": \"N\"}", "dedupe_signature": "6e7c512fcaedf9348e4e4e3745e58f54784672309942cf1a9d554fbff248198d", "difficulty": "medium", "final_answer": {"answer": [0.8767, 1.7976], "unit": "N"}, "id": "vector_components_003901_2_64", "license": "Apache-2.0", "prompt": "A vector has magnitude 2 N at 64 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=64 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 64, "magnitude": 2.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [2.6, -17.5], \"unit\": \"dimensionless\"}", "dedupe_signature": "794a3df4ba8a256e2f3ae6d6bafd3422d744230d41886a3a269f2caa8e50aeec", "difficulty": "medium", "final_answer": {"answer": [2.6, -17.5], "unit": "dimensionless"}, "id": "line_two_point_003902_9.75_23.5_2.6_-17.5", "license": "Apache-2.0", "prompt": "A line passes through points (9.75, 7.85) and (23.5, 43.6). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 9.75, "x2": 23.5, "y1": 7.850000000000001, "y2": 43.6}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. speed squared over acceleration has units of meters\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "8fbdfe9abf75ec9f23e45dc479507d2e08600adca5d13026f02f307f966d5ab0", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_003903_consistent_741d4e34_888889", "license": "Apache-2.0", "prompt": "In lab notebook case 888889, check dimensional consistency for R = v^2 * sin(theta) / g. The left side has dimensions m and the right side has dimensions m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nspeed squared over acceleration has units of meters\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "R = v^2 * sin(theta) / g"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef pairwise_ratios_003904(numerators, denominators):\n    if len(numerators) != len(denominators):\n        raise ValueError('length mismatch')\n    out = []\n    for numerator, denominator in zip(numerators, denominators):\n        if denominator == 0:\n            raise ValueError('zero denominator')\n        out.append(numerator / denominator)\n    return out\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"pairwise_ratios_003904\"}", "dedupe_signature": "db5db8350df6914f2ce175facef4e4a464c987e76dbc2b8516c3f6ecfea1a82e", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "pairwise_ratios_003904"}, "id": "code_003904_pairwise_ratios_003904", "license": "Apache-2.0", "prompt": "Write a Python function pairwise_ratios_003904(numerators, denominators) that returns a list of n/d values. Raise ValueError if lengths differ or any denominator is zero. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "pairwise_ratios_003904"}, "verifier": {"function": "pairwise_ratios_003904", "tests": ["assert pairwise_ratios_003904([2, 9], [4, 3]) == [0.5, 3.0]", "try:\n    pairwise_ratios_003904([1], [0])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass", "try:\n    pairwise_ratios_003904([1, 2], [1])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: volume.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"volume\"]}", "dedupe_signature": "933072b8be2421996514d899cc61011d0a085c41ef7a9568a5b6086841f3f8d7", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["volume"]}, "id": "abstain_003905_volume", "license": "Apache-2.0", "prompt": "Compute pressure from the ideal gas law. The prompt gives n=0.7 mol and T=344 K, but does not give volume. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: volume.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["volume"]}, "verifier": {"missing": ["volume"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 12.55^2 and multiply by 0.5 * 9.1.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 716.6364, \"unit\": \"J\"}", "dedupe_signature": "d17d3207a40a88d95e730610615fc9f8990f98b60a46835c56c64f186f431b52", "difficulty": "easy", "final_answer": {"answer": 716.6364, "unit": "J"}, "id": "ke_003907_9.1_12.55", "license": "Apache-2.0", "prompt": "A body of mass 9.1 kg moves at 12.55 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 12.55^2 and multiply by 0.5 * 9.1.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 9.1, "velocity": 12.55}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=44 degrees through the sine of 2 theta.\n3. Substitute v=50.2 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 256.7283, \"unit\": \"m\"}", "dedupe_signature": "86d270dc382b28cadfe0c3699183654245cdc0db6a39c378f66cf355e2c41224", "difficulty": "medium", "final_answer": {"answer": 256.7283, "unit": "m"}, "id": "projectile_range_003908_50.2_44", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 50.2 m/s and angle 44 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=44 degrees through the sine of 2 theta.\nSubstitute v=50.2 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 44, "gravity": 9.81, "speed": 50.2}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 3.6 * 8.314 * 322 / 115.5.\nFinal: {\"answer\": 83.4423, \"unit\": \"kPa\"}", "dedupe_signature": "c8397f9fbd4c582e05942bb9ccbaa4fa638f49657fb4770af37b65b7b4d1946e", "difficulty": "medium", "final_answer": {"answer": 83.4423, "unit": "kPa"}, "id": "ideal_gas_003909_3.6_322_115.5", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=3.6 mol, T=322 K, and V=115.5 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 3.6 * 8.314 * 322 / 115.5.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 3.6, "temp_k": 322, "volume_l": 115.5}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 230 * 4.18 * 60.\nFinal: {\"answer\": 57684.0, \"unit\": \"J\"}", "dedupe_signature": "9cacea2878348448604829452ed1cd4b4beba3e4cc8fb7e4f47424d61a18b973", "difficulty": "easy", "final_answer": {"answer": 57684.0, "unit": "J"}, "id": "heat_q_003910_230_4.18_60", "license": "Apache-2.0", "prompt": "A 230 g sample has specific heat 4.18 J/(g*K). How much heat is needed to raise its temperature by 60 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 230 * 4.18 * 60.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 60, "heat_capacity": 4.18, "mass_g": 230}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=239.1 V and R=31.8 ohm.\nFinal: {\"answer\": 1797.7613, \"unit\": \"W\"}", "dedupe_signature": "fc9ad9bbcb227558339848e255cc542475c0dd72efd54adea41517a33933bd6a", "difficulty": "easy", "final_answer": {"answer": 1797.7613, "unit": "W"}, "id": "ohm_power_003911_239.1_31.8", "license": "Apache-2.0", "prompt": "A resistor has resistance 31.8 ohm and voltage 239.1 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=239.1 V and R=31.8 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 31.8, "voltage": 239.1}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=971 mg, t=257 h, and T_half=26.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 1.169, \"unit\": \"mg\"}", "dedupe_signature": "8a7ea3603aa582c5923584bb6c8665fce26bae1a5c93f6f36b60ba4d9a9e9819", "difficulty": "medium", "final_answer": {"answer": 1.169, "unit": "mg"}, "id": "half_life_003912_971_26.5_257", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 971 mg. Its half-life is 26.5 hours. How many mg remain after 257 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=971 mg, t=257 h, and T_half=26.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 257.0, "half_life": 26.5, "initial_amount": 971.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 6.41 mol * 44.01 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 282.1041, \"unit\": \"g\"}", "dedupe_signature": "1601bf4aecf476ecb15297427600ca37846edb143688f32d1fad48eede66bfb6", "difficulty": "medium", "final_answer": {"answer": 282.1041, "unit": "g"}, "id": "stoich_mass_003913_carbon_dioxide_6.41", "license": "Apache-2.0", "prompt": "A sample contains 6.41 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 6.41 mol * 44.01 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "carbon dioxide", "molar_mass": 44.01, "moles": 6.41}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 3465 mL to 3.465 L.\n3. Compute M = 3.095 / 3.465.\nFinal: {\"answer\": 0.8932, \"unit\": \"mol/L\"}", "dedupe_signature": "d4338b749d1148d71b66824b7c52038e155728603dc6da3a783b031728ae04c3", "difficulty": "medium", "final_answer": {"answer": 0.8932, "unit": "mol/L"}, "id": "molarity_003914_3.095_3465", "license": "Apache-2.0", "prompt": "A solution contains 3.095 mol of solute in 3465 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 3465 mL to 3.465 L.\nCompute M = 3.095 / 3.465.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 3.095, "volume_ml": 3465}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(0.8)=-2.86 and f(9.1)=-8.67.\n3. The interval width is 8.3.\nFinal: {\"answer\": -47.8495, \"unit\": \"area_units\"}", "dedupe_signature": "3988c5bfe3e17e318a9eae1369b30c0b8882f7f3152a76c8c55f3326b33f5104", "difficulty": "medium", "final_answer": {"answer": -47.8495, "unit": "area_units"}, "id": "trapz_linear_003916_-0.7_-2.3_0.8_9.1", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-0.7x+-2.3 from x=0.8 to x=9.1. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(0.8)=-2.86 and f(9.1)=-8.67.\nThe interval width is 8.3.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -2.3, "slope": -0.7, "x0": 0.8, "x1": 9.100000000000001}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.4 and add it to the current value.\nFinal: {\"answer\": [-1.0, -0.78, 0.36], \"unit\": \"temperature_units\"}", "dedupe_signature": "50258994f744ec9c7609bacd6f9364ce316bd7349da99ff27ad054fb9d17835d", "difficulty": "hard", "final_answer": {"answer": [-1.0, -0.78, 0.36], "unit": "temperature_units"}, "id": "heat_step_003917_0.4_-0.55_-1.3_-1.3_0.0_2.2", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-0.55, right=2.2; current interior values are [-1.3, -1.3, 0.0]. Use r=0.4. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.4 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-1.3, -1.3, 0.0], "left": -0.55, "r": 0.4, "right": 2.2}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=205 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-64.801, -30.2172], \"unit\": \"N\"}", "dedupe_signature": "f5163673b5f773a5a4c3b52676a1493be0b20ef785e55f243c33493191cda805", "difficulty": "medium", "final_answer": {"answer": [-64.801, -30.2172], "unit": "N"}, "id": "vector_components_003919_71.5_205", "license": "Apache-2.0", "prompt": "A vector has magnitude 71.5 N at 205 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=205 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 205, "magnitude": 71.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. energy divided by length is force, not spring constant\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "8b82f224fa965cc2d5ff241fecddb72698c4b8be180be84e7c7e61fa0d56ef35", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_003921_inconsistent_56040f5d_231839", "license": "Apache-2.0", "prompt": "In sensor calibration case 231839, check dimensional consistency for k = E / x. The left side has dimensions N/m and the right side has dimensions J/m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nenergy divided by length is force, not spring constant\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "k = E / x"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef center_values_003922(values):\n    if not values:\n        raise ValueError('center_values requires at least one value')\n    mean = sum(values) / len(values)\n    return [value - mean for value in values]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"center_values_003922\"}", "dedupe_signature": "9147f42c195dd2225daacb7133221c098876a7f4e0d2557fee227f6bb325df03", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "center_values_003922"}, "id": "code_003922_center_values_003922", "license": "Apache-2.0", "prompt": "Write a Python function center_values_003922(values) that subtracts the arithmetic mean from each value and returns a new list. Raise ValueError for an empty input. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "center_values_003922"}, "verifier": {"function": "center_values_003922", "tests": ["out = center_values_003922([1, 2, 3]); assert out == [-1, 0, 1]", "assert center_values_003922([5]) == [0]", "try:\n    center_values_003922([])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: left_boundary, right_boundary.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"left_boundary\", \"right_boundary\"]}", "dedupe_signature": "b7413e8394358989c6cf2178bfd7aa1fee5cd18f4a3e0ef58a0fc1a1cd024716", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["left_boundary", "right_boundary"]}, "id": "abstain_003923_left_boundary_right_boundary", "license": "Apache-2.0", "prompt": "Solve the 1D heat equation after one finite-difference step. The prompt gives r=0.02 and interior values [1.3, -0.2, 1.3], but gives no boundary values. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: left_boundary, right_boundary.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["left_boundary", "right_boundary"]}, "verifier": {"missing": ["left_boundary", "right_boundary"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 7.85 kg and a = 2.85 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 22.3725, \"unit\": \"N\"}", "dedupe_signature": "f4118e53d7d512c32bbef002c96d889cbe588b976fa3d5a837d21d887e8c45d1", "difficulty": "easy", "final_answer": {"answer": 22.3725, "unit": "N"}, "id": "force_003924_7.85_2.85", "license": "Apache-2.0", "prompt": "A cart has mass 7.85 kg and measured acceleration 2.85 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 7.85 kg and a = 2.85 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 2.85, "mass": 7.85}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 0.65^2 and multiply by 0.5 * 12.3.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 2.5984, \"unit\": \"J\"}", "dedupe_signature": "b89f433e2d217bcc8c59c8d543317bab972e9f146279c55d2206496495053c84", "difficulty": "easy", "final_answer": {"answer": 2.5984, "unit": "J"}, "id": "ke_003925_12.3_0.65", "license": "Apache-2.0", "prompt": "A body of mass 12.3 kg moves at 0.65 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 0.65^2 and multiply by 0.5 * 12.3.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 12.3, "velocity": 0.65}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=56 degrees through the sine of 2 theta.\n3. Substitute v=45.8 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 198.2567, \"unit\": \"m\"}", "dedupe_signature": "10097ef3441f4ce5c72a3f8e4a124ee227a557e622792cbf87b86e53fc20236b", "difficulty": "medium", "final_answer": {"answer": 198.2567, "unit": "m"}, "id": "projectile_range_003926_45.8_56", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 45.8 m/s and angle 56 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=56 degrees through the sine of 2 theta.\nSubstitute v=45.8 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 56, "gravity": 9.81, "speed": 45.8}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 0.62 * 8.314 * 587 / 30.4.\nFinal: {\"answer\": 99.5328, \"unit\": \"kPa\"}", "dedupe_signature": "621f534563679674ab11941b30a6b08e9901243acbbb47227ae31e2e800b035a", "difficulty": "medium", "final_answer": {"answer": 99.5328, "unit": "kPa"}, "id": "ideal_gas_003927_0.62_587_30.4", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=0.62 mol, T=587 K, and V=30.4 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 0.62 * 8.314 * 587 / 30.4.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 0.62, "temp_k": 587, "volume_l": 30.4}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 720 * 4.39 * 23.\nFinal: {\"answer\": 72698.4, \"unit\": \"J\"}", "dedupe_signature": "2da63aa330009c723b463aa47f2d26262a3c0a172a4e2f75a538fc5ac4010a47", "difficulty": "easy", "final_answer": {"answer": 72698.4, "unit": "J"}, "id": "heat_q_003928_720_4.39_23", "license": "Apache-2.0", "prompt": "A 720 g sample has specific heat 4.39 J/(g*K). How much heat is needed to raise its temperature by 23 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 720 * 4.39 * 23.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 23, "heat_capacity": 4.39, "mass_g": 720}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=153.5 V and R=53.9 ohm.\nFinal: {\"answer\": 437.1475, \"unit\": \"W\"}", "dedupe_signature": "36426005df1e563e9ee9b1fb12c50af40d37576e8ad918690a1f1a8255a9d365", "difficulty": "easy", "final_answer": {"answer": 437.1475, "unit": "W"}, "id": "ohm_power_003929_153.5_53.9", "license": "Apache-2.0", "prompt": "A resistor has resistance 53.9 ohm and voltage 153.5 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=153.5 V and R=53.9 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 53.9, "voltage": 153.5}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=398.5 mg, t=236 h, and T_half=2.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 0.0, \"unit\": \"mg\"}", "dedupe_signature": "aaaa4e41cd026ed57c3cc74e73fdc6583a3ca11945aa96f5aee7c2b555774ee8", "difficulty": "medium", "final_answer": {"answer": 0.0, "unit": "mg"}, "id": "half_life_003930_398.5_2.5_236", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 398.5 mg. Its half-life is 2.5 hours. How many mg remain after 236 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=398.5 mg, t=236 h, and T_half=2.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 236.0, "half_life": 2.5, "initial_amount": 398.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 2825 mL to 2.825 L.\n3. Compute M = 0.78 / 2.825.\nFinal: {\"answer\": 0.2761, \"unit\": \"mol/L\"}", "dedupe_signature": "7af4a363ac77d52b1720d2e8e30f6d03d1c2051ab61ac78a11e7ae400bc1e677", "difficulty": "medium", "final_answer": {"answer": 0.2761, "unit": "mol/L"}, "id": "molarity_003932_0.78_2825", "license": "Apache-2.0", "prompt": "A solution contains 0.78 mol of solute in 2825 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 2825 mL to 2.825 L.\nCompute M = 0.78 / 2.825.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 0.78, "volume_ml": 2825}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.21 y, so each step multiplies y by 1 - h*0.21.\n3. Apply that update for 12 steps and round the final state.\nFinal: {\"answer\": 0.2009, \"unit\": \"state_units\"}", "dedupe_signature": "da8d363b9462762189a4fdbaf6ba30680a72a57f6ae928934f26da32e6556bb5", "difficulty": "medium", "final_answer": {"answer": 0.2009, "unit": "state_units"}, "id": "euler_decay_003933_73.5_0.21_1.85_12", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.21 y with y(0)=73.5, step size h=1.85, for 12 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.21 y, so each step multiplies y by 1 - h*0.21.\nApply that update for 12 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 73.5, "rate": 0.21, "step": 1.85, "steps": 12}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(3.2)=26.26 and f(6.2)=40.66.\n3. The interval width is 3.\nFinal: {\"answer\": 100.38, \"unit\": \"area_units\"}", "dedupe_signature": "5cec612e4a45227420e8a672aba9b88006541026ce12d1b440a9e1cb439038b3", "difficulty": "medium", "final_answer": {"answer": 100.38, "unit": "area_units"}, "id": "trapz_linear_003934_4.8_10.9_3.2_6.2", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=4.8x+10.9 from x=3.2 to x=6.2. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(3.2)=26.26 and f(6.2)=40.66.\nThe interval width is 3.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 10.9, "slope": 4.8, "x0": 3.2, "x1": 6.2}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.26 and add it to the current value.\nFinal: {\"answer\": [-0.864, 0.198, 1.0], \"unit\": \"temperature_units\"}", "dedupe_signature": "aacc04c7aba22cdf530be8560f5b5353d222bb3eae44a9b7c15f8637bde5cf09", "difficulty": "hard", "final_answer": {"answer": [-0.864, 0.198, 1.0], "unit": "temperature_units"}, "id": "heat_step_003935_0.26_-1.55_-1.8_1.55_-0.3_2.85", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-1.55, right=2.85; current interior values are [-1.8, 1.55, -0.3]. Use r=0.26. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.26 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-1.8, 1.55, -0.3], "left": -1.55, "r": 0.26, "right": 2.85}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 100 centimeters in one meter.\n2. Apply the conversion factor directly to the given value.\n3. Compute 2589.0 / 100.\nFinal: {\"answer\": 25.89, \"unit\": \"m\"}", "dedupe_signature": "48768d670d02c3da6e93be5cc22676f23ff9ee74ddea38ab32b9521b28b64e58", "difficulty": "easy", "final_answer": {"answer": 25.89, "unit": "m"}, "id": "unit_convert_003936_cm_to_m_2589", "license": "Apache-2.0", "prompt": "Convert 2589 cm to m. Return the converted value with unit.", "reasoning_trace": "There are 100 centimeters in one meter.\nApply the conversion factor directly to the given value.\nCompute 2589.0 / 100.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 2589.0}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=262 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-58.731, -417.8931], \"unit\": \"N\"}", "dedupe_signature": "42ca9c9c8fc4950904477a16ea8a25dbd56901bc000a0b915bb224a3447a5871", "difficulty": "medium", "final_answer": {"answer": [-58.731, -417.8931], "unit": "N"}, "id": "vector_components_003937_422_262", "license": "Apache-2.0", "prompt": "A vector has magnitude 422 N at 262 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=262 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 262, "magnitude": 422.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-6.5, 19.0], \"unit\": \"dimensionless\"}", "dedupe_signature": "83ae362ef90f3b8a0451856e422d5156b1a76620bf0481cd8085ff026306232e", "difficulty": "medium", "final_answer": {"answer": [-6.5, 19.0], "unit": "dimensionless"}, "id": "line_two_point_003938_15.75_30.25_-6.5_19", "license": "Apache-2.0", "prompt": "A line passes through points (15.75, -83.375) and (30.25, -177.625). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 15.75, "x2": 30.25, "y1": -83.375, "y2": -177.625}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. amount times volume is not concentration\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "d79d3476b1c44a3d5b81cbe2e0b79487a6b297666ae8852f8669a99df5b80dcc", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_003939_inconsistent_74ac0b02_646506", "license": "Apache-2.0", "prompt": "In quality-control check case 646506, check dimensional consistency for C = n * V. The left side has dimensions mol/L and the right side has dimensions mol*L. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\namount times volume is not concentration\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "C = n * V"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef clamp_003940(x, lo, hi):\n    if lo > hi:\n        raise ValueError('lo must be <= hi')\n    return min(max(x, lo), hi)\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"clamp_003940\"}", "dedupe_signature": "2660871c730534c3847411eec45c37d7893b638deda4a047708e558a917abd7b", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "clamp_003940"}, "id": "code_003940_clamp_003940", "license": "Apache-2.0", "prompt": "Write a Python function clamp_003940(x, lo, hi) that clips x into the inclusive interval [lo, hi]. It must raise ValueError if lo > hi. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "clamp_003940"}, "verifier": {"function": "clamp_003940", "tests": ["assert clamp_003940(5, 0, 10) == 5", "assert clamp_003940(-2, 0, 10) == 0", "assert clamp_003940(12, 0, 10) == 10", "try:\n    clamp_003940(1, 3, 2)\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 13.75 kg and a = 3.15 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 43.3125, \"unit\": \"N\"}", "dedupe_signature": "ab44de8a2a858dfd00f800fd1585c9044db1debc807f28c0c67a29287a06d765", "difficulty": "easy", "final_answer": {"answer": 43.3125, "unit": "N"}, "id": "force_003942_13.75_3.15", "license": "Apache-2.0", "prompt": "A cart has mass 13.75 kg and measured acceleration 3.15 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 13.75 kg and a = 3.15 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 3.15, "mass": 13.75}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 34.4^2 and multiply by 0.5 * 18.8.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 11123.584, \"unit\": \"J\"}", "dedupe_signature": "b1aa8680e9519d025edd1ed7c343485f8b5361d2683f3fc1fade8179fd43721a", "difficulty": "easy", "final_answer": {"answer": 11123.584, "unit": "J"}, "id": "ke_003943_18.8_34.4", "license": "Apache-2.0", "prompt": "A body of mass 18.8 kg moves at 34.4 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 34.4^2 and multiply by 0.5 * 18.8.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 18.8, "velocity": 34.4}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=12 degrees through the sine of 2 theta.\n3. Substitute v=54.5 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 123.1508, \"unit\": \"m\"}", "dedupe_signature": "673081593583903f278a6b55713aa49ca3ea2837f22ea10a1c09655ba9262a03", "difficulty": "medium", "final_answer": {"answer": 123.1508, "unit": "m"}, "id": "projectile_range_003944_54.5_12", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 54.5 m/s and angle 12 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=12 degrees through the sine of 2 theta.\nSubstitute v=54.5 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 12, "gravity": 9.81, "speed": 54.5}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 1.07 * 8.314 * 535 / 115.8.\nFinal: {\"answer\": 41.0997, \"unit\": \"kPa\"}", "dedupe_signature": "7ce83d032309ec42641ac6f52c65fe1a1fe31d6326be1e378561952c37dfd3c6", "difficulty": "medium", "final_answer": {"answer": 41.0997, "unit": "kPa"}, "id": "ideal_gas_003945_1.07_535_115.8", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=1.07 mol, T=535 K, and V=115.8 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 1.07 * 8.314 * 535 / 115.8.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 1.07, "temp_k": 535, "volume_l": 115.8}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 75 * 4.415 * 51.\nFinal: {\"answer\": 16887.375, \"unit\": \"J\"}", "dedupe_signature": "12a6dca4c831a8b65b908a330a0e402adc47466a766418c9a46f1a28740c7653", "difficulty": "easy", "final_answer": {"answer": 16887.375, "unit": "J"}, "id": "heat_q_003946_75_4.415_51", "license": "Apache-2.0", "prompt": "A 75 g sample has specific heat 4.415 J/(g*K). How much heat is needed to raise its temperature by 51 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 75 * 4.415 * 51.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 51, "heat_capacity": 4.415, "mass_g": 75}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=57.9 V and R=152.7 ohm.\nFinal: {\"answer\": 21.9542, \"unit\": \"W\"}", "dedupe_signature": "e276cb82f9e62eca29fefe000134a64ebbb641783aaf0e4ad99d993953d100f6", "difficulty": "easy", "final_answer": {"answer": 21.9542, "unit": "W"}, "id": "ohm_power_003947_57.9_152.7", "license": "Apache-2.0", "prompt": "A resistor has resistance 152.7 ohm and voltage 57.9 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=57.9 V and R=152.7 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 152.7, "voltage": 57.9}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 4.76 mol * 58.44 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 278.1744, \"unit\": \"g\"}", "dedupe_signature": "c7a5b2483ed2aabf5da8e58e3e3e29632de23c615f60be7b11c99b334dcd62d1", "difficulty": "medium", "final_answer": {"answer": 278.1744, "unit": "g"}, "id": "stoich_mass_003949_sodium_chloride_4.76", "license": "Apache-2.0", "prompt": "A sample contains 4.76 mol of sodium chloride. Using molar mass 58.44 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 4.76 mol * 58.44 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "sodium chloride", "molar_mass": 58.44, "moles": 4.76}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 3395 mL to 3.395 L.\n3. Compute M = 1.925 / 3.395.\nFinal: {\"answer\": 0.567, \"unit\": \"mol/L\"}", "dedupe_signature": "4e5975f0ada47bc294c6d81076d36d79fe2b6b75a5e01295296dfb2745c85cf8", "difficulty": "medium", "final_answer": {"answer": 0.567, "unit": "mol/L"}, "id": "molarity_003950_1.925_3395", "license": "Apache-2.0", "prompt": "A solution contains 1.925 mol of solute in 3395 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 3395 mL to 3.395 L.\nCompute M = 1.925 / 3.395.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 1.925, "volume_ml": 3395}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.8 y, so each step multiplies y by 1 - h*0.8.\n3. Apply that update for 3 steps and round the final state.\nFinal: {\"answer\": -0.0015, \"unit\": \"state_units\"}", "dedupe_signature": "b258736395f7e9f880173b24834505fc246ef10a1707eac63245dae969e216a6", "difficulty": "medium", "final_answer": {"answer": -0.0015, "unit": "state_units"}, "id": "euler_decay_003951_23.5_0.8_1.3_3", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.8 y with y(0)=23.5, step size h=1.3, for 3 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.8 y, so each step multiplies y by 1 - h*0.8.\nApply that update for 3 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 23.5, "rate": 0.8, "step": 1.3, "steps": 3}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(6.6)=12.32 and f(8.4)=20.78.\n3. The interval width is 1.8.\nFinal: {\"answer\": 29.79, \"unit\": \"area_units\"}", "dedupe_signature": "59ba1b357d5dc137b8422623c1b469fbaa951077f7c0ab7db7cf032542227e9f", "difficulty": "medium", "final_answer": {"answer": 29.79, "unit": "area_units"}, "id": "trapz_linear_003952_4.7_-18.7_6.6_8.4", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=4.7x+-18.7 from x=6.6 to x=8.4. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(6.6)=12.32 and f(8.4)=20.78.\nThe interval width is 1.8.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -18.7, "slope": 4.7, "x0": 6.6, "x1": 8.4}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.32 and add it to the current value.\nFinal: {\"answer\": [-0.472, -0.38, -0.5], \"unit\": \"temperature_units\"}", "dedupe_signature": "da27a7bb89ea9be2f701545dd66e20d39dc4708dfe4530d36c11f065cd2bac0e", "difficulty": "hard", "final_answer": {"answer": [-0.472, -0.38, -0.5], "unit": "temperature_units"}, "id": "heat_step_003953_0.32_0.25_-0.2_-1.5_0.7_-0.85", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=0.25, right=-0.85; current interior values are [-0.2, -1.5, 0.7]. Use r=0.32. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.32 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-0.2, -1.5, 0.7], "left": 0.25, "r": 0.32, "right": -0.85}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 12791.0 / 1000.\nFinal: {\"answer\": 12.791, \"unit\": \"kg\"}", "dedupe_signature": "ec4ccac9192b2d40efc67aa735c93e4d4f517c9d28025220a066298c66bac660", "difficulty": "easy", "final_answer": {"answer": 12.791, "unit": "kg"}, "id": "unit_convert_003954_g_to_kg_12791", "license": "Apache-2.0", "prompt": "Convert 12791 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 12791.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 12791.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=172 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-411.4564, 57.8264], \"unit\": \"N\"}", "dedupe_signature": "4e1f2a801d710e2eaead6e14deabe438ba40da040859b4fae57253ad7d05e230", "difficulty": "medium", "final_answer": {"answer": [-411.4564, 57.8264], "unit": "N"}, "id": "vector_components_003955_415.5_172", "license": "Apache-2.0", "prompt": "A vector has magnitude 415.5 N at 172 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=172 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 172, "magnitude": 415.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: rate_constant, number_of_steps.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"rate_constant\", \"number_of_steps\"]}", "dedupe_signature": "4eab7232fa49d3ecd8b2c8c62a6bea226b05776570728def2accd25694044193", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["rate_constant", "number_of_steps"]}, "id": "abstain_003959_rate_constant_number_of_steps", "license": "Apache-2.0", "prompt": "Use explicit Euler for dy/dt = -k y. The prompt gives y(0)=17.5 and h=0.8, but omits both k and the number of steps. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: rate_constant, number_of_steps.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["rate_constant", "number_of_steps"]}, "verifier": {"missing": ["rate_constant", "number_of_steps"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=37 degrees through the sine of 2 theta.\n3. Substitute v=42.2 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 174.5008, \"unit\": \"m\"}", "dedupe_signature": "63ce0730105fe3d97d566380455bc623e1e2da3b92950e76b0a0fd8fe8bd053b", "difficulty": "medium", "final_answer": {"answer": 174.5008, "unit": "m"}, "id": "projectile_range_003962_42.2_37", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 42.2 m/s and angle 37 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=37 degrees through the sine of 2 theta.\nSubstitute v=42.2 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 37, "gravity": 9.81, "speed": 42.2}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 4.5 * 8.314 * 545 / 112.5.\nFinal: {\"answer\": 181.2452, \"unit\": \"kPa\"}", "dedupe_signature": "5d62ed9250458e180ae068f71afa00509679f2a98f456e09eaeb0f63f6c57018", "difficulty": "medium", "final_answer": {"answer": 181.2452, "unit": "kPa"}, "id": "ideal_gas_003963_4.5_545_112.5", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=4.5 mol, T=545 K, and V=112.5 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 4.5 * 8.314 * 545 / 112.5.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 4.5, "temp_k": 545, "volume_l": 112.5}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1145 * 3.105 * 41.\nFinal: {\"answer\": 145764.225, \"unit\": \"J\"}", "dedupe_signature": "2a40fe91d7baa3c1c2f4a1dd860d309716e713cd41ae25e864308e0335f7e79a", "difficulty": "easy", "final_answer": {"answer": 145764.225, "unit": "J"}, "id": "heat_q_003964_1145_3.105_41", "license": "Apache-2.0", "prompt": "A 1145 g sample has specific heat 3.105 J/(g*K). How much heat is needed to raise its temperature by 41 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1145 * 3.105 * 41.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 41, "heat_capacity": 3.105, "mass_g": 1145}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=121.5 V and R=190 ohm.\nFinal: {\"answer\": 77.6961, \"unit\": \"W\"}", "dedupe_signature": "255aaed8e036d76776878dcfc7942613eb00869213951de4e6e004fa4312b77a", "difficulty": "easy", "final_answer": {"answer": 77.6961, "unit": "W"}, "id": "ohm_power_003965_121.5_190", "license": "Apache-2.0", "prompt": "A resistor has resistance 190 ohm and voltage 121.5 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=121.5 V and R=190 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 190.0, "voltage": 121.5}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=155.5 mg, t=302.5 h, and T_half=58.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 4.3164, \"unit\": \"mg\"}", "dedupe_signature": "76833b95138f83f33d050835930faca280d4ad7fe4147be128992532d8921f51", "difficulty": "medium", "final_answer": {"answer": 4.3164, "unit": "mg"}, "id": "half_life_003966_155.5_58.5_302.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 155.5 mg. Its half-life is 58.5 hours. How many mg remain after 302.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=155.5 mg, t=302.5 h, and T_half=58.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 302.5, "half_life": 58.5, "initial_amount": 155.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 5.47 mol * 58.44 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 319.6668, \"unit\": \"g\"}", "dedupe_signature": "6824a8d33b75ecdfda13101a56cf598a469a3974f9f057a89991a6748f02b10d", "difficulty": "medium", "final_answer": {"answer": 319.6668, "unit": "g"}, "id": "stoich_mass_003967_sodium_chloride_5.47", "license": "Apache-2.0", "prompt": "A sample contains 5.47 mol of sodium chloride. Using molar mass 58.44 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 5.47 mol * 58.44 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "sodium chloride", "molar_mass": 58.44, "moles": 5.47}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 4410 mL to 4.41 L.\n3. Compute M = 1.315 / 4.41.\nFinal: {\"answer\": 0.2982, \"unit\": \"mol/L\"}", "dedupe_signature": "c4bcc454211eba0e4537a854bb22e4c5d0abd1e0fd365172c8a09e6823411254", "difficulty": "medium", "final_answer": {"answer": 0.2982, "unit": "mol/L"}, "id": "molarity_003968_1.315_4410", "license": "Apache-2.0", "prompt": "A solution contains 1.315 mol of solute in 4410 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 4410 mL to 4.41 L.\nCompute M = 1.315 / 4.41.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 1.315, "volume_ml": 4410}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.89 y, so each step multiplies y by 1 - h*0.89.\n3. Apply that update for 5 steps and round the final state.\nFinal: {\"answer\": -0.0013, \"unit\": \"state_units\"}", "dedupe_signature": "cb7f00aa2072cc08307388d52ccb307dac7e2f942db1b0d92db44f60f3deb11d", "difficulty": "medium", "final_answer": {"answer": -0.0013, "unit": "state_units"}, "id": "euler_decay_003969_72_0.89_1.25_5", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.89 y with y(0)=72, step size h=1.25, for 5 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.89 y, so each step multiplies y by 1 - h*0.89.\nApply that update for 5 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 72.0, "rate": 0.89, "step": 1.25, "steps": 5}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(1.4)=-16.76 and f(10.6)=-61.84.\n3. The interval width is 9.2.\nFinal: {\"answer\": -361.56, \"unit\": \"area_units\"}", "dedupe_signature": "7d210d1d316afa008d03552347a4f5b97ccaa6e6d6797b50a640207c8f5cf070", "difficulty": "medium", "final_answer": {"answer": -361.56, "unit": "area_units"}, "id": "trapz_linear_003970_-4.9_-9.9_1.4_10.6", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-4.9x+-9.9 from x=1.4 to x=10.6. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(1.4)=-16.76 and f(10.6)=-61.84.\nThe interval width is 9.2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -9.9, "slope": -4.9, "x0": 1.4, "x1": 10.6}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.14 and add it to the current value.\nFinal: {\"answer\": [0.516, 2.059, 0.759], \"unit\": \"temperature_units\"}", "dedupe_signature": "34bba616e4a13ffa233ca8c25bef41f8eb206ea74d4cbdc2b52cd53542d33ba5", "difficulty": "hard", "final_answer": {"answer": [0.516, 2.059, 0.759], "unit": "temperature_units"}, "id": "heat_step_003971_0.14_1.35_-0.1_2.85_0.15_1.8", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.35, right=1.8; current interior values are [-0.1, 2.85, 0.15]. Use r=0.14. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.14 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-0.1, 2.85, 0.15], "left": 1.35, "r": 0.14, "right": 1.8}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 42565.0 / 1000.\nFinal: {\"answer\": 42.565, \"unit\": \"kg\"}", "dedupe_signature": "a23d4a019bd5365d16effda0f1a04179e7c384f3f7278e425d09eb0210cbd6b8", "difficulty": "easy", "final_answer": {"answer": 42.565, "unit": "kg"}, "id": "unit_convert_003972_g_to_kg_42565", "license": "Apache-2.0", "prompt": "Convert 42565 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 42565.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 42565.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [3.6, 20.5], \"unit\": \"dimensionless\"}", "dedupe_signature": "522655f71e1f4cb75eb8e9eb6b981c70539ac3a644cd8a036dcab23ade783c74", "difficulty": "medium", "final_answer": {"answer": [3.6, 20.5], "unit": "dimensionless"}, "id": "line_two_point_003974_-0.5_6.5_3.6_20.5", "license": "Apache-2.0", "prompt": "A line passes through points (-0.5, 18.7) and (6.5, 43.9). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -0.5, "x2": 6.5, "y1": 18.7, "y2": 43.900000000000006}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. density times acceleration times height gives kg/(m*s^2), or pascal\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "b87ac719259fcb234b413396d27c8e6dea8c7c8595ecc3a8d7358e3bee123330", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_003975_consistent_b7d3eed1_875320", "license": "Apache-2.0", "prompt": "In sensor calibration case 875320, check dimensional consistency for p = rho * g * h. The left side has dimensions Pa and the right side has dimensions Pa. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\ndensity times acceleration times height gives kg/(m*s^2), or pascal\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "p = rho * g * h"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef clamp_003976(x, lo, hi):\n    if lo > hi:\n        raise ValueError('lo must be <= hi')\n    return min(max(x, lo), hi)\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"clamp_003976\"}", "dedupe_signature": "99cd33615146902dabccae12d0d9b388385a930135d12a840aad8045caef4c62", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "clamp_003976"}, "id": "code_003976_clamp_003976", "license": "Apache-2.0", "prompt": "Write a Python function clamp_003976(x, lo, hi) that clips x into the inclusive interval [lo, hi]. It must raise ValueError if lo > hi. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "clamp_003976"}, "verifier": {"function": "clamp_003976", "tests": ["assert clamp_003976(5, 0, 10) == 5", "assert clamp_003976(-2, 0, 10) == 0", "assert clamp_003976(12, 0, 10) == 10", "try:\n    clamp_003976(1, 3, 2)\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: recurrence, objective, tie_breaking_rule.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"recurrence\", \"objective\", \"tie_breaking_rule\"]}", "dedupe_signature": "3bb495cd703cb6a9088f15e2cfdf704d160fdb1061a2f60ee0e7b46b685fde98", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["recurrence", "objective", "tie_breaking_rule"]}, "id": "abstain_003977_recurrence_objective_tie_breaking_rule", "license": "Apache-2.0", "prompt": "Write a dynamic-programming solver for a segmentation scoring problem with 1215 items and budget 95770, but the recurrence, objective, and tie-breaking rule are all absent. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: recurrence, objective, tie_breaking_rule.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["recurrence", "objective", "tie_breaking_rule"]}, "verifier": {"missing": ["recurrence", "objective", "tie_breaking_rule"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 11.45^2 and multiply by 0.5 * 6.8.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 445.7485, \"unit\": \"J\"}", "dedupe_signature": "13f7cee2993c9c9dac7bebf0814be480d913a54be31609ef4534ebdb0143b6cf", "difficulty": "easy", "final_answer": {"answer": 445.7485, "unit": "J"}, "id": "ke_003979_6.8_11.45", "license": "Apache-2.0", "prompt": "A body of mass 6.8 kg moves at 11.45 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 11.45^2 and multiply by 0.5 * 6.8.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 6.8, "velocity": 11.45}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=32 degrees through the sine of 2 theta.\n3. Substitute v=75.1 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 516.7388, \"unit\": \"m\"}", "dedupe_signature": "5d4d8d15a0dfd63fcd30aa2fab56117d2b7fb9198439f5fc07de193ea6bd19fd", "difficulty": "medium", "final_answer": {"answer": 516.7388, "unit": "m"}, "id": "projectile_range_003980_75.1_32", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 75.1 m/s and angle 32 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=32 degrees through the sine of 2 theta.\nSubstitute v=75.1 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 32, "gravity": 9.81, "speed": 75.1}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 3.37 * 8.314 * 503 / 38.4.\nFinal: {\"answer\": 367.009, \"unit\": \"kPa\"}", "dedupe_signature": "ca6128db059076ea76a619ce5bb957180c2592eec1c59efeadc44e13e60d9e59", "difficulty": "medium", "final_answer": {"answer": 367.009, "unit": "kPa"}, "id": "ideal_gas_003981_3.37_503_38.4", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=3.37 mol, T=503 K, and V=38.4 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 3.37 * 8.314 * 503 / 38.4.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 3.37, "temp_k": 503, "volume_l": 38.4}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1115 * 3.13 * 76.\nFinal: {\"answer\": 265236.2, \"unit\": \"J\"}", "dedupe_signature": "b543798a5adcf133b97f8057a3e5485aed93cd96b576824de56568b3893c35b3", "difficulty": "easy", "final_answer": {"answer": 265236.2, "unit": "J"}, "id": "heat_q_003982_1115_3.13_76", "license": "Apache-2.0", "prompt": "A 1115 g sample has specific heat 3.13 J/(g*K). How much heat is needed to raise its temperature by 76 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1115 * 3.13 * 76.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 76, "heat_capacity": 3.13, "mass_g": 1115}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=27.2 V and R=87.3 ohm.\nFinal: {\"answer\": 8.4747, \"unit\": \"W\"}", "dedupe_signature": "0bcd70679f56ec5f15342e506b1f02a0a0b6eba60179f5c22537cf6330c6867a", "difficulty": "easy", "final_answer": {"answer": 8.4747, "unit": "W"}, "id": "ohm_power_003983_27.2_87.3", "license": "Apache-2.0", "prompt": "A resistor has resistance 87.3 ohm and voltage 27.2 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=27.2 V and R=87.3 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 87.3, "voltage": 27.2}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=115.5 mg, t=255 h, and T_half=92 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 16.9124, \"unit\": \"mg\"}", "dedupe_signature": "0c4bddc0e4847c7c8a1e8f0289441c7f9b605723dc587eb5b62f62dd8d95c416", "difficulty": "medium", "final_answer": {"answer": 16.9124, "unit": "mg"}, "id": "half_life_003984_115.5_92_255", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 115.5 mg. Its half-life is 92 hours. How many mg remain after 255 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=115.5 mg, t=255 h, and T_half=92 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 255.0, "half_life": 92.0, "initial_amount": 115.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 1.06 mol * 180.156 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 190.9654, \"unit\": \"g\"}", "dedupe_signature": "a86fd7ad8731e806182c5004841dd2c4d2f4aac4520a7eeaf2472230ab94141c", "difficulty": "medium", "final_answer": {"answer": 190.9654, "unit": "g"}, "id": "stoich_mass_003985_glucose_1.06", "license": "Apache-2.0", "prompt": "A sample contains 1.06 mol of glucose. Using molar mass 180.156 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 1.06 mol * 180.156 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "glucose", "molar_mass": 180.156, "moles": 1.06}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 4825 mL to 4.825 L.\n3. Compute M = 0.175 / 4.825.\nFinal: {\"answer\": 0.0363, \"unit\": \"mol/L\"}", "dedupe_signature": "b78535ac56b2b483d21cf02dc40cfe711a473b74647d2ddf3796c302f74c5f67", "difficulty": "medium", "final_answer": {"answer": 0.0363, "unit": "mol/L"}, "id": "molarity_003986_0.175_4825", "license": "Apache-2.0", "prompt": "A solution contains 0.175 mol of solute in 4825 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 4825 mL to 4.825 L.\nCompute M = 0.175 / 4.825.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 0.175, "volume_ml": 4825}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.92 y, so each step multiplies y by 1 - h*0.92.\n3. Apply that update for 3 steps and round the final state.\nFinal: {\"answer\": -2.5111, \"unit\": \"state_units\"}", "dedupe_signature": "bc75fbc896d3b19e6a514fbc7a80c36549a3d671a229ddb28ee5e74866fc6c79", "difficulty": "medium", "final_answer": {"answer": -2.5111, "unit": "state_units"}, "id": "euler_decay_003987_6_0.92_1.9_3", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.92 y with y(0)=6, step size h=1.9, for 3 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.92 y, so each step multiplies y by 1 - h*0.92.\nApply that update for 3 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 6.0, "rate": 0.92, "step": 1.9, "steps": 3}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(1.6)=-20.96 and f(7)=-32.3.\n3. The interval width is 5.4.\nFinal: {\"answer\": -143.802, \"unit\": \"area_units\"}", "dedupe_signature": "1212190375b4dd35c6ab094e565f734cb17084a887c0a03906439437f5007ae2", "difficulty": "medium", "final_answer": {"answer": -143.802, "unit": "area_units"}, "id": "trapz_linear_003988_-2.1_-17.6_1.6_7", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-2.1x+-17.6 from x=1.6 to x=7. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(1.6)=-20.96 and f(7)=-32.3.\nThe interval width is 5.4.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -17.6, "slope": -2.1, "x0": 1.6, "x1": 7.0}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.04 and add it to the current value.\nFinal: {\"answer\": [-0.956, 0.878, -0.93], \"unit\": \"temperature_units\"}", "dedupe_signature": "4f0086a42e751d17a0c7b346147ada5217f29b2127346c6e6e93a07d40e6cd6e", "difficulty": "hard", "final_answer": {"answer": [-0.956, 0.878, -0.93], "unit": "temperature_units"}, "id": "heat_step_003989_0.04_-0.8_-1.05_1.05_-1.15_2.15", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-0.8, right=2.15; current interior values are [-1.05, 1.05, -1.15]. Use r=0.04. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.04 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-1.05, 1.05, -1.15], "left": -0.8, "r": 0.04, "right": 2.15}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 100 centimeters in one meter.\n2. Apply the conversion factor directly to the given value.\n3. Compute 2601.5 / 100.\nFinal: {\"answer\": 26.015, \"unit\": \"m\"}", "dedupe_signature": "d8c68497b0fa72ae16e41e5c545c909b2e0c7d24997d57d0308dccf0e991300e", "difficulty": "easy", "final_answer": {"answer": 26.015, "unit": "m"}, "id": "unit_convert_003990_cm_to_m_2601.5", "license": "Apache-2.0", "prompt": "Convert 2601.5 cm to m. Return the converted value with unit.", "reasoning_trace": "There are 100 centimeters in one meter.\nApply the conversion factor directly to the given value.\nCompute 2601.5 / 100.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 2601.5}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=7 degrees and keep the unit as newtons.\nFinal: {\"answer\": [251.6104, 30.8939], \"unit\": \"N\"}", "dedupe_signature": "f422636d2c2adbb168400652acad9ff2141ad96687edc42f4fd1396169e23fe1", "difficulty": "medium", "final_answer": {"answer": [251.6104, 30.8939], "unit": "N"}, "id": "vector_components_003991_253.5_7", "license": "Apache-2.0", "prompt": "A vector has magnitude 253.5 N at 7 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=7 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 7, "magnitude": 253.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. lever arm times force has torque dimensions\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "8061f09d6236558a6f06c7cb408ec98f0f1416a5e4bce3f7c7dfb71285993208", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_003993_consistent_5ca82cb9_296503", "license": "Apache-2.0", "prompt": "In lab notebook case 296503, check dimensional consistency for tau = r * F. The left side has dimensions N*m and the right side has dimensions N*m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nlever arm times force has torque dimensions\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "tau = r * F"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef weighted_sum_003994(values, weights):\n    if len(values) != len(weights):\n        raise ValueError('length mismatch')\n    return sum(value * weight for value, weight in zip(values, weights))\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"weighted_sum_003994\"}", "dedupe_signature": "83c0a2db76535db0f085a756c7d2c5315b22e820d7d9c22d73696799695026a2", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "weighted_sum_003994"}, "id": "code_003994_weighted_sum_003994", "license": "Apache-2.0", "prompt": "Write a Python function weighted_sum_003994(values, weights) that returns sum(value*weight). Raise ValueError when the two inputs have different lengths. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "weighted_sum_003994"}, "verifier": {"function": "weighted_sum_003994", "tests": ["assert weighted_sum_003994([2, 3], [4, 5]) == 23", "assert weighted_sum_003994([], []) == 0", "try:\n    weighted_sum_003994([1], [1, 2])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: required_fields, allowed_transformations.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"required_fields\", \"allowed_transformations\"]}", "dedupe_signature": "c2fff698b79cc67c3ea2fc0c80ff92243fc5184aaf6adf9df633a062bc17e375", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["required_fields", "allowed_transformations"]}, "id": "abstain_003995_required_fields_allowed_transformations", "license": "Apache-2.0", "prompt": "Write a sanitizer for valid field sensor records in release 992062, but the prompt does not state which fields are required or which transformations are allowed. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: required_fields, allowed_transformations.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["required_fields", "allowed_transformations"]}, "verifier": {"missing": ["required_fields", "allowed_transformations"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 6.75 kg and a = 7.85 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 52.9875, \"unit\": \"N\"}", "dedupe_signature": "96bd6ac4afcccda73b5aa0e03e9885ba32ac948ea23aa5bcd7df78ebc50689d8", "difficulty": "easy", "final_answer": {"answer": 52.9875, "unit": "N"}, "id": "force_003996_6.75_7.85", "license": "Apache-2.0", "prompt": "A cart has mass 6.75 kg and measured acceleration 7.85 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 6.75 kg and a = 7.85 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 7.85, "mass": 6.75}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 23.65^2 and multiply by 0.5 * 15.25.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 4264.8341, \"unit\": \"J\"}", "dedupe_signature": "b9865ad9a7c14218424ede75303d2c6e696b7430a4c90f6e59ab89426fc7d59b", "difficulty": "easy", "final_answer": {"answer": 4264.8341, "unit": "J"}, "id": "ke_003997_15.25_23.65", "license": "Apache-2.0", "prompt": "A body of mass 15.25 kg moves at 23.65 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 23.65^2 and multiply by 0.5 * 15.25.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 15.25, "velocity": 23.65}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=6 degrees through the sine of 2 theta.\n3. Substitute v=59.9 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 76.0438, \"unit\": \"m\"}", "dedupe_signature": "e3c8099ce28457d006a6bdeb43f2b1babc7495530bf68bc0849848aeba611891", "difficulty": "medium", "final_answer": {"answer": 76.0438, "unit": "m"}, "id": "projectile_range_003998_59.9_6", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 59.9 m/s and angle 6 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=6 degrees through the sine of 2 theta.\nSubstitute v=59.9 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 6, "gravity": 9.81, "speed": 59.9}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1780 * 2.19 * 97.\nFinal: {\"answer\": 378125.4, \"unit\": \"J\"}", "dedupe_signature": "ec8ef13c252729eacc0309ef3b5f2076434d16e23cea503fdd5222ed5c5a4bb7", "difficulty": "easy", "final_answer": {"answer": 378125.4, "unit": "J"}, "id": "heat_q_004000_1780_2.19_97", "license": "Apache-2.0", "prompt": "A 1780 g sample has specific heat 2.19 J/(g*K). How much heat is needed to raise its temperature by 97 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1780 * 2.19 * 97.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 97, "heat_capacity": 2.19, "mass_g": 1780}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=126.4 V and R=94.8 ohm.\nFinal: {\"answer\": 168.5333, \"unit\": \"W\"}", "dedupe_signature": "edf2649f17c2853e2a2a6c92b9572bde8d360317788ca276ce710369354a5385", "difficulty": "easy", "final_answer": {"answer": 168.5333, "unit": "W"}, "id": "ohm_power_004001_126.4_94.8", "license": "Apache-2.0", "prompt": "A resistor has resistance 94.8 ohm and voltage 126.4 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=126.4 V and R=94.8 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 94.8, "voltage": 126.4}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=888 mg, t=272.5 h, and T_half=14.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 0.002, \"unit\": \"mg\"}", "dedupe_signature": "817231b50f2a03fc6980335f93d8d37d0e948472747051e14d9550c6f7a17fd3", "difficulty": "medium", "final_answer": {"answer": 0.002, "unit": "mg"}, "id": "half_life_004002_888_14.5_272.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 888 mg. Its half-life is 14.5 hours. How many mg remain after 272.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=888 mg, t=272.5 h, and T_half=14.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 272.5, "half_life": 14.5, "initial_amount": 888.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 1.07 mol * 180.156 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 192.7669, \"unit\": \"g\"}", "dedupe_signature": "1731d10682784ad9b0f6cf5a5239076721125be68666a3df2e13bbd88356df09", "difficulty": "medium", "final_answer": {"answer": 192.7669, "unit": "g"}, "id": "stoich_mass_004003_glucose_1.07", "license": "Apache-2.0", "prompt": "A sample contains 1.07 mol of glucose. Using molar mass 180.156 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 1.07 mol * 180.156 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "glucose", "molar_mass": 180.156, "moles": 1.07}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 3520 mL to 3.52 L.\n3. Compute M = 2.93 / 3.52.\nFinal: {\"answer\": 0.8324, \"unit\": \"mol/L\"}", "dedupe_signature": "2f7bcaebd011f5a15076885ac62f821d3dc2b967eeeb27f08166f42b14817860", "difficulty": "medium", "final_answer": {"answer": 0.8324, "unit": "mol/L"}, "id": "molarity_004004_2.93_3520", "license": "Apache-2.0", "prompt": "A solution contains 2.93 mol of solute in 3520 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 3520 mL to 3.52 L.\nCompute M = 2.93 / 3.52.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 2.93, "volume_ml": 3520}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.29 y, so each step multiplies y by 1 - h*0.29.\n3. Apply that update for 8 steps and round the final state.\nFinal: {\"answer\": 3.5194, \"unit\": \"state_units\"}", "dedupe_signature": "d5e4d302b211e99675fd218847e2b1fd28dd2ca4f2d501614977d6b443f806b1", "difficulty": "medium", "final_answer": {"answer": 3.5194, "unit": "state_units"}, "id": "euler_decay_004005_54.5_0.29_1_8", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.29 y with y(0)=54.5, step size h=1, for 8 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.29 y, so each step multiplies y by 1 - h*0.29.\nApply that update for 8 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 54.5, "rate": 0.29, "step": 1.0, "steps": 8}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(8.5)=77.65 and f(11.1)=96.11.\n3. The interval width is 2.6.\nFinal: {\"answer\": 225.888, \"unit\": \"area_units\"}", "dedupe_signature": "08407b53f8b8fb885f76715df7382a09ed95c61b5a3f7a02a779db31910f73c2", "difficulty": "medium", "final_answer": {"answer": 225.888, "unit": "area_units"}, "id": "trapz_linear_004006_7.1_17.3_8.5_11.1", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=7.1x+17.3 from x=8.5 to x=11.1. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(8.5)=77.65 and f(11.1)=96.11.\nThe interval width is 2.6.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 17.3, "slope": 7.1, "x0": 8.5, "x1": 11.1}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=273 degrees and keep the unit as newtons.\nFinal: {\"answer\": [22.426, -427.9128], \"unit\": \"N\"}", "dedupe_signature": "08d675f13e26193927d36b33b70f699e907902468d3151083753e181bacb32ea", "difficulty": "medium", "final_answer": {"answer": [22.426, -427.9128], "unit": "N"}, "id": "vector_components_004009_428.5_273", "license": "Apache-2.0", "prompt": "A vector has magnitude 428.5 N at 273 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=273 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 273, "magnitude": 428.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [0.3, 19.25], \"unit\": \"dimensionless\"}", "dedupe_signature": "7184d2dc1e17227062bb4724f808461e9364195fb7da66ef5bbfa97c1c8d4f3b", "difficulty": "medium", "final_answer": {"answer": [0.3, 19.25], "unit": "dimensionless"}, "id": "line_two_point_004010_17.25_19.25_0.3_19.25", "license": "Apache-2.0", "prompt": "A line passes through points (17.25, 24.425) and (19.25, 25.025). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 17.25, "x2": 19.25, "y1": 24.425, "y2": 25.025}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. amount times volume is not concentration\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "cf798ff38515d9a9c9ac98d94e563c6a4f72583719a3a3c556a810da1e0823c9", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_004011_inconsistent_74ac0b02_67694", "license": "Apache-2.0", "prompt": "In model card equation case 67694, check dimensional consistency for C = n * V. The left side has dimensions mol/L and the right side has dimensions mol*L. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\namount times volume is not concentration\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "C = n * V"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef weighted_sum_004012(values, weights):\n    if len(values) != len(weights):\n        raise ValueError('length mismatch')\n    return sum(value * weight for value, weight in zip(values, weights))\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"weighted_sum_004012\"}", "dedupe_signature": "305190723c909086dc8191c936d9149761fc3437845c45cfc16165d3a0f1b1aa", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "weighted_sum_004012"}, "id": "code_004012_weighted_sum_004012", "license": "Apache-2.0", "prompt": "Write a Python function weighted_sum_004012(values, weights) that returns sum(value*weight). Raise ValueError when the two inputs have different lengths. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "weighted_sum_004012"}, "verifier": {"function": "weighted_sum_004012", "tests": ["assert weighted_sum_004012([2, 3], [4, 5]) == 23", "assert weighted_sum_004012([], []) == 0", "try:\n    weighted_sum_004012([1], [1, 2])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: volume.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"volume\"]}", "dedupe_signature": "a3f5a485655e2cd90f7872518b370267d6cc6d419296bf7156a61f57b81a7c92", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["volume"]}, "id": "abstain_004013_volume", "license": "Apache-2.0", "prompt": "Compute pressure from the ideal gas law. The prompt gives n=0.56 mol and T=319 K, but does not give volume. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: volume.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["volume"]}, "verifier": {"missing": ["volume"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 9.9 kg and a = 9.3 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 92.07, \"unit\": \"N\"}", "dedupe_signature": "932dd5bdf7fdfc74cedd021793755d5ac8b4a4d0a0e9441e492969fa5c4fef24", "difficulty": "easy", "final_answer": {"answer": 92.07, "unit": "N"}, "id": "force_004014_9.9_9.3", "license": "Apache-2.0", "prompt": "A cart has mass 9.9 kg and measured acceleration 9.3 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 9.9 kg and a = 9.3 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 9.3, "mass": 9.9}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 18.65^2 and multiply by 0.5 * 12.15.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 2113.0217, \"unit\": \"J\"}", "dedupe_signature": "52678954b0be878ec48ce72171db23d3bedad526e83c44a124a242c1c839c0d8", "difficulty": "easy", "final_answer": {"answer": 2113.0217, "unit": "J"}, "id": "ke_004015_12.15_18.65", "license": "Apache-2.0", "prompt": "A body of mass 12.15 kg moves at 18.65 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 18.65^2 and multiply by 0.5 * 12.15.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 12.15, "velocity": 18.65}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1770 * 0.905 * 52.\nFinal: {\"answer\": 83296.2, \"unit\": \"J\"}", "dedupe_signature": "9d08446f7cc66939092eb5d7659834add2a5d68f63733a3d945381ab136cb38e", "difficulty": "easy", "final_answer": {"answer": 83296.2, "unit": "J"}, "id": "heat_q_004018_1770_0.905_52", "license": "Apache-2.0", "prompt": "A 1770 g sample has specific heat 0.905 J/(g*K). How much heat is needed to raise its temperature by 52 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1770 * 0.905 * 52.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 52, "heat_capacity": 0.905, "mass_g": 1770}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=103.2 V and R=177.6 ohm.\nFinal: {\"answer\": 59.9676, \"unit\": \"W\"}", "dedupe_signature": "a8301d6ec2995a95adab8b95b0ef7968eb04fd760da29161740cad244638daab", "difficulty": "easy", "final_answer": {"answer": 59.9676, "unit": "W"}, "id": "ohm_power_004019_103.2_177.6", "license": "Apache-2.0", "prompt": "A resistor has resistance 177.6 ohm and voltage 103.2 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=103.2 V and R=177.6 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 177.6, "voltage": 103.2}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 5.62 mol * 44.01 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 247.3362, \"unit\": \"g\"}", "dedupe_signature": "90b3b7f2b98d71c216eecfcf3880737561dc2d945d88e81330a3e3474c6c1e88", "difficulty": "medium", "final_answer": {"answer": 247.3362, "unit": "g"}, "id": "stoich_mass_004021_carbon_dioxide_5.62", "license": "Apache-2.0", "prompt": "A sample contains 5.62 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 5.62 mol * 44.01 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "carbon dioxide", "molar_mass": 44.01, "moles": 5.62}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 4960 mL to 4.96 L.\n3. Compute M = 0.805 / 4.96.\nFinal: {\"answer\": 0.1623, \"unit\": \"mol/L\"}", "dedupe_signature": "69c016069cda73fe06e50f6606a4354343a65e24b663babc9e684346c6e56d2a", "difficulty": "medium", "final_answer": {"answer": 0.1623, "unit": "mol/L"}, "id": "molarity_004022_0.805_4960", "license": "Apache-2.0", "prompt": "A solution contains 0.805 mol of solute in 4960 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 4960 mL to 4.96 L.\nCompute M = 0.805 / 4.96.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 0.805, "volume_ml": 4960}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.49 y, so each step multiplies y by 1 - h*0.49.\n3. Apply that update for 6 steps and round the final state.\nFinal: {\"answer\": 0.5855, \"unit\": \"state_units\"}", "dedupe_signature": "3569ca622886e756db724fe5a498d22464b9685537bd329cd9bf114032a2644b", "difficulty": "medium", "final_answer": {"answer": 0.5855, "unit": "state_units"}, "id": "euler_decay_004023_61_0.49_1.1_6", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.49 y with y(0)=61, step size h=1.1, for 6 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.49 y, so each step multiplies y by 1 - h*0.49.\nApply that update for 6 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 61.0, "rate": 0.49, "step": 1.1, "steps": 6}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.34 and add it to the current value.\nFinal: {\"answer\": [1.393, 0.088, 0.841], \"unit\": \"temperature_units\"}", "dedupe_signature": "79fdcf9e786e3eba3ba2df2129bed7c44379cdd4398bc262b8469216c2223fd8", "difficulty": "hard", "final_answer": {"answer": [1.393, 0.088, 0.841], "unit": "temperature_units"}, "id": "heat_step_004025_0.34_2.5_0.05_1.55_-1.25_2.1", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=2.5, right=2.1; current interior values are [0.05, 1.55, -1.25]. Use r=0.34. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.34 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [0.05, 1.55, -1.25], "left": 2.5, "r": 0.34, "right": 2.1}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 100 centimeters in one meter.\n2. Apply the conversion factor directly to the given value.\n3. Compute 3200.0 / 100.\nFinal: {\"answer\": 32.0, \"unit\": \"m\"}", "dedupe_signature": "672ece0850ce123802c50579498ee85a5a2cde50c12396c35754c97456cadefe", "difficulty": "easy", "final_answer": {"answer": 32.0, "unit": "m"}, "id": "unit_convert_004026_cm_to_m_3200", "license": "Apache-2.0", "prompt": "Convert 3200 cm to m. Return the converted value with unit.", "reasoning_trace": "There are 100 centimeters in one meter.\nApply the conversion factor directly to the given value.\nCompute 3200.0 / 100.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 3200.0}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=27 degrees and keep the unit as newtons.\nFinal: {\"answer\": [240.5718, 122.5774], \"unit\": \"N\"}", "dedupe_signature": "990a3926881fb2cd65d7c388b281b543bc94332569401d441d543e3c676faf5c", "difficulty": "medium", "final_answer": {"answer": [240.5718, 122.5774], "unit": "N"}, "id": "vector_components_004027_270_27", "license": "Apache-2.0", "prompt": "A vector has magnitude 270 N at 27 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=27 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 27, "magnitude": 270.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. volt squared divided by ohm is watt\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "083ad4ea6714701996d3dfe82e885d39f6f331e09eb176e3f2bad88488b31dc6", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_004029_consistent_82e93f3d_426930", "license": "Apache-2.0", "prompt": "In quality-control check case 426930, check dimensional consistency for P = V^2 / R. The left side has dimensions W and the right side has dimensions W. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nvolt squared divided by ohm is watt\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "P = V^2 / R"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef threshold_flags_004030(values, threshold):\n    return [value >= threshold for value in values]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"threshold_flags_004030\"}", "dedupe_signature": "50996d0aebb926addaef47c77b72777541aa9c54cd24227d2604c52dc571537a", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "threshold_flags_004030"}, "id": "code_004030_threshold_flags_004030", "license": "Apache-2.0", "prompt": "Write a Python function threshold_flags_004030(values, threshold) that returns a list of booleans showing whether each value is greater than or equal to threshold. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "threshold_flags_004030"}, "verifier": {"function": "threshold_flags_004030", "tests": ["assert threshold_flags_004030([1, 2, 3], 2) == [False, True, True]", "assert threshold_flags_004030([], 5) == []", "assert threshold_flags_004030([-1, 0], 0) == [False, True]"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: volume.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"volume\"]}", "dedupe_signature": "8bf4c701a505a504ea7d9573a9e9dc3daf9b30226a6cdabebbcf11c732c121c7", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["volume"]}, "id": "abstain_004031_volume", "license": "Apache-2.0", "prompt": "Compute pressure from the ideal gas law. The prompt gives n=5.59 mol and T=490 K, but does not give volume. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: volume.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["volume"]}, "verifier": {"missing": ["volume"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 22.15 kg and a = 13.05 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 289.0575, \"unit\": \"N\"}", "dedupe_signature": "cc7f3cc1142e9daa9d68d6c2afeb00adb9f3506f765257e1a44391fc60bc6cd7", "difficulty": "easy", "final_answer": {"answer": 289.0575, "unit": "N"}, "id": "force_004032_22.15_13.05", "license": "Apache-2.0", "prompt": "A cart has mass 22.15 kg and measured acceleration 13.05 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 22.15 kg and a = 13.05 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 13.05, "mass": 22.15}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 9.4^2 and multiply by 0.5 * 24.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 1060.32, \"unit\": \"J\"}", "dedupe_signature": "9351a56e76fa159096052919fa810302ac8255050aedfd81025b02c8de3b5807", "difficulty": "easy", "final_answer": {"answer": 1060.32, "unit": "J"}, "id": "ke_004033_24_9.4", "license": "Apache-2.0", "prompt": "A body of mass 24 kg moves at 9.4 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 9.4^2 and multiply by 0.5 * 24.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 24.0, "velocity": 9.4}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=9 degrees through the sine of 2 theta.\n3. Substitute v=30.8 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 29.8824, \"unit\": \"m\"}", "dedupe_signature": "8b34e50de2fd73f4efc6ec70018de1b4ca123e5cb3da763c4193cc765f19ed1b", "difficulty": "medium", "final_answer": {"answer": 29.8824, "unit": "m"}, "id": "projectile_range_004034_30.8_9", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 30.8 m/s and angle 9 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=9 degrees through the sine of 2 theta.\nSubstitute v=30.8 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 9, "gravity": 9.81, "speed": 30.8}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 605 * 4.095 * 94.\nFinal: {\"answer\": 232882.65, \"unit\": \"J\"}", "dedupe_signature": "cb079c614197c9bae10063d2c8e4953a1393790641caba89071bfcf01c746fbd", "difficulty": "easy", "final_answer": {"answer": 232882.65, "unit": "J"}, "id": "heat_q_004036_605_4.095_94", "license": "Apache-2.0", "prompt": "A 605 g sample has specific heat 4.095 J/(g*K). How much heat is needed to raise its temperature by 94 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 605 * 4.095 * 94.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 94, "heat_capacity": 4.095, "mass_g": 605}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=78.4 V and R=82.1 ohm.\nFinal: {\"answer\": 74.8667, \"unit\": \"W\"}", "dedupe_signature": "0141cdd3f78d14db4c100d74401e3fc07010f81f2fc8c5cc0760fc818d653e4f", "difficulty": "easy", "final_answer": {"answer": 74.8667, "unit": "W"}, "id": "ohm_power_004037_78.4_82.1", "license": "Apache-2.0", "prompt": "A resistor has resistance 82.1 ohm and voltage 78.4 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=78.4 V and R=82.1 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 82.1, "voltage": 78.4}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=790 mg, t=154.5 h, and T_half=53 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 104.7361, \"unit\": \"mg\"}", "dedupe_signature": "8a9496c012c2fcbc7e1f35d8f4069d153885d929ff52c58f518747da07d65c69", "difficulty": "medium", "final_answer": {"answer": 104.7361, "unit": "mg"}, "id": "half_life_004038_790_53_154.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 790 mg. Its half-life is 53 hours. How many mg remain after 154.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=790 mg, t=154.5 h, and T_half=53 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 154.5, "half_life": 53.0, "initial_amount": 790.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 5.57 mol * 100.087 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 557.4846, \"unit\": \"g\"}", "dedupe_signature": "00d94714ff423a06139853a6e12201c410d45c9468e9595b2d731fa3485129f7", "difficulty": "medium", "final_answer": {"answer": 557.4846, "unit": "g"}, "id": "stoich_mass_004039_calcium_carbonate_5.57", "license": "Apache-2.0", "prompt": "A sample contains 5.57 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 5.57 mol * 100.087 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "calcium carbonate", "molar_mass": 100.087, "moles": 5.57}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 185 mL to 0.185 L.\n3. Compute M = 0.525 / 0.185.\nFinal: {\"answer\": 2.8378, \"unit\": \"mol/L\"}", "dedupe_signature": "ac33ba499108f629519a4c1cc74f1c98a60193d935e39f29e4441e2a7fe9f170", "difficulty": "medium", "final_answer": {"answer": 2.8378, "unit": "mol/L"}, "id": "molarity_004040_0.525_185", "license": "Apache-2.0", "prompt": "A solution contains 0.525 mol of solute in 185 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 185 mL to 0.185 L.\nCompute M = 0.525 / 0.185.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 0.525, "volume_ml": 185}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.79 y, so each step multiplies y by 1 - h*0.79.\n3. Apply that update for 12 steps and round the final state.\nFinal: {\"answer\": 0.0, \"unit\": \"state_units\"}", "dedupe_signature": "bab6bb54527e64306686543495bc9608f3f62bfbc22f5b1cee6557448f398678", "difficulty": "medium", "final_answer": {"answer": 0.0, "unit": "state_units"}, "id": "euler_decay_004041_20.5_0.79_1.35_12", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.79 y with y(0)=20.5, step size h=1.35, for 12 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.79 y, so each step multiplies y by 1 - h*0.79.\nApply that update for 12 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 20.5, "rate": 0.79, "step": 1.35, "steps": 12}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.12 and add it to the current value.\nFinal: {\"answer\": [0.052, -1.246, -1.632], \"unit\": \"temperature_units\"}", "dedupe_signature": "253d2193b9ab38fe2c5a65d14eeb3c46aa0f1d2c69de7a7ee655b1862bf0cf00", "difficulty": "hard", "final_answer": {"answer": [0.052, -1.246, -1.632], "unit": "temperature_units"}, "id": "heat_step_004043_0.12_3.0_-0.2_-1.3_-1.95_0.05", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=3, right=0.05; current interior values are [-0.2, -1.3, -1.95]. Use r=0.12. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.12 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-0.2, -1.3, -1.95], "left": 3.0, "r": 0.12, "right": 0.05}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 100 centimeters in one meter.\n2. Apply the conversion factor directly to the given value.\n3. Compute 4327.5 / 100.\nFinal: {\"answer\": 43.275, \"unit\": \"m\"}", "dedupe_signature": "75bf9357956bcaa39182463458d185d86912952f288a96f3fa4a844a1bcb7ede", "difficulty": "easy", "final_answer": {"answer": 43.275, "unit": "m"}, "id": "unit_convert_004044_cm_to_m_4327.5", "license": "Apache-2.0", "prompt": "Convert 4327.5 cm to m. Return the converted value with unit.", "reasoning_trace": "There are 100 centimeters in one meter.\nApply the conversion factor directly to the given value.\nCompute 4327.5 / 100.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 4327.5}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=134 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-297.3138, 307.8774], \"unit\": \"N\"}", "dedupe_signature": "39777b3d85d3e1739ea3843b1924a4b08b825500b6e4308595331aa64dc1c3a5", "difficulty": "medium", "final_answer": {"answer": [-297.3138, 307.8774], "unit": "N"}, "id": "vector_components_004045_428_134", "license": "Apache-2.0", "prompt": "A vector has magnitude 428 N at 134 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=134 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 134, "magnitude": 428.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [1.65, -24.0], \"unit\": \"dimensionless\"}", "dedupe_signature": "9c222916a6719c37ddf2f6621683b1a6167c6f2b727fa06facc190e0c52ee6a2", "difficulty": "medium", "final_answer": {"answer": [1.65, -24.0], "unit": "dimensionless"}, "id": "line_two_point_004046_0_1.5_1.65_-24", "license": "Apache-2.0", "prompt": "A line passes through points (0, -24) and (1.5, -21.525). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 0.0, "x2": 1.5, "y1": -24.0, "y2": -21.525}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. density times acceleration times height gives kg/(m*s^2), or pascal\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "846619239b7cb72be11285fdad7d115a4e5141e7fbf75be601c9a13bc28c8a49", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_004047_consistent_b7d3eed1_637547", "license": "Apache-2.0", "prompt": "In simulation spec case 637547, check dimensional consistency for p = rho * g * h. The left side has dimensions Pa and the right side has dimensions Pa. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\ndensity times acceleration times height gives kg/(m*s^2), or pascal\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "p = rho * g * h"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef weighted_sum_004048(values, weights):\n    if len(values) != len(weights):\n        raise ValueError('length mismatch')\n    return sum(value * weight for value, weight in zip(values, weights))\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"weighted_sum_004048\"}", "dedupe_signature": "e5a6db45491e2184d0d3e7a4d51c68fdbcb406b805a5e47ba706ffb904e4a7be", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "weighted_sum_004048"}, "id": "code_004048_weighted_sum_004048", "license": "Apache-2.0", "prompt": "Write a Python function weighted_sum_004048(values, weights) that returns sum(value*weight). Raise ValueError when the two inputs have different lengths. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "weighted_sum_004048"}, "verifier": {"function": "weighted_sum_004048", "tests": ["assert weighted_sum_004048([2, 3], [4, 5]) == 23", "assert weighted_sum_004048([], []) == 0", "try:\n    weighted_sum_004048([1], [1, 2])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: target_schema, valid_examples.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"target_schema\", \"valid_examples\"]}", "dedupe_signature": "e33bf463e81609fa978eaebc1fdfd8507188a721edab8227f9612bd2ba93f0ff", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["target_schema", "valid_examples"]}, "id": "abstain_004049_target_schema_valid_examples", "license": "Apache-2.0", "prompt": "Write a parser that converts each mobile clinical record from batch 406004 into the correct schema, but the prompt does not include the target schema or examples. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: target_schema, valid_examples.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["target_schema", "valid_examples"]}, "verifier": {"missing": ["target_schema", "valid_examples"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 10.45 kg and a = 3 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 31.35, \"unit\": \"N\"}", "dedupe_signature": "fc2f7757d96ee43b260c3799b1b24f5f7c4641aae7df63cb5f7b269912733e05", "difficulty": "easy", "final_answer": {"answer": 31.35, "unit": "N"}, "id": "force_004050_10.45_3", "license": "Apache-2.0", "prompt": "A cart has mass 10.45 kg and measured acceleration 3 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 10.45 kg and a = 3 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 3.0, "mass": 10.45}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 3.45^2 and multiply by 0.5 * 13.4.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 79.7468, \"unit\": \"J\"}", "dedupe_signature": "7c0c398bb5eb353aaf6fac298bfd40fa2f2020e7aa43485cfd6d0c86a2ed7488", "difficulty": "easy", "final_answer": {"answer": 79.7468, "unit": "J"}, "id": "ke_004051_13.4_3.45", "license": "Apache-2.0", "prompt": "A body of mass 13.4 kg moves at 3.45 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 3.45^2 and multiply by 0.5 * 13.4.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 13.4, "velocity": 3.45}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=78 degrees through the sine of 2 theta.\n3. Substitute v=56.7 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 133.2939, \"unit\": \"m\"}", "dedupe_signature": "87bb9c85f5d04cb4a07076ad9add85bd2946157a172ac5999382a9f9c95f317b", "difficulty": "medium", "final_answer": {"answer": 133.2939, "unit": "m"}, "id": "projectile_range_004052_56.7_78", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 56.7 m/s and angle 78 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=78 degrees through the sine of 2 theta.\nSubstitute v=56.7 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 78, "gravity": 9.81, "speed": 56.7}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 3.22 * 8.314 * 584 / 25.7.\nFinal: {\"answer\": 608.3389, \"unit\": \"kPa\"}", "dedupe_signature": "fa5dedc1a12ee3d0b08872edf9ebf87bfc9ca9d20909460f254e2926ceb2bfb6", "difficulty": "medium", "final_answer": {"answer": 608.3389, "unit": "kPa"}, "id": "ideal_gas_004053_3.22_584_25.7", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=3.22 mol, T=584 K, and V=25.7 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 3.22 * 8.314 * 584 / 25.7.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 3.22, "temp_k": 584, "volume_l": 25.7}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=34.2 V and R=58.9 ohm.\nFinal: {\"answer\": 19.8581, \"unit\": \"W\"}", "dedupe_signature": "7f74026e2dd12fff306a263a989d9f135530080039d7c7991cc88ff5ca1a4fdb", "difficulty": "easy", "final_answer": {"answer": 19.8581, "unit": "W"}, "id": "ohm_power_004055_34.2_58.9", "license": "Apache-2.0", "prompt": "A resistor has resistance 58.9 ohm and voltage 34.2 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=34.2 V and R=58.9 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 58.9, "voltage": 34.2}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=657.5 mg, t=202.5 h, and T_half=29.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 5.6429, \"unit\": \"mg\"}", "dedupe_signature": "09f20bde725a8fa7059c99ec31334c223e25326cfddab5f8d02ab5936f15cf90", "difficulty": "medium", "final_answer": {"answer": 5.6429, "unit": "mg"}, "id": "half_life_004056_657.5_29.5_202.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 657.5 mg. Its half-life is 29.5 hours. How many mg remain after 202.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=657.5 mg, t=202.5 h, and T_half=29.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 202.5, "half_life": 29.5, "initial_amount": 657.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 6.21 mol * 18.015 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 111.8732, \"unit\": \"g\"}", "dedupe_signature": "8b5e5e2c9418103c94af45d933128428cfddcd913644f670d41a99c8c7fe71a1", "difficulty": "medium", "final_answer": {"answer": 111.8732, "unit": "g"}, "id": "stoich_mass_004057_water_6.21", "license": "Apache-2.0", "prompt": "A sample contains 6.21 mol of water. Using molar mass 18.015 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 6.21 mol * 18.015 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "water", "molar_mass": 18.015, "moles": 6.21}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 2335 mL to 2.335 L.\n3. Compute M = 2.365 / 2.335.\nFinal: {\"answer\": 1.0128, \"unit\": \"mol/L\"}", "dedupe_signature": "bf471b7607e1eeabbdedcccd9157864e74626e10ead4937098e85e66af8d1c6c", "difficulty": "medium", "final_answer": {"answer": 1.0128, "unit": "mol/L"}, "id": "molarity_004058_2.365_2335", "license": "Apache-2.0", "prompt": "A solution contains 2.365 mol of solute in 2335 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 2335 mL to 2.335 L.\nCompute M = 2.365 / 2.335.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 2.365, "volume_ml": 2335}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.58 y, so each step multiplies y by 1 - h*0.58.\n3. Apply that update for 5 steps and round the final state.\nFinal: {\"answer\": 0.1439, \"unit\": \"state_units\"}", "dedupe_signature": "ccbd4f5c5bee71855d9977bbfd44b4162e04e55e057b9676203cf126af9bbc07", "difficulty": "medium", "final_answer": {"answer": 0.1439, "unit": "state_units"}, "id": "euler_decay_004059_2.5_0.58_0.75_5", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.58 y with y(0)=2.5, step size h=0.75, for 5 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.58 y, so each step multiplies y by 1 - h*0.58.\nApply that update for 5 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 2.5, "rate": 0.58, "step": 0.75, "steps": 5}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(6.7)=25.58 and f(15.4)=72.56.\n3. The interval width is 8.7.\nFinal: {\"answer\": 426.909, \"unit\": \"area_units\"}", "dedupe_signature": "75030adf3455525381b649cafd93bfc95e0a97dc525925554c185cade28e765a", "difficulty": "medium", "final_answer": {"answer": 426.909, "unit": "area_units"}, "id": "trapz_linear_004060_5.4_-10.6_6.7_15.4", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=5.4x+-10.6 from x=6.7 to x=15.4. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(6.7)=25.58 and f(15.4)=72.56.\nThe interval width is 8.7.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -10.6, "slope": 5.4, "x0": 6.7, "x1": 15.399999999999999}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.06 and add it to the current value.\nFinal: {\"answer\": [1.65, 2.508, 0.682], \"unit\": \"temperature_units\"}", "dedupe_signature": "8fa5c6c14302efaf8216070129f9742df61df0c6fb283668b2863d6c5bbd2ab8", "difficulty": "hard", "final_answer": {"answer": [1.65, 2.508, 0.682], "unit": "temperature_units"}, "id": "heat_step_004061_0.06_-1.6_1.8_2.7_0.4_2.8", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-1.6, right=2.8; current interior values are [1.8, 2.7, 0.4]. Use r=0.06. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.06 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [1.8, 2.7, 0.4], "left": -1.6, "r": 0.06, "right": 2.8}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 18648.0 / 1000.\nFinal: {\"answer\": 18.648, \"unit\": \"kg\"}", "dedupe_signature": "9b4585940ce08ce45d8db3b7bf7af4d971c14deec7604f2703a69024ebc6858f", "difficulty": "easy", "final_answer": {"answer": 18.648, "unit": "kg"}, "id": "unit_convert_004062_g_to_kg_18648", "license": "Apache-2.0", "prompt": "Convert 18648 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 18648.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 18648.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=275 degrees and keep the unit as newtons.\nFinal: {\"answer\": [17.7362, -202.7256], \"unit\": \"N\"}", "dedupe_signature": "29afa82863cc04ce1d435006cc1b10f106442e2a0ccb41741c6199a919ef9664", "difficulty": "medium", "final_answer": {"answer": [17.7362, -202.7256], "unit": "N"}, "id": "vector_components_004063_203.5_275", "license": "Apache-2.0", "prompt": "A vector has magnitude 203.5 N at 275 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=275 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 275, "magnitude": 203.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [0.8, -22.0], \"unit\": \"dimensionless\"}", "dedupe_signature": "5bcf4a82358c5c576485887c4ec1413a6aa43d931a6c39d0bc1a24b53d4f61e2", "difficulty": "medium", "final_answer": {"answer": [0.8, -22.0], "unit": "dimensionless"}, "id": "line_two_point_004064_6_9_0.8_-22", "license": "Apache-2.0", "prompt": "A line passes through points (6, -17.2) and (9, -14.8). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 6.0, "x2": 9.0, "y1": -17.2, "y2": -14.8}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. velocity divided by time is acceleration\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "5ac7f85fc4fada3ac30543547deca5749275114483851866def1a52c98bb7f31", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_004065_inconsistent_c1271127_81840", "license": "Apache-2.0", "prompt": "In simulation spec case 81840, check dimensional consistency for x = v / t. The left side has dimensions m and the right side has dimensions m/s^2. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nvelocity divided by time is acceleration\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "x = v / t"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 12.65 kg and a = 4.25 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 53.7625, \"unit\": \"N\"}", "dedupe_signature": "9b05ed442010a5a298743c3d832eca6ddc0c8339c2fcf5cfe9d5b77a206a85e7", "difficulty": "easy", "final_answer": {"answer": 53.7625, "unit": "N"}, "id": "force_004068_12.65_4.25", "license": "Apache-2.0", "prompt": "A cart has mass 12.65 kg and measured acceleration 4.25 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 12.65 kg and a = 4.25 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 4.25, "mass": 12.65}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 22.65^2 and multiply by 0.5 * 17.65.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 4527.4236, \"unit\": \"J\"}", "dedupe_signature": "f94e2397eb00391b823fd029a3f020de1d3fc19cecbd00036102775989de94d5", "difficulty": "easy", "final_answer": {"answer": 4527.4236, "unit": "J"}, "id": "ke_004069_17.65_22.65", "license": "Apache-2.0", "prompt": "A body of mass 17.65 kg moves at 22.65 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 22.65^2 and multiply by 0.5 * 17.65.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 17.65, "velocity": 22.65}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=38 degrees through the sine of 2 theta.\n3. Substitute v=61.5 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 374.098, \"unit\": \"m\"}", "dedupe_signature": "cc3d5bdc51ed3dce8ce14657b89640ce88158127f3dd44e220139999a8f506ac", "difficulty": "medium", "final_answer": {"answer": 374.098, "unit": "m"}, "id": "projectile_range_004070_61.5_38", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 61.5 m/s and angle 38 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=38 degrees through the sine of 2 theta.\nSubstitute v=61.5 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 38, "gravity": 9.81, "speed": 61.5}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 2.37 * 8.314 * 420 / 56.9.\nFinal: {\"answer\": 145.4439, \"unit\": \"kPa\"}", "dedupe_signature": "cecc2cde1a9aea566e3bc32ee8f0ac72404537e4030d53d1a03187c99d4060d1", "difficulty": "medium", "final_answer": {"answer": 145.4439, "unit": "kPa"}, "id": "ideal_gas_004071_2.37_420_56.9", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=2.37 mol, T=420 K, and V=56.9 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 2.37 * 8.314 * 420 / 56.9.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 2.37, "temp_k": 420, "volume_l": 56.9}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1495 * 0.56 * 10.\nFinal: {\"answer\": 8372.0, \"unit\": \"J\"}", "dedupe_signature": "9387849d8daebaa2d639e3e1a16e84b8fd27895479e404ed795de5f468f219ae", "difficulty": "easy", "final_answer": {"answer": 8372.0, "unit": "J"}, "id": "heat_q_004072_1495_0.56_10", "license": "Apache-2.0", "prompt": "A 1495 g sample has specific heat 0.56 J/(g*K). How much heat is needed to raise its temperature by 10 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1495 * 0.56 * 10.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 10, "heat_capacity": 0.56, "mass_g": 1495}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=44.6 V and R=19.9 ohm.\nFinal: {\"answer\": 99.9578, \"unit\": \"W\"}", "dedupe_signature": "0458d744868a7dfe224e706950b3ae40fdffe07ff0fdfe4f6d17f6cf14a7882f", "difficulty": "easy", "final_answer": {"answer": 99.9578, "unit": "W"}, "id": "ohm_power_004073_44.6_19.9", "license": "Apache-2.0", "prompt": "A resistor has resistance 19.9 ohm and voltage 44.6 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=44.6 V and R=19.9 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 19.9, "voltage": 44.6}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=72 mg, t=31 h, and T_half=89.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 56.6324, \"unit\": \"mg\"}", "dedupe_signature": "06042c412e3cda875df3e98aa725050808ff2a66bab0f46b587fa7e09168c6f2", "difficulty": "medium", "final_answer": {"answer": 56.6324, "unit": "mg"}, "id": "half_life_004074_72_89.5_31", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 72 mg. Its half-life is 89.5 hours. How many mg remain after 31 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=72 mg, t=31 h, and T_half=89.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 31.0, "half_life": 89.5, "initial_amount": 72.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 2210 mL to 2.21 L.\n3. Compute M = 2.375 / 2.21.\nFinal: {\"answer\": 1.0747, \"unit\": \"mol/L\"}", "dedupe_signature": "17f9204b296a0e085e2fb827367ebdec148bd9b8004199667eefec8a9f70c9e5", "difficulty": "medium", "final_answer": {"answer": 1.0747, "unit": "mol/L"}, "id": "molarity_004076_2.375_2210", "license": "Apache-2.0", "prompt": "A solution contains 2.375 mol of solute in 2210 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 2210 mL to 2.21 L.\nCompute M = 2.375 / 2.21.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 2.375, "volume_ml": 2210}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(9.5)=10.7 and f(18.1)=36.5.\n3. The interval width is 8.6.\nFinal: {\"answer\": 202.96, \"unit\": \"area_units\"}", "dedupe_signature": "9b22a44ddfe110c0a7f90321ff63ca7268b5bc0ca9e9669c7533508a9425f859", "difficulty": "medium", "final_answer": {"answer": 202.96, "unit": "area_units"}, "id": "trapz_linear_004078_3_-17.8_9.5_18.1", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=3x+-17.8 from x=9.5 to x=18.1. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(9.5)=10.7 and f(18.1)=36.5.\nThe interval width is 8.6.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -17.8, "slope": 3.0, "x0": 9.5, "x1": 18.1}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kelvin equals Celsius plus 273.15.\n2. Apply the conversion factor directly to the given value.\n3. Compute 98.5 + 273.15.\nFinal: {\"answer\": 371.65, \"unit\": \"K\"}", "dedupe_signature": "35d84f8a1e19a7c5cf959d1dcb5ca6dddeb4e0b29ba1f1458dc1e89dd3f58d30", "difficulty": "easy", "final_answer": {"answer": 371.65, "unit": "K"}, "id": "unit_convert_004080_c_to_k_98.5", "license": "Apache-2.0", "prompt": "Convert 98.5 degC to K. Return the converted value with unit.", "reasoning_trace": "Kelvin equals Celsius plus 273.15.\nApply the conversion factor directly to the given value.\nCompute 98.5 + 273.15.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 98.5}, "verifier": {"formula": "value + 273.15", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [8.65, -25.0], \"unit\": \"dimensionless\"}", "dedupe_signature": "b342fcc42140fcf03ed9ff2c2382d7a8e6fd9aff5453139897889226d6b18b27", "difficulty": "medium", "final_answer": {"answer": [8.65, -25.0], "unit": "dimensionless"}, "id": "line_two_point_004082_17.5_23.25_8.65_-25", "license": "Apache-2.0", "prompt": "A line passes through points (17.5, 126.375) and (23.25, 176.113). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 17.5, "x2": 23.25, "y1": 126.375, "y2": 176.1125}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. amount times volume is not concentration\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "c9e65d4a9a4e840160459d6cdc9d648aa562dfbd3177b989c39015543512d007", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_004083_inconsistent_74ac0b02_436059", "license": "Apache-2.0", "prompt": "In field worksheet case 436059, check dimensional consistency for C = n * V. The left side has dimensions mol/L and the right side has dimensions mol*L. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\namount times volume is not concentration\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "C = n * V"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef safe_mean_004084(values):\n    if not values:\n        raise ValueError('safe_mean requires at least one value')\n    return sum(values) / len(values)\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"safe_mean_004084\"}", "dedupe_signature": "01bffe77ef46586beb83acb32261b4fb868dea2900335c42a73246b8e5a858aa", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "safe_mean_004084"}, "id": "code_004084_safe_mean_004084", "license": "Apache-2.0", "prompt": "Write a Python function safe_mean_004084(values) that returns the arithmetic mean. It must raise ValueError for an empty input and must not mutate the input list. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "safe_mean_004084"}, "verifier": {"function": "safe_mean_004084", "tests": ["assert safe_mean_004084([2, 4, 6]) == 4", "xs = [1, 2, 3]; assert safe_mean_004084(xs) == 2 and xs == [1, 2, 3]", "try:\n    safe_mean_004084([])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 17.4 kg and a = 0.6 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 10.44, \"unit\": \"N\"}", "dedupe_signature": "ac820eae46209124d28528bd7ea0920b04c649967683a55a80b82c1d5420c2f1", "difficulty": "easy", "final_answer": {"answer": 10.44, "unit": "N"}, "id": "force_004086_17.4_0.6", "license": "Apache-2.0", "prompt": "A cart has mass 17.4 kg and measured acceleration 0.6 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 17.4 kg and a = 0.6 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 0.6, "mass": 17.4}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=81 degrees through the sine of 2 theta.\n3. Substitute v=19.2 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 11.6122, \"unit\": \"m\"}", "dedupe_signature": "bacd109a672577f9a0dc5a7093089904a2f48f358822f77f213da4ba50181aee", "difficulty": "medium", "final_answer": {"answer": 11.6122, "unit": "m"}, "id": "projectile_range_004088_19.2_81", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 19.2 m/s and angle 81 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=81 degrees through the sine of 2 theta.\nSubstitute v=19.2 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 81, "gravity": 9.81, "speed": 19.2}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 3.18 * 8.314 * 607 / 60.8.\nFinal: {\"answer\": 263.9504, \"unit\": \"kPa\"}", "dedupe_signature": "70764bf61f4c05c53f48ff3812884f42f5a5713f8956d4ebd5066867c97cc06e", "difficulty": "medium", "final_answer": {"answer": 263.9504, "unit": "kPa"}, "id": "ideal_gas_004089_3.18_607_60.8", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=3.18 mol, T=607 K, and V=60.8 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 3.18 * 8.314 * 607 / 60.8.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 3.18, "temp_k": 607, "volume_l": 60.8}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1855 * 2.965 * 37.\nFinal: {\"answer\": 203502.775, \"unit\": \"J\"}", "dedupe_signature": "cb4ed1c8f2ba1196abb53d205c4eb3e8d1b30d7473d5c8ce702ffa4b722bef3a", "difficulty": "easy", "final_answer": {"answer": 203502.775, "unit": "J"}, "id": "heat_q_004090_1855_2.965_37", "license": "Apache-2.0", "prompt": "A 1855 g sample has specific heat 2.965 J/(g*K). How much heat is needed to raise its temperature by 37 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1855 * 2.965 * 37.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 37, "heat_capacity": 2.965, "mass_g": 1855}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=168.8 V and R=103.7 ohm.\nFinal: {\"answer\": 274.768, \"unit\": \"W\"}", "dedupe_signature": "9cb51798726881a71fbe459cce4890829d25b5c1241ce3e14272c1bd5c00d23e", "difficulty": "easy", "final_answer": {"answer": 274.768, "unit": "W"}, "id": "ohm_power_004091_168.8_103.7", "license": "Apache-2.0", "prompt": "A resistor has resistance 103.7 ohm and voltage 168.8 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=168.8 V and R=103.7 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 103.7, "voltage": 168.8}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=879.5 mg, t=78 h, and T_half=81.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 453.0368, \"unit\": \"mg\"}", "dedupe_signature": "8fc3198a1df5ae01290e8a129d634354d29c883540a36de21f3462b36a202861", "difficulty": "medium", "final_answer": {"answer": 453.0368, "unit": "mg"}, "id": "half_life_004092_879.5_81.5_78", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 879.5 mg. Its half-life is 81.5 hours. How many mg remain after 78 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=879.5 mg, t=78 h, and T_half=81.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 78.0, "half_life": 81.5, "initial_amount": 879.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 6.91 mol * 44.01 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 304.1091, \"unit\": \"g\"}", "dedupe_signature": "1b5ff2567abf7547a6a2b182f1161dfded5bab92f409b2d7badf9d4f16ef0e9a", "difficulty": "medium", "final_answer": {"answer": 304.1091, "unit": "g"}, "id": "stoich_mass_004093_carbon_dioxide_6.91", "license": "Apache-2.0", "prompt": "A sample contains 6.91 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 6.91 mol * 44.01 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "carbon dioxide", "molar_mass": 44.01, "moles": 6.91}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.28 y, so each step multiplies y by 1 - h*0.28.\n3. Apply that update for 9 steps and round the final state.\nFinal: {\"answer\": 2.3531, \"unit\": \"state_units\"}", "dedupe_signature": "25d312e9903349f057a90ffd8a732df22f900558b1b38ba7a5a970e62d5adf39", "difficulty": "medium", "final_answer": {"answer": 2.3531, "unit": "state_units"}, "id": "euler_decay_004095_54_0.28_1.05_9", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.28 y with y(0)=54, step size h=1.05, for 9 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.28 y, so each step multiplies y by 1 - h*0.28.\nApply that update for 9 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 54.0, "rate": 0.28, "step": 1.05, "steps": 9}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-9.2)=-63.96 and f(-6.3)=-47.14.\n3. The interval width is 2.9.\nFinal: {\"answer\": -161.095, \"unit\": \"area_units\"}", "dedupe_signature": "c342ef270f62d76ba79f5e68a8e8b3c88c001696f36eb1df311787ff00b00711", "difficulty": "medium", "final_answer": {"answer": -161.095, "unit": "area_units"}, "id": "trapz_linear_004096_5.8_-10.6_-9.2_-6.3", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=5.8x+-10.6 from x=-9.2 to x=-6.3. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-9.2)=-63.96 and f(-6.3)=-47.14.\nThe interval width is 2.9.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -10.6, "slope": 5.8, "x0": -9.2, "x1": -6.299999999999999}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kelvin equals Celsius plus 273.15.\n2. Apply the conversion factor directly to the given value.\n3. Compute -24.5 + 273.15.\nFinal: {\"answer\": 248.65, \"unit\": \"K\"}", "dedupe_signature": "1b9d422026cdecffe58cc6e4ac8cbc5abb52ff226a8af20fc1ce16e7f65df5b1", "difficulty": "easy", "final_answer": {"answer": 248.65, "unit": "K"}, "id": "unit_convert_004098_c_to_k_-24.5", "license": "Apache-2.0", "prompt": "Convert -24.5 degC to K. Return the converted value with unit.", "reasoning_trace": "Kelvin equals Celsius plus 273.15.\nApply the conversion factor directly to the given value.\nCompute -24.5 + 273.15.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": -24.5}, "verifier": {"formula": "value + 273.15", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [8.4, -22.25], \"unit\": \"dimensionless\"}", "dedupe_signature": "4460d240257d2bafc3454678d71023122f60d6f1179a20cf60130c27770d24e2", "difficulty": "medium", "final_answer": {"answer": [8.4, -22.25], "unit": "dimensionless"}, "id": "line_two_point_004100_-15.5_-8.75_8.4_-22.25", "license": "Apache-2.0", "prompt": "A line passes through points (-15.5, -152.45) and (-8.75, -95.75). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -15.5, "x2": -8.75, "y1": -152.45000000000002, "y2": -95.75}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. lever arm times force has torque dimensions\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "86bb17941f71e68b38bbf5ed03cf2ce1c64e83436cad7ac9a1f944c3194dc2b6", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_004101_consistent_5ca82cb9_346220", "license": "Apache-2.0", "prompt": "In student derivation case 346220, check dimensional consistency for tau = r * F. The left side has dimensions N*m and the right side has dimensions N*m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nlever arm times force has torque dimensions\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "tau = r * F"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef weighted_sum_004102(values, weights):\n    if len(values) != len(weights):\n        raise ValueError('length mismatch')\n    return sum(value * weight for value, weight in zip(values, weights))\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"weighted_sum_004102\"}", "dedupe_signature": "aaad65dee8198da6139908dca8be58cb900dd02bfc3b3ff6819ebcdbeaeb77cf", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "weighted_sum_004102"}, "id": "code_004102_weighted_sum_004102", "license": "Apache-2.0", "prompt": "Write a Python function weighted_sum_004102(values, weights) that returns sum(value*weight). Raise ValueError when the two inputs have different lengths. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "weighted_sum_004102"}, "verifier": {"function": "weighted_sum_004102", "tests": ["assert weighted_sum_004102([2, 3], [4, 5]) == 23", "assert weighted_sum_004102([], []) == 0", "try:\n    weighted_sum_004102([1], [1, 2])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: target_schema, valid_examples.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"target_schema\", \"valid_examples\"]}", "dedupe_signature": "26d8c35cc4b384e2d4cc0dc25afb63479581f3f556ae421614cb56d949570f6c", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["target_schema", "valid_examples"]}, "id": "abstain_004103_target_schema_valid_examples", "license": "Apache-2.0", "prompt": "Write a parser that converts each registry experiment record from batch 286702 into the correct schema, but the prompt does not include the target schema or examples. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: target_schema, valid_examples.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["target_schema", "valid_examples"]}, "verifier": {"missing": ["target_schema", "valid_examples"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 1.71 * 8.314 * 253 / 1.6.\nFinal: {\"answer\": 2248.0536, \"unit\": \"kPa\"}", "dedupe_signature": "ad6a75fef1c68b3992a61ca80de3ca5c73a46a8e4a9107b3500315a8c865a3e6", "difficulty": "medium", "final_answer": {"answer": 2248.0536, "unit": "kPa"}, "id": "ideal_gas_004107_1.71_253_1.6", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=1.71 mol, T=253 K, and V=1.6 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 1.71 * 8.314 * 253 / 1.6.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 1.71, "temp_k": 253, "volume_l": 1.6}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=50.3 V and R=151 ohm.\nFinal: {\"answer\": 16.7556, \"unit\": \"W\"}", "dedupe_signature": "26c5c01d76b2eba18d810b55db8d90445aea84000797239c3391d6b621d32fbc", "difficulty": "easy", "final_answer": {"answer": 16.7556, "unit": "W"}, "id": "ohm_power_004109_50.3_151", "license": "Apache-2.0", "prompt": "A resistor has resistance 151 ohm and voltage 50.3 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=50.3 V and R=151 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 151.0, "voltage": 50.3}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=164 mg, t=319.5 h, and T_half=31 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 0.1295, \"unit\": \"mg\"}", "dedupe_signature": "e5e545eedbee2884ffed861abc0bfb08157657f8d78efe670e18b479213b5476", "difficulty": "medium", "final_answer": {"answer": 0.1295, "unit": "mg"}, "id": "half_life_004110_164_31_319.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 164 mg. Its half-life is 31 hours. How many mg remain after 319.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=164 mg, t=319.5 h, and T_half=31 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 319.5, "half_life": 31.0, "initial_amount": 164.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 4105 mL to 4.105 L.\n3. Compute M = 4.995 / 4.105.\nFinal: {\"answer\": 1.2168, \"unit\": \"mol/L\"}", "dedupe_signature": "ccb6891af35ea167ac854bdab828170aca79665e0e93b3eb42b7354c6e2200ea", "difficulty": "medium", "final_answer": {"answer": 1.2168, "unit": "mol/L"}, "id": "molarity_004112_4.995_4105", "license": "Apache-2.0", "prompt": "A solution contains 4.995 mol of solute in 4105 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 4105 mL to 4.105 L.\nCompute M = 4.995 / 4.105.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 4.995, "volume_ml": 4105}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.18 y, so each step multiplies y by 1 - h*0.18.\n3. Apply that update for 7 steps and round the final state.\nFinal: {\"answer\": 3.322, \"unit\": \"state_units\"}", "dedupe_signature": "0396b651a357955b01ab0966c7c47b2dc13182a4c4112e3ac64ae68c9f646f31", "difficulty": "medium", "final_answer": {"answer": 3.322, "unit": "state_units"}, "id": "euler_decay_004113_68.5_0.18_1.95_7", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.18 y with y(0)=68.5, step size h=1.95, for 7 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.18 y, so each step multiplies y by 1 - h*0.18.\nApply that update for 7 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 68.5, "rate": 0.18, "step": 1.95, "steps": 7}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-8.2)=4.08 and f(-7.2)=3.68.\n3. The interval width is 1.\nFinal: {\"answer\": 3.88, \"unit\": \"area_units\"}", "dedupe_signature": "54dc8751f24415a59fc5736d0f9023dee6e58fe8fb34721b8b2832a337300019", "difficulty": "medium", "final_answer": {"answer": 3.88, "unit": "area_units"}, "id": "trapz_linear_004114_-0.4_0.8_-8.2_-7.2", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-0.4x+0.8 from x=-8.2 to x=-7.2. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-8.2)=4.08 and f(-7.2)=3.68.\nThe interval width is 1.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 0.8, "slope": -0.4, "x0": -8.2, "x1": -7.199999999999999}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=235 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-138.5187, -197.8252], \"unit\": \"N\"}", "dedupe_signature": "7d301ca999c5edfa0a52790104fc39fb6b93e6496ee404d7d1a65860c52f37dd", "difficulty": "medium", "final_answer": {"answer": [-138.5187, -197.8252], "unit": "N"}, "id": "vector_components_004117_241.5_235", "license": "Apache-2.0", "prompt": "A vector has magnitude 241.5 N at 235 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=235 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 235, "magnitude": 241.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [5.95, 17.0], \"unit\": \"dimensionless\"}", "dedupe_signature": "aa4da07f44c1e75a2a2423aabce002658507f59f0b0f350ce66f6fd097a25c7d", "difficulty": "medium", "final_answer": {"answer": [5.95, 17.0], "unit": "dimensionless"}, "id": "line_two_point_004118_-9.5_1.75_5.95_17", "license": "Apache-2.0", "prompt": "A line passes through points (-9.5, -39.525) and (1.75, 27.4125). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -9.5, "x2": 1.75, "y1": -39.525, "y2": 27.4125}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. amount times volume is not concentration\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "486ccfd3cad5b7ddff5f235c1ed745c34d40705b671f750a864e5127ddae96cd", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_004119_inconsistent_74ac0b02_900786", "license": "Apache-2.0", "prompt": "In simulation spec case 900786, check dimensional consistency for C = n * V. The left side has dimensions mol/L and the right side has dimensions mol*L. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\namount times volume is not concentration\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "C = n * V"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef weighted_sum_004120(values, weights):\n    if len(values) != len(weights):\n        raise ValueError('length mismatch')\n    return sum(value * weight for value, weight in zip(values, weights))\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"weighted_sum_004120\"}", "dedupe_signature": "d4f4333e650d5fd69c90b91b9a0f8f91bb7c4414617d7a179c17d61ddf8443d9", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "weighted_sum_004120"}, "id": "code_004120_weighted_sum_004120", "license": "Apache-2.0", "prompt": "Write a Python function weighted_sum_004120(values, weights) that returns sum(value*weight). Raise ValueError when the two inputs have different lengths. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "weighted_sum_004120"}, "verifier": {"function": "weighted_sum_004120", "tests": ["assert weighted_sum_004120([2, 3], [4, 5]) == 23", "assert weighted_sum_004120([], []) == 0", "try:\n    weighted_sum_004120([1], [1, 2])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: left_boundary, right_boundary.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"left_boundary\", \"right_boundary\"]}", "dedupe_signature": "d960ccf3c9d403789461cbec1408f32eca29bfeeb7398f8c9df9d4618c2f89d5", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["left_boundary", "right_boundary"]}, "id": "abstain_004121_left_boundary_right_boundary", "license": "Apache-2.0", "prompt": "Solve the 1D heat equation after one finite-difference step. The prompt gives r=0.08 and interior values [1.15, -1.55, -0.55], but gives no boundary values. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: left_boundary, right_boundary.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["left_boundary", "right_boundary"]}, "verifier": {"missing": ["left_boundary", "right_boundary"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 18.85 kg and a = 15.85 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 298.7725, \"unit\": \"N\"}", "dedupe_signature": "7eed2aaa0d7fa6e792042e85037890f0aa82dfd82491e075acdf370598d73666", "difficulty": "easy", "final_answer": {"answer": 298.7725, "unit": "N"}, "id": "force_004122_18.85_15.85", "license": "Apache-2.0", "prompt": "A cart has mass 18.85 kg and measured acceleration 15.85 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 18.85 kg and a = 15.85 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 15.85, "mass": 18.85}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 7.8^2 and multiply by 0.5 * 19.65.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 597.753, \"unit\": \"J\"}", "dedupe_signature": "b7bb30e4076964930946b994cb4078dd98bab04b315b6b03465575c757774718", "difficulty": "easy", "final_answer": {"answer": 597.753, "unit": "J"}, "id": "ke_004123_19.65_7.8", "license": "Apache-2.0", "prompt": "A body of mass 19.65 kg moves at 7.8 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 7.8^2 and multiply by 0.5 * 19.65.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 19.65, "velocity": 7.8}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 2.89 * 8.314 * 281 / 7.4.\nFinal: {\"answer\": 912.3941, \"unit\": \"kPa\"}", "dedupe_signature": "6fc9878469ddce345510a70069c16da0d9a69072f15d6e89367c829150bd15bd", "difficulty": "medium", "final_answer": {"answer": 912.3941, "unit": "kPa"}, "id": "ideal_gas_004125_2.89_281_7.4", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=2.89 mol, T=281 K, and V=7.4 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 2.89 * 8.314 * 281 / 7.4.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 2.89, "temp_k": 281, "volume_l": 7.4}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1850 * 2.67 * 35.\nFinal: {\"answer\": 172882.5, \"unit\": \"J\"}", "dedupe_signature": "a6530e42a67fdb2964fde94cb6bb51c927cde94134b856e3d8f29c89290cdb5e", "difficulty": "easy", "final_answer": {"answer": 172882.5, "unit": "J"}, "id": "heat_q_004126_1850_2.67_35", "license": "Apache-2.0", "prompt": "A 1850 g sample has specific heat 2.67 J/(g*K). How much heat is needed to raise its temperature by 35 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1850 * 2.67 * 35.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 35, "heat_capacity": 2.67, "mass_g": 1850}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=104.7 V and R=61.8 ohm.\nFinal: {\"answer\": 177.3801, \"unit\": \"W\"}", "dedupe_signature": "48717393cefaf41e92793268df4cbb3555f441788fb5f06d40f0715f76aa3c0a", "difficulty": "easy", "final_answer": {"answer": 177.3801, "unit": "W"}, "id": "ohm_power_004127_104.7_61.8", "license": "Apache-2.0", "prompt": "A resistor has resistance 61.8 ohm and voltage 104.7 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=104.7 V and R=61.8 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 61.8, "voltage": 104.7}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=504.5 mg, t=86.5 h, and T_half=60 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 185.7275, \"unit\": \"mg\"}", "dedupe_signature": "b6f6b48341a0e291cb4045941d1394fe198b1431c1bae24bb01a4d9659419f14", "difficulty": "medium", "final_answer": {"answer": 185.7275, "unit": "mg"}, "id": "half_life_004128_504.5_60_86.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 504.5 mg. Its half-life is 60 hours. How many mg remain after 86.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=504.5 mg, t=86.5 h, and T_half=60 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 86.5, "half_life": 60.0, "initial_amount": 504.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 4.66 mol * 100.087 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 466.4054, \"unit\": \"g\"}", "dedupe_signature": "69a1903a5222567d32b517e3a6dc4961068f95aae1f1882493764c01beac5943", "difficulty": "medium", "final_answer": {"answer": 466.4054, "unit": "g"}, "id": "stoich_mass_004129_calcium_carbonate_4.66", "license": "Apache-2.0", "prompt": "A sample contains 4.66 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 4.66 mol * 100.087 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "calcium carbonate", "molar_mass": 100.087, "moles": 4.66}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 3335 mL to 3.335 L.\n3. Compute M = 1.925 / 3.335.\nFinal: {\"answer\": 0.5772, \"unit\": \"mol/L\"}", "dedupe_signature": "9511a31e724f4cf67caab97db01ee2ab85f4fdd8166022c47dba443ec5f11dfb", "difficulty": "medium", "final_answer": {"answer": 0.5772, "unit": "mol/L"}, "id": "molarity_004130_1.925_3335", "license": "Apache-2.0", "prompt": "A solution contains 1.925 mol of solute in 3335 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 3335 mL to 3.335 L.\nCompute M = 1.925 / 3.335.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 1.925, "volume_ml": 3335}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.71 y, so each step multiplies y by 1 - h*0.71.\n3. Apply that update for 11 steps and round the final state.\nFinal: {\"answer\": 0.0, \"unit\": \"state_units\"}", "dedupe_signature": "2da0b421ff2bd934a9eb4758a7998b8050e5d470c224582f85d8cf99dcd94c3b", "difficulty": "medium", "final_answer": {"answer": 0.0, "unit": "state_units"}, "id": "euler_decay_004131_28_0.71_1.25_11", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.71 y with y(0)=28, step size h=1.25, for 11 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.71 y, so each step multiplies y by 1 - h*0.71.\nApply that update for 11 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 28.0, "rate": 0.71, "step": 1.25, "steps": 11}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(6.1)=-35.5 and f(8.4)=-49.3.\n3. The interval width is 2.3.\nFinal: {\"answer\": -97.52, \"unit\": \"area_units\"}", "dedupe_signature": "563e1149622495b9d53a3e89db3dbabd23487c33689c319249bc8ed5a93dfa2a", "difficulty": "medium", "final_answer": {"answer": -97.52, "unit": "area_units"}, "id": "trapz_linear_004132_-6_1.1_6.1_8.4", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-6x+1.1 from x=6.1 to x=8.4. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(6.1)=-35.5 and f(8.4)=-49.3.\nThe interval width is 2.3.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 1.1, "slope": -6.0, "x0": 6.1, "x1": 8.399999999999999}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.34 and add it to the current value.\nFinal: {\"answer\": [0.18, -0.549, -1.297], \"unit\": \"temperature_units\"}", "dedupe_signature": "3555743151d5145ebddf42e0a7e96d816a6c90852f3c6fac9579fb711dd7ebb4", "difficulty": "hard", "final_answer": {"answer": [0.18, -0.549, -1.297], "unit": "temperature_units"}, "id": "heat_step_004133_0.34_1.65_0.35_-1.45_-0.6_-1.8", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.65, right=-1.8; current interior values are [0.35, -1.45, -0.6]. Use r=0.34. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.34 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [0.35, -1.45, -0.6], "left": 1.65, "r": 0.34, "right": -1.8}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=352 degrees and keep the unit as newtons.\nFinal: {\"answer\": [382.2435, -53.7208], \"unit\": \"N\"}", "dedupe_signature": "3a9097693e63121c8880da38291fddeeb0fa17a94ec282cdc6d796ab0469bbbc", "difficulty": "medium", "final_answer": {"answer": [382.2435, -53.7208], "unit": "N"}, "id": "vector_components_004135_386_352", "license": "Apache-2.0", "prompt": "A vector has magnitude 386 N at 352 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=352 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 352, "magnitude": 386.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [7.35, 5.5], \"unit\": \"dimensionless\"}", "dedupe_signature": "8906a19cb016ac030a29d65008cfd9b1cda3547f0535be92ee8cda92eaf05ba3", "difficulty": "medium", "final_answer": {"answer": [7.35, 5.5], "unit": "dimensionless"}, "id": "line_two_point_004136_-5.75_-1.75_7.35_5.5", "license": "Apache-2.0", "prompt": "A line passes through points (-5.75, -36.7625) and (-1.75, -7.3625). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -5.75, "x2": -1.75, "y1": -36.762499999999996, "y2": -7.362499999999999}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef running_total_004138(values):\n    total = 0\n    out = []\n    for value in values:\n        total += value\n        out.append(total)\n    return out\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"running_total_004138\"}", "dedupe_signature": "8bdc9139f9f90494713b1d458ae6c7f72839f4241b187991c1a131d5d6267c24", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "running_total_004138"}, "id": "code_004138_running_total_004138", "license": "Apache-2.0", "prompt": "Write a Python function running_total_004138(values) that returns cumulative sums as a new list. It must not mutate the input list. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "running_total_004138"}, "verifier": {"function": "running_total_004138", "tests": ["assert running_total_004138([1, 2, 3]) == [1, 3, 6]", "xs = [4, -1, 2]; assert running_total_004138(xs) == [4, 3, 5] and xs == [4, -1, 2]", "assert running_total_004138([]) == []"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: volume.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"volume\"]}", "dedupe_signature": "de4eb74cabb132dd74ec4c8bd6376c3f2ba0acab344a64bf7ae9e4d4b3b01632", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["volume"]}, "id": "abstain_004139_volume", "license": "Apache-2.0", "prompt": "Compute pressure from the ideal gas law. The prompt gives n=0.73 mol and T=319 K, but does not give volume. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: volume.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["volume"]}, "verifier": {"missing": ["volume"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 12.55 kg and a = 9.15 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 114.8325, \"unit\": \"N\"}", "dedupe_signature": "6b452d1e3393e52edcb7ef128d96bd7d7306b7117807f78c04b7d5b79d50c57f", "difficulty": "easy", "final_answer": {"answer": 114.8325, "unit": "N"}, "id": "force_004140_12.55_9.15", "license": "Apache-2.0", "prompt": "A cart has mass 12.55 kg and measured acceleration 9.15 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 12.55 kg and a = 9.15 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 9.15, "mass": 12.55}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 11.15^2 and multiply by 0.5 * 24.25.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 1507.4103, \"unit\": \"J\"}", "dedupe_signature": "efb0582bd835e0dd870e81ef499709180471fd7e0d30db93da91c335a514e877", "difficulty": "easy", "final_answer": {"answer": 1507.4103, "unit": "J"}, "id": "ke_004141_24.25_11.15", "license": "Apache-2.0", "prompt": "A body of mass 24.25 kg moves at 11.15 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 11.15^2 and multiply by 0.5 * 24.25.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 24.25, "velocity": 11.15}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=25 degrees through the sine of 2 theta.\n3. Substitute v=14.7 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 16.8741, \"unit\": \"m\"}", "dedupe_signature": "10f299bf0be3a522c53035a424029c13a77d1b50fdaeb1246f73cc4d78055e11", "difficulty": "medium", "final_answer": {"answer": 16.8741, "unit": "m"}, "id": "projectile_range_004142_14.7_25", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 14.7 m/s and angle 25 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=25 degrees through the sine of 2 theta.\nSubstitute v=14.7 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 25, "gravity": 9.81, "speed": 14.7}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 0.49 * 8.314 * 476 / 102.7.\nFinal: {\"answer\": 18.8818, \"unit\": \"kPa\"}", "dedupe_signature": "2b7aaf7563a15c703df6269a15ef1771846c7d7a60e56bd3b8da2564240995df", "difficulty": "medium", "final_answer": {"answer": 18.8818, "unit": "kPa"}, "id": "ideal_gas_004143_0.49_476_102.7", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=0.49 mol, T=476 K, and V=102.7 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 0.49 * 8.314 * 476 / 102.7.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 0.49, "temp_k": 476, "volume_l": 102.7}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 410 * 3.635 * 105.\nFinal: {\"answer\": 156486.75, \"unit\": \"J\"}", "dedupe_signature": "fbd2e9cd28709ffb16b52015364d2a73a99c9a73dab2cf4850a45016dcc4eb86", "difficulty": "easy", "final_answer": {"answer": 156486.75, "unit": "J"}, "id": "heat_q_004144_410_3.635_105", "license": "Apache-2.0", "prompt": "A 410 g sample has specific heat 3.635 J/(g*K). How much heat is needed to raise its temperature by 105 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 410 * 3.635 * 105.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 105, "heat_capacity": 3.635, "mass_g": 410}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=112.7 V and R=193.7 ohm.\nFinal: {\"answer\": 65.572, \"unit\": \"W\"}", "dedupe_signature": "15ed187a9fb5dd1ca0da3b5991fc8d69130fc802de7209c249598bb9057a29f1", "difficulty": "easy", "final_answer": {"answer": 65.572, "unit": "W"}, "id": "ohm_power_004145_112.7_193.7", "license": "Apache-2.0", "prompt": "A resistor has resistance 193.7 ohm and voltage 112.7 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=112.7 V and R=193.7 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 193.7, "voltage": 112.7}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(5.4)=27.48 and f(8.5)=48.25.\n3. The interval width is 3.1.\nFinal: {\"answer\": 117.3815, \"unit\": \"area_units\"}", "dedupe_signature": "3ff7b2e8d93ba77aa9c26a374017a17bc339b0000622abd7d8c6b53f8f51653f", "difficulty": "medium", "final_answer": {"answer": 117.3815, "unit": "area_units"}, "id": "trapz_linear_004150_6.7_-8.7_5.4_8.5", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=6.7x+-8.7 from x=5.4 to x=8.5. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(5.4)=27.48 and f(8.5)=48.25.\nThe interval width is 3.1.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -8.7, "slope": 6.7, "x0": 5.4, "x1": 8.5}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.44 and add it to the current value.\nFinal: {\"answer\": [0.55, 0.194, 0.25], \"unit\": \"temperature_units\"}", "dedupe_signature": "7be93754829aabff0cfb5b66c9b163394c81a1bf1a403059b0af385615aabd66", "difficulty": "hard", "final_answer": {"answer": [0.55, 0.194, 0.25], "unit": "temperature_units"}, "id": "heat_step_004151_0.44_0.4_0.55_0.7_-0.3_-0.05", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=0.4, right=-0.05; current interior values are [0.55, 0.7, -0.3]. Use r=0.44. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.44 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [0.55, 0.7, -0.3], "left": 0.4, "r": 0.44, "right": -0.05}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 21501.0 / 1000.\nFinal: {\"answer\": 21.501, \"unit\": \"kg\"}", "dedupe_signature": "3909f1cac0d93916d02bced287eb9707c66b4b76664cf51f81a65d83c8e21ad7", "difficulty": "easy", "final_answer": {"answer": 21.501, "unit": "kg"}, "id": "unit_convert_004152_g_to_kg_21501", "license": "Apache-2.0", "prompt": "Convert 21501 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 21501.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 21501.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=109 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-38.7426, 112.5167], \"unit\": \"N\"}", "dedupe_signature": "65a39e5ddcf9ad365a442513d7f106d0f31dc16640e0869321e4cf4c49ee64e7", "difficulty": "medium", "final_answer": {"answer": [-38.7426, 112.5167], "unit": "N"}, "id": "vector_components_004153_119_109", "license": "Apache-2.0", "prompt": "A vector has magnitude 119 N at 109 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=109 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 109, "magnitude": 119.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [5.6, -2.75], \"unit\": \"dimensionless\"}", "dedupe_signature": "486e42acd628f5600d79c0db9e11251b5f479fa3f153873c22b28912eb2c0612", "difficulty": "medium", "final_answer": {"answer": [5.6, -2.75], "unit": "dimensionless"}, "id": "line_two_point_004154_12.25_18.75_5.6_-2.75", "license": "Apache-2.0", "prompt": "A line passes through points (12.25, 65.85) and (18.75, 102.25). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 12.25, "x2": 18.75, "y1": 65.85, "y2": 102.25}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. mass times acceleration has newton dimensions\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "2f8d787e97ee4544f35d26d9ac04df00663d910b954d5d64b5a6f2d4abc2b3dc", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_004155_consistent_03f5e041_659591", "license": "Apache-2.0", "prompt": "In simulation spec case 659591, check dimensional consistency for F = m * a. The left side has dimensions kg*m/s^2 and the right side has dimensions kg*m/s^2. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nmass times acceleration has newton dimensions\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "F = m * a"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef safe_mean_004156(values):\n    if not values:\n        raise ValueError('safe_mean requires at least one value')\n    return sum(values) / len(values)\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"safe_mean_004156\"}", "dedupe_signature": "5724fb694a626db1e2c31addce004b727984eb244743843679cf30ea89bdf880", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "safe_mean_004156"}, "id": "code_004156_safe_mean_004156", "license": "Apache-2.0", "prompt": "Write a Python function safe_mean_004156(values) that returns the arithmetic mean. It must raise ValueError for an empty input and must not mutate the input list. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "safe_mean_004156"}, "verifier": {"function": "safe_mean_004156", "tests": ["assert safe_mean_004156([2, 4, 6]) == 4", "xs = [1, 2, 3]; assert safe_mean_004156(xs) == 2 and xs == [1, 2, 3]", "try:\n    safe_mean_004156([])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: rate_constant, number_of_steps.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"rate_constant\", \"number_of_steps\"]}", "dedupe_signature": "7e406ae7050363da0985b808f332a1fc15c56a67299596c3bfc35326bfe297ff", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["rate_constant", "number_of_steps"]}, "id": "abstain_004157_rate_constant_number_of_steps", "license": "Apache-2.0", "prompt": "Use explicit Euler for dy/dt = -k y. The prompt gives y(0)=59.5 and h=1, but omits both k and the number of steps. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: rate_constant, number_of_steps.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["rate_constant", "number_of_steps"]}, "verifier": {"missing": ["rate_constant", "number_of_steps"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 19.85 kg and a = 5.75 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 114.1375, \"unit\": \"N\"}", "dedupe_signature": "66acd1fe9d0242dd709a112225f1bdd0356d526b0536d575b75138783ebbe477", "difficulty": "easy", "final_answer": {"answer": 114.1375, "unit": "N"}, "id": "force_004158_19.85_5.75", "license": "Apache-2.0", "prompt": "A cart has mass 19.85 kg and measured acceleration 5.75 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 19.85 kg and a = 5.75 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 5.75, "mass": 19.85}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 28.25^2 and multiply by 0.5 * 0.9.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 359.1281, \"unit\": \"J\"}", "dedupe_signature": "4c95eff8fee9eaa966b325465438b8c8005768bb8711fb91b5f0870f446d4a10", "difficulty": "easy", "final_answer": {"answer": 359.1281, "unit": "J"}, "id": "ke_004159_0.9_28.25", "license": "Apache-2.0", "prompt": "A body of mass 0.9 kg moves at 28.25 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 28.25^2 and multiply by 0.5 * 0.9.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 0.9, "velocity": 28.25}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=37 degrees through the sine of 2 theta.\n3. Substitute v=45.5 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 202.8595, \"unit\": \"m\"}", "dedupe_signature": "2599fb844e1f02b047e991c3f8e29dd1075a6a3ae6550ac6dd69e5c57d0afdaf", "difficulty": "medium", "final_answer": {"answer": 202.8595, "unit": "m"}, "id": "projectile_range_004160_45.5_37", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 45.5 m/s and angle 37 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=37 degrees through the sine of 2 theta.\nSubstitute v=45.5 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 37, "gravity": 9.81, "speed": 45.5}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 2.98 * 8.314 * 345 / 100.4.\nFinal: {\"answer\": 85.1357, \"unit\": \"kPa\"}", "dedupe_signature": "428256b272794d5d400b6ac78a888e2a593dc2d4039254d36e3b637be2433a3e", "difficulty": "medium", "final_answer": {"answer": 85.1357, "unit": "kPa"}, "id": "ideal_gas_004161_2.98_345_100.4", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=2.98 mol, T=345 K, and V=100.4 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 2.98 * 8.314 * 345 / 100.4.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 2.98, "temp_k": 345, "volume_l": 100.4}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 230 * 3.73 * 11.\nFinal: {\"answer\": 9436.9, \"unit\": \"J\"}", "dedupe_signature": "bfce32991435d08a7e64ba1d7c839ecefd84727983de5f9cbe74e49d4880ba80", "difficulty": "easy", "final_answer": {"answer": 9436.9, "unit": "J"}, "id": "heat_q_004162_230_3.73_11", "license": "Apache-2.0", "prompt": "A 230 g sample has specific heat 3.73 J/(g*K). How much heat is needed to raise its temperature by 11 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 230 * 3.73 * 11.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 11, "heat_capacity": 3.73, "mass_g": 230}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=864 mg, t=266 h, and T_half=43.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 12.4662, \"unit\": \"mg\"}", "dedupe_signature": "82c06afee950affe9d569aeed4e9863d41ac683d5758e9c1f6e40575ea79d795", "difficulty": "medium", "final_answer": {"answer": 12.4662, "unit": "mg"}, "id": "half_life_004164_864_43.5_266", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 864 mg. Its half-life is 43.5 hours. How many mg remain after 266 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=864 mg, t=266 h, and T_half=43.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 266.0, "half_life": 43.5, "initial_amount": 864.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 3.25 mol * 100.087 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 325.2828, \"unit\": \"g\"}", "dedupe_signature": "95ad929d4a1fe037d613168e6545b7968920c188845ed5fb542fcc756ba443b3", "difficulty": "medium", "final_answer": {"answer": 325.2828, "unit": "g"}, "id": "stoich_mass_004165_calcium_carbonate_3.25", "license": "Apache-2.0", "prompt": "A sample contains 3.25 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 3.25 mol * 100.087 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "calcium carbonate", "molar_mass": 100.087, "moles": 3.25}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 4970 mL to 4.97 L.\n3. Compute M = 2.135 / 4.97.\nFinal: {\"answer\": 0.4296, \"unit\": \"mol/L\"}", "dedupe_signature": "48df4cebc77da28a7dc3c14ceb389774750f0dc51ba643b4045e31e36419a8a8", "difficulty": "medium", "final_answer": {"answer": 0.4296, "unit": "mol/L"}, "id": "molarity_004166_2.135_4970", "license": "Apache-2.0", "prompt": "A solution contains 2.135 mol of solute in 4970 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 4970 mL to 4.97 L.\nCompute M = 2.135 / 4.97.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 2.135, "volume_ml": 4970}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-2.7)=1.7 and f(3.7)=-49.5.\n3. The interval width is 6.4.\nFinal: {\"answer\": -152.96, \"unit\": \"area_units\"}", "dedupe_signature": "11fb8a489922ce27fb11043b55471eb183b9d0d99754d1d5d38e30399dac8266", "difficulty": "medium", "final_answer": {"answer": -152.96, "unit": "area_units"}, "id": "trapz_linear_004168_-8_-19.9_-2.7_3.7", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-8x+-19.9 from x=-2.7 to x=3.7. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-2.7)=1.7 and f(3.7)=-49.5.\nThe interval width is 6.4.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -19.9, "slope": -8.0, "x0": -2.7, "x1": 3.7}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.06 and add it to the current value.\nFinal: {\"answer\": [0.115, 1.406, 2.509], \"unit\": \"temperature_units\"}", "dedupe_signature": "f5a0d87fae888e6000624673946421ad86bfca3ed6d099c0e1c77ec43a13eed3", "difficulty": "hard", "final_answer": {"answer": [0.115, 1.406, 2.509], "unit": "temperature_units"}, "id": "heat_step_004169_0.06_-0.95_0.1_1.4_2.8_-0.65", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-0.95, right=-0.65; current interior values are [0.1, 1.4, 2.8]. Use r=0.06. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.06 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [0.1, 1.4, 2.8], "left": -0.95, "r": 0.06, "right": -0.65}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kelvin equals Celsius plus 273.15.\n2. Apply the conversion factor directly to the given value.\n3. Compute 151.5 + 273.15.\nFinal: {\"answer\": 424.65, \"unit\": \"K\"}", "dedupe_signature": "c916ffac5ee74d5731b6e646dd2037a209089175b01181a90a3293587512fe29", "difficulty": "easy", "final_answer": {"answer": 424.65, "unit": "K"}, "id": "unit_convert_004170_c_to_k_151.5", "license": "Apache-2.0", "prompt": "Convert 151.5 degC to K. Return the converted value with unit.", "reasoning_trace": "Kelvin equals Celsius plus 273.15.\nApply the conversion factor directly to the given value.\nCompute 151.5 + 273.15.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 151.5}, "verifier": {"formula": "value + 273.15", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=341 degrees and keep the unit as newtons.\nFinal: {\"answer\": [253.8717, -87.415], \"unit\": \"N\"}", "dedupe_signature": "6d2acc764d088879bde34271810243bc32f98212038026e3467252f603f33ce3", "difficulty": "medium", "final_answer": {"answer": [253.8717, -87.415], "unit": "N"}, "id": "vector_components_004171_268.5_341", "license": "Apache-2.0", "prompt": "A vector has magnitude 268.5 N at 341 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=341 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 341, "magnitude": 268.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-9.55, -25.75], \"unit\": \"dimensionless\"}", "dedupe_signature": "3223298549b0852401a762be1b67929e3a745f80cd8bf4fe4180ceb295c46860", "difficulty": "medium", "final_answer": {"answer": [-9.55, -25.75], "unit": "dimensionless"}, "id": "line_two_point_004172_-8.75_4.5_-9.55_-25.75", "license": "Apache-2.0", "prompt": "A line passes through points (-8.75, 57.8125) and (4.5, -68.725). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -8.75, "x2": 4.5, "y1": 57.8125, "y2": -68.725}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. volt squared divided by ohm is watt\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "70e8f55c3e987f2c18d6b893684fdc8ec669931851017c6aea2d7f3a755a7ccb", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_004173_consistent_82e93f3d_897298", "license": "Apache-2.0", "prompt": "In field worksheet case 897298, check dimensional consistency for P = V^2 / R. The left side has dimensions W and the right side has dimensions W. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nvolt squared divided by ohm is watt\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "P = V^2 / R"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: target_schema, valid_examples.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"target_schema\", \"valid_examples\"]}", "dedupe_signature": "0a088b1380ede55f767861ea8dd28cb2d317bfa050fdae0570b021145d7d4df4", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["target_schema", "valid_examples"]}, "id": "abstain_004175_target_schema_valid_examples", "license": "Apache-2.0", "prompt": "Write a parser that converts each registry survey record from batch 728508 into the correct schema, but the prompt does not include the target schema or examples. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: target_schema, valid_examples.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["target_schema", "valid_examples"]}, "verifier": {"missing": ["target_schema", "valid_examples"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 20.55 kg and a = 11.5 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 236.325, \"unit\": \"N\"}", "dedupe_signature": "504c1e121a007735ebdd6dac3dd52664aeb984d581a56a043ad5e324ab803b8d", "difficulty": "easy", "final_answer": {"answer": 236.325, "unit": "N"}, "id": "force_004176_20.55_11.5", "license": "Apache-2.0", "prompt": "A cart has mass 20.55 kg and measured acceleration 11.5 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 20.55 kg and a = 11.5 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 11.5, "mass": 20.55}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 12.55^2 and multiply by 0.5 * 17.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 1338.7713, \"unit\": \"J\"}", "dedupe_signature": "a70a4271b6aae206606cd5820bb8b299872c87ae8ffe77346499e76c0c59766d", "difficulty": "easy", "final_answer": {"answer": 1338.7713, "unit": "J"}, "id": "ke_004177_17_12.55", "license": "Apache-2.0", "prompt": "A body of mass 17 kg moves at 12.55 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 12.55^2 and multiply by 0.5 * 17.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 17.0, "velocity": 12.55}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=73 degrees through the sine of 2 theta.\n3. Substitute v=66.3 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 250.5646, \"unit\": \"m\"}", "dedupe_signature": "5c0be9552d285f800b5503399c570156f320d539ef2cc8cbb8b9a17e9d447a9c", "difficulty": "medium", "final_answer": {"answer": 250.5646, "unit": "m"}, "id": "projectile_range_004178_66.3_73", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 66.3 m/s and angle 73 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=73 degrees through the sine of 2 theta.\nSubstitute v=66.3 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 73, "gravity": 9.81, "speed": 66.3}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 1.26 * 8.314 * 366 / 85.1.\nFinal: {\"answer\": 45.0539, \"unit\": \"kPa\"}", "dedupe_signature": "ecc406788fede46386faa45b3421cdbbd877280bcca609b08d1bdb2f20a6b7a5", "difficulty": "medium", "final_answer": {"answer": 45.0539, "unit": "kPa"}, "id": "ideal_gas_004179_1.26_366_85.1", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=1.26 mol, T=366 K, and V=85.1 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 1.26 * 8.314 * 366 / 85.1.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 1.26, "temp_k": 366, "volume_l": 85.1}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1590 * 1.955 * 21.\nFinal: {\"answer\": 65277.45, \"unit\": \"J\"}", "dedupe_signature": "5c32f32d70ae251587a45e883058e6beb46ad8957d08853658fb0671d1c3fd57", "difficulty": "easy", "final_answer": {"answer": 65277.45, "unit": "J"}, "id": "heat_q_004180_1590_1.955_21", "license": "Apache-2.0", "prompt": "A 1590 g sample has specific heat 1.955 J/(g*K). How much heat is needed to raise its temperature by 21 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1590 * 1.955 * 21.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 21, "heat_capacity": 1.955, "mass_g": 1590}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=137.4 V and R=83.9 ohm.\nFinal: {\"answer\": 225.015, \"unit\": \"W\"}", "dedupe_signature": "b1266d12cabe2a6deb5760942dfedba8421c38d11f865b973a93133b6d4754d4", "difficulty": "easy", "final_answer": {"answer": 225.015, "unit": "W"}, "id": "ohm_power_004181_137.4_83.9", "license": "Apache-2.0", "prompt": "A resistor has resistance 83.9 ohm and voltage 137.4 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=137.4 V and R=83.9 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 83.9, "voltage": 137.4}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=322.5 mg, t=61.5 h, and T_half=115 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 222.6097, \"unit\": \"mg\"}", "dedupe_signature": "0b1634685c976392f98ce8343ad96899e33d97b9ec9283bd353342d993e4b4bc", "difficulty": "medium", "final_answer": {"answer": 222.6097, "unit": "mg"}, "id": "half_life_004182_322.5_115_61.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 322.5 mg. Its half-life is 115 hours. How many mg remain after 61.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=322.5 mg, t=61.5 h, and T_half=115 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 61.5, "half_life": 115.0, "initial_amount": 322.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 5.44 mol * 180.156 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 980.0486, \"unit\": \"g\"}", "dedupe_signature": "aa56919949e2ae3e0f2794c097ee0084434d51ef0f9abc4976535aecb9ec3f73", "difficulty": "medium", "final_answer": {"answer": 980.0486, "unit": "g"}, "id": "stoich_mass_004183_glucose_5.44", "license": "Apache-2.0", "prompt": "A sample contains 5.44 mol of glucose. Using molar mass 180.156 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 5.44 mol * 180.156 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "glucose", "molar_mass": 180.156, "moles": 5.44}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 2075 mL to 2.075 L.\n3. Compute M = 0.345 / 2.075.\nFinal: {\"answer\": 0.1663, \"unit\": \"mol/L\"}", "dedupe_signature": "75aebb1ff7f8c5130a68108380abbee28b8bea35f7ad8b09f6397e522c40c41d", "difficulty": "medium", "final_answer": {"answer": 0.1663, "unit": "mol/L"}, "id": "molarity_004184_0.345_2075", "license": "Apache-2.0", "prompt": "A solution contains 0.345 mol of solute in 2075 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 2075 mL to 2.075 L.\nCompute M = 0.345 / 2.075.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 0.345, "volume_ml": 2075}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.34 and add it to the current value.\nFinal: {\"answer\": [-0.026, -0.321, 0.674], \"unit\": \"temperature_units\"}", "dedupe_signature": "61d24f9ae19edc58f2725b86eb6f5e1b58985adf8e9835357773edc3b9fa54d9", "difficulty": "hard", "final_answer": {"answer": [-0.026, -0.321, 0.674], "unit": "temperature_units"}, "id": "heat_step_004187_0.34_2.1_-0.4_-1.8_1.15_2.7", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=2.1, right=2.7; current interior values are [-0.4, -1.8, 1.15]. Use r=0.34. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.34 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-0.4, -1.8, 1.15], "left": 2.1, "r": 0.34, "right": 2.7}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 100 centimeters in one meter.\n2. Apply the conversion factor directly to the given value.\n3. Compute 4021.5 / 100.\nFinal: {\"answer\": 40.215, \"unit\": \"m\"}", "dedupe_signature": "33e2f68f783a59d08ea53b75315043691fef7decd49fe2c8d3a3d089bb67b3a4", "difficulty": "easy", "final_answer": {"answer": 40.215, "unit": "m"}, "id": "unit_convert_004188_cm_to_m_4021.5", "license": "Apache-2.0", "prompt": "Convert 4021.5 cm to m. Return the converted value with unit.", "reasoning_trace": "There are 100 centimeters in one meter.\nApply the conversion factor directly to the given value.\nCompute 4021.5 / 100.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 4021.5}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=287 degrees and keep the unit as newtons.\nFinal: {\"answer\": [89.9043, -294.0637], \"unit\": \"N\"}", "dedupe_signature": "de318ccb7cc5b6a854e6592f7aad5cb8bca536101092db64f8ad085245540f76", "difficulty": "medium", "final_answer": {"answer": [89.9043, -294.0637], "unit": "N"}, "id": "vector_components_004189_307.5_287", "license": "Apache-2.0", "prompt": "A vector has magnitude 307.5 N at 287 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=287 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 287, "magnitude": 307.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-2.65, -9.5], \"unit\": \"dimensionless\"}", "dedupe_signature": "13e5755abef1ac6ae1b0a26a87a5d62e20b6ab6d3d18c7cde4589d7bfea69887", "difficulty": "medium", "final_answer": {"answer": [-2.65, -9.5], "unit": "dimensionless"}, "id": "line_two_point_004190_-5.75_2.75_-2.65_-9.5", "license": "Apache-2.0", "prompt": "A line passes through points (-5.75, 5.7375) and (2.75, -16.7875). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -5.75, "x2": 2.75, "y1": 5.737499999999999, "y2": -16.7875}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. amount times volume is not concentration\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "73ab9bdc36ef0bf275263cb5f51d43c06fbcec4e54edfe21e4b5c17be948c2b1", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_004191_inconsistent_74ac0b02_295054", "license": "Apache-2.0", "prompt": "In student derivation case 295054, check dimensional consistency for C = n * V. The left side has dimensions mol/L and the right side has dimensions mol*L. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\namount times volume is not concentration\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "C = n * V"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef threshold_flags_004192(values, threshold):\n    return [value >= threshold for value in values]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"threshold_flags_004192\"}", "dedupe_signature": "246a77d744f74119a35f6d71a3c1efaa0970726a9aeafe366a54c87315e1aaed", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "threshold_flags_004192"}, "id": "code_004192_threshold_flags_004192", "license": "Apache-2.0", "prompt": "Write a Python function threshold_flags_004192(values, threshold) that returns a list of booleans showing whether each value is greater than or equal to threshold. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "threshold_flags_004192"}, "verifier": {"function": "threshold_flags_004192", "tests": ["assert threshold_flags_004192([1, 2, 3], 2) == [False, True, True]", "assert threshold_flags_004192([], 5) == []", "assert threshold_flags_004192([-1, 0], 0) == [False, True]"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: target_schema, valid_examples.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"target_schema\", \"valid_examples\"]}", "dedupe_signature": "90720777fff8fab098386235fb92faa092f15db265884fc0199bac980f425592", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["target_schema", "valid_examples"]}, "id": "abstain_004193_target_schema_valid_examples", "license": "Apache-2.0", "prompt": "Write a parser that converts each mobile ledger record from batch 593043 into the correct schema, but the prompt does not include the target schema or examples. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: target_schema, valid_examples.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["target_schema", "valid_examples"]}, "verifier": {"missing": ["target_schema", "valid_examples"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 0.5 kg and a = 2.55 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 1.275, \"unit\": \"N\"}", "dedupe_signature": "d81af0bab8c43f935e888b30c94ea4e8de958b0ee8871341bf6b276f7060fdb1", "difficulty": "easy", "final_answer": {"answer": 1.275, "unit": "N"}, "id": "force_004194_0.5_2.55", "license": "Apache-2.0", "prompt": "A cart has mass 0.5 kg and measured acceleration 2.55 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 0.5 kg and a = 2.55 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 2.55, "mass": 0.5}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 28.05^2 and multiply by 0.5 * 3.3.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 1298.2241, \"unit\": \"J\"}", "dedupe_signature": "31574331d2c9b1db38a087c0b14511d557d9a7307070772bad7f01fdeaba5cfe", "difficulty": "easy", "final_answer": {"answer": 1298.2241, "unit": "J"}, "id": "ke_004195_3.3_28.05", "license": "Apache-2.0", "prompt": "A body of mass 3.3 kg moves at 28.05 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 28.05^2 and multiply by 0.5 * 3.3.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 3.3, "velocity": 28.05}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=58 degrees through the sine of 2 theta.\n3. Substitute v=64.6 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 382.3457, \"unit\": \"m\"}", "dedupe_signature": "fa12cc76c8dc1d041a3c75938bd76fe0f23b3cdd9651ce88a24d32b65aa3721f", "difficulty": "medium", "final_answer": {"answer": 382.3457, "unit": "m"}, "id": "projectile_range_004196_64.6_58", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 64.6 m/s and angle 58 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=58 degrees through the sine of 2 theta.\nSubstitute v=64.6 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 58, "gravity": 9.81, "speed": 64.6}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 1.92 * 8.314 * 459 / 22.2.\nFinal: {\"answer\": 330.0433, \"unit\": \"kPa\"}", "dedupe_signature": "bcb292fab06d49aa8dd57c5f8812b6c464e193e5308a1c66fab94121dcc5f6a3", "difficulty": "medium", "final_answer": {"answer": 330.0433, "unit": "kPa"}, "id": "ideal_gas_004197_1.92_459_22.2", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=1.92 mol, T=459 K, and V=22.2 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 1.92 * 8.314 * 459 / 22.2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 1.92, "temp_k": 459, "volume_l": 22.2}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 465 * 0.89 * 98.\nFinal: {\"answer\": 40557.3, \"unit\": \"J\"}", "dedupe_signature": "45f9040553c47981f84308bccf1374bd7708e082e32e6414cf343fbcf314a0ae", "difficulty": "easy", "final_answer": {"answer": 40557.3, "unit": "J"}, "id": "heat_q_004198_465_0.89_98", "license": "Apache-2.0", "prompt": "A 465 g sample has specific heat 0.89 J/(g*K). How much heat is needed to raise its temperature by 98 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 465 * 0.89 * 98.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 98, "heat_capacity": 0.89, "mass_g": 465}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=150.8 V and R=150.4 ohm.\nFinal: {\"answer\": 151.2011, \"unit\": \"W\"}", "dedupe_signature": "9212dac89aea88ead0b5028ec50896d4406fd2b57c8c33995d72afaad69f996d", "difficulty": "easy", "final_answer": {"answer": 151.2011, "unit": "W"}, "id": "ohm_power_004199_150.8_150.4", "license": "Apache-2.0", "prompt": "A resistor has resistance 150.4 ohm and voltage 150.8 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=150.8 V and R=150.4 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 150.4, "voltage": 150.8}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 6.73 mol * 180.156 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 1212.4499, \"unit\": \"g\"}", "dedupe_signature": "e8aa2e4e8f4bbbe3032209f687ee33ade2e5b2ce51441889c77e96a9b3722d9a", "difficulty": "medium", "final_answer": {"answer": 1212.4499, "unit": "g"}, "id": "stoich_mass_004201_glucose_6.73", "license": "Apache-2.0", "prompt": "A sample contains 6.73 mol of glucose. Using molar mass 180.156 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 6.73 mol * 180.156 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "glucose", "molar_mass": 180.156, "moles": 6.73}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 1000 mL to 1 L.\n3. Compute M = 3.57 / 1.\nFinal: {\"answer\": 3.57, \"unit\": \"mol/L\"}", "dedupe_signature": "395f1173304fa087987295ef99c8c2fb62f0c34884d4e3c45757659921107eee", "difficulty": "medium", "final_answer": {"answer": 3.57, "unit": "mol/L"}, "id": "molarity_004202_3.57_1000", "license": "Apache-2.0", "prompt": "A solution contains 3.57 mol of solute in 1000 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 1000 mL to 1 L.\nCompute M = 3.57 / 1.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 3.57, "volume_ml": 1000}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.08 y, so each step multiplies y by 1 - h*0.08.\n3. Apply that update for 10 steps and round the final state.\nFinal: {\"answer\": 2.6228, \"unit\": \"state_units\"}", "dedupe_signature": "c3c76c9eb5e80088c814fd60de9f7ced46c9b14dfdc4c1042f0749614b6d5c31", "difficulty": "medium", "final_answer": {"answer": 2.6228, "unit": "state_units"}, "id": "euler_decay_004203_9_0.08_1.45_10", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.08 y with y(0)=9, step size h=1.45, for 10 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.08 y, so each step multiplies y by 1 - h*0.08.\nApply that update for 10 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 9.0, "rate": 0.08, "step": 1.45, "steps": 10}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.36 and add it to the current value.\nFinal: {\"answer\": [1.312, 1.462, -0.254], \"unit\": \"temperature_units\"}", "dedupe_signature": "94d745cd0b961f29137dde6c65879983c465145acf7deb3977a1427ae9271892", "difficulty": "hard", "final_answer": {"answer": [1.312, 1.462, -0.254], "unit": "temperature_units"}, "id": "heat_step_004205_0.36_1.4_2.95_-0.05_1.15_-1.55", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.4, right=-1.55; current interior values are [2.95, -0.05, 1.15]. Use r=0.36. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.36 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [2.95, -0.05, 1.15], "left": 1.4, "r": 0.36, "right": -1.55}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-1.5, 8.25], \"unit\": \"dimensionless\"}", "dedupe_signature": "9193c99f8c3b13d7a4cf05dd38ee679a4ea5219a1f79e8bc4454d6875ac750ee", "difficulty": "medium", "final_answer": {"answer": [-1.5, 8.25], "unit": "dimensionless"}, "id": "line_two_point_004208_17.25_19.25_-1.5_8.25", "license": "Apache-2.0", "prompt": "A line passes through points (17.25, -17.625) and (19.25, -20.625). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 17.25, "x2": 19.25, "y1": -17.625, "y2": -20.625}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef clamp_004210(x, lo, hi):\n    if lo > hi:\n        raise ValueError('lo must be <= hi')\n    return min(max(x, lo), hi)\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"clamp_004210\"}", "dedupe_signature": "ac395fcac762469156b6d3cdae382e3f29d81d904bf0b052a8e1f00eca3ea238", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "clamp_004210"}, "id": "code_004210_clamp_004210", "license": "Apache-2.0", "prompt": "Write a Python function clamp_004210(x, lo, hi) that clips x into the inclusive interval [lo, hi]. It must raise ValueError if lo > hi. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "clamp_004210"}, "verifier": {"function": "clamp_004210", "tests": ["assert clamp_004210(5, 0, 10) == 5", "assert clamp_004210(-2, 0, 10) == 0", "assert clamp_004210(12, 0, 10) == 10", "try:\n    clamp_004210(1, 3, 2)\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: required_fields, allowed_transformations.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"required_fields\", \"allowed_transformations\"]}", "dedupe_signature": "91b7230a5ceaf8bfed7f1cd5c134ad91573868a5a150ad68302d527ffcae07f3", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["required_fields", "allowed_transformations"]}, "id": "abstain_004211_required_fields_allowed_transformations", "license": "Apache-2.0", "prompt": "Write a sanitizer for valid mobile invoice records in release 338249, but the prompt does not state which fields are required or which transformations are allowed. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: required_fields, allowed_transformations.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["required_fields", "allowed_transformations"]}, "verifier": {"missing": ["required_fields", "allowed_transformations"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 21.35^2 and multiply by 0.5 * 27.3.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 6221.9771, \"unit\": \"J\"}", "dedupe_signature": "08ef1049981c971df0730cc04b5be8fad20cc2ca2a43c645fe1f54a773c350f2", "difficulty": "easy", "final_answer": {"answer": 6221.9771, "unit": "J"}, "id": "ke_004213_27.3_21.35", "license": "Apache-2.0", "prompt": "A body of mass 27.3 kg moves at 21.35 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 21.35^2 and multiply by 0.5 * 27.3.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 27.3, "velocity": 21.35}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=37 degrees through the sine of 2 theta.\n3. Substitute v=20.5 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 41.1794, \"unit\": \"m\"}", "dedupe_signature": "7f6f554c6226e72337d6d18da33570acee72bd0f0f3b976651fdeee3ca62098d", "difficulty": "medium", "final_answer": {"answer": 41.1794, "unit": "m"}, "id": "projectile_range_004214_20.5_37", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 20.5 m/s and angle 37 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=37 degrees through the sine of 2 theta.\nSubstitute v=20.5 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 37, "gravity": 9.81, "speed": 20.5}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 545 * 0.665 * 2.\nFinal: {\"answer\": 724.85, \"unit\": \"J\"}", "dedupe_signature": "faf36d7642a895073b04709e062fcf0cff3a0eff1bdb8a7298cc6ddb499f4cfb", "difficulty": "easy", "final_answer": {"answer": 724.85, "unit": "J"}, "id": "heat_q_004216_545_0.665_2", "license": "Apache-2.0", "prompt": "A 545 g sample has specific heat 0.665 J/(g*K). How much heat is needed to raise its temperature by 2 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 545 * 0.665 * 2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 2, "heat_capacity": 0.665, "mass_g": 545}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=175.1 V and R=169.6 ohm.\nFinal: {\"answer\": 180.7784, \"unit\": \"W\"}", "dedupe_signature": "23b6962675cee235788b107c1bba6d2359c14afe2283088784a29122615635a7", "difficulty": "easy", "final_answer": {"answer": 180.7784, "unit": "W"}, "id": "ohm_power_004217_175.1_169.6", "license": "Apache-2.0", "prompt": "A resistor has resistance 169.6 ohm and voltage 175.1 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=175.1 V and R=169.6 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 169.6, "voltage": 175.1}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=293.5 mg, t=268.5 h, and T_half=24 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 0.1258, \"unit\": \"mg\"}", "dedupe_signature": "e0f87137931719f15391019fa9f62cfb28990efd6397e3184f0f4a3d4e484296", "difficulty": "medium", "final_answer": {"answer": 0.1258, "unit": "mg"}, "id": "half_life_004218_293.5_24_268.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 293.5 mg. Its half-life is 24 hours. How many mg remain after 268.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=293.5 mg, t=268.5 h, and T_half=24 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 268.5, "half_life": 24.0, "initial_amount": 293.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 2.15 mol * 58.44 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 125.646, \"unit\": \"g\"}", "dedupe_signature": "fb3c20bcf1fcb04328a138e9f56e382ffb71f5e40273b1781ada97987a08601b", "difficulty": "medium", "final_answer": {"answer": 125.646, "unit": "g"}, "id": "stoich_mass_004219_sodium_chloride_2.15", "license": "Apache-2.0", "prompt": "A sample contains 2.15 mol of sodium chloride. Using molar mass 58.44 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 2.15 mol * 58.44 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "sodium chloride", "molar_mass": 58.44, "moles": 2.15}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 1670 mL to 1.67 L.\n3. Compute M = 0.015 / 1.67.\nFinal: {\"answer\": 0.009, \"unit\": \"mol/L\"}", "dedupe_signature": "d4df2b3e833f30fe72ea5ed3982daab5ad4015e15758fae11cd9d80f0845d2b0", "difficulty": "medium", "final_answer": {"answer": 0.009, "unit": "mol/L"}, "id": "molarity_004220_0.015_1670", "license": "Apache-2.0", "prompt": "A solution contains 0.015 mol of solute in 1670 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 1670 mL to 1.67 L.\nCompute M = 0.015 / 1.67.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 0.015, "volume_ml": 1670}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.88 y, so each step multiplies y by 1 - h*0.88.\n3. Apply that update for 2 steps and round the final state.\nFinal: {\"answer\": 12.2351, \"unit\": \"state_units\"}", "dedupe_signature": "72e4bef1fea8fba2cf6a96e37f8d272d3349a7b7c6859355915256e2009ae617", "difficulty": "medium", "final_answer": {"answer": 12.2351, "unit": "state_units"}, "id": "euler_decay_004221_73.5_0.88_1.6_2", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.88 y with y(0)=73.5, step size h=1.6, for 2 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.88 y, so each step multiplies y by 1 - h*0.88.\nApply that update for 2 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 73.5, "rate": 0.88, "step": 1.6, "steps": 2}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-7.5)=63.4 and f(-5.7)=51.52.\n3. The interval width is 1.8.\nFinal: {\"answer\": 103.428, \"unit\": \"area_units\"}", "dedupe_signature": "bc02775d7400b175b2615e4bae3df4dbec7802ea2881ef76ee1b04149437fe1e", "difficulty": "medium", "final_answer": {"answer": 103.428, "unit": "area_units"}, "id": "trapz_linear_004222_-6.6_13.9_-7.5_-5.7", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-6.6x+13.9 from x=-7.5 to x=-5.7. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-7.5)=63.4 and f(-5.7)=51.52.\nThe interval width is 1.8.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 13.9, "slope": -6.6, "x0": -7.5, "x1": -5.7}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.08 and add it to the current value.\nFinal: {\"answer\": [0.58, 0.548, 2.72], \"unit\": \"temperature_units\"}", "dedupe_signature": "4173aacefeaae0a15e42c68e8f9ba6310d8fb3543a60d7153cd3936fceb3da4c", "difficulty": "hard", "final_answer": {"answer": [0.58, 0.548, 2.72], "unit": "temperature_units"}, "id": "heat_step_004223_0.08_-0.4_0.7_0.3_3.0_2.2", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-0.4, right=2.2; current interior values are [0.7, 0.3, 3.0]. Use r=0.08. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.08 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [0.7, 0.3, 3.0], "left": -0.4, "r": 0.08, "right": 2.2}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. grams cancel with J/(g*K), and kelvin cancels, leaving joules\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "cae0840dfe55834ebea989add679ae5390e76e82626dbf068a062400ea78e6ce", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_004227_consistent_4153435f_869217", "license": "Apache-2.0", "prompt": "In simulation spec case 869217, check dimensional consistency for Q = m * c * DeltaT. The left side has dimensions J and the right side has dimensions J. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\ngrams cancel with J/(g*K), and kelvin cancels, leaving joules\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "Q = m * c * DeltaT"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef weighted_sum_004228(values, weights):\n    if len(values) != len(weights):\n        raise ValueError('length mismatch')\n    return sum(value * weight for value, weight in zip(values, weights))\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"weighted_sum_004228\"}", "dedupe_signature": "019ecfda09699a232eb88ba3f4cfbef2ce54a8e2fcbb84878024c3b1ea12cbb0", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "weighted_sum_004228"}, "id": "code_004228_weighted_sum_004228", "license": "Apache-2.0", "prompt": "Write a Python function weighted_sum_004228(values, weights) that returns sum(value*weight). Raise ValueError when the two inputs have different lengths. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "weighted_sum_004228"}, "verifier": {"function": "weighted_sum_004228", "tests": ["assert weighted_sum_004228([2, 3], [4, 5]) == 23", "assert weighted_sum_004228([], []) == 0", "try:\n    weighted_sum_004228([1], [1, 2])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: recurrence, objective, tie_breaking_rule.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"recurrence\", \"objective\", \"tie_breaking_rule\"]}", "dedupe_signature": "3621de3dac5a738d9d942504a0f54b6296536e5bf5895772f8ddeb1a5fed1932", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["recurrence", "objective", "tie_breaking_rule"]}, "id": "abstain_004229_recurrence_objective_tie_breaking_rule", "license": "Apache-2.0", "prompt": "Write a dynamic-programming solver for a knapsack scoring problem with 597 items and budget 94505, but the recurrence, objective, and tie-breaking rule are all absent. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: recurrence, objective, tie_breaking_rule.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["recurrence", "objective", "tie_breaking_rule"]}, "verifier": {"missing": ["recurrence", "objective", "tie_breaking_rule"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 15.7 kg and a = 3.7 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 58.09, \"unit\": \"N\"}", "dedupe_signature": "157d1f4bc72d5bdebcd41713c6fd440655bd2cbd05c8a9f569470209c23faee4", "difficulty": "easy", "final_answer": {"answer": 58.09, "unit": "N"}, "id": "force_004230_15.7_3.7", "license": "Apache-2.0", "prompt": "A cart has mass 15.7 kg and measured acceleration 3.7 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 15.7 kg and a = 3.7 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 3.7, "mass": 15.7}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 29.55^2 and multiply by 0.5 * 12.2.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 5326.5352, \"unit\": \"J\"}", "dedupe_signature": "26708b585515d304ca2ab867ee5cd5bb04b089540d10b588a2ef029032c73e19", "difficulty": "easy", "final_answer": {"answer": 5326.5352, "unit": "J"}, "id": "ke_004231_12.2_29.55", "license": "Apache-2.0", "prompt": "A body of mass 12.2 kg moves at 29.55 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 29.55^2 and multiply by 0.5 * 12.2.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 12.2, "velocity": 29.55}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=62 degrees through the sine of 2 theta.\n3. Substitute v=43.6 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 160.6491, \"unit\": \"m\"}", "dedupe_signature": "22a500e786a57fbf6b993fce55dd62d3659087d1d7603097eb449a8aedd97ab9", "difficulty": "medium", "final_answer": {"answer": 160.6491, "unit": "m"}, "id": "projectile_range_004232_43.6_62", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 43.6 m/s and angle 62 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=62 degrees through the sine of 2 theta.\nSubstitute v=43.6 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 62, "gravity": 9.81, "speed": 43.6}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 3.19 * 8.314 * 571 / 55.6.\nFinal: {\"answer\": 272.3717, \"unit\": \"kPa\"}", "dedupe_signature": "b02c0706bf6c44f02321d6599164cd03c29c8b216c7b05f51126dd159f606f9a", "difficulty": "medium", "final_answer": {"answer": 272.3717, "unit": "kPa"}, "id": "ideal_gas_004233_3.19_571_55.6", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=3.19 mol, T=571 K, and V=55.6 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 3.19 * 8.314 * 571 / 55.6.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 3.19, "temp_k": 571, "volume_l": 55.6}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=205.6 V and R=132.5 ohm.\nFinal: {\"answer\": 319.0291, \"unit\": \"W\"}", "dedupe_signature": "5556195e87b8d04bb8abcab7c7bb5a85a0ba8084b302b91275424fc14ab88e57", "difficulty": "easy", "final_answer": {"answer": 319.0291, "unit": "W"}, "id": "ohm_power_004235_205.6_132.5", "license": "Apache-2.0", "prompt": "A resistor has resistance 132.5 ohm and voltage 205.6 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=205.6 V and R=132.5 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 132.5, "voltage": 205.6}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=782.5 mg, t=166 h, and T_half=39.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 42.5007, \"unit\": \"mg\"}", "dedupe_signature": "7857a7bc55511b849f5f68fc49da72b74de63b5354899e37981ce30a250f4ea6", "difficulty": "medium", "final_answer": {"answer": 42.5007, "unit": "mg"}, "id": "half_life_004236_782.5_39.5_166", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 782.5 mg. Its half-life is 39.5 hours. How many mg remain after 166 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=782.5 mg, t=166 h, and T_half=39.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 166.0, "half_life": 39.5, "initial_amount": 782.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 0.53 mol * 100.087 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 53.0461, \"unit\": \"g\"}", "dedupe_signature": "5a27f8f9da2c8b829fe7b5d0be441266069475cb423555423aa65136f6c414d4", "difficulty": "medium", "final_answer": {"answer": 53.0461, "unit": "g"}, "id": "stoich_mass_004237_calcium_carbonate_0.53", "license": "Apache-2.0", "prompt": "A sample contains 0.53 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 0.53 mol * 100.087 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "calcium carbonate", "molar_mass": 100.087, "moles": 0.53}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-6.1)=-14.28 and f(1.1)=-8.52.\n3. The interval width is 7.2.\nFinal: {\"answer\": -82.08, \"unit\": \"area_units\"}", "dedupe_signature": "8fe4e0fd840b35e921fb0b7101bb3f81d4ef70556ea3cf600ce3ce9df9bfe987", "difficulty": "medium", "final_answer": {"answer": -82.08, "unit": "area_units"}, "id": "trapz_linear_004240_0.8_-9.4_-6.1_1.1", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=0.8x+-9.4 from x=-6.1 to x=1.1. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-6.1)=-14.28 and f(1.1)=-8.52.\nThe interval width is 7.2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -9.4, "slope": 0.8, "x0": -6.1, "x1": 1.1000000000000005}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.1 and add it to the current value.\nFinal: {\"answer\": [-1.19, 1.11, 1.765], \"unit\": \"temperature_units\"}", "dedupe_signature": "f828097be5481187d60a7663b486bdb0833876d381dd36aba64d44e3dcf7fc92", "difficulty": "hard", "final_answer": {"answer": [-1.19, 1.11, 1.765], "unit": "temperature_units"}, "id": "heat_step_004241_0.1_2.7_-2.0_1.4_1.9_1.05", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=2.7, right=1.05; current interior values are [-2.0, 1.4, 1.9]. Use r=0.1. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.1 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-2.0, 1.4, 1.9], "left": 2.7, "r": 0.1, "right": 1.05}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kelvin equals Celsius plus 273.15.\n2. Apply the conversion factor directly to the given value.\n3. Compute -38.0 + 273.15.\nFinal: {\"answer\": 235.15, \"unit\": \"K\"}", "dedupe_signature": "f305289f5be966e4b7f9d4f38938e93f11ae3914b03f718e1a7160817da45990", "difficulty": "easy", "final_answer": {"answer": 235.15, "unit": "K"}, "id": "unit_convert_004242_c_to_k_-38", "license": "Apache-2.0", "prompt": "Convert -38 degC to K. Return the converted value with unit.", "reasoning_trace": "Kelvin equals Celsius plus 273.15.\nApply the conversion factor directly to the given value.\nCompute -38.0 + 273.15.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": -38.0}, "verifier": {"formula": "value + 273.15", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=203 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-440.0013, -186.7695], \"unit\": \"N\"}", "dedupe_signature": "9897064cc1035b823112d15a8fcd674815a9ac438c5bfc7efe7a2c6afe2d3492", "difficulty": "medium", "final_answer": {"answer": [-440.0013, -186.7695], "unit": "N"}, "id": "vector_components_004243_478_203", "license": "Apache-2.0", "prompt": "A vector has magnitude 478 N at 203 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=203 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 203, "magnitude": 478.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-6.85, 13.5], \"unit\": \"dimensionless\"}", "dedupe_signature": "69b2bf4f80605a14aaeedadce90dab91dca28a08b634d329269676a8228161c1", "difficulty": "medium", "final_answer": {"answer": [-6.85, 13.5], "unit": "dimensionless"}, "id": "line_two_point_004244_3.75_15.75_-6.85_13.5", "license": "Apache-2.0", "prompt": "A line passes through points (3.75, -12.1875) and (15.75, -94.3875). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 3.75, "x2": 15.75, "y1": -12.1875, "y2": -94.38749999999999}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. volt squared divided by ohm is watt\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "a7787cf4a5cc3f44b864fa58f30eebcc51d72fa50125b3db95be2059de246a26", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_004245_consistent_82e93f3d_79729", "license": "Apache-2.0", "prompt": "In student derivation case 79729, check dimensional consistency for P = V^2 / R. The left side has dimensions W and the right side has dimensions W. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nvolt squared divided by ohm is watt\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "P = V^2 / R"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef pairwise_ratios_004246(numerators, denominators):\n    if len(numerators) != len(denominators):\n        raise ValueError('length mismatch')\n    out = []\n    for numerator, denominator in zip(numerators, denominators):\n        if denominator == 0:\n            raise ValueError('zero denominator')\n        out.append(numerator / denominator)\n    return out\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"pairwise_ratios_004246\"}", "dedupe_signature": "60729f27bff8101f155d18ebc864532fbf691ad32fd2f11992c0d21687754ef9", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "pairwise_ratios_004246"}, "id": "code_004246_pairwise_ratios_004246", "license": "Apache-2.0", "prompt": "Write a Python function pairwise_ratios_004246(numerators, denominators) that returns a list of n/d values. Raise ValueError if lengths differ or any denominator is zero. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "pairwise_ratios_004246"}, "verifier": {"function": "pairwise_ratios_004246", "tests": ["assert pairwise_ratios_004246([2, 9], [4, 3]) == [0.5, 3.0]", "try:\n    pairwise_ratios_004246([1], [0])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass", "try:\n    pairwise_ratios_004246([1, 2], [1])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: target_schema, valid_examples.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"target_schema\", \"valid_examples\"]}", "dedupe_signature": "bbbd1020f64cc289723bab3d78670c0c460c3ffe62630ba76aa21dcbc4462ad9", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["target_schema", "valid_examples"]}, "id": "abstain_004247_target_schema_valid_examples", "license": "Apache-2.0", "prompt": "Write a parser that converts each registry clinical record from batch 983533 into the correct schema, but the prompt does not include the target schema or examples. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: target_schema, valid_examples.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["target_schema", "valid_examples"]}, "verifier": {"missing": ["target_schema", "valid_examples"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 7.65 kg and a = 3.65 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 27.9225, \"unit\": \"N\"}", "dedupe_signature": "ae61da238a8cd9e5627b17a412eff967f43d5b3780e508556a12b60d31e89e7d", "difficulty": "easy", "final_answer": {"answer": 27.9225, "unit": "N"}, "id": "force_004248_7.65_3.65", "license": "Apache-2.0", "prompt": "A cart has mass 7.65 kg and measured acceleration 3.65 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 7.65 kg and a = 3.65 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 3.65, "mass": 7.65}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=33 degrees through the sine of 2 theta.\n3. Substitute v=6.6 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 4.0565, \"unit\": \"m\"}", "dedupe_signature": "3196ddd1827d700dd5e5f35dcdd8f6a4c75b82fd7b4a2753b5085061cd8d9d72", "difficulty": "medium", "final_answer": {"answer": 4.0565, "unit": "m"}, "id": "projectile_range_004250_6.6_33", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 6.6 m/s and angle 33 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=33 degrees through the sine of 2 theta.\nSubstitute v=6.6 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 33, "gravity": 9.81, "speed": 6.6}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 5.43 * 8.314 * 484 / 34.3.\nFinal: {\"answer\": 637.0318, \"unit\": \"kPa\"}", "dedupe_signature": "5b0a60c7f5facd0d6302815e0772701d5acab065f741f526d2ba62b1ae6a8c3e", "difficulty": "medium", "final_answer": {"answer": 637.0318, "unit": "kPa"}, "id": "ideal_gas_004251_5.43_484_34.3", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=5.43 mol, T=484 K, and V=34.3 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 5.43 * 8.314 * 484 / 34.3.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 5.43, "temp_k": 484, "volume_l": 34.3}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1755 * 2.85 * 74.\nFinal: {\"answer\": 370129.5, \"unit\": \"J\"}", "dedupe_signature": "931461b6b1570bd2d1f61dde6b68c58119cb70997d9f26cd66e5dfc0f23ae1ce", "difficulty": "easy", "final_answer": {"answer": 370129.5, "unit": "J"}, "id": "heat_q_004252_1755_2.85_74", "license": "Apache-2.0", "prompt": "A 1755 g sample has specific heat 2.85 J/(g*K). How much heat is needed to raise its temperature by 74 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1755 * 2.85 * 74.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 74, "heat_capacity": 2.85, "mass_g": 1755}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=809 mg, t=339.5 h, and T_half=30 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 0.3172, \"unit\": \"mg\"}", "dedupe_signature": "743678593c0ef43054fb52e39d4ecc7881ac870de0f2f8ad555c5fbfdaa00ca3", "difficulty": "medium", "final_answer": {"answer": 0.3172, "unit": "mg"}, "id": "half_life_004254_809_30_339.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 809 mg. Its half-life is 30 hours. How many mg remain after 339.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=809 mg, t=339.5 h, and T_half=30 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 339.5, "half_life": 30.0, "initial_amount": 809.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 1700 mL to 1.7 L.\n3. Compute M = 1.42 / 1.7.\nFinal: {\"answer\": 0.8353, \"unit\": \"mol/L\"}", "dedupe_signature": "0543fc66b3e74e2a6123ddc3d9faff03a6f7ce1d5e03b8d218d46434179bcd94", "difficulty": "medium", "final_answer": {"answer": 0.8353, "unit": "mol/L"}, "id": "molarity_004256_1.42_1700", "license": "Apache-2.0", "prompt": "A solution contains 1.42 mol of solute in 1700 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 1700 mL to 1.7 L.\nCompute M = 1.42 / 1.7.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 1.42, "volume_ml": 1700}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.54 y, so each step multiplies y by 1 - h*0.54.\n3. Apply that update for 3 steps and round the final state.\nFinal: {\"answer\": 47.8939, \"unit\": \"state_units\"}", "dedupe_signature": "03136c75868986d51e2d072a834e742a10d8f02360e241e49ce68251b51dcbf1", "difficulty": "medium", "final_answer": {"answer": 47.8939, "unit": "state_units"}, "id": "euler_decay_004257_74_0.54_0.25_3", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.54 y with y(0)=74, step size h=0.25, for 3 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.54 y, so each step multiplies y by 1 - h*0.54.\nApply that update for 3 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 74.0, "rate": 0.54, "step": 0.25, "steps": 3}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-8.4)=-30.48 and f(-3.7)=-17.79.\n3. The interval width is 4.7.\nFinal: {\"answer\": -113.4345, \"unit\": \"area_units\"}", "dedupe_signature": "4bd3ee88461f22c8eb849115149544e852466336b6c116ab28efc49cbd1bd10d", "difficulty": "medium", "final_answer": {"answer": -113.4345, "unit": "area_units"}, "id": "trapz_linear_004258_2.7_-7.8_-8.4_-3.7", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=2.7x+-7.8 from x=-8.4 to x=-3.7. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-8.4)=-30.48 and f(-3.7)=-17.79.\nThe interval width is 4.7.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -7.8, "slope": 2.7, "x0": -8.4, "x1": -3.7}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.04 and add it to the current value.\nFinal: {\"answer\": [-1.132, -1.634, -0.582], \"unit\": \"temperature_units\"}", "dedupe_signature": "aa6da467eee910cb262556d4cfe392f67d5dc66028ce6e141bbcae662db2d7fc", "difficulty": "hard", "final_answer": {"answer": [-1.132, -1.634, -0.582], "unit": "temperature_units"}, "id": "heat_step_004259_0.04_1.0_-1.2_-1.7_-0.55_-0.2", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1, right=-0.2; current interior values are [-1.2, -1.7, -0.55]. Use r=0.04. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.04 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-1.2, -1.7, -0.55], "left": 1.0, "r": 0.04, "right": -0.2}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=43 degrees and keep the unit as newtons.\nFinal: {\"answer\": [203.682, 189.9365], \"unit\": \"N\"}", "dedupe_signature": "2083304ccc0943ce471483519b4a47c6a570bbef563306cde0ae8cba82b09899", "difficulty": "medium", "final_answer": {"answer": [203.682, 189.9365], "unit": "N"}, "id": "vector_components_004261_278.5_43", "license": "Apache-2.0", "prompt": "A vector has magnitude 278.5 N at 43 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=43 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 43, "magnitude": 278.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [9.5, -14.25], \"unit\": \"dimensionless\"}", "dedupe_signature": "cc1b162ca65ad67f087f7c885a0a8990ea6c8c51930a593b694598e713b60e34", "difficulty": "medium", "final_answer": {"answer": [9.5, -14.25], "unit": "dimensionless"}, "id": "line_two_point_004262_-20_-15.25_9.5_-14.25", "license": "Apache-2.0", "prompt": "A line passes through points (-20, -204.25) and (-15.25, -159.125). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -20.0, "x2": -15.25, "y1": -204.25, "y2": -159.125}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. m*v is momentum, not energy\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "11f90d6a969765c5cb8881ab798e91ae6b661fbdfd7b667205ca29301b89e866", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_004263_inconsistent_1e14b074_888342", "license": "Apache-2.0", "prompt": "In simulation spec case 888342, check dimensional consistency for E = m * v. The left side has dimensions kg*m^2/s^2 and the right side has dimensions kg*m/s. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nm*v is momentum, not energy\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "E = m * v"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef threshold_flags_004264(values, threshold):\n    return [value >= threshold for value in values]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"threshold_flags_004264\"}", "dedupe_signature": "b0c5ae529bc3e8b26dc3a5266d80c311975d93d2cedca817267a7f7cdec52c4d", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "threshold_flags_004264"}, "id": "code_004264_threshold_flags_004264", "license": "Apache-2.0", "prompt": "Write a Python function threshold_flags_004264(values, threshold) that returns a list of booleans showing whether each value is greater than or equal to threshold. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "threshold_flags_004264"}, "verifier": {"function": "threshold_flags_004264", "tests": ["assert threshold_flags_004264([1, 2, 3], 2) == [False, True, True]", "assert threshold_flags_004264([], 5) == []", "assert threshold_flags_004264([-1, 0], 0) == [False, True]"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: launch_angle_or_vertical_velocity.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"launch_angle_or_vertical_velocity\"]}", "dedupe_signature": "04059a8afc8ba2183232980201e0008c30531af09edc08f0535e8bf3732e267c", "difficulty": "easy", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["launch_angle_or_vertical_velocity"]}, "id": "abstain_004265_launch_angle_or_vertical_velocity", "license": "Apache-2.0", "prompt": "Compute projectile range on level ground. The prompt gives initial speed 16 m/s but does not give launch angle or vertical velocity. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: launch_angle_or_vertical_velocity.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["launch_angle_or_vertical_velocity"]}, "verifier": {"missing": ["launch_angle_or_vertical_velocity"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 7.3 kg and a = 12.15 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 88.695, \"unit\": \"N\"}", "dedupe_signature": "a238232c7aa4fc28bf0fcb2d66a4cdf7c3ffde1c22348a890adca871c22f81e3", "difficulty": "easy", "final_answer": {"answer": 88.695, "unit": "N"}, "id": "force_004266_7.3_12.15", "license": "Apache-2.0", "prompt": "A cart has mass 7.3 kg and measured acceleration 12.15 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 7.3 kg and a = 12.15 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 12.15, "mass": 7.3}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=43 degrees through the sine of 2 theta.\n3. Substitute v=74.4 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 562.8824, \"unit\": \"m\"}", "dedupe_signature": "89fe9bd29d81344f41340fd4dbd406aa00dc43fd4341dc3e73f5975d5c0197d9", "difficulty": "medium", "final_answer": {"answer": 562.8824, "unit": "m"}, "id": "projectile_range_004268_74.4_43", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 74.4 m/s and angle 43 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=43 degrees through the sine of 2 theta.\nSubstitute v=74.4 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 43, "gravity": 9.81, "speed": 74.4}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 3.29 * 8.314 * 301 / 7.5.\nFinal: {\"answer\": 1097.7695, \"unit\": \"kPa\"}", "dedupe_signature": "8979f58baf2838bc2cb2a3df09a51f4d7c00ff4fbd82a254b50fb9fe4a4fed2a", "difficulty": "medium", "final_answer": {"answer": 1097.7695, "unit": "kPa"}, "id": "ideal_gas_004269_3.29_301_7.5", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=3.29 mol, T=301 K, and V=7.5 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 3.29 * 8.314 * 301 / 7.5.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 3.29, "temp_k": 301, "volume_l": 7.5}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1520 * 1.775 * 115.\nFinal: {\"answer\": 310270.0, \"unit\": \"J\"}", "dedupe_signature": "4a3410c4e22fa1f46966417db8a9089d1f5e20dc60577cdb01976ca451ffa57b", "difficulty": "easy", "final_answer": {"answer": 310270.0, "unit": "J"}, "id": "heat_q_004270_1520_1.775_115", "license": "Apache-2.0", "prompt": "A 1520 g sample has specific heat 1.775 J/(g*K). How much heat is needed to raise its temperature by 115 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1520 * 1.775 * 115.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 115, "heat_capacity": 1.775, "mass_g": 1520}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=223.2 V and R=72.5 ohm.\nFinal: {\"answer\": 687.1481, \"unit\": \"W\"}", "dedupe_signature": "c9cbe17f7f98fb665783dfad72b81dcbc9bf4c3ea1cfe59708e54af74163fe92", "difficulty": "easy", "final_answer": {"answer": 687.1481, "unit": "W"}, "id": "ohm_power_004271_223.2_72.5", "license": "Apache-2.0", "prompt": "A resistor has resistance 72.5 ohm and voltage 223.2 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=223.2 V and R=72.5 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 72.5, "voltage": 223.2}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=732.5 mg, t=241.5 h, and T_half=84.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 101.034, \"unit\": \"mg\"}", "dedupe_signature": "5d90082febe2263db2568cd2e09de1f74368468c6c1d4bacd39022b96a8ea87e", "difficulty": "medium", "final_answer": {"answer": 101.034, "unit": "mg"}, "id": "half_life_004272_732.5_84.5_241.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 732.5 mg. Its half-life is 84.5 hours. How many mg remain after 241.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=732.5 mg, t=241.5 h, and T_half=84.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 241.5, "half_life": 84.5, "initial_amount": 732.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 1.53 mol * 44.01 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 67.3353, \"unit\": \"g\"}", "dedupe_signature": "071eb757e6507bb6fe21b3bce8be8a5d2f6a5f1ad70059873a771b8cc9db560c", "difficulty": "medium", "final_answer": {"answer": 67.3353, "unit": "g"}, "id": "stoich_mass_004273_carbon_dioxide_1.53", "license": "Apache-2.0", "prompt": "A sample contains 1.53 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 1.53 mol * 44.01 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "carbon dioxide", "molar_mass": 44.01, "moles": 1.53}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 2610 mL to 2.61 L.\n3. Compute M = 1.18 / 2.61.\nFinal: {\"answer\": 0.4521, \"unit\": \"mol/L\"}", "dedupe_signature": "593eaa1061a0dd2ca77647e79a793366689a7032e676ae228496c07af1e04f6c", "difficulty": "medium", "final_answer": {"answer": 0.4521, "unit": "mol/L"}, "id": "molarity_004274_1.18_2610", "license": "Apache-2.0", "prompt": "A solution contains 1.18 mol of solute in 2610 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 2610 mL to 2.61 L.\nCompute M = 1.18 / 2.61.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 1.18, "volume_ml": 2610}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-5.1)=28.48 and f(-4.9)=27.12.\n3. The interval width is 0.2.\nFinal: {\"answer\": 5.56, \"unit\": \"area_units\"}", "dedupe_signature": "2547564e31e55f32a5a54101430835e4f9e6fb6a0049deb802ffb59434d32dd2", "difficulty": "medium", "final_answer": {"answer": 5.56, "unit": "area_units"}, "id": "trapz_linear_004276_-6.8_-6.2_-5.1_-4.9", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-6.8x+-6.2 from x=-5.1 to x=-4.9. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-5.1)=28.48 and f(-4.9)=27.12.\nThe interval width is 0.2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -6.2, "slope": -6.8, "x0": -5.1, "x1": -4.8999999999999995}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.14 and add it to the current value.\nFinal: {\"answer\": [-1.434, -0.428, 1.765], \"unit\": \"temperature_units\"}", "dedupe_signature": "b1464633c10bca928c5fbed263f84819aff3fb157e930782354582bb54fbcc67", "difficulty": "hard", "final_answer": {"answer": [-1.434, -0.428, 1.765], "unit": "temperature_units"}, "id": "heat_step_004277_0.14_-0.75_-1.7_-0.75_2.5_0.5", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-0.75, right=0.5; current interior values are [-1.7, -0.75, 2.5]. Use r=0.14. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.14 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-1.7, -0.75, 2.5], "left": -0.75, "r": 0.14, "right": 0.5}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 24512.0 / 1000.\nFinal: {\"answer\": 24.512, \"unit\": \"kg\"}", "dedupe_signature": "70879afc15c041ca1d2c8246ff1865dae42f3ac19a3f4e21305608b623e0e45c", "difficulty": "easy", "final_answer": {"answer": 24.512, "unit": "kg"}, "id": "unit_convert_004278_g_to_kg_24512", "license": "Apache-2.0", "prompt": "Convert 24512 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 24512.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 24512.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-9.55, 1.25], \"unit\": \"dimensionless\"}", "dedupe_signature": "c7c9746262aed9b96768a1389c54cb900d0f2e38d1c0b95191788c5c3edadb18", "difficulty": "medium", "final_answer": {"answer": [-9.55, 1.25], "unit": "dimensionless"}, "id": "line_two_point_004280_12.25_27_-9.55_1.25", "license": "Apache-2.0", "prompt": "A line passes through points (12.25, -115.738) and (27, -256.6). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 12.25, "x2": 27.0, "y1": -115.73750000000001, "y2": -256.6}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef running_total_004282(values):\n    total = 0\n    out = []\n    for value in values:\n        total += value\n        out.append(total)\n    return out\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"running_total_004282\"}", "dedupe_signature": "f843d248e976505db8875561bc7b880c4aa00c3611fe6534830240e1d0cf538e", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "running_total_004282"}, "id": "code_004282_running_total_004282", "license": "Apache-2.0", "prompt": "Write a Python function running_total_004282(values) that returns cumulative sums as a new list. It must not mutate the input list. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "running_total_004282"}, "verifier": {"function": "running_total_004282", "tests": ["assert running_total_004282([1, 2, 3]) == [1, 3, 6]", "xs = [4, -1, 2]; assert running_total_004282(xs) == [4, 3, 5] and xs == [4, -1, 2]", "assert running_total_004282([]) == []"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: recurrence, objective, tie_breaking_rule.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"recurrence\", \"objective\", \"tie_breaking_rule\"]}", "dedupe_signature": "7568efa0ce2d61fca988d4021912e490d5263e751a9eca744051f8da9217b10f", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["recurrence", "objective", "tie_breaking_rule"]}, "id": "abstain_004283_recurrence_objective_tie_breaking_rule", "license": "Apache-2.0", "prompt": "Write a dynamic-programming solver for a segmentation scoring problem with 1083 items and budget 27660, but the recurrence, objective, and tie-breaking rule are all absent. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: recurrence, objective, tie_breaking_rule.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["recurrence", "objective", "tie_breaking_rule"]}, "verifier": {"missing": ["recurrence", "objective", "tie_breaking_rule"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 18.65 kg and a = 6.6 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 123.09, \"unit\": \"N\"}", "dedupe_signature": "3b39cb48c38ac7d33f89b3aee01d7dd9c7e12e27c8ee6c1b91a43fe4c3937a64", "difficulty": "easy", "final_answer": {"answer": 123.09, "unit": "N"}, "id": "force_004284_18.65_6.6", "license": "Apache-2.0", "prompt": "A cart has mass 18.65 kg and measured acceleration 6.6 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 18.65 kg and a = 6.6 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 6.6, "mass": 18.65}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 0.9^2 and multiply by 0.5 * 26.15.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 10.5907, \"unit\": \"J\"}", "dedupe_signature": "bd1d152f98cb72b5ea0fac860e7dcecb3bac27b01222040db98dfa6168a963e1", "difficulty": "easy", "final_answer": {"answer": 10.5907, "unit": "J"}, "id": "ke_004285_26.15_0.9", "license": "Apache-2.0", "prompt": "A body of mass 26.15 kg moves at 0.9 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 0.9^2 and multiply by 0.5 * 26.15.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 26.15, "velocity": 0.9}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=56 degrees through the sine of 2 theta.\n3. Substitute v=79.6 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 598.8568, \"unit\": \"m\"}", "dedupe_signature": "33934a371ac8074a9591809c09b395e97b1f8778239b73674c9eefb511d15c0a", "difficulty": "medium", "final_answer": {"answer": 598.8568, "unit": "m"}, "id": "projectile_range_004286_79.6_56", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 79.6 m/s and angle 56 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=56 degrees through the sine of 2 theta.\nSubstitute v=79.6 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 56, "gravity": 9.81, "speed": 79.6}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 1.07 * 8.314 * 342 / 85.0.\nFinal: {\"answer\": 35.7932, \"unit\": \"kPa\"}", "dedupe_signature": "fadc6047f2400a63107acc90a8e11115ec14981170b75501318b48e1bc552446", "difficulty": "medium", "final_answer": {"answer": 35.7932, "unit": "kPa"}, "id": "ideal_gas_004287_1.07_342_85.0", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=1.07 mol, T=342 K, and V=85.0 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 1.07 * 8.314 * 342 / 85.0.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 1.07, "temp_k": 342, "volume_l": 85.0}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 485 * 2 * 62.\nFinal: {\"answer\": 60140.0, \"unit\": \"J\"}", "dedupe_signature": "7f1962dbd8e9501e3468f7fb432d100815ddbb1467dc74ea536001df30d3f901", "difficulty": "easy", "final_answer": {"answer": 60140.0, "unit": "J"}, "id": "heat_q_004288_485_2_62", "license": "Apache-2.0", "prompt": "A 485 g sample has specific heat 2 J/(g*K). How much heat is needed to raise its temperature by 62 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 485 * 2 * 62.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 62, "heat_capacity": 2.0, "mass_g": 485}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=53.5 V and R=75.8 ohm.\nFinal: {\"answer\": 37.7606, \"unit\": \"W\"}", "dedupe_signature": "5b418559253b88909a771fe1886a7113ce05576217b3f0f3bf16fcb5532e19bc", "difficulty": "easy", "final_answer": {"answer": 37.7606, "unit": "W"}, "id": "ohm_power_004289_53.5_75.8", "license": "Apache-2.0", "prompt": "A resistor has resistance 75.8 ohm and voltage 53.5 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=53.5 V and R=75.8 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 75.8, "voltage": 53.5}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=284.5 mg, t=322 h, and T_half=67 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 10.1705, \"unit\": \"mg\"}", "dedupe_signature": "377d8db6875c99c680cc6879e049e8181486df91b50aee38f4b03e2d73fa4fd1", "difficulty": "medium", "final_answer": {"answer": 10.1705, "unit": "mg"}, "id": "half_life_004290_284.5_67_322", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 284.5 mg. Its half-life is 67 hours. How many mg remain after 322 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=284.5 mg, t=322 h, and T_half=67 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 322.0, "half_life": 67.0, "initial_amount": 284.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 4.35 mol * 58.44 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 254.214, \"unit\": \"g\"}", "dedupe_signature": "9d27f3e6ef42dbf5dd15f6ff335ff7a9855254bf6b01997874a3ca46963fb445", "difficulty": "medium", "final_answer": {"answer": 254.214, "unit": "g"}, "id": "stoich_mass_004291_sodium_chloride_4.35", "license": "Apache-2.0", "prompt": "A sample contains 4.35 mol of sodium chloride. Using molar mass 58.44 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 4.35 mol * 58.44 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "sodium chloride", "molar_mass": 58.44, "moles": 4.35}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 2915 mL to 2.915 L.\n3. Compute M = 1.33 / 2.915.\nFinal: {\"answer\": 0.4563, \"unit\": \"mol/L\"}", "dedupe_signature": "2cb880733ee93558181e538ca897ae865d90bd5e284ba79948d35490ca664e1e", "difficulty": "medium", "final_answer": {"answer": 0.4563, "unit": "mol/L"}, "id": "molarity_004292_1.33_2915", "license": "Apache-2.0", "prompt": "A solution contains 1.33 mol of solute in 2915 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 2915 mL to 2.915 L.\nCompute M = 1.33 / 2.915.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 1.33, "volume_ml": 2915}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.6 y, so each step multiplies y by 1 - h*0.6.\n3. Apply that update for 4 steps and round the final state.\nFinal: {\"answer\": 13.7897, \"unit\": \"state_units\"}", "dedupe_signature": "aac7642c38b03219cab347295f137ce29eb1383b9ed57d7c91cd792143319d97", "difficulty": "medium", "final_answer": {"answer": 13.7897, "unit": "state_units"}, "id": "euler_decay_004293_30.5_0.6_0.3_4", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.6 y with y(0)=30.5, step size h=0.3, for 4 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.6 y, so each step multiplies y by 1 - h*0.6.\nApply that update for 4 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 30.5, "rate": 0.6, "step": 0.3, "steps": 4}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(9.3)=9.07 and f(15.6)=14.74.\n3. The interval width is 6.3.\nFinal: {\"answer\": 75.0015, \"unit\": \"area_units\"}", "dedupe_signature": "ac4b909cd44665bf81531df1ab1152bea298f0e6fc2d320fb85835ebbaec6c3d", "difficulty": "medium", "final_answer": {"answer": 75.0015, "unit": "area_units"}, "id": "trapz_linear_004294_0.9_0.7_9.3_15.6", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=0.9x+0.7 from x=9.3 to x=15.6. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(9.3)=9.07 and f(15.6)=14.74.\nThe interval width is 6.3.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 0.7, "slope": 0.9, "x0": 9.3, "x1": 15.600000000000001}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 100 centimeters in one meter.\n2. Apply the conversion factor directly to the given value.\n3. Compute 3978.5 / 100.\nFinal: {\"answer\": 39.785, \"unit\": \"m\"}", "dedupe_signature": "442fda24d219ebb87298188663ea109e2a0b6a673b4bbc267d86bebdf9cf44ed", "difficulty": "easy", "final_answer": {"answer": 39.785, "unit": "m"}, "id": "unit_convert_004296_cm_to_m_3978.5", "license": "Apache-2.0", "prompt": "Convert 3978.5 cm to m. Return the converted value with unit.", "reasoning_trace": "There are 100 centimeters in one meter.\nApply the conversion factor directly to the given value.\nCompute 3978.5 / 100.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 3978.5}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=120 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-123.25, 213.4753], \"unit\": \"N\"}", "dedupe_signature": "f6596b2d20ed999eeecc64c4d70b28b27b20446ccb7c68810a9d435f5e7b0eba", "difficulty": "medium", "final_answer": {"answer": [-123.25, 213.4753], "unit": "N"}, "id": "vector_components_004297_246.5_120", "license": "Apache-2.0", "prompt": "A vector has magnitude 246.5 N at 120 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=120 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 120, "magnitude": 246.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-7.45, 14.5], \"unit\": \"dimensionless\"}", "dedupe_signature": "172f35d22dc526912678cf944b3a8df62b5b2145a2689f919a849be7f230e433", "difficulty": "medium", "final_answer": {"answer": [-7.45, 14.5], "unit": "dimensionless"}, "id": "line_two_point_004298_5.75_15_-7.45_14.5", "license": "Apache-2.0", "prompt": "A line passes through points (5.75, -28.3375) and (15, -97.25). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 5.75, "x2": 15.0, "y1": -28.3375, "y2": -97.25}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. amount times volume is not concentration\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "f433655f7e4a21a061541e92f8e1bb59c2cfb2dfcc96d0135387d9ec1c66d5c2", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_004299_inconsistent_74ac0b02_474100", "license": "Apache-2.0", "prompt": "In lab notebook case 474100, check dimensional consistency for C = n * V. The left side has dimensions mol/L and the right side has dimensions mol*L. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\namount times volume is not concentration\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "C = n * V"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef pairwise_ratios_004300(numerators, denominators):\n    if len(numerators) != len(denominators):\n        raise ValueError('length mismatch')\n    out = []\n    for numerator, denominator in zip(numerators, denominators):\n        if denominator == 0:\n            raise ValueError('zero denominator')\n        out.append(numerator / denominator)\n    return out\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"pairwise_ratios_004300\"}", "dedupe_signature": "f94f0be26319f44a81fa0bc2441542675eca3ce25233f241caab1204e334b270", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "pairwise_ratios_004300"}, "id": "code_004300_pairwise_ratios_004300", "license": "Apache-2.0", "prompt": "Write a Python function pairwise_ratios_004300(numerators, denominators) that returns a list of n/d values. Raise ValueError if lengths differ or any denominator is zero. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "pairwise_ratios_004300"}, "verifier": {"function": "pairwise_ratios_004300", "tests": ["assert pairwise_ratios_004300([2, 9], [4, 3]) == [0.5, 3.0]", "try:\n    pairwise_ratios_004300([1], [0])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass", "try:\n    pairwise_ratios_004300([1, 2], [1])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: recurrence, objective, tie_breaking_rule.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"recurrence\", \"objective\", \"tie_breaking_rule\"]}", "dedupe_signature": "5e851e46480dbb0f614bbb71053b8febc49dbb5291a7efe2ccc8a262c940bf38", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["recurrence", "objective", "tie_breaking_rule"]}, "id": "abstain_004301_recurrence_objective_tie_breaking_rule", "license": "Apache-2.0", "prompt": "Write a dynamic-programming solver for a alignment scoring problem with 981 items and budget 18770, but the recurrence, objective, and tie-breaking rule are all absent. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: recurrence, objective, tie_breaking_rule.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["recurrence", "objective", "tie_breaking_rule"]}, "verifier": {"missing": ["recurrence", "objective", "tie_breaking_rule"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 21.1 kg and a = 7.4 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 156.14, \"unit\": \"N\"}", "dedupe_signature": "249f67fb950ea498cdced5126b73be78691da06ca960166182b66acf2a6e416e", "difficulty": "easy", "final_answer": {"answer": 156.14, "unit": "N"}, "id": "force_004302_21.1_7.4", "license": "Apache-2.0", "prompt": "A cart has mass 21.1 kg and measured acceleration 7.4 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 21.1 kg and a = 7.4 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 7.4, "mass": 21.1}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 38.5^2 and multiply by 0.5 * 13.05.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 9671.6812, \"unit\": \"J\"}", "dedupe_signature": "4c2b9e8dd1c4ea1eb8c188b071d51ca32efef3a61ad60920c28e8addeeb8f6b6", "difficulty": "easy", "final_answer": {"answer": 9671.6812, "unit": "J"}, "id": "ke_004303_13.05_38.5", "license": "Apache-2.0", "prompt": "A body of mass 13.05 kg moves at 38.5 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 38.5^2 and multiply by 0.5 * 13.05.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 13.05, "velocity": 38.5}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=73 degrees through the sine of 2 theta.\n3. Substitute v=83.6 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 398.387, \"unit\": \"m\"}", "dedupe_signature": "bae286873cd341ae2c1bb3df48fea0cd6ffbd3803eaaaf0cf723317ea7a675e4", "difficulty": "medium", "final_answer": {"answer": 398.387, "unit": "m"}, "id": "projectile_range_004304_83.6_73", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 83.6 m/s and angle 73 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=73 degrees through the sine of 2 theta.\nSubstitute v=83.6 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 73, "gravity": 9.81, "speed": 83.6}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 3.71 * 8.314 * 464 / 88.4.\nFinal: {\"answer\": 161.901, \"unit\": \"kPa\"}", "dedupe_signature": "ba1dace821f0c4bbed5926366678e2607a0a085228e697e645b66018c6a46aca", "difficulty": "medium", "final_answer": {"answer": 161.901, "unit": "kPa"}, "id": "ideal_gas_004305_3.71_464_88.4", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=3.71 mol, T=464 K, and V=88.4 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 3.71 * 8.314 * 464 / 88.4.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 3.71, "temp_k": 464, "volume_l": 88.4}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 475 * 2.275 * 7.\nFinal: {\"answer\": 7564.375, \"unit\": \"J\"}", "dedupe_signature": "485165c8c9060f70be9a726216c9330eccb7356e4935f82c73e795b86c1467f1", "difficulty": "easy", "final_answer": {"answer": 7564.375, "unit": "J"}, "id": "heat_q_004306_475_2.275_7", "license": "Apache-2.0", "prompt": "A 475 g sample has specific heat 2.275 J/(g*K). How much heat is needed to raise its temperature by 7 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 475 * 2.275 * 7.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 7, "heat_capacity": 2.275, "mass_g": 475}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=70.3 V and R=147.2 ohm.\nFinal: {\"answer\": 33.574, \"unit\": \"W\"}", "dedupe_signature": "f0336b12c9040fff32181953481edf77065cd810749c687c721ca7b82b53e678", "difficulty": "easy", "final_answer": {"answer": 33.574, "unit": "W"}, "id": "ohm_power_004307_70.3_147.2", "license": "Apache-2.0", "prompt": "A resistor has resistance 147.2 ohm and voltage 70.3 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=70.3 V and R=147.2 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 147.2, "voltage": 70.3}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=253 mg, t=13 h, and T_half=94 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 229.8734, \"unit\": \"mg\"}", "dedupe_signature": "574d7671a544ed458759e33a135eed607fde2f89fdd847fd1d91d49771863691", "difficulty": "medium", "final_answer": {"answer": 229.8734, "unit": "mg"}, "id": "half_life_004308_253_94_13", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 253 mg. Its half-life is 94 hours. How many mg remain after 13 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=253 mg, t=13 h, and T_half=94 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 13.0, "half_life": 94.0, "initial_amount": 253.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 0.92 mol * 44.01 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 40.4892, \"unit\": \"g\"}", "dedupe_signature": "22baa3f14841d0c1a1a5bffc5f2a735784b81523399eafc3e25ee043f8fa51e1", "difficulty": "medium", "final_answer": {"answer": 40.4892, "unit": "g"}, "id": "stoich_mass_004309_carbon_dioxide_0.92", "license": "Apache-2.0", "prompt": "A sample contains 0.92 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 0.92 mol * 44.01 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "carbon dioxide", "molar_mass": 44.01, "moles": 0.92}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 3000 mL to 3 L.\n3. Compute M = 2.73 / 3.\nFinal: {\"answer\": 0.91, \"unit\": \"mol/L\"}", "dedupe_signature": "fe043ff45358fce1d9393f6f7911854272d7128b9aa7a2e6730b25f71b7c0329", "difficulty": "medium", "final_answer": {"answer": 0.91, "unit": "mol/L"}, "id": "molarity_004310_2.73_3000", "license": "Apache-2.0", "prompt": "A solution contains 2.73 mol of solute in 3000 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 3000 mL to 3 L.\nCompute M = 2.73 / 3.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 2.73, "volume_ml": 3000}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-5.8)=48.38 and f(1.2)=5.68.\n3. The interval width is 7.\nFinal: {\"answer\": 189.21, \"unit\": \"area_units\"}", "dedupe_signature": "2d19fdbb6fed2bdc0745aea184d7d377a54dd37457c5893ab2a9ff12fbe99799", "difficulty": "medium", "final_answer": {"answer": 189.21, "unit": "area_units"}, "id": "trapz_linear_004312_-6.1_13_-5.8_1.2", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-6.1x+13 from x=-5.8 to x=1.2. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-5.8)=48.38 and f(1.2)=5.68.\nThe interval width is 7.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 13.0, "slope": -6.1, "x0": -5.8, "x1": 1.2000000000000002}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.12 and add it to the current value.\nFinal: {\"answer\": [0.112, 0.956, 0.828], \"unit\": \"temperature_units\"}", "dedupe_signature": "fdfde3398fb2df018de6ee1c294446edb8bc17f9c9747a44213520aad0dc889e", "difficulty": "hard", "final_answer": {"answer": [0.112, 0.956, 0.828], "unit": "temperature_units"}, "id": "heat_step_004313_0.12_-0.8_0.1_1.1_0.9_0.1", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-0.8, right=0.1; current interior values are [0.1, 1.1, 0.9]. Use r=0.12. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.12 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [0.1, 1.1, 0.9], "left": -0.8, "r": 0.12, "right": 0.1}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 100 centimeters in one meter.\n2. Apply the conversion factor directly to the given value.\n3. Compute 395.5 / 100.\nFinal: {\"answer\": 3.955, \"unit\": \"m\"}", "dedupe_signature": "fe92e1d98410096cd6ef2bad872315241baaf3c0f9400718e16adba9980e0ce2", "difficulty": "easy", "final_answer": {"answer": 3.955, "unit": "m"}, "id": "unit_convert_004314_cm_to_m_395.5", "license": "Apache-2.0", "prompt": "Convert 395.5 cm to m. Return the converted value with unit.", "reasoning_trace": "There are 100 centimeters in one meter.\nApply the conversion factor directly to the given value.\nCompute 395.5 / 100.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 395.5}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=179 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-468.4286, 8.1765], \"unit\": \"N\"}", "dedupe_signature": "491f2eac1f2910fd717b49cbb5e42ac0af4fde34d0b5d2a85837ff3fcdac0a4c", "difficulty": "medium", "final_answer": {"answer": [-468.4286, 8.1765], "unit": "N"}, "id": "vector_components_004315_468.5_179", "license": "Apache-2.0", "prompt": "A vector has magnitude 468.5 N at 179 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=179 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 179, "magnitude": 468.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef finite_differences_004318(values):\n    return [values[i + 1] - values[i] for i in range(len(values) - 1)]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"finite_differences_004318\"}", "dedupe_signature": "27a0037e7fcc3237309883d83b5f9a9bf7b9b4f17bff0895aba717ba8784a2a2", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "finite_differences_004318"}, "id": "code_004318_finite_differences_004318", "license": "Apache-2.0", "prompt": "Write a Python function finite_differences_004318(values) that returns the list of successive differences values[i+1] - values[i]. It must return [] for fewer than two values. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "finite_differences_004318"}, "verifier": {"function": "finite_differences_004318", "tests": ["assert finite_differences_004318([1, 4, 9, 16]) == [3, 5, 7]", "assert finite_differences_004318([5]) == []", "assert finite_differences_004318([]) == []"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: recurrence, objective, tie_breaking_rule.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"recurrence\", \"objective\", \"tie_breaking_rule\"]}", "dedupe_signature": "e2d085828e90bee532e4e8296429a63553f8cc4a5e5a536b38dab6cab65dbbfa", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["recurrence", "objective", "tie_breaking_rule"]}, "id": "abstain_004319_recurrence_objective_tie_breaking_rule", "license": "Apache-2.0", "prompt": "Write a dynamic-programming solver for a alignment scoring problem with 4792 items and budget 34085, but the recurrence, objective, and tie-breaking rule are all absent. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: recurrence, objective, tie_breaking_rule.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["recurrence", "objective", "tie_breaking_rule"]}, "verifier": {"missing": ["recurrence", "objective", "tie_breaking_rule"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 23.55^2 and multiply by 0.5 * 14.8.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 4104.0585, \"unit\": \"J\"}", "dedupe_signature": "09b07565ee02ff1cd4eae5702e1f4c9f3481b46f34289906fc71f5edffb9515a", "difficulty": "easy", "final_answer": {"answer": 4104.0585, "unit": "J"}, "id": "ke_004321_14.8_23.55", "license": "Apache-2.0", "prompt": "A body of mass 14.8 kg moves at 23.55 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 23.55^2 and multiply by 0.5 * 14.8.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 14.8, "velocity": 23.55}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 1.89 * 8.314 * 534 / 77.6.\nFinal: {\"answer\": 108.1313, \"unit\": \"kPa\"}", "dedupe_signature": "0bac83233062c2a99033d55b1a89b1f8a733f8ccb7320b609e66fe918d9a5d03", "difficulty": "medium", "final_answer": {"answer": 108.1313, "unit": "kPa"}, "id": "ideal_gas_004323_1.89_534_77.6", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=1.89 mol, T=534 K, and V=77.6 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 1.89 * 8.314 * 534 / 77.6.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 1.89, "temp_k": 534, "volume_l": 77.6}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 830 * 4.495 * 56.\nFinal: {\"answer\": 208927.6, \"unit\": \"J\"}", "dedupe_signature": "51eadbf8e417544df95e3a90a158304d8dae50d30052c23f49d36fc190337d1a", "difficulty": "easy", "final_answer": {"answer": 208927.6, "unit": "J"}, "id": "heat_q_004324_830_4.495_56", "license": "Apache-2.0", "prompt": "A 830 g sample has specific heat 4.495 J/(g*K). How much heat is needed to raise its temperature by 56 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 830 * 4.495 * 56.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 56, "heat_capacity": 4.495, "mass_g": 830}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=191.6 V and R=193.4 ohm.\nFinal: {\"answer\": 189.8168, \"unit\": \"W\"}", "dedupe_signature": "f42071a3c936d9246efede96f4927c5540299f89286eca04deba21c7204ae21a", "difficulty": "easy", "final_answer": {"answer": 189.8168, "unit": "W"}, "id": "ohm_power_004325_191.6_193.4", "license": "Apache-2.0", "prompt": "A resistor has resistance 193.4 ohm and voltage 191.6 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=191.6 V and R=193.4 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 193.4, "voltage": 191.6}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=149 mg, t=59.5 h, and T_half=53 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 68.4286, \"unit\": \"mg\"}", "dedupe_signature": "3c0b5933a16ec0c18e2266f3cce16a75b7334c9bd77d8ce8dbe7e924d1b317cc", "difficulty": "medium", "final_answer": {"answer": 68.4286, "unit": "mg"}, "id": "half_life_004326_149_53_59.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 149 mg. Its half-life is 53 hours. How many mg remain after 59.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=149 mg, t=59.5 h, and T_half=53 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 59.5, "half_life": 53.0, "initial_amount": 149.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.7 y, so each step multiplies y by 1 - h*0.7.\n3. Apply that update for 9 steps and round the final state.\nFinal: {\"answer\": 0.0, \"unit\": \"state_units\"}", "dedupe_signature": "dcbe850f61282fff70ba67bca09308d8dbec7731c2b7813376523c4326d18fc0", "difficulty": "medium", "final_answer": {"answer": 0.0, "unit": "state_units"}, "id": "euler_decay_004329_69.5_0.7_1.3_9", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.7 y with y(0)=69.5, step size h=1.3, for 9 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.7 y, so each step multiplies y by 1 - h*0.7.\nApply that update for 9 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 69.5, "rate": 0.7, "step": 1.3, "steps": 9}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-6.6)=-41.32 and f(0.3)=4.91.\n3. The interval width is 6.9.\nFinal: {\"answer\": -125.6145, \"unit\": \"area_units\"}", "dedupe_signature": "7b124acb8533d2953ed0b99d24384800e143f75e4d4bfb914bbe21cd9743151d", "difficulty": "medium", "final_answer": {"answer": -125.6145, "unit": "area_units"}, "id": "trapz_linear_004330_6.7_2.9_-6.6_0.3", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=6.7x+2.9 from x=-6.6 to x=0.3. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-6.6)=-41.32 and f(0.3)=4.91.\nThe interval width is 6.9.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 2.9, "slope": 6.7, "x0": -6.6, "x1": 0.3000000000000007}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.14 and add it to the current value.\nFinal: {\"answer\": [0.455, -1.193, -1.026], \"unit\": \"temperature_units\"}", "dedupe_signature": "f56e07daf21524b56a98cd6b45518cbb8f2fe78fa5fa5742a7e5cf90572ebd98", "difficulty": "hard", "final_answer": {"answer": [0.455, -1.193, -1.026], "unit": "temperature_units"}, "id": "heat_step_004331_0.14_3.0_0.35_-1.55_-0.9_-1.15", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=3, right=-1.15; current interior values are [0.35, -1.55, -0.9]. Use r=0.14. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.14 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [0.35, -1.55, -0.9], "left": 3.0, "r": 0.14, "right": -1.15}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=52 degrees and keep the unit as newtons.\nFinal: {\"answer\": [32.9379, 42.1586], \"unit\": \"N\"}", "dedupe_signature": "4fb6cfdda487dba89be9497dc02f801e142d10dc102e5ec9abfc6636b9696df9", "difficulty": "medium", "final_answer": {"answer": [32.9379, 42.1586], "unit": "N"}, "id": "vector_components_004333_53.5_52", "license": "Apache-2.0", "prompt": "A vector has magnitude 53.5 N at 52 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=52 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 52, "magnitude": 53.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [8.4, 12.0], \"unit\": \"dimensionless\"}", "dedupe_signature": "f6f3dcccb222f6f4d795e84c7a8dc9a5bd0b60b000d1af74b0d9e6b62eb61cb0", "difficulty": "medium", "final_answer": {"answer": [8.4, 12.0], "unit": "dimensionless"}, "id": "line_two_point_004334_5.5_17.5_8.4_12", "license": "Apache-2.0", "prompt": "A line passes through points (5.5, 58.2) and (17.5, 159). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 5.5, "x2": 17.5, "y1": 58.2, "y2": 159.0}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. lever arm times force has torque dimensions\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "c6442c3f4d8e7f0501e1a52fba53ecb170bd0bd8aef564903ed9e3bf42abb603", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_004335_consistent_5ca82cb9_344643", "license": "Apache-2.0", "prompt": "In sensor calibration case 344643, check dimensional consistency for tau = r * F. The left side has dimensions N*m and the right side has dimensions N*m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nlever arm times force has torque dimensions\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "tau = r * F"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef finite_differences_004336(values):\n    return [values[i + 1] - values[i] for i in range(len(values) - 1)]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"finite_differences_004336\"}", "dedupe_signature": "ed3037bfae01870de631606352643cc989a0009f32b888fe8b4515477a691d63", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "finite_differences_004336"}, "id": "code_004336_finite_differences_004336", "license": "Apache-2.0", "prompt": "Write a Python function finite_differences_004336(values) that returns the list of successive differences values[i+1] - values[i]. It must return [] for fewer than two values. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "finite_differences_004336"}, "verifier": {"function": "finite_differences_004336", "tests": ["assert finite_differences_004336([1, 4, 9, 16]) == [3, 5, 7]", "assert finite_differences_004336([5]) == []", "assert finite_differences_004336([]) == []"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: recurrence, objective, tie_breaking_rule.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"recurrence\", \"objective\", \"tie_breaking_rule\"]}", "dedupe_signature": "b604d2b5b45e72b2f69c2a9fd0c5a1e8a05bf5e543cc95f0254f62ae78a2ad8d", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["recurrence", "objective", "tie_breaking_rule"]}, "id": "abstain_004337_recurrence_objective_tie_breaking_rule", "license": "Apache-2.0", "prompt": "Write a dynamic-programming solver for a segmentation scoring problem with 2504 items and budget 54640, but the recurrence, objective, and tie-breaking rule are all absent. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: recurrence, objective, tie_breaking_rule.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["recurrence", "objective", "tie_breaking_rule"]}, "verifier": {"missing": ["recurrence", "objective", "tie_breaking_rule"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=16 degrees through the sine of 2 theta.\n3. Substitute v=69.3 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 259.4222, \"unit\": \"m\"}", "dedupe_signature": "ac4ae02cbc9efc75926e79949a277d0ce7677e21ba3f206f95837ba2b9dd15b7", "difficulty": "medium", "final_answer": {"answer": 259.4222, "unit": "m"}, "id": "projectile_range_004340_69.3_16", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 69.3 m/s and angle 16 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=16 degrees through the sine of 2 theta.\nSubstitute v=69.3 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 16, "gravity": 9.81, "speed": 69.3}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 0.18 * 8.314 * 420 / 92.6.\nFinal: {\"answer\": 6.7877, \"unit\": \"kPa\"}", "dedupe_signature": "21a765069e4b6e89541f241c297ad34a24950801a583bb7faea3205f17ace503", "difficulty": "medium", "final_answer": {"answer": 6.7877, "unit": "kPa"}, "id": "ideal_gas_004341_0.18_420_92.6", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=0.18 mol, T=420 K, and V=92.6 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 0.18 * 8.314 * 420 / 92.6.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 0.18, "temp_k": 420, "volume_l": 92.6}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1360 * 1.595 * 78.\nFinal: {\"answer\": 169197.6, \"unit\": \"J\"}", "dedupe_signature": "866d3131bb2693824041dd31186ceee94069abe086827f84fa02d9caf77ef41c", "difficulty": "easy", "final_answer": {"answer": 169197.6, "unit": "J"}, "id": "heat_q_004342_1360_1.595_78", "license": "Apache-2.0", "prompt": "A 1360 g sample has specific heat 1.595 J/(g*K). How much heat is needed to raise its temperature by 78 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1360 * 1.595 * 78.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 78, "heat_capacity": 1.595, "mass_g": 1360}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=585 mg, t=322.5 h, and T_half=19.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 0.0061, \"unit\": \"mg\"}", "dedupe_signature": "c083c0d26e1e0a3fcc711c578166dd0455531cacd8975c4809d24c5dfb91961e", "difficulty": "medium", "final_answer": {"answer": 0.0061, "unit": "mg"}, "id": "half_life_004344_585_19.5_322.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 585 mg. Its half-life is 19.5 hours. How many mg remain after 322.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=585 mg, t=322.5 h, and T_half=19.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 322.5, "half_life": 19.5, "initial_amount": 585.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 7.88 mol * 44.01 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 346.7988, \"unit\": \"g\"}", "dedupe_signature": "24ebe357ef6b8f1a00d6145d9407cd9f9f9f912fc9dccef86c87424dd44c5ab5", "difficulty": "medium", "final_answer": {"answer": 346.7988, "unit": "g"}, "id": "stoich_mass_004345_carbon_dioxide_7.88", "license": "Apache-2.0", "prompt": "A sample contains 7.88 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 7.88 mol * 44.01 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "carbon dioxide", "molar_mass": 44.01, "moles": 7.88}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 4275 mL to 4.275 L.\n3. Compute M = 2.425 / 4.275.\nFinal: {\"answer\": 0.5673, \"unit\": \"mol/L\"}", "dedupe_signature": "6e8d484c0e703ddf36374686a3adfa347e4f522912dd183343330a90d945b603", "difficulty": "medium", "final_answer": {"answer": 0.5673, "unit": "mol/L"}, "id": "molarity_004346_2.425_4275", "license": "Apache-2.0", "prompt": "A solution contains 2.425 mol of solute in 4275 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 4275 mL to 4.275 L.\nCompute M = 2.425 / 4.275.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 2.425, "volume_ml": 4275}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.11 y, so each step multiplies y by 1 - h*0.11.\n3. Apply that update for 8 steps and round the final state.\nFinal: {\"answer\": 13.3218, \"unit\": \"state_units\"}", "dedupe_signature": "e85d574bf06f19c334fad611e8c4e602e63a25382dc3da4397f05dffa7cd21d1", "difficulty": "medium", "final_answer": {"answer": 13.3218, "unit": "state_units"}, "id": "euler_decay_004347_43.5_0.11_1.25_8", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.11 y with y(0)=43.5, step size h=1.25, for 8 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.11 y, so each step multiplies y by 1 - h*0.11.\nApply that update for 8 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 43.5, "rate": 0.11, "step": 1.25, "steps": 8}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-4.9)=-28.62 and f(4.9)=18.42.\n3. The interval width is 9.8.\nFinal: {\"answer\": -49.98, \"unit\": \"area_units\"}", "dedupe_signature": "e96660df29e45082f98cf0076ae0eafb9472d54a808e4c4e1013571884688ca6", "difficulty": "medium", "final_answer": {"answer": -49.98, "unit": "area_units"}, "id": "trapz_linear_004348_4.8_-5.1_-4.9_4.9", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=4.8x+-5.1 from x=-4.9 to x=4.9. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-4.9)=-28.62 and f(4.9)=18.42.\nThe interval width is 9.8.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -5.1, "slope": 4.8, "x0": -4.9, "x1": 4.9}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.08 and add it to the current value.\nFinal: {\"answer\": [-1.044, -0.878, 0.06], \"unit\": \"temperature_units\"}", "dedupe_signature": "7445471bb40eeda1023fc5cebe5c858ea0a2b6fe7fa19e4c640d77b1776e55fc", "difficulty": "hard", "final_answer": {"answer": [-1.044, -0.878, 0.06], "unit": "temperature_units"}, "id": "heat_step_004349_0.08_1.55_-1.3_-0.95_0.3_-1.45", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.55, right=-1.45; current interior values are [-1.3, -0.95, 0.3]. Use r=0.08. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.08 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-1.3, -0.95, 0.3], "left": 1.55, "r": 0.08, "right": -1.45}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=116 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-146.416, 300.1972], \"unit\": \"N\"}", "dedupe_signature": "367bddbae6461e62f594f02843123bd9cdcc77e4fcdde9bb7b7513e93a2d3843", "difficulty": "medium", "final_answer": {"answer": [-146.416, 300.1972], "unit": "N"}, "id": "vector_components_004351_334_116", "license": "Apache-2.0", "prompt": "A vector has magnitude 334 N at 116 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=116 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 116, "magnitude": 334.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [4.05, -3.5], \"unit\": \"dimensionless\"}", "dedupe_signature": "eca15d968cb1843c629b361db8e235ecfb94a32034133f3bb66dcad6e3c82707", "difficulty": "medium", "final_answer": {"answer": [4.05, -3.5], "unit": "dimensionless"}, "id": "line_two_point_004352_-15.75_-10.75_4.05_-3.5", "license": "Apache-2.0", "prompt": "A line passes through points (-15.75, -67.2875) and (-10.75, -47.0375). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -15.75, "x2": -10.75, "y1": -67.2875, "y2": -47.0375}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef center_values_004354(values):\n    if not values:\n        raise ValueError('center_values requires at least one value')\n    mean = sum(values) / len(values)\n    return [value - mean for value in values]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"center_values_004354\"}", "dedupe_signature": "ebeeb6a47dc3dbd84b3ebc36d7424ddd7cee60c2bb25b112c7310542056ca245", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "center_values_004354"}, "id": "code_004354_center_values_004354", "license": "Apache-2.0", "prompt": "Write a Python function center_values_004354(values) that subtracts the arithmetic mean from each value and returns a new list. Raise ValueError for an empty input. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "center_values_004354"}, "verifier": {"function": "center_values_004354", "tests": ["out = center_values_004354([1, 2, 3]); assert out == [-1, 0, 1]", "assert center_values_004354([5]) == [0]", "try:\n    center_values_004354([])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: volume.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"volume\"]}", "dedupe_signature": "36762fc5c3720bb1c0e39138a3c91ff17df8a29a3ce7da1af33ec545ec1259bb", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["volume"]}, "id": "abstain_004355_volume", "license": "Apache-2.0", "prompt": "Compute pressure from the ideal gas law. The prompt gives n=4.21 mol and T=300 K, but does not give volume. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: volume.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["volume"]}, "verifier": {"missing": ["volume"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 25 kg and a = 6.15 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 153.75, \"unit\": \"N\"}", "dedupe_signature": "4eb12b5d4d14a3e52b8c796a8f96867bd342c869188fff533462e839348842d0", "difficulty": "easy", "final_answer": {"answer": 153.75, "unit": "N"}, "id": "force_004356_25_6.15", "license": "Apache-2.0", "prompt": "A cart has mass 25 kg and measured acceleration 6.15 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 25 kg and a = 6.15 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 6.15, "mass": 25.0}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 16.1^2 and multiply by 0.5 * 21.65.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 2805.9483, \"unit\": \"J\"}", "dedupe_signature": "9ab6a02d395c6e81fbe4aec751f056f754cda2f69e16b974d04bceca843d19b8", "difficulty": "easy", "final_answer": {"answer": 2805.9483, "unit": "J"}, "id": "ke_004357_21.65_16.1", "license": "Apache-2.0", "prompt": "A body of mass 21.65 kg moves at 16.1 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 16.1^2 and multiply by 0.5 * 21.65.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 21.65, "velocity": 16.1}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=9 degrees through the sine of 2 theta.\n3. Substitute v=50.7 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 80.971, \"unit\": \"m\"}", "dedupe_signature": "3da1f369db6551cb87eac4b36b8a752aaf3b16185bbca9ac16c21259d02cb04c", "difficulty": "medium", "final_answer": {"answer": 80.971, "unit": "m"}, "id": "projectile_range_004358_50.7_9", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 50.7 m/s and angle 9 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=9 degrees through the sine of 2 theta.\nSubstitute v=50.7 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 9, "gravity": 9.81, "speed": 50.7}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 2.85 * 8.314 * 601 / 118.4.\nFinal: {\"answer\": 120.2756, \"unit\": \"kPa\"}", "dedupe_signature": "90a6bc4908ccc6ecd99c2e3ce1f6c93c4fa9670008bcd4b46e92ab5229a2a26c", "difficulty": "medium", "final_answer": {"answer": 120.2756, "unit": "kPa"}, "id": "ideal_gas_004359_2.85_601_118.4", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=2.85 mol, T=601 K, and V=118.4 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 2.85 * 8.314 * 601 / 118.4.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 2.85, "temp_k": 601, "volume_l": 118.4}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=201.1 V and R=129.9 ohm.\nFinal: {\"answer\": 311.3257, \"unit\": \"W\"}", "dedupe_signature": "c6057630fb91273f7f8c4fa5f52272314dda7e82f43720e81b56d10588579822", "difficulty": "easy", "final_answer": {"answer": 311.3257, "unit": "W"}, "id": "ohm_power_004361_201.1_129.9", "license": "Apache-2.0", "prompt": "A resistor has resistance 129.9 ohm and voltage 201.1 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=201.1 V and R=129.9 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 129.9, "voltage": 201.1}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=142 mg, t=8.5 h, and T_half=82.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 132.2127, \"unit\": \"mg\"}", "dedupe_signature": "26895a9bb6461be433b52deb8569c49cb7c18dd28e3c7211e618373217ed7a29", "difficulty": "medium", "final_answer": {"answer": 132.2127, "unit": "mg"}, "id": "half_life_004362_142_82.5_8.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 142 mg. Its half-life is 82.5 hours. How many mg remain after 8.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=142 mg, t=8.5 h, and T_half=82.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 8.5, "half_life": 82.5, "initial_amount": 142.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 0.14 mol * 180.156 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 25.2218, \"unit\": \"g\"}", "dedupe_signature": "021c9ffa7b56fd512d13dff808caf173bc8c315c10daa3b58a0bfb74e564c0f2", "difficulty": "medium", "final_answer": {"answer": 25.2218, "unit": "g"}, "id": "stoich_mass_004363_glucose_0.14", "license": "Apache-2.0", "prompt": "A sample contains 0.14 mol of glucose. Using molar mass 180.156 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 0.14 mol * 180.156 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "glucose", "molar_mass": 180.156, "moles": 0.14}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 2060 mL to 2.06 L.\n3. Compute M = 1.065 / 2.06.\nFinal: {\"answer\": 0.517, \"unit\": \"mol/L\"}", "dedupe_signature": "bf7509f10e6beddf1b7559382b49d5bbf3d770e1431be79c80ce6375b00dcadf", "difficulty": "medium", "final_answer": {"answer": 0.517, "unit": "mol/L"}, "id": "molarity_004364_1.065_2060", "license": "Apache-2.0", "prompt": "A solution contains 1.065 mol of solute in 2060 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 2060 mL to 2.06 L.\nCompute M = 1.065 / 2.06.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 1.065, "volume_ml": 2060}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(9.9)=33.94 and f(15.7)=60.62.\n3. The interval width is 5.8.\nFinal: {\"answer\": 274.224, \"unit\": \"area_units\"}", "dedupe_signature": "515d2b1cf61b90d754813899f97e72bc8ce9d3783f6fe2d7e03f690d410e6bad", "difficulty": "medium", "final_answer": {"answer": 274.224, "unit": "area_units"}, "id": "trapz_linear_004366_4.6_-11.6_9.9_15.7", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=4.6x+-11.6 from x=9.9 to x=15.7. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(9.9)=33.94 and f(15.7)=60.62.\nThe interval width is 5.8.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -11.6, "slope": 4.6, "x0": 9.9, "x1": 15.7}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.18 and add it to the current value.\nFinal: {\"answer\": [-0.857, 0.924, 1.224], \"unit\": \"temperature_units\"}", "dedupe_signature": "c8e7eb63cb92ccc77f1894fc6ccd5e8776f699c621473e463a68957809a4bbe3", "difficulty": "hard", "final_answer": {"answer": [-0.857, 0.924, 1.224], "unit": "temperature_units"}, "id": "heat_step_004367_0.18_0.85_-2.0_1.5_1.8_-1.1", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=0.85, right=-1.1; current interior values are [-2.0, 1.5, 1.8]. Use r=0.18. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.18 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-2.0, 1.5, 1.8], "left": 0.85, "r": 0.18, "right": -1.1}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kelvin equals Celsius plus 273.15.\n2. Apply the conversion factor directly to the given value.\n3. Compute 64.5 + 273.15.\nFinal: {\"answer\": 337.65, \"unit\": \"K\"}", "dedupe_signature": "58e6a49e7efa28df70cd397129e13da403c0d7a40767e55c3e5ebadb66c72710", "difficulty": "easy", "final_answer": {"answer": 337.65, "unit": "K"}, "id": "unit_convert_004368_c_to_k_64.5", "license": "Apache-2.0", "prompt": "Convert 64.5 degC to K. Return the converted value with unit.", "reasoning_trace": "Kelvin equals Celsius plus 273.15.\nApply the conversion factor directly to the given value.\nCompute 64.5 + 273.15.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 64.5}, "verifier": {"formula": "value + 273.15", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=29 degrees and keep the unit as newtons.\nFinal: {\"answer\": [386.1446, 214.0434], \"unit\": \"N\"}", "dedupe_signature": "20b4701a7d6a7c9ea0c970c7188962560f2ed30216a9ba541a522f1cb299f849", "difficulty": "medium", "final_answer": {"answer": [386.1446, 214.0434], "unit": "N"}, "id": "vector_components_004369_441.5_29", "license": "Apache-2.0", "prompt": "A vector has magnitude 441.5 N at 29 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=29 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 29, "magnitude": 441.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-4.6, 25.75], \"unit\": \"dimensionless\"}", "dedupe_signature": "7e1e7ca4d517ef5aadd895e582192a6635cbf0e3662c83e383b9fb98fd93c1d6", "difficulty": "medium", "final_answer": {"answer": [-4.6, 25.75], "unit": "dimensionless"}, "id": "line_two_point_004370_14.25_20_-4.6_25.75", "license": "Apache-2.0", "prompt": "A line passes through points (14.25, -39.8) and (20, -66.25). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 14.25, "x2": 20.0, "y1": -39.8, "y2": -66.25}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. mass times acceleration has newton dimensions\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "dcb4b4d75413c2fd12cd0c790dca65a1e46720fb0a3377399b437981a561fa4e", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_004371_consistent_03f5e041_296400", "license": "Apache-2.0", "prompt": "In quality-control check case 296400, check dimensional consistency for F = m * a. The left side has dimensions kg*m/s^2 and the right side has dimensions kg*m/s^2. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nmass times acceleration has newton dimensions\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "F = m * a"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef pairwise_ratios_004372(numerators, denominators):\n    if len(numerators) != len(denominators):\n        raise ValueError('length mismatch')\n    out = []\n    for numerator, denominator in zip(numerators, denominators):\n        if denominator == 0:\n            raise ValueError('zero denominator')\n        out.append(numerator / denominator)\n    return out\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"pairwise_ratios_004372\"}", "dedupe_signature": "d1f44d006e52f08ddfb75a2c51d9abf66b5a44a9b0c3874aa8e24ebf7c1fcbdb", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "pairwise_ratios_004372"}, "id": "code_004372_pairwise_ratios_004372", "license": "Apache-2.0", "prompt": "Write a Python function pairwise_ratios_004372(numerators, denominators) that returns a list of n/d values. Raise ValueError if lengths differ or any denominator is zero. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "pairwise_ratios_004372"}, "verifier": {"function": "pairwise_ratios_004372", "tests": ["assert pairwise_ratios_004372([2, 9], [4, 3]) == [0.5, 3.0]", "try:\n    pairwise_ratios_004372([1], [0])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass", "try:\n    pairwise_ratios_004372([1, 2], [1])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: launch_angle_or_vertical_velocity.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"launch_angle_or_vertical_velocity\"]}", "dedupe_signature": "8798b17ade8d8e9b7fbb1b823316f4010eeaab528e1518c3ae377a28827baf2c", "difficulty": "easy", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["launch_angle_or_vertical_velocity"]}, "id": "abstain_004373_launch_angle_or_vertical_velocity", "license": "Apache-2.0", "prompt": "Compute projectile range on level ground. The prompt gives initial speed 23 m/s but does not give launch angle or vertical velocity. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: launch_angle_or_vertical_velocity.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["launch_angle_or_vertical_velocity"]}, "verifier": {"missing": ["launch_angle_or_vertical_velocity"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 18.85^2 and multiply by 0.5 * 6.05.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 1074.8506, \"unit\": \"J\"}", "dedupe_signature": "9c8a23d242aa39eb5cbb040b16dc0d50a9f02e7a818a0c78df730773d8d3f547", "difficulty": "easy", "final_answer": {"answer": 1074.8506, "unit": "J"}, "id": "ke_004375_6.05_18.85", "license": "Apache-2.0", "prompt": "A body of mass 6.05 kg moves at 18.85 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 18.85^2 and multiply by 0.5 * 6.05.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 6.05, "velocity": 18.85}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=17 degrees through the sine of 2 theta.\n3. Substitute v=40.5 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 93.4981, \"unit\": \"m\"}", "dedupe_signature": "6f53329197f76fa4bc60de60ab10fc030ae008c8a47d8c290e7281fae9988a60", "difficulty": "medium", "final_answer": {"answer": 93.4981, "unit": "m"}, "id": "projectile_range_004376_40.5_17", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 40.5 m/s and angle 17 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=17 degrees through the sine of 2 theta.\nSubstitute v=40.5 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 17, "gravity": 9.81, "speed": 40.5}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 4.37 * 8.314 * 249 / 104.1.\nFinal: {\"answer\": 86.9041, \"unit\": \"kPa\"}", "dedupe_signature": "b654eec39d453f900325b46604d8e2732b174c81816c13cba456fdf90f300854", "difficulty": "medium", "final_answer": {"answer": 86.9041, "unit": "kPa"}, "id": "ideal_gas_004377_4.37_249_104.1", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=4.37 mol, T=249 K, and V=104.1 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 4.37 * 8.314 * 249 / 104.1.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 4.37, "temp_k": 249, "volume_l": 104.1}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1615 * 3.73 * 21.\nFinal: {\"answer\": 126502.95, \"unit\": \"J\"}", "dedupe_signature": "03a315301d943cd96973087224eff90a566e23c24614a24ab5206e38e5a518ed", "difficulty": "easy", "final_answer": {"answer": 126502.95, "unit": "J"}, "id": "heat_q_004378_1615_3.73_21", "license": "Apache-2.0", "prompt": "A 1615 g sample has specific heat 3.73 J/(g*K). How much heat is needed to raise its temperature by 21 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1615 * 3.73 * 21.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 21, "heat_capacity": 3.73, "mass_g": 1615}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=27.3 V and R=10.4 ohm.\nFinal: {\"answer\": 71.6625, \"unit\": \"W\"}", "dedupe_signature": "95efaa832dce7d02cb14f508b5af33f3206a01d409b7f7352f70a34213e4a134", "difficulty": "easy", "final_answer": {"answer": 71.6625, "unit": "W"}, "id": "ohm_power_004379_27.3_10.4", "license": "Apache-2.0", "prompt": "A resistor has resistance 10.4 ohm and voltage 27.3 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=27.3 V and R=10.4 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 10.4, "voltage": 27.3}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=649 mg, t=255 h, and T_half=63 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 39.2455, \"unit\": \"mg\"}", "dedupe_signature": "05d54d056381a2251cfe242877a4ef2b0a69f049b0303b9382abb7b11f831f5c", "difficulty": "medium", "final_answer": {"answer": 39.2455, "unit": "mg"}, "id": "half_life_004380_649_63_255", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 649 mg. Its half-life is 63 hours. How many mg remain after 255 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=649 mg, t=255 h, and T_half=63 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 255.0, "half_life": 63.0, "initial_amount": 649.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 5.33 mol * 18.015 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 96.02, \"unit\": \"g\"}", "dedupe_signature": "7c65c2c01b04482da4d6860155d0bd93918ac8b419ff3c689c5ea61499261d57", "difficulty": "medium", "final_answer": {"answer": 96.02, "unit": "g"}, "id": "stoich_mass_004381_water_5.33", "license": "Apache-2.0", "prompt": "A sample contains 5.33 mol of water. Using molar mass 18.015 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 5.33 mol * 18.015 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "water", "molar_mass": 18.015, "moles": 5.33}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 4540 mL to 4.54 L.\n3. Compute M = 0.75 / 4.54.\nFinal: {\"answer\": 0.1652, \"unit\": \"mol/L\"}", "dedupe_signature": "a93f7bfdd03d92d2c7c48d16c51a427219d6eb43d57854338378b473420be7a1", "difficulty": "medium", "final_answer": {"answer": 0.1652, "unit": "mol/L"}, "id": "molarity_004382_0.75_4540", "license": "Apache-2.0", "prompt": "A solution contains 0.75 mol of solute in 4540 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 4540 mL to 4.54 L.\nCompute M = 0.75 / 4.54.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 0.75, "volume_ml": 4540}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.51 y, so each step multiplies y by 1 - h*0.51.\n3. Apply that update for 9 steps and round the final state.\nFinal: {\"answer\": 0.3797, \"unit\": \"state_units\"}", "dedupe_signature": "14a79630d733e1a999ff7c42d068c0cb9c5cc0cfdafb86ce2444fcf3c3715290", "difficulty": "medium", "final_answer": {"answer": 0.3797, "unit": "state_units"}, "id": "euler_decay_004383_1_0.51_0.2_9", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.51 y with y(0)=1, step size h=0.2, for 9 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.51 y, so each step multiplies y by 1 - h*0.51.\nApply that update for 9 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 1.0, "rate": 0.51, "step": 0.2, "steps": 9}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-2.3)=32.27 and f(2.3)=-4.07.\n3. The interval width is 4.6.\nFinal: {\"answer\": 64.86, \"unit\": \"area_units\"}", "dedupe_signature": "734fd3c2a347910572c25e64bb81358af081b727a7032ce65b1ab8f426517973", "difficulty": "medium", "final_answer": {"answer": 64.86, "unit": "area_units"}, "id": "trapz_linear_004384_-7.9_14.1_-2.3_2.3", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-7.9x+14.1 from x=-2.3 to x=2.3. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-2.3)=32.27 and f(2.3)=-4.07.\nThe interval width is 4.6.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 14.1, "slope": -7.9, "x0": -2.3, "x1": 2.3}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.02 and add it to the current value.\nFinal: {\"answer\": [-1.755, 1.507, -1.878], \"unit\": \"temperature_units\"}", "dedupe_signature": "735cf4820847681b5cb4ad22640e080e437c4260175c5e5888e5dd47e8ebe026", "difficulty": "hard", "final_answer": {"answer": [-1.755, 1.507, -1.878], "unit": "temperature_units"}, "id": "heat_step_004385_0.02_-0.6_-1.85_1.65_-2.0_0.45", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-0.6, right=0.45; current interior values are [-1.85, 1.65, -2.0]. Use r=0.02. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.02 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-1.85, 1.65, -2.0], "left": -0.6, "r": 0.02, "right": 0.45}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 100 centimeters in one meter.\n2. Apply the conversion factor directly to the given value.\n3. Compute 4891.5 / 100.\nFinal: {\"answer\": 48.915, \"unit\": \"m\"}", "dedupe_signature": "1a3e00224d93c8a023549624e97a051c19b86cfb7f8abd88af028f46e61c5dd4", "difficulty": "easy", "final_answer": {"answer": 48.915, "unit": "m"}, "id": "unit_convert_004386_cm_to_m_4891.5", "license": "Apache-2.0", "prompt": "Convert 4891.5 cm to m. Return the converted value with unit.", "reasoning_trace": "There are 100 centimeters in one meter.\nApply the conversion factor directly to the given value.\nCompute 4891.5 / 100.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 4891.5}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=137 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-236.9586, 220.9675], \"unit\": \"N\"}", "dedupe_signature": "f58d64e52e9e95cc930ba966b796dbe0323bd2ac649711e2f5a167fac0e4f347", "difficulty": "medium", "final_answer": {"answer": [-236.9586, 220.9675], "unit": "N"}, "id": "vector_components_004387_324_137", "license": "Apache-2.0", "prompt": "A vector has magnitude 324 N at 137 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=137 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 137, "magnitude": 324.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-7.95, 5.75], \"unit\": \"dimensionless\"}", "dedupe_signature": "b02c58702e36b4d6525c0350acfb5f087c5134702b7cb65ebccbb504c5c56c7b", "difficulty": "medium", "final_answer": {"answer": [-7.95, 5.75], "unit": "dimensionless"}, "id": "line_two_point_004388_4.25_8.25_-7.95_5.75", "license": "Apache-2.0", "prompt": "A line passes through points (4.25, -28.0375) and (8.25, -59.8375). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 4.25, "x2": 8.25, "y1": -28.0375, "y2": -59.837500000000006}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. density times acceleration times height gives kg/(m*s^2), or pascal\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "637a30443d81b7005fbe3bf5fa859958dc3443c435020940b432609169e84580", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_004389_consistent_b7d3eed1_534558", "license": "Apache-2.0", "prompt": "In field worksheet case 534558, check dimensional consistency for p = rho * g * h. The left side has dimensions Pa and the right side has dimensions Pa. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\ndensity times acceleration times height gives kg/(m*s^2), or pascal\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "p = rho * g * h"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef clamp_004390(x, lo, hi):\n    if lo > hi:\n        raise ValueError('lo must be <= hi')\n    return min(max(x, lo), hi)\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"clamp_004390\"}", "dedupe_signature": "3a091df7ec0b8f5a154700cff9b82f140ededaf330f7f2be68ccc69bb9a53319", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "clamp_004390"}, "id": "code_004390_clamp_004390", "license": "Apache-2.0", "prompt": "Write a Python function clamp_004390(x, lo, hi) that clips x into the inclusive interval [lo, hi]. It must raise ValueError if lo > hi. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "clamp_004390"}, "verifier": {"function": "clamp_004390", "tests": ["assert clamp_004390(5, 0, 10) == 5", "assert clamp_004390(-2, 0, 10) == 0", "assert clamp_004390(12, 0, 10) == 10", "try:\n    clamp_004390(1, 3, 2)\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 16.8^2 and multiply by 0.5 * 12.65.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 1785.168, \"unit\": \"J\"}", "dedupe_signature": "facc041ad7efe0ddb62b60f4566dad00a1e79d1be04e603c28d06509b431191b", "difficulty": "easy", "final_answer": {"answer": 1785.168, "unit": "J"}, "id": "ke_004393_12.65_16.8", "license": "Apache-2.0", "prompt": "A body of mass 12.65 kg moves at 16.8 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 16.8^2 and multiply by 0.5 * 12.65.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 12.65, "velocity": 16.8}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=77 degrees through the sine of 2 theta.\n3. Substitute v=50.5 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 113.9609, \"unit\": \"m\"}", "dedupe_signature": "e61f67a12ffe8e8a533c7126a02ed74df47c7abdadd278d03839ff6312d89370", "difficulty": "medium", "final_answer": {"answer": 113.9609, "unit": "m"}, "id": "projectile_range_004394_50.5_77", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 50.5 m/s and angle 77 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=77 degrees through the sine of 2 theta.\nSubstitute v=50.5 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 77, "gravity": 9.81, "speed": 50.5}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 1.56 * 8.314 * 341 / 16.8.\nFinal: {\"answer\": 263.2569, \"unit\": \"kPa\"}", "dedupe_signature": "ef5e4fc01029808d5bfee0978375b194fe82b2012bcff0f565736efc2927a4ad", "difficulty": "medium", "final_answer": {"answer": 263.2569, "unit": "kPa"}, "id": "ideal_gas_004395_1.56_341_16.8", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=1.56 mol, T=341 K, and V=16.8 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 1.56 * 8.314 * 341 / 16.8.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 1.56, "temp_k": 341, "volume_l": 16.8}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=180.8 V and R=77.1 ohm.\nFinal: {\"answer\": 423.9772, \"unit\": \"W\"}", "dedupe_signature": "2f8f2ed212b34b61910304a83e4ee43032db28b57b0d37483ebe3a3bdf018e24", "difficulty": "easy", "final_answer": {"answer": 423.9772, "unit": "W"}, "id": "ohm_power_004397_180.8_77.1", "license": "Apache-2.0", "prompt": "A resistor has resistance 77.1 ohm and voltage 180.8 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=180.8 V and R=77.1 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 77.1, "voltage": 180.8}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=678.5 mg, t=182 h, and T_half=91.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 170.9149, \"unit\": \"mg\"}", "dedupe_signature": "c06d9a918be591ef13807d47405fd04e412f0cbbd42a5d169cd9dc2c3a6c12cb", "difficulty": "medium", "final_answer": {"answer": 170.9149, "unit": "mg"}, "id": "half_life_004398_678.5_91.5_182", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 678.5 mg. Its half-life is 91.5 hours. How many mg remain after 182 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=678.5 mg, t=182 h, and T_half=91.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 182.0, "half_life": 91.5, "initial_amount": 678.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 0.82 mol * 180.156 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 147.7279, \"unit\": \"g\"}", "dedupe_signature": "6d55f5fbd7bdee689a0700d0b8353e1f571215117306966587f0b88a32e615b9", "difficulty": "medium", "final_answer": {"answer": 147.7279, "unit": "g"}, "id": "stoich_mass_004399_glucose_0.82", "license": "Apache-2.0", "prompt": "A sample contains 0.82 mol of glucose. Using molar mass 180.156 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 0.82 mol * 180.156 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "glucose", "molar_mass": 180.156, "moles": 0.82}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 1635 mL to 1.635 L.\n3. Compute M = 2.47 / 1.635.\nFinal: {\"answer\": 1.5107, \"unit\": \"mol/L\"}", "dedupe_signature": "5f95ff6d4f37d775047f512f8deae1b1014c4b7d64341aa35e9eff44c8cde616", "difficulty": "medium", "final_answer": {"answer": 1.5107, "unit": "mol/L"}, "id": "molarity_004400_2.47_1635", "license": "Apache-2.0", "prompt": "A solution contains 2.47 mol of solute in 1635 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 1635 mL to 1.635 L.\nCompute M = 2.47 / 1.635.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 2.47, "volume_ml": 1635}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-1)=15.3 and f(1.5)=2.3.\n3. The interval width is 2.5.\nFinal: {\"answer\": 22.0, \"unit\": \"area_units\"}", "dedupe_signature": "0a84d6cf0d61ab2bc3607aec78d54f5cbc752b64c458be2c7f7b1e48f378654f", "difficulty": "medium", "final_answer": {"answer": 22.0, "unit": "area_units"}, "id": "trapz_linear_004402_-5.2_10.1_-1_1.5", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-5.2x+10.1 from x=-1 to x=1.5. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-1)=15.3 and f(1.5)=2.3.\nThe interval width is 2.5.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 10.1, "slope": -5.2, "x0": -1.0, "x1": 1.5}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.16 and add it to the current value.\nFinal: {\"answer\": [1.216, 0.04, -0.79], \"unit\": \"temperature_units\"}", "dedupe_signature": "5494a0659cfbb368b66c8fe0b08f3fbba3098e6ba1743c3b354e2079b56c08de", "difficulty": "hard", "final_answer": {"answer": [1.216, 0.04, -0.79], "unit": "temperature_units"}, "id": "heat_step_004403_0.16_1.65_1.4_0.0_-1.15_-0.05", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.65, right=-0.05; current interior values are [1.4, 0.0, -1.15]. Use r=0.16. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.16 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [1.4, 0.0, -1.15], "left": 1.65, "r": 0.16, "right": -0.05}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=224 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-352.8362, -340.7299], \"unit\": \"N\"}", "dedupe_signature": "bbe8ecfa73b94572cb0fde4796292644d2cbcfb7b533c252a70c936b5ad405df", "difficulty": "medium", "final_answer": {"answer": [-352.8362, -340.7299], "unit": "N"}, "id": "vector_components_004405_490.5_224", "license": "Apache-2.0", "prompt": "A vector has magnitude 490.5 N at 224 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=224 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 224, "magnitude": 490.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [8.9, 27.0], \"unit\": \"dimensionless\"}", "dedupe_signature": "1019a1eab167f03b9ac52f5c463428dad2276266dbd1cd298426f627e7ac3e25", "difficulty": "medium", "final_answer": {"answer": [8.9, 27.0], "unit": "dimensionless"}, "id": "line_two_point_004406_-14.5_-1.25_8.9_27", "license": "Apache-2.0", "prompt": "A line passes through points (-14.5, -102.05) and (-1.25, 15.875). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -14.5, "x2": -1.25, "y1": -102.05000000000001, "y2": 15.875}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. energy divided by length is force, not spring constant\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "51a7676900bb0f6cab8840310e4744e4e58ffaff74e5172370611fd27689ca73", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_004407_inconsistent_56040f5d_532640", "license": "Apache-2.0", "prompt": "In lab notebook case 532640, check dimensional consistency for k = E / x. The left side has dimensions N/m and the right side has dimensions J/m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nenergy divided by length is force, not spring constant\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "k = E / x"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: left_boundary, right_boundary.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"left_boundary\", \"right_boundary\"]}", "dedupe_signature": "7dfcaa7e0c68861aa7c5fb5e2f3ca909bb159ee81e8a67796bb85274792b56d8", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["left_boundary", "right_boundary"]}, "id": "abstain_004409_left_boundary_right_boundary", "license": "Apache-2.0", "prompt": "Solve the 1D heat equation after one finite-difference step. The prompt gives r=0.16 and interior values [0.35, 2.2, -0.45], but gives no boundary values. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: left_boundary, right_boundary.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["left_boundary", "right_boundary"]}, "verifier": {"missing": ["left_boundary", "right_boundary"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 7.75 kg and a = 14.45 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 111.9875, \"unit\": \"N\"}", "dedupe_signature": "463f5598fe93b19334b8781cc4b340625ba2a52cd7ac0c2d87d0649bfb356820", "difficulty": "easy", "final_answer": {"answer": 111.9875, "unit": "N"}, "id": "force_004410_7.75_14.45", "license": "Apache-2.0", "prompt": "A cart has mass 7.75 kg and measured acceleration 14.45 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 7.75 kg and a = 14.45 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 14.45, "mass": 7.75}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 8.6^2 and multiply by 0.5 * 12.75.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 471.495, \"unit\": \"J\"}", "dedupe_signature": "07406477ee496f59f00b951b83b2d009faa9255fb2f8fd670c6e6678bf15de6a", "difficulty": "easy", "final_answer": {"answer": 471.495, "unit": "J"}, "id": "ke_004411_12.75_8.6", "license": "Apache-2.0", "prompt": "A body of mass 12.75 kg moves at 8.6 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 8.6^2 and multiply by 0.5 * 12.75.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 12.75, "velocity": 8.6}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=82 degrees through the sine of 2 theta.\n3. Substitute v=58.7 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 96.8156, \"unit\": \"m\"}", "dedupe_signature": "817c556fffc61df493354ffd9d65287690687a8c1a7be29ebb43510c651b2ca1", "difficulty": "medium", "final_answer": {"answer": 96.8156, "unit": "m"}, "id": "projectile_range_004412_58.7_82", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 58.7 m/s and angle 82 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=82 degrees through the sine of 2 theta.\nSubstitute v=58.7 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 82, "gravity": 9.81, "speed": 58.7}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 5.46 * 8.314 * 385 / 15.1.\nFinal: {\"answer\": 1157.4079, \"unit\": \"kPa\"}", "dedupe_signature": "e4ab5a89b22e0425eb82ad79bfa1e12ea310287678884ddecebd2152f4dc4691", "difficulty": "medium", "final_answer": {"answer": 1157.4079, "unit": "kPa"}, "id": "ideal_gas_004413_5.46_385_15.1", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=5.46 mol, T=385 K, and V=15.1 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 5.46 * 8.314 * 385 / 15.1.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 5.46, "temp_k": 385, "volume_l": 15.1}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1610 * 0.685 * 45.\nFinal: {\"answer\": 49628.25, \"unit\": \"J\"}", "dedupe_signature": "9d21ca8b7cf8b4f4a3e0d9f7a44dd2226bffda438fa5b65b81740b6d6e9fa192", "difficulty": "easy", "final_answer": {"answer": 49628.25, "unit": "J"}, "id": "heat_q_004414_1610_0.685_45", "license": "Apache-2.0", "prompt": "A 1610 g sample has specific heat 0.685 J/(g*K). How much heat is needed to raise its temperature by 45 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1610 * 0.685 * 45.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 45, "heat_capacity": 0.685, "mass_g": 1610}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=105.3 V and R=153.8 ohm.\nFinal: {\"answer\": 72.0942, \"unit\": \"W\"}", "dedupe_signature": "2a96aaedd792cfcdfa6880b0d62292ca2eea93cb55e4925a4669e0c07163528f", "difficulty": "easy", "final_answer": {"answer": 72.0942, "unit": "W"}, "id": "ohm_power_004415_105.3_153.8", "license": "Apache-2.0", "prompt": "A resistor has resistance 153.8 ohm and voltage 105.3 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=105.3 V and R=153.8 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 153.8, "voltage": 105.3}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=39 mg, t=102 h, and T_half=105 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 19.89, \"unit\": \"mg\"}", "dedupe_signature": "43dc265b054788ea73cbf1333f823291c3a07ebc5b268450f0abe181135eb725", "difficulty": "medium", "final_answer": {"answer": 19.89, "unit": "mg"}, "id": "half_life_004416_39_105_102", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 39 mg. Its half-life is 105 hours. How many mg remain after 102 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=39 mg, t=102 h, and T_half=105 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 102.0, "half_life": 105.0, "initial_amount": 39.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 2.17 mol * 180.156 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 390.9385, \"unit\": \"g\"}", "dedupe_signature": "9b0312b156dbf7609d0c3f08efeaec1d770313dd1337baa29e822a3b3f6ce341", "difficulty": "medium", "final_answer": {"answer": 390.9385, "unit": "g"}, "id": "stoich_mass_004417_glucose_2.17", "license": "Apache-2.0", "prompt": "A sample contains 2.17 mol of glucose. Using molar mass 180.156 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 2.17 mol * 180.156 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "glucose", "molar_mass": 180.156, "moles": 2.17}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 2400 mL to 2.4 L.\n3. Compute M = 0.175 / 2.4.\nFinal: {\"answer\": 0.0729, \"unit\": \"mol/L\"}", "dedupe_signature": "4be6264e66b2b6869a2932a492c84fc8ff08a7d847409d821f7fe2f8159a8d5e", "difficulty": "medium", "final_answer": {"answer": 0.0729, "unit": "mol/L"}, "id": "molarity_004418_0.175_2400", "license": "Apache-2.0", "prompt": "A solution contains 0.175 mol of solute in 2400 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 2400 mL to 2.4 L.\nCompute M = 0.175 / 2.4.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 0.175, "volume_ml": 2400}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.54 y, so each step multiplies y by 1 - h*0.54.\n3. Apply that update for 2 steps and round the final state.\nFinal: {\"answer\": 19.5505, \"unit\": \"state_units\"}", "dedupe_signature": "e3fa1c161201823dd8cf11b25dff05ace1f4ca414f7ea59f4518aa150ec4fed1", "difficulty": "medium", "final_answer": {"answer": 19.5505, "unit": "state_units"}, "id": "euler_decay_004419_74_0.54_0.9_2", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.54 y with y(0)=74, step size h=0.9, for 2 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.54 y, so each step multiplies y by 1 - h*0.54.\nApply that update for 2 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 74.0, "rate": 0.54, "step": 0.9, "steps": 2}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(6.7)=25.95 and f(9.1)=39.15.\n3. The interval width is 2.4.\nFinal: {\"answer\": 78.12, \"unit\": \"area_units\"}", "dedupe_signature": "5459842ee9dae394cd3d8865e2c61a24326c7415e4923306e36a8f52d20e12c2", "difficulty": "medium", "final_answer": {"answer": 78.12, "unit": "area_units"}, "id": "trapz_linear_004420_5.5_-10.9_6.7_9.1", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=5.5x+-10.9 from x=6.7 to x=9.1. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(6.7)=25.95 and f(9.1)=39.15.\nThe interval width is 2.4.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -10.9, "slope": 5.5, "x0": 6.7, "x1": 9.1}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.22 and add it to the current value.\nFinal: {\"answer\": [2.369, 2.483, 1.743], \"unit\": \"temperature_units\"}", "dedupe_signature": "0052176e3206eecbdef5e278fe13fe48525b9c8009677e1ae1aaac485ba93f0b", "difficulty": "hard", "final_answer": {"answer": [2.369, 2.483, 1.743], "unit": "temperature_units"}, "id": "heat_step_004421_0.22_1.15_2.6_3.0_1.05_2.25", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.15, right=2.25; current interior values are [2.6, 3.0, 1.05]. Use r=0.22. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.22 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [2.6, 3.0, 1.05], "left": 1.15, "r": 0.22, "right": 2.25}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 10148.0 / 1000.\nFinal: {\"answer\": 10.148, \"unit\": \"kg\"}", "dedupe_signature": "e2e911b7d8725b8fa98d65199684810000153eee3032f51c17a42d1779c54e88", "difficulty": "easy", "final_answer": {"answer": 10.148, "unit": "kg"}, "id": "unit_convert_004422_g_to_kg_10148", "license": "Apache-2.0", "prompt": "Convert 10148 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 10148.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 10148.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [2.9, -5.5], \"unit\": \"dimensionless\"}", "dedupe_signature": "61520d5c7a93eb5746ed0a8acc6ff1ba550f5ae6df3e86938766d325c2caf6ff", "difficulty": "medium", "final_answer": {"answer": [2.9, -5.5], "unit": "dimensionless"}, "id": "line_two_point_004424_-20_-18.5_2.9_-5.5", "license": "Apache-2.0", "prompt": "A line passes through points (-20, -63.5) and (-18.5, -59.15). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -20.0, "x2": -18.5, "y1": -63.5, "y2": -59.15}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. volt squared divided by ohm is watt\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "01265f08e7a765261144c3bd7e6e57fbb9869f477dd012c15dbd26d4ecc444fa", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_004425_consistent_82e93f3d_831068", "license": "Apache-2.0", "prompt": "In field worksheet case 831068, check dimensional consistency for P = V^2 / R. The left side has dimensions W and the right side has dimensions W. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nvolt squared divided by ohm is watt\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "P = V^2 / R"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef running_total_004426(values):\n    total = 0\n    out = []\n    for value in values:\n        total += value\n        out.append(total)\n    return out\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"running_total_004426\"}", "dedupe_signature": "3443df7558094fd1d40d733bec88d66da16bbfbe06c92264787e07b50c5d30d9", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "running_total_004426"}, "id": "code_004426_running_total_004426", "license": "Apache-2.0", "prompt": "Write a Python function running_total_004426(values) that returns cumulative sums as a new list. It must not mutate the input list. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "running_total_004426"}, "verifier": {"function": "running_total_004426", "tests": ["assert running_total_004426([1, 2, 3]) == [1, 3, 6]", "xs = [4, -1, 2]; assert running_total_004426(xs) == [4, 3, 5] and xs == [4, -1, 2]", "assert running_total_004426([]) == []"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: required_fields, allowed_transformations.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"required_fields\", \"allowed_transformations\"]}", "dedupe_signature": "a80a84bfa5c3e8e420a149d8542dc614c9b4684e7300bdbb831aed794aa44db2", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["required_fields", "allowed_transformations"]}, "id": "abstain_004427_required_fields_allowed_transformations", "license": "Apache-2.0", "prompt": "Write a sanitizer for valid warehouse invoice records in release 242098, but the prompt does not state which fields are required or which transformations are allowed. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: required_fields, allowed_transformations.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["required_fields", "allowed_transformations"]}, "verifier": {"missing": ["required_fields", "allowed_transformations"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 0.95 kg and a = 1.95 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 1.8525, \"unit\": \"N\"}", "dedupe_signature": "935df56f6036a197d6ed87bd0eea6c1c003e6c8595aa5df46e4638a145c0fbbc", "difficulty": "easy", "final_answer": {"answer": 1.8525, "unit": "N"}, "id": "force_004428_0.95_1.95", "license": "Apache-2.0", "prompt": "A cart has mass 0.95 kg and measured acceleration 1.95 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 0.95 kg and a = 1.95 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 1.95, "mass": 0.95}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 27.7^2 and multiply by 0.5 * 17.6.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 6752.152, \"unit\": \"J\"}", "dedupe_signature": "260d403274f01c5d09a0836cb275db0723cbfb9b4fd9c9b7f5df3efbf02f45a2", "difficulty": "easy", "final_answer": {"answer": 6752.152, "unit": "J"}, "id": "ke_004429_17.6_27.7", "license": "Apache-2.0", "prompt": "A body of mass 17.6 kg moves at 27.7 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 27.7^2 and multiply by 0.5 * 17.6.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 17.6, "velocity": 27.7}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=49 degrees through the sine of 2 theta.\n3. Substitute v=34.7 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 121.5466, \"unit\": \"m\"}", "dedupe_signature": "1d2b58b548aa0d08ec43c01ee0aaffe8d7b483bfddabff3d698bd2c370a97c8f", "difficulty": "medium", "final_answer": {"answer": 121.5466, "unit": "m"}, "id": "projectile_range_004430_34.7_49", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 34.7 m/s and angle 49 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=49 degrees through the sine of 2 theta.\nSubstitute v=34.7 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 49, "gravity": 9.81, "speed": 34.7}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 0.58 * 8.314 * 522 / 13.6.\nFinal: {\"answer\": 185.0843, \"unit\": \"kPa\"}", "dedupe_signature": "5a5955dbb45683464a75e6bdefe40164fecd8088d594f8848713ca20e6f39c16", "difficulty": "medium", "final_answer": {"answer": 185.0843, "unit": "kPa"}, "id": "ideal_gas_004431_0.58_522_13.6", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=0.58 mol, T=522 K, and V=13.6 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 0.58 * 8.314 * 522 / 13.6.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 0.58, "temp_k": 522, "volume_l": 13.6}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 595 * 1.89 * 70.\nFinal: {\"answer\": 78718.5, \"unit\": \"J\"}", "dedupe_signature": "42a995926cf84601a62f5ced4d174d37d47f6cf3d9f53603225ca0ed2a5091c9", "difficulty": "easy", "final_answer": {"answer": 78718.5, "unit": "J"}, "id": "heat_q_004432_595_1.89_70", "license": "Apache-2.0", "prompt": "A 595 g sample has specific heat 1.89 J/(g*K). How much heat is needed to raise its temperature by 70 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 595 * 1.89 * 70.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 70, "heat_capacity": 1.89, "mass_g": 595}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=999.5 mg, t=255.5 h, and T_half=99.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 168.5723, \"unit\": \"mg\"}", "dedupe_signature": "eaf3e58dd48944b36ecfa4b92dce3c36c30e7f70ad4c8cf7e732a5807bb4248d", "difficulty": "medium", "final_answer": {"answer": 168.5723, "unit": "mg"}, "id": "half_life_004434_999.5_99.5_255.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 999.5 mg. Its half-life is 99.5 hours. How many mg remain after 255.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=999.5 mg, t=255.5 h, and T_half=99.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 255.5, "half_life": 99.5, "initial_amount": 999.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 3.11 mol * 18.015 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 56.0266, \"unit\": \"g\"}", "dedupe_signature": "0ae7ccecff7035a5b3232f3ebcf08ce2f99b5eef4aa8ed66521ea809d21de9c8", "difficulty": "medium", "final_answer": {"answer": 56.0266, "unit": "g"}, "id": "stoich_mass_004435_water_3.11", "license": "Apache-2.0", "prompt": "A sample contains 3.11 mol of water. Using molar mass 18.015 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 3.11 mol * 18.015 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "water", "molar_mass": 18.015, "moles": 3.11}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 4050 mL to 4.05 L.\n3. Compute M = 4.355 / 4.05.\nFinal: {\"answer\": 1.0753, \"unit\": \"mol/L\"}", "dedupe_signature": "00116fea3b02053ceb85857ac7133fdaa4ab7d5224127136e2cb4613048a21a3", "difficulty": "medium", "final_answer": {"answer": 1.0753, "unit": "mol/L"}, "id": "molarity_004436_4.355_4050", "license": "Apache-2.0", "prompt": "A solution contains 4.355 mol of solute in 4050 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 4050 mL to 4.05 L.\nCompute M = 4.355 / 4.05.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 4.355, "volume_ml": 4050}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(5.8)=2.32 and f(6.1)=3.04.\n3. The interval width is 0.3.\nFinal: {\"answer\": 0.804, \"unit\": \"area_units\"}", "dedupe_signature": "dc675e40448c6639ab3cadae071576681d5ef1b976519f81cc45fc2ac28065a5", "difficulty": "medium", "final_answer": {"answer": 0.804, "unit": "area_units"}, "id": "trapz_linear_004438_2.4_-11.6_5.8_6.1", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=2.4x+-11.6 from x=5.8 to x=6.1. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(5.8)=2.32 and f(6.1)=3.04.\nThe interval width is 0.3.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -11.6, "slope": 2.4, "x0": 5.8, "x1": 6.1}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.14 and add it to the current value.\nFinal: {\"answer\": [1.884, 0.284, -0.099], \"unit\": \"temperature_units\"}", "dedupe_signature": "d24d0e437bd8f30d05978172914b600c58cc74e1cc7cbdd760261299a4f6a42c", "difficulty": "hard", "final_answer": {"answer": [1.884, 0.284, -0.099], "unit": "temperature_units"}, "id": "heat_step_004439_0.14_-1.05_2.85_-0.15_-0.05_-0.3", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-1.05, right=-0.3; current interior values are [2.85, -0.15, -0.05]. Use r=0.14. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.14 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [2.85, -0.15, -0.05], "left": -1.05, "r": 0.14, "right": -0.3}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [2.2, 19.0], \"unit\": \"dimensionless\"}", "dedupe_signature": "7fbc5d4cd6272768afab92211dd95330a69517e86a2a7e5f097380b0e5197bc9", "difficulty": "medium", "final_answer": {"answer": [2.2, 19.0], "unit": "dimensionless"}, "id": "line_two_point_004442_-17.5_-7.75_2.2_19", "license": "Apache-2.0", "prompt": "A line passes through points (-17.5, -19.5) and (-7.75, 1.95). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -17.5, "x2": -7.75, "y1": -19.5, "y2": 1.9499999999999993}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. lever arm times force has torque dimensions\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "54878774caaf09448f19ba3437935896217ac0b8ae00dc130aa7c57eda8f645c", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_004443_consistent_5ca82cb9_228146", "license": "Apache-2.0", "prompt": "In field worksheet case 228146, check dimensional consistency for tau = r * F. The left side has dimensions N*m and the right side has dimensions N*m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nlever arm times force has torque dimensions\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "tau = r * F"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\nimport math\n\ndef unit_vector_004444(x, y):\n    norm = math.hypot(x, y)\n    if norm == 0:\n        raise ValueError('zero vector has no direction')\n    return (x / norm, y / norm)\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"unit_vector_004444\"}", "dedupe_signature": "2e9d27a4f6c64449196c894310423bbd17b12b25bedc8343c4b008bd3c6ec357", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "unit_vector_004444"}, "id": "code_004444_unit_vector_004444", "license": "Apache-2.0", "prompt": "Write a Python function unit_vector_004444(x, y) that returns the 2D unit vector as a tuple. Raise ValueError for the zero vector. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "unit_vector_004444"}, "verifier": {"function": "unit_vector_004444", "tests": ["ux, uy = unit_vector_004444(3, 4); assert abs(ux - 0.6) < 1e-12 and abs(uy - 0.8) < 1e-12", "assert unit_vector_004444(0, 5) == (0, 1)", "try:\n    unit_vector_004444(0, 0)\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: recurrence, objective, tie_breaking_rule.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"recurrence\", \"objective\", \"tie_breaking_rule\"]}", "dedupe_signature": "c9741847779fcf0bc890f0ca54ad875a2d92b1c5ca2db1358ea2d599377cb7c1", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["recurrence", "objective", "tie_breaking_rule"]}, "id": "abstain_004445_recurrence_objective_tie_breaking_rule", "license": "Apache-2.0", "prompt": "Write a dynamic-programming solver for a scheduler scoring problem with 3755 items and budget 585, but the recurrence, objective, and tie-breaking rule are all absent. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: recurrence, objective, tie_breaking_rule.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["recurrence", "objective", "tie_breaking_rule"]}, "verifier": {"missing": ["recurrence", "objective", "tie_breaking_rule"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=52 degrees through the sine of 2 theta.\n3. Substitute v=26.7 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 70.5111, \"unit\": \"m\"}", "dedupe_signature": "b837bb59bc2fb1de738282c40333060ad5e2709331c9076b3956392f1e09227f", "difficulty": "medium", "final_answer": {"answer": 70.5111, "unit": "m"}, "id": "projectile_range_004448_26.7_52", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 26.7 m/s and angle 52 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=52 degrees through the sine of 2 theta.\nSubstitute v=26.7 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 52, "gravity": 9.81, "speed": 26.7}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1700 * 1 * 42.\nFinal: {\"answer\": 71400.0, \"unit\": \"J\"}", "dedupe_signature": "00e13c1007dcf98f5de357966546cf560f2a0f3c89c5dd93574dff195bb42fdf", "difficulty": "easy", "final_answer": {"answer": 71400.0, "unit": "J"}, "id": "heat_q_004450_1700_1_42", "license": "Apache-2.0", "prompt": "A 1700 g sample has specific heat 1 J/(g*K). How much heat is needed to raise its temperature by 42 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1700 * 1 * 42.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 42, "heat_capacity": 1.0, "mass_g": 1700}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=186.9 V and R=132.8 ohm.\nFinal: {\"answer\": 263.0392, \"unit\": \"W\"}", "dedupe_signature": "500dbcfa4ef8f35debd2dcd1214547b943bb7c79b1122d9e9a3bc3e9c9e50a3d", "difficulty": "easy", "final_answer": {"answer": 263.0392, "unit": "W"}, "id": "ohm_power_004451_186.9_132.8", "license": "Apache-2.0", "prompt": "A resistor has resistance 132.8 ohm and voltage 186.9 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=186.9 V and R=132.8 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 132.8, "voltage": 186.9}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=814 mg, t=5.5 h, and T_half=84 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 777.8827, \"unit\": \"mg\"}", "dedupe_signature": "aedee202315778fae8df3aa6fa5d7042c585e04156520da0dee1842c8921b231", "difficulty": "medium", "final_answer": {"answer": 777.8827, "unit": "mg"}, "id": "half_life_004452_814_84_5.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 814 mg. Its half-life is 84 hours. How many mg remain after 5.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=814 mg, t=5.5 h, and T_half=84 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 5.5, "half_life": 84.0, "initial_amount": 814.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 3.45 mol * 44.01 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 151.8345, \"unit\": \"g\"}", "dedupe_signature": "1b3d70b180aef4c0791de57d6005977b3c8e535ce87c9454b6f7825fd513a9fc", "difficulty": "medium", "final_answer": {"answer": 151.8345, "unit": "g"}, "id": "stoich_mass_004453_carbon_dioxide_3.45", "license": "Apache-2.0", "prompt": "A sample contains 3.45 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 3.45 mol * 44.01 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "carbon dioxide", "molar_mass": 44.01, "moles": 3.45}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 3500 mL to 3.5 L.\n3. Compute M = 1.015 / 3.5.\nFinal: {\"answer\": 0.29, \"unit\": \"mol/L\"}", "dedupe_signature": "e5de20caf6a20bd0cfff4deac8855929e5f85b83843ca4cb511d6b5847dc441e", "difficulty": "medium", "final_answer": {"answer": 0.29, "unit": "mol/L"}, "id": "molarity_004454_1.015_3500", "license": "Apache-2.0", "prompt": "A solution contains 1.015 mol of solute in 3500 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 3500 mL to 3.5 L.\nCompute M = 1.015 / 3.5.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 1.015, "volume_ml": 3500}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.31 y, so each step multiplies y by 1 - h*0.31.\n3. Apply that update for 12 steps and round the final state.\nFinal: {\"answer\": 0.1384, \"unit\": \"state_units\"}", "dedupe_signature": "f10db742b2349364147682bac83662ae1275d6e4a755912a91a15e472dc3d12e", "difficulty": "medium", "final_answer": {"answer": 0.1384, "unit": "state_units"}, "id": "euler_decay_004455_67.5_0.31_1.3_12", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.31 y with y(0)=67.5, step size h=1.3, for 12 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.31 y, so each step multiplies y by 1 - h*0.31.\nApply that update for 12 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 67.5, "rate": 0.31, "step": 1.3, "steps": 12}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-3.7)=-28.01 and f(0.1)=-4.07.\n3. The interval width is 3.8.\nFinal: {\"answer\": -60.952, \"unit\": \"area_units\"}", "dedupe_signature": "f66d37f2a8e360b2e0ab3cebf00f78d68dc1671e5fbceaffe917c22f4ced4e1d", "difficulty": "medium", "final_answer": {"answer": -60.952, "unit": "area_units"}, "id": "trapz_linear_004456_6.3_-4.7_-3.7_0.1", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=6.3x+-4.7 from x=-3.7 to x=0.1. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-3.7)=-28.01 and f(0.1)=-4.07.\nThe interval width is 3.8.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -4.7, "slope": 6.3, "x0": -3.7, "x1": 0.09999999999999964}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.36 and add it to the current value.\nFinal: {\"answer\": [1.668, 1.728, 0.658], \"unit\": \"temperature_units\"}", "dedupe_signature": "e277466f08e8bd4a5cfb507a1477cfeed48caae699f265bc68e820c287a475f9", "difficulty": "hard", "final_answer": {"answer": [1.668, 1.728, 0.658], "unit": "temperature_units"}, "id": "heat_step_004457_0.36_2.9_1.65_0.45_2.8_-0.8", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=2.9, right=-0.8; current interior values are [1.65, 0.45, 2.8]. Use r=0.36. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.36 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [1.65, 0.45, 2.8], "left": 2.9, "r": 0.36, "right": -0.8}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 100 centimeters in one meter.\n2. Apply the conversion factor directly to the given value.\n3. Compute 4318.0 / 100.\nFinal: {\"answer\": 43.18, \"unit\": \"m\"}", "dedupe_signature": "b696373f38b833fa3838d101ad4b94ab4dd7c9a2802e5b1905c64cc7ba8626d8", "difficulty": "easy", "final_answer": {"answer": 43.18, "unit": "m"}, "id": "unit_convert_004458_cm_to_m_4318", "license": "Apache-2.0", "prompt": "Convert 4318 cm to m. Return the converted value with unit.", "reasoning_trace": "There are 100 centimeters in one meter.\nApply the conversion factor directly to the given value.\nCompute 4318.0 / 100.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 4318.0}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=247 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-146.3288, -344.7291], \"unit\": \"N\"}", "dedupe_signature": "89803e4c00b02629b029ecfcd9bf5e0ed07c27e2dfa34e3774b6a6c1fa08374e", "difficulty": "medium", "final_answer": {"answer": [-146.3288, -344.7291], "unit": "N"}, "id": "vector_components_004459_374.5_247", "license": "Apache-2.0", "prompt": "A vector has magnitude 374.5 N at 247 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=247 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 247, "magnitude": 374.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-2.7, 7.5], \"unit\": \"dimensionless\"}", "dedupe_signature": "64a585a778d2b0d101a73c4661850e4812a59c1701e6985d2568cbd3265795bd", "difficulty": "medium", "final_answer": {"answer": [-2.7, 7.5], "unit": "dimensionless"}, "id": "line_two_point_004460_16.5_25.75_-2.7_7.5", "license": "Apache-2.0", "prompt": "A line passes through points (16.5, -37.05) and (25.75, -62.025). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 16.5, "x2": 25.75, "y1": -37.050000000000004, "y2": -62.025000000000006}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. lever arm times force has torque dimensions\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "22a8f2de483339a204e3d407bf33a7cc10b0f457953f1d2433416f779c155ef9", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_004461_consistent_5ca82cb9_4077", "license": "Apache-2.0", "prompt": "In model card equation case 4077, check dimensional consistency for tau = r * F. The left side has dimensions N*m and the right side has dimensions N*m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nlever arm times force has torque dimensions\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "tau = r * F"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef normalize_004462(values):\n    total = sum(values)\n    if total == 0:\n        raise ValueError('cannot normalize zero-sum values')\n    return [v / total for v in values]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"normalize_004462\"}", "dedupe_signature": "92faf128d36e38daed8dbfc95226ac21ddc65e60fa22abcf94dc97b53ef913c9", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "normalize_004462"}, "id": "code_004462_normalize_004462", "license": "Apache-2.0", "prompt": "Write a Python function normalize_004462(values) that returns a new list whose values sum to 1. Raise ValueError if the sum is zero. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "normalize_004462"}, "verifier": {"function": "normalize_004462", "tests": ["out = normalize_004462([2, 3, 5]); assert len(out) == 3", "assert abs(sum(normalize_004462([2, 3, 5])) - 1.0) < 1e-12", "assert normalize_004462([1, 1]) == [0.5, 0.5]", "try:\n    normalize_004462([1, -1])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: rate_constant, number_of_steps.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"rate_constant\", \"number_of_steps\"]}", "dedupe_signature": "c9827c8f58af0224d663140c779649428006af3993993cbad1127fc8781cec71", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["rate_constant", "number_of_steps"]}, "id": "abstain_004463_rate_constant_number_of_steps", "license": "Apache-2.0", "prompt": "Use explicit Euler for dy/dt = -k y. The prompt gives y(0)=53.5 and h=0.6, but omits both k and the number of steps. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: rate_constant, number_of_steps.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["rate_constant", "number_of_steps"]}, "verifier": {"missing": ["rate_constant", "number_of_steps"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 18.55 kg and a = 15.4 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 285.67, \"unit\": \"N\"}", "dedupe_signature": "b6a8113860777e5e8707ad07113364a0e332eaa59c96ef6ae4c3363bf2faa2a0", "difficulty": "easy", "final_answer": {"answer": 285.67, "unit": "N"}, "id": "force_004464_18.55_15.4", "license": "Apache-2.0", "prompt": "A cart has mass 18.55 kg and measured acceleration 15.4 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 18.55 kg and a = 15.4 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 15.4, "mass": 18.55}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=71 degrees through the sine of 2 theta.\n3. Substitute v=72 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 325.3404, \"unit\": \"m\"}", "dedupe_signature": "704b80efe88f4b375a32e23071c5b8cafa5265d7dcd30d8d6fad1d32a1f6ee0d", "difficulty": "medium", "final_answer": {"answer": 325.3404, "unit": "m"}, "id": "projectile_range_004466_72_71", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 72 m/s and angle 71 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=71 degrees through the sine of 2 theta.\nSubstitute v=72 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 71, "gravity": 9.81, "speed": 72.0}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 190 * 4.15 * 8.\nFinal: {\"answer\": 6308.0, \"unit\": \"J\"}", "dedupe_signature": "0d912370a635498619cf82624ddd3852bd2082a9d9da82f22f50aed41e0c399f", "difficulty": "easy", "final_answer": {"answer": 6308.0, "unit": "J"}, "id": "heat_q_004468_190_4.15_8", "license": "Apache-2.0", "prompt": "A 190 g sample has specific heat 4.15 J/(g*K). How much heat is needed to raise its temperature by 8 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 190 * 4.15 * 8.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 8, "heat_capacity": 4.15, "mass_g": 190}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=103.6 V and R=186.8 ohm.\nFinal: {\"answer\": 57.457, \"unit\": \"W\"}", "dedupe_signature": "036c8d0cabf80edc25d610f1d66f2ee276555486528e1645c43a8bf8a43c2558", "difficulty": "easy", "final_answer": {"answer": 57.457, "unit": "W"}, "id": "ohm_power_004469_103.6_186.8", "license": "Apache-2.0", "prompt": "A resistor has resistance 186.8 ohm and voltage 103.6 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=103.6 V and R=186.8 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 186.8, "voltage": 103.6}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=903 mg, t=24.5 h, and T_half=39 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 584.2237, \"unit\": \"mg\"}", "dedupe_signature": "6b18fd585c0927519809f7d59681ecf5e9d9083a017e0ef1e73ecdab485e7403", "difficulty": "medium", "final_answer": {"answer": 584.2237, "unit": "mg"}, "id": "half_life_004470_903_39_24.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 903 mg. Its half-life is 39 hours. How many mg remain after 24.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=903 mg, t=24.5 h, and T_half=39 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 24.5, "half_life": 39.0, "initial_amount": 903.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 6.64 mol * 58.44 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 388.0416, \"unit\": \"g\"}", "dedupe_signature": "920b6d7e0ec6092cd24d81545070076fa6e91494a0f230f40f8597aca5a1eb24", "difficulty": "medium", "final_answer": {"answer": 388.0416, "unit": "g"}, "id": "stoich_mass_004471_sodium_chloride_6.64", "license": "Apache-2.0", "prompt": "A sample contains 6.64 mol of sodium chloride. Using molar mass 58.44 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 6.64 mol * 58.44 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "sodium chloride", "molar_mass": 58.44, "moles": 6.64}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 4780 mL to 4.78 L.\n3. Compute M = 3.59 / 4.78.\nFinal: {\"answer\": 0.751, \"unit\": \"mol/L\"}", "dedupe_signature": "4a607db7354dca5cd3aff79bca7afb24952dc9c829186ed74d3c45eb40662045", "difficulty": "medium", "final_answer": {"answer": 0.751, "unit": "mol/L"}, "id": "molarity_004472_3.59_4780", "license": "Apache-2.0", "prompt": "A solution contains 3.59 mol of solute in 4780 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 4780 mL to 4.78 L.\nCompute M = 3.59 / 4.78.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 3.59, "volume_ml": 4780}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.11 y, so each step multiplies y by 1 - h*0.11.\n3. Apply that update for 4 steps and round the final state.\nFinal: {\"answer\": 26.9861, \"unit\": \"state_units\"}", "dedupe_signature": "9690782b92b762e89d2efa4e65079dcf430b33fd5afe3f9ba964251ca24567e0", "difficulty": "medium", "final_answer": {"answer": 26.9861, "unit": "state_units"}, "id": "euler_decay_004473_57_0.11_1.55_4", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.11 y with y(0)=57, step size h=1.55, for 4 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.11 y, so each step multiplies y by 1 - h*0.11.\nApply that update for 4 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 57.0, "rate": 0.11, "step": 1.55, "steps": 4}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(4.3)=33.97 and f(12.5)=82.35.\n3. The interval width is 8.2.\nFinal: {\"answer\": 476.912, \"unit\": \"area_units\"}", "dedupe_signature": "ab6637e9a07c640b6cf33f0c7c7fc9cd3cd1425331edcda9a5cc016e822d595e", "difficulty": "medium", "final_answer": {"answer": 476.912, "unit": "area_units"}, "id": "trapz_linear_004474_5.9_8.6_4.3_12.5", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=5.9x+8.6 from x=4.3 to x=12.5. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(4.3)=33.97 and f(12.5)=82.35.\nThe interval width is 8.2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 8.6, "slope": 5.9, "x0": 4.3, "x1": 12.5}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.18 and add it to the current value.\nFinal: {\"answer\": [2.313, 2.372, 1.258], \"unit\": \"temperature_units\"}", "dedupe_signature": "4256105c8a9018094ceaa61f632e914aa11eb405daf2fed7d66ba496be9e8b2a", "difficulty": "hard", "final_answer": {"answer": [2.313, 2.372, 1.258], "unit": "temperature_units"}, "id": "heat_step_004475_0.18_0.5_2.7_2.75_0.7_1.75", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=0.5, right=1.75; current interior values are [2.7, 2.75, 0.7]. Use r=0.18. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.18 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [2.7, 2.75, 0.7], "left": 0.5, "r": 0.18, "right": 1.75}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kelvin equals Celsius plus 273.15.\n2. Apply the conversion factor directly to the given value.\n3. Compute -15.5 + 273.15.\nFinal: {\"answer\": 257.65, \"unit\": \"K\"}", "dedupe_signature": "6f77b5aad104637c01e4d6e9a837e2c8c22c12f735b714dab0ae0304261d0f19", "difficulty": "easy", "final_answer": {"answer": 257.65, "unit": "K"}, "id": "unit_convert_004476_c_to_k_-15.5", "license": "Apache-2.0", "prompt": "Convert -15.5 degC to K. Return the converted value with unit.", "reasoning_trace": "Kelvin equals Celsius plus 273.15.\nApply the conversion factor directly to the given value.\nCompute -15.5 + 273.15.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": -15.5}, "verifier": {"formula": "value + 273.15", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=60 degrees and keep the unit as newtons.\nFinal: {\"answer\": [81.25, 140.7291], \"unit\": \"N\"}", "dedupe_signature": "6b6ed2d86a3695fd0fa08b67fe86cd9a30cb59ebc01c58fca29c977c7c0eb316", "difficulty": "medium", "final_answer": {"answer": [81.25, 140.7291], "unit": "N"}, "id": "vector_components_004477_162.5_60", "license": "Apache-2.0", "prompt": "A vector has magnitude 162.5 N at 60 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=60 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 60, "magnitude": 162.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [8.4, 7.75], \"unit\": \"dimensionless\"}", "dedupe_signature": "180a9402696f21f73c1486c58df422e2db3f78727c7103ce88a08b94aa4aec81", "difficulty": "medium", "final_answer": {"answer": [8.4, 7.75], "unit": "dimensionless"}, "id": "line_two_point_004478_-3.75_7_8.4_7.75", "license": "Apache-2.0", "prompt": "A line passes through points (-3.75, -23.75) and (7, 66.55). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -3.75, "x2": 7.0, "y1": -23.75, "y2": 66.55000000000001}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef finite_differences_004480(values):\n    return [values[i + 1] - values[i] for i in range(len(values) - 1)]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"finite_differences_004480\"}", "dedupe_signature": "724e6657059944180ff45f6d8bfc1f9b4fca211d3ea82ef0bdc9a2a9ec742abc", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "finite_differences_004480"}, "id": "code_004480_finite_differences_004480", "license": "Apache-2.0", "prompt": "Write a Python function finite_differences_004480(values) that returns the list of successive differences values[i+1] - values[i]. It must return [] for fewer than two values. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "finite_differences_004480"}, "verifier": {"function": "finite_differences_004480", "tests": ["assert finite_differences_004480([1, 4, 9, 16]) == [3, 5, 7]", "assert finite_differences_004480([5]) == []", "assert finite_differences_004480([]) == []"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: launch_angle_or_vertical_velocity.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"launch_angle_or_vertical_velocity\"]}", "dedupe_signature": "1cd1e161444948ee2d0a06477adcfce2c9ffaaffa46c72e5baa8c49dd576750c", "difficulty": "easy", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["launch_angle_or_vertical_velocity"]}, "id": "abstain_004481_launch_angle_or_vertical_velocity", "license": "Apache-2.0", "prompt": "Compute projectile range on level ground. The prompt gives initial speed 52.3 m/s but does not give launch angle or vertical velocity. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: launch_angle_or_vertical_velocity.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["launch_angle_or_vertical_velocity"]}, "verifier": {"missing": ["launch_angle_or_vertical_velocity"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 7.2 kg and a = 1.65 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 11.88, \"unit\": \"N\"}", "dedupe_signature": "b815b31c89f4415c88f145eae3aada54fe36ff6397beab2e5a09ba90e7b6562d", "difficulty": "easy", "final_answer": {"answer": 11.88, "unit": "N"}, "id": "force_004482_7.2_1.65", "license": "Apache-2.0", "prompt": "A cart has mass 7.2 kg and measured acceleration 1.65 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 7.2 kg and a = 1.65 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 1.65, "mass": 7.2}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=21 degrees through the sine of 2 theta.\n3. Substitute v=75.2 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 385.7248, \"unit\": \"m\"}", "dedupe_signature": "1966839e05dd25aadcbe0d3a8ccc099c9e6df27d1896d205e0f72025d1fbfd69", "difficulty": "medium", "final_answer": {"answer": 385.7248, "unit": "m"}, "id": "projectile_range_004484_75.2_21", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 75.2 m/s and angle 21 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=21 degrees through the sine of 2 theta.\nSubstitute v=75.2 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 21, "gravity": 9.81, "speed": 75.2}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 5.34 * 8.314 * 267 / 40.9.\nFinal: {\"answer\": 289.8273, \"unit\": \"kPa\"}", "dedupe_signature": "d09dabfda609b716ef8f55bb87c13702d7bbf33be965cf565ca6520404f9c5f8", "difficulty": "medium", "final_answer": {"answer": 289.8273, "unit": "kPa"}, "id": "ideal_gas_004485_5.34_267_40.9", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=5.34 mol, T=267 K, and V=40.9 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 5.34 * 8.314 * 267 / 40.9.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 5.34, "temp_k": 267, "volume_l": 40.9}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 575 * 0.675 * 66.\nFinal: {\"answer\": 25616.25, \"unit\": \"J\"}", "dedupe_signature": "26de8efe1aa2ba557a0c8b97a2cbc923f9ea7b5bb006a329f33384013736ba38", "difficulty": "easy", "final_answer": {"answer": 25616.25, "unit": "J"}, "id": "heat_q_004486_575_0.675_66", "license": "Apache-2.0", "prompt": "A 575 g sample has specific heat 0.675 J/(g*K). How much heat is needed to raise its temperature by 66 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 575 * 0.675 * 66.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 66, "heat_capacity": 0.675, "mass_g": 575}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=79 mg, t=291.5 h, and T_half=25.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 0.0286, \"unit\": \"mg\"}", "dedupe_signature": "147c171970dcb612074d79ea26ef23e5caea8d36ccab4bf9deb274684d6c4c61", "difficulty": "medium", "final_answer": {"answer": 0.0286, "unit": "mg"}, "id": "half_life_004488_79_25.5_291.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 79 mg. Its half-life is 25.5 hours. How many mg remain after 291.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=79 mg, t=291.5 h, and T_half=25.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 291.5, "half_life": 25.5, "initial_amount": 79.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 7.18 mol * 44.01 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 315.9918, \"unit\": \"g\"}", "dedupe_signature": "02b0b0ba73aa45f7acd374f7c2ea27d98ccd87d921ea80a5609cbbbccb7a5915", "difficulty": "medium", "final_answer": {"answer": 315.9918, "unit": "g"}, "id": "stoich_mass_004489_carbon_dioxide_7.18", "license": "Apache-2.0", "prompt": "A sample contains 7.18 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 7.18 mol * 44.01 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "carbon dioxide", "molar_mass": 44.01, "moles": 7.18}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 645 mL to 0.645 L.\n3. Compute M = 0.985 / 0.645.\nFinal: {\"answer\": 1.5271, \"unit\": \"mol/L\"}", "dedupe_signature": "62e944fe682297ad41c2531e63ed3503e9bdfb7fbf93597a759728c1603415cb", "difficulty": "medium", "final_answer": {"answer": 1.5271, "unit": "mol/L"}, "id": "molarity_004490_0.985_645", "license": "Apache-2.0", "prompt": "A solution contains 0.985 mol of solute in 645 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 645 mL to 0.645 L.\nCompute M = 0.985 / 0.645.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 0.985, "volume_ml": 645}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.69 y, so each step multiplies y by 1 - h*0.69.\n3. Apply that update for 6 steps and round the final state.\nFinal: {\"answer\": 0.0003, \"unit\": \"state_units\"}", "dedupe_signature": "63bd1fa6529a384eb40573f99a0054655e246060a883b0b508ae97f18d4e8dc7", "difficulty": "medium", "final_answer": {"answer": 0.0003, "unit": "state_units"}, "id": "euler_decay_004491_44_0.69_1.25_6", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.69 y with y(0)=44, step size h=1.25, for 6 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.69 y, so each step multiplies y by 1 - h*0.69.\nApply that update for 6 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 44.0, "rate": 0.69, "step": 1.25, "steps": 6}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(6.3)=-0.77 and f(14.2)=7.92.\n3. The interval width is 7.9.\nFinal: {\"answer\": 28.2425, \"unit\": \"area_units\"}", "dedupe_signature": "c7c474167342543d92d02d67fd0ff265b3f7769f994ae0ce5453632e1a8295bc", "difficulty": "medium", "final_answer": {"answer": 28.2425, "unit": "area_units"}, "id": "trapz_linear_004492_1.1_-7.7_6.3_14.2", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=1.1x+-7.7 from x=6.3 to x=14.2. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(6.3)=-0.77 and f(14.2)=7.92.\nThe interval width is 7.9.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -7.7, "slope": 1.1, "x0": 6.3, "x1": 14.2}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.24 and add it to the current value.\nFinal: {\"answer\": [1.204, 1.654, 0.978], \"unit\": \"temperature_units\"}", "dedupe_signature": "e09c6d51fdc3216a8eb361d18d3ca7b92797b6a97092861cf092ae46ca15094d", "difficulty": "hard", "final_answer": {"answer": [1.204, 1.654, 0.978], "unit": "temperature_units"}, "id": "heat_step_004493_0.24_2.8_-0.2_2.65_1.35_-1.5", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=2.8, right=-1.5; current interior values are [-0.2, 2.65, 1.35]. Use r=0.24. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.24 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-0.2, 2.65, 1.35], "left": 2.8, "r": 0.24, "right": -1.5}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 100 centimeters in one meter.\n2. Apply the conversion factor directly to the given value.\n3. Compute 1041.0 / 100.\nFinal: {\"answer\": 10.41, \"unit\": \"m\"}", "dedupe_signature": "2fb4a557d0a62efc2a071cd7fe214f6e42e196df92abd6db7c16566601a378b1", "difficulty": "easy", "final_answer": {"answer": 10.41, "unit": "m"}, "id": "unit_convert_004494_cm_to_m_1041", "license": "Apache-2.0", "prompt": "Convert 1041 cm to m. Return the converted value with unit.", "reasoning_trace": "There are 100 centimeters in one meter.\nApply the conversion factor directly to the given value.\nCompute 1041.0 / 100.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 1041.0}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-6.85, -13.25], \"unit\": \"dimensionless\"}", "dedupe_signature": "7ea84125ab838151f85aad2967d6fb2afae8ad68f924130f59e1225b2d31b18b", "difficulty": "medium", "final_answer": {"answer": [-6.85, -13.25], "unit": "dimensionless"}, "id": "line_two_point_004496_-9.25_-6_-6.85_-13.25", "license": "Apache-2.0", "prompt": "A line passes through points (-9.25, 50.1125) and (-6, 27.85). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -9.25, "x2": -6.0, "y1": 50.1125, "y2": 27.849999999999994}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. speed squared over acceleration has units of meters\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "fbbb9a40f980634160288f7d9d5427ac119b1756ed2b6bd506324a470d4e6388", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_004497_consistent_741d4e34_560054", "license": "Apache-2.0", "prompt": "In simulation spec case 560054, check dimensional consistency for R = v^2 * sin(theta) / g. The left side has dimensions m and the right side has dimensions m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nspeed squared over acceleration has units of meters\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "R = v^2 * sin(theta) / g"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef threshold_flags_004498(values, threshold):\n    return [value >= threshold for value in values]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"threshold_flags_004498\"}", "dedupe_signature": "96c05d84e56b2feb2380a94fd0db3c8a12022f90c2814ec6cd2a6c012fd3708d", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "threshold_flags_004498"}, "id": "code_004498_threshold_flags_004498", "license": "Apache-2.0", "prompt": "Write a Python function threshold_flags_004498(values, threshold) that returns a list of booleans showing whether each value is greater than or equal to threshold. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "threshold_flags_004498"}, "verifier": {"function": "threshold_flags_004498", "tests": ["assert threshold_flags_004498([1, 2, 3], 2) == [False, True, True]", "assert threshold_flags_004498([], 5) == []", "assert threshold_flags_004498([-1, 0], 0) == [False, True]"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: required_fields, allowed_transformations.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"required_fields\", \"allowed_transformations\"]}", "dedupe_signature": "e9c2222529648ccc810bd907467aebdf99dc6b09327f6b8d7f4418af37eb5af7", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["required_fields", "allowed_transformations"]}, "id": "abstain_004499_required_fields_allowed_transformations", "license": "Apache-2.0", "prompt": "Write a sanitizer for valid warehouse experiment records in release 284060, but the prompt does not state which fields are required or which transformations are allowed. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: required_fields, allowed_transformations.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["required_fields", "allowed_transformations"]}, "verifier": {"missing": ["required_fields", "allowed_transformations"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 20.45 kg and a = 12.3 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 251.535, \"unit\": \"N\"}", "dedupe_signature": "9e891e49fe3902d20c9cae9ef4d28817c96a41774e2a6f3c20c55ac253dac349", "difficulty": "easy", "final_answer": {"answer": 251.535, "unit": "N"}, "id": "force_004500_20.45_12.3", "license": "Apache-2.0", "prompt": "A cart has mass 20.45 kg and measured acceleration 12.3 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 20.45 kg and a = 12.3 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 12.3, "mass": 20.45}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 30.25^2 and multiply by 0.5 * 29.8.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 13634.4312, \"unit\": \"J\"}", "dedupe_signature": "5422c44636fe8b4eb8469af89cdd85a138b9b2460869143ce0f40a9d71428335", "difficulty": "easy", "final_answer": {"answer": 13634.4312, "unit": "J"}, "id": "ke_004501_29.8_30.25", "license": "Apache-2.0", "prompt": "A body of mass 29.8 kg moves at 30.25 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 30.25^2 and multiply by 0.5 * 29.8.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 29.8, "velocity": 30.25}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 0.48 * 8.314 * 539 / 71.4.\nFinal: {\"answer\": 30.126, \"unit\": \"kPa\"}", "dedupe_signature": "d3b844e0ed3a112ce652afc909a3bd3274a5ffa770d579f26d1c5092ad7e7bbe", "difficulty": "medium", "final_answer": {"answer": 30.126, "unit": "kPa"}, "id": "ideal_gas_004503_0.48_539_71.4", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=0.48 mol, T=539 K, and V=71.4 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 0.48 * 8.314 * 539 / 71.4.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 0.48, "temp_k": 539, "volume_l": 71.4}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1450 * 1.465 * 14.\nFinal: {\"answer\": 29739.5, \"unit\": \"J\"}", "dedupe_signature": "c2e0843b8f6a9f38e1f3a0e1ade0cc44c3c501a299ad64a27db469cc613dd76b", "difficulty": "easy", "final_answer": {"answer": 29739.5, "unit": "J"}, "id": "heat_q_004504_1450_1.465_14", "license": "Apache-2.0", "prompt": "A 1450 g sample has specific heat 1.465 J/(g*K). How much heat is needed to raise its temperature by 14 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1450 * 1.465 * 14.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 14, "heat_capacity": 1.465, "mass_g": 1450}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=168.6 V and R=173.2 ohm.\nFinal: {\"answer\": 164.1222, \"unit\": \"W\"}", "dedupe_signature": "1e9f118cf718bd8b0eda0fa670516f424ef2a93d8f15fce9a29822e49a9781c4", "difficulty": "easy", "final_answer": {"answer": 164.1222, "unit": "W"}, "id": "ohm_power_004505_168.6_173.2", "license": "Apache-2.0", "prompt": "A resistor has resistance 173.2 ohm and voltage 168.6 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=168.6 V and R=173.2 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 173.2, "voltage": 168.6}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=764.5 mg, t=190.5 h, and T_half=37 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 21.5516, \"unit\": \"mg\"}", "dedupe_signature": "19b9d01d85f39579f87f0b296e7bdf18267914f10250f39b860a391aaca480ff", "difficulty": "medium", "final_answer": {"answer": 21.5516, "unit": "mg"}, "id": "half_life_004506_764.5_37_190.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 764.5 mg. Its half-life is 37 hours. How many mg remain after 190.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=764.5 mg, t=190.5 h, and T_half=37 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 190.5, "half_life": 37.0, "initial_amount": 764.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 4.33 mol * 44.01 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 190.5633, \"unit\": \"g\"}", "dedupe_signature": "bb93dd8a6af3531b80e15601ca0c208707ea984693e35ff2c7f69501b3f03dc6", "difficulty": "medium", "final_answer": {"answer": 190.5633, "unit": "g"}, "id": "stoich_mass_004507_carbon_dioxide_4.33", "license": "Apache-2.0", "prompt": "A sample contains 4.33 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 4.33 mol * 44.01 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "carbon dioxide", "molar_mass": 44.01, "moles": 4.33}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.41 y, so each step multiplies y by 1 - h*0.41.\n3. Apply that update for 12 steps and round the final state.\nFinal: {\"answer\": 0.0, \"unit\": \"state_units\"}", "dedupe_signature": "30c32039f802ab857576f863c9dc638bd3599ad2478295b736b29794e42541c0", "difficulty": "medium", "final_answer": {"answer": 0.0, "unit": "state_units"}, "id": "euler_decay_004509_5_0.41_1.85_12", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.41 y with y(0)=5, step size h=1.85, for 12 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.41 y, so each step multiplies y by 1 - h*0.41.\nApply that update for 12 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 5.0, "rate": 0.41, "step": 1.85, "steps": 12}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.42 and add it to the current value.\nFinal: {\"answer\": [0.65, 0.345, -1.048], \"unit\": \"temperature_units\"}", "dedupe_signature": "283d50c3749e7c3e9fc8cff60bde51b9c9baf37fe948479b2c90c8f398aa85bc", "difficulty": "hard", "final_answer": {"answer": [0.65, 0.345, -1.048], "unit": "temperature_units"}, "id": "heat_step_004511_0.42_2.95_0.65_-1.65_0.8_-1.15", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=2.95, right=-1.15; current interior values are [0.65, -1.65, 0.8]. Use r=0.42. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.42 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [0.65, -1.65, 0.8], "left": 2.95, "r": 0.42, "right": -1.15}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 29688.0 / 1000.\nFinal: {\"answer\": 29.688, \"unit\": \"kg\"}", "dedupe_signature": "bdd0e59ca1b445ad43ecc4ed85ddf463bb0873e1c1658f64376dd1c85aab7142", "difficulty": "easy", "final_answer": {"answer": 29.688, "unit": "kg"}, "id": "unit_convert_004512_g_to_kg_29688", "license": "Apache-2.0", "prompt": "Convert 29688 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 29688.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 29688.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. velocity times time gives distance, not acceleration\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "da55ce7633581f16429b9cad7528798df1f115d3890c2baa1ea18852c9c84d2d", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_004515_inconsistent_7481c798_223845", "license": "Apache-2.0", "prompt": "In simulation spec case 223845, check dimensional consistency for a = v * t. The left side has dimensions m/s^2 and the right side has dimensions m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nvelocity times time gives distance, not acceleration\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "a = v * t"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef normalize_004516(values):\n    total = sum(values)\n    if total == 0:\n        raise ValueError('cannot normalize zero-sum values')\n    return [v / total for v in values]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"normalize_004516\"}", "dedupe_signature": "91f830f16c74f32925460f4d37d22491a91f67445caa21f1852ff0e518f58a40", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "normalize_004516"}, "id": "code_004516_normalize_004516", "license": "Apache-2.0", "prompt": "Write a Python function normalize_004516(values) that returns a new list whose values sum to 1. Raise ValueError if the sum is zero. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "normalize_004516"}, "verifier": {"function": "normalize_004516", "tests": ["out = normalize_004516([2, 3, 5]); assert len(out) == 3", "assert abs(sum(normalize_004516([2, 3, 5])) - 1.0) < 1e-12", "assert normalize_004516([1, 1]) == [0.5, 0.5]", "try:\n    normalize_004516([1, -1])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: target_schema, valid_examples.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"target_schema\", \"valid_examples\"]}", "dedupe_signature": "f3a7142fd0011c468e7f317f8bb40e1fd4e6ba6a5886537f9523bf04d8e01c3e", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["target_schema", "valid_examples"]}, "id": "abstain_004517_target_schema_valid_examples", "license": "Apache-2.0", "prompt": "Write a parser that converts each field survey record from batch 471846 into the correct schema, but the prompt does not include the target schema or examples. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: target_schema, valid_examples.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["target_schema", "valid_examples"]}, "verifier": {"missing": ["target_schema", "valid_examples"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 16.55 kg and a = 1.25 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 20.6875, \"unit\": \"N\"}", "dedupe_signature": "09d374b56666fd53913fdbb576e3b552228cce3262f83f5792e1b6378c1f1c67", "difficulty": "easy", "final_answer": {"answer": 20.6875, "unit": "N"}, "id": "force_004518_16.55_1.25", "license": "Apache-2.0", "prompt": "A cart has mass 16.55 kg and measured acceleration 1.25 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 16.55 kg and a = 1.25 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 1.25, "mass": 16.55}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 1.15 * 8.314 * 258 / 94.3.\nFinal: {\"answer\": 26.1587, \"unit\": \"kPa\"}", "dedupe_signature": "555394fee414111c3de1f15e36ce9da4a4966627578d0f2652e921d93806c7c2", "difficulty": "medium", "final_answer": {"answer": 26.1587, "unit": "kPa"}, "id": "ideal_gas_004521_1.15_258_94.3", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=1.15 mol, T=258 K, and V=94.3 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 1.15 * 8.314 * 258 / 94.3.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 1.15, "temp_k": 258, "volume_l": 94.3}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 145 * 3.53 * 15.\nFinal: {\"answer\": 7677.75, \"unit\": \"J\"}", "dedupe_signature": "5ee14b58a04955f499eefa66eaaa25c92302bbe81056b92f9da4969995884d08", "difficulty": "easy", "final_answer": {"answer": 7677.75, "unit": "J"}, "id": "heat_q_004522_145_3.53_15", "license": "Apache-2.0", "prompt": "A 145 g sample has specific heat 3.53 J/(g*K). How much heat is needed to raise its temperature by 15 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 145 * 3.53 * 15.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 15, "heat_capacity": 3.53, "mass_g": 145}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=66.2 V and R=14.7 ohm.\nFinal: {\"answer\": 298.1252, \"unit\": \"W\"}", "dedupe_signature": "b29dd0d9c757c0d12b56b00a5bbc3c57d48b72bda46b8d87e1e057540aa47179", "difficulty": "easy", "final_answer": {"answer": 298.1252, "unit": "W"}, "id": "ohm_power_004523_66.2_14.7", "license": "Apache-2.0", "prompt": "A resistor has resistance 14.7 ohm and voltage 66.2 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=66.2 V and R=14.7 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 14.7, "voltage": 66.2}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=145.5 mg, t=44 h, and T_half=71 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 94.6911, \"unit\": \"mg\"}", "dedupe_signature": "dc444d29578593e367712fff9016a93950049e49f37b9301642623c53a890fed", "difficulty": "medium", "final_answer": {"answer": 94.6911, "unit": "mg"}, "id": "half_life_004524_145.5_71_44", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 145.5 mg. Its half-life is 71 hours. How many mg remain after 44 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=145.5 mg, t=44 h, and T_half=71 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 44.0, "half_life": 71.0, "initial_amount": 145.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 1855 mL to 1.855 L.\n3. Compute M = 0.865 / 1.855.\nFinal: {\"answer\": 0.4663, \"unit\": \"mol/L\"}", "dedupe_signature": "3c558ba21c2ad9f3738a2c196b6b993c35652fedbaef8a66115cf1619dd4c9ce", "difficulty": "medium", "final_answer": {"answer": 0.4663, "unit": "mol/L"}, "id": "molarity_004526_0.865_1855", "license": "Apache-2.0", "prompt": "A solution contains 0.865 mol of solute in 1855 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 1855 mL to 1.855 L.\nCompute M = 0.865 / 1.855.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 0.865, "volume_ml": 1855}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.06 y, so each step multiplies y by 1 - h*0.06.\n3. Apply that update for 7 steps and round the final state.\nFinal: {\"answer\": 6.3272, \"unit\": \"state_units\"}", "dedupe_signature": "aaeb324d434ab124a7bda63372f633ebc4d7d4085885fdb6a92a27c4ca8e389a", "difficulty": "medium", "final_answer": {"answer": 6.3272, "unit": "state_units"}, "id": "euler_decay_004527_7.5_0.06_0.4_7", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.06 y with y(0)=7.5, step size h=0.4, for 7 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.06 y, so each step multiplies y by 1 - h*0.06.\nApply that update for 7 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 7.5, "rate": 0.06, "step": 0.4, "steps": 7}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(5.6)=46.34 and f(9.9)=67.41.\n3. The interval width is 4.3.\nFinal: {\"answer\": 244.5625, \"unit\": \"area_units\"}", "dedupe_signature": "845d7daa0e6c0b6bbce587d8d75e30f97aeb6eb3a6b401b75de437d364f4dafa", "difficulty": "medium", "final_answer": {"answer": 244.5625, "unit": "area_units"}, "id": "trapz_linear_004528_4.9_18.9_5.6_9.9", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=4.9x+18.9 from x=5.6 to x=9.9. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(5.6)=46.34 and f(9.9)=67.41.\nThe interval width is 4.3.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 18.9, "slope": 4.9, "x0": 5.6, "x1": 9.899999999999999}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.06 and add it to the current value.\nFinal: {\"answer\": [1.254, -0.307, 1.309], \"unit\": \"temperature_units\"}", "dedupe_signature": "badcb08dafdb81ae43b1e5faa23a010dca5028b3ad03c4ed4cdd6f9ed17f0397", "difficulty": "hard", "final_answer": {"answer": [1.254, -0.307, 1.309], "unit": "temperature_units"}, "id": "heat_step_004529_0.06_1.65_1.35_-0.55_1.6_-1.1", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.65, right=-1.1; current interior values are [1.35, -0.55, 1.6]. Use r=0.06. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.06 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [1.35, -0.55, 1.6], "left": 1.65, "r": 0.06, "right": -1.1}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kelvin equals Celsius plus 273.15.\n2. Apply the conversion factor directly to the given value.\n3. Compute 141.0 + 273.15.\nFinal: {\"answer\": 414.15, \"unit\": \"K\"}", "dedupe_signature": "c61191454ca5e1e6acfca7eabb703e80f13783f49ba9ee09a78b9a1332d84083", "difficulty": "easy", "final_answer": {"answer": 414.15, "unit": "K"}, "id": "unit_convert_004530_c_to_k_141", "license": "Apache-2.0", "prompt": "Convert 141 degC to K. Return the converted value with unit.", "reasoning_trace": "Kelvin equals Celsius plus 273.15.\nApply the conversion factor directly to the given value.\nCompute 141.0 + 273.15.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 141.0}, "verifier": {"formula": "value + 273.15", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=21 degrees and keep the unit as newtons.\nFinal: {\"answer\": [253.4671, 97.2969], \"unit\": \"N\"}", "dedupe_signature": "481b385c17b92993df0120e3c84421ff2c4c66b13f688d1e59d504e840ee78ac", "difficulty": "medium", "final_answer": {"answer": [253.4671, 97.2969], "unit": "N"}, "id": "vector_components_004531_271.5_21", "license": "Apache-2.0", "prompt": "A vector has magnitude 271.5 N at 21 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=21 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 21, "magnitude": 271.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef normalize_004534(values):\n    total = sum(values)\n    if total == 0:\n        raise ValueError('cannot normalize zero-sum values')\n    return [v / total for v in values]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"normalize_004534\"}", "dedupe_signature": "f8fa5e441df6d9f4bf2b3d648fb24c01838065a01bdd4592b810453d424e1842", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "normalize_004534"}, "id": "code_004534_normalize_004534", "license": "Apache-2.0", "prompt": "Write a Python function normalize_004534(values) that returns a new list whose values sum to 1. Raise ValueError if the sum is zero. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "normalize_004534"}, "verifier": {"function": "normalize_004534", "tests": ["out = normalize_004534([2, 3, 5]); assert len(out) == 3", "assert abs(sum(normalize_004534([2, 3, 5])) - 1.0) < 1e-12", "assert normalize_004534([1, 1]) == [0.5, 0.5]", "try:\n    normalize_004534([1, -1])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: volume.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"volume\"]}", "dedupe_signature": "700be5940baac0393a2f7cb912d320802f7e8c9099a5dcb72803dbdc37611721", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["volume"]}, "id": "abstain_004535_volume", "license": "Apache-2.0", "prompt": "Compute pressure from the ideal gas law. The prompt gives n=3.93 mol and T=291 K, but does not give volume. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: volume.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["volume"]}, "verifier": {"missing": ["volume"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 9.35 kg and a = 8.85 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 82.7475, \"unit\": \"N\"}", "dedupe_signature": "3a1797102b75a08ad0999bc1565e3cecb15157162c3696062d5da64a2a652c8e", "difficulty": "easy", "final_answer": {"answer": 82.7475, "unit": "N"}, "id": "force_004536_9.35_8.85", "license": "Apache-2.0", "prompt": "A cart has mass 9.35 kg and measured acceleration 8.85 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 9.35 kg and a = 8.85 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 8.85, "mass": 9.35}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 6.35^2 and multiply by 0.5 * 19.2.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 387.096, \"unit\": \"J\"}", "dedupe_signature": "a77ca2fee23cf4d37016f479596af3381e1a9b2dc9bb059e3d1a81ea9495da19", "difficulty": "easy", "final_answer": {"answer": 387.096, "unit": "J"}, "id": "ke_004537_19.2_6.35", "license": "Apache-2.0", "prompt": "A body of mass 19.2 kg moves at 6.35 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 6.35^2 and multiply by 0.5 * 19.2.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 19.2, "velocity": 6.35}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 4.49 * 8.314 * 387 / 8.8.\nFinal: {\"answer\": 1641.6654, \"unit\": \"kPa\"}", "dedupe_signature": "946fae93a85efce6495da3170202cc8a20cb35f783caa74506c6e0db7ed004cd", "difficulty": "medium", "final_answer": {"answer": 1641.6654, "unit": "kPa"}, "id": "ideal_gas_004539_4.49_387_8.8", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=4.49 mol, T=387 K, and V=8.8 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 4.49 * 8.314 * 387 / 8.8.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 4.49, "temp_k": 387, "volume_l": 8.8}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=52.4 V and R=178.1 ohm.\nFinal: {\"answer\": 15.417, \"unit\": \"W\"}", "dedupe_signature": "0893c0f2b3d79b3cf2ca587ea70d16d521d8aa209089baecc41a302f36da1e0a", "difficulty": "easy", "final_answer": {"answer": 15.417, "unit": "W"}, "id": "ohm_power_004541_52.4_178.1", "license": "Apache-2.0", "prompt": "A resistor has resistance 178.1 ohm and voltage 52.4 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=52.4 V and R=178.1 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 178.1, "voltage": 52.4}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=66.5 mg, t=179 h, and T_half=47 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 4.7462, \"unit\": \"mg\"}", "dedupe_signature": "31160a2b3a6127486914d5d0ed31e83bfb5ddf0c2436d22ba38a6dbaac271675", "difficulty": "medium", "final_answer": {"answer": 4.7462, "unit": "mg"}, "id": "half_life_004542_66.5_47_179", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 66.5 mg. Its half-life is 47 hours. How many mg remain after 179 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=66.5 mg, t=179 h, and T_half=47 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 179.0, "half_life": 47.0, "initial_amount": 66.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 7.26 mol * 100.087 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 726.6316, \"unit\": \"g\"}", "dedupe_signature": "c4d4763e7e7c05841caff5b2fb4b4786dd2518da39f9116f7647823a2757eadc", "difficulty": "medium", "final_answer": {"answer": 726.6316, "unit": "g"}, "id": "stoich_mass_004543_calcium_carbonate_7.26", "license": "Apache-2.0", "prompt": "A sample contains 7.26 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 7.26 mol * 100.087 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "calcium carbonate", "molar_mass": 100.087, "moles": 7.26}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.34 y, so each step multiplies y by 1 - h*0.34.\n3. Apply that update for 3 steps and round the final state.\nFinal: {\"answer\": 8.1747, \"unit\": \"state_units\"}", "dedupe_signature": "62fc1a381b0350b294ce14b8ea3698108448f7046dec9f6ec7d0917937acc351", "difficulty": "medium", "final_answer": {"answer": 8.1747, "unit": "state_units"}, "id": "euler_decay_004545_43_0.34_1.25_3", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.34 y with y(0)=43, step size h=1.25, for 3 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.34 y, so each step multiplies y by 1 - h*0.34.\nApply that update for 3 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 43.0, "rate": 0.34, "step": 1.25, "steps": 3}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.26 and add it to the current value.\nFinal: {\"answer\": [2.184, 2.164, 1.122], \"unit\": \"temperature_units\"}", "dedupe_signature": "8ca7d7a4bc821a32676354d7f198d488cdc69d4c02a55c93aa0ab8aa6cca0705", "difficulty": "hard", "final_answer": {"answer": [2.184, 2.164, 1.122], "unit": "temperature_units"}, "id": "heat_step_004547_0.26_1.15_2.6_2.45_1.2_-0.35", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.15, right=-0.35; current interior values are [2.6, 2.45, 1.2]. Use r=0.26. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.26 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [2.6, 2.45, 1.2], "left": 1.15, "r": 0.26, "right": -0.35}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 1726.0 / 1000.\nFinal: {\"answer\": 1.726, \"unit\": \"kg\"}", "dedupe_signature": "2461f7195d996946be54b45e0725fe8ad531c1703d294408ce8537a477a8a023", "difficulty": "easy", "final_answer": {"answer": 1.726, "unit": "kg"}, "id": "unit_convert_004548_g_to_kg_1726", "license": "Apache-2.0", "prompt": "Convert 1726 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 1726.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 1726.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=273 degrees and keep the unit as newtons.\nFinal: {\"answer\": [3.742, -71.402], \"unit\": \"N\"}", "dedupe_signature": "668b063d712fd143c8c2b1c4d4ff1188de070579a4dcf43207a869ecdd5eb1d9", "difficulty": "medium", "final_answer": {"answer": [3.742, -71.402], "unit": "N"}, "id": "vector_components_004549_71.5_273", "license": "Apache-2.0", "prompt": "A vector has magnitude 71.5 N at 273 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=273 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 273, "magnitude": 71.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-2.15, 10.25], \"unit\": \"dimensionless\"}", "dedupe_signature": "3e2c3d709df086410f45c7f7565f0a360643543c54063054f9b59a459306df2b", "difficulty": "medium", "final_answer": {"answer": [-2.15, 10.25], "unit": "dimensionless"}, "id": "line_two_point_004550_8.5_9.25_-2.15_10.25", "license": "Apache-2.0", "prompt": "A line passes through points (8.5, -8.025) and (9.25, -9.6375). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 8.5, "x2": 9.25, "y1": -8.024999999999999, "y2": -9.6375}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. amount times volume is not concentration\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "d60cd3bda90f07ae0a256065726d7c9c76de288a40cb0910ba9092a3cca64d5f", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_004551_inconsistent_74ac0b02_593625", "license": "Apache-2.0", "prompt": "In field worksheet case 593625, check dimensional consistency for C = n * V. The left side has dimensions mol/L and the right side has dimensions mol*L. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\namount times volume is not concentration\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "C = n * V"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef threshold_flags_004552(values, threshold):\n    return [value >= threshold for value in values]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"threshold_flags_004552\"}", "dedupe_signature": "4df5ce9f4e372b2430d9381c684342a6d38c1570b080bdfb9a0f45780219e540", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "threshold_flags_004552"}, "id": "code_004552_threshold_flags_004552", "license": "Apache-2.0", "prompt": "Write a Python function threshold_flags_004552(values, threshold) that returns a list of booleans showing whether each value is greater than or equal to threshold. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "threshold_flags_004552"}, "verifier": {"function": "threshold_flags_004552", "tests": ["assert threshold_flags_004552([1, 2, 3], 2) == [False, True, True]", "assert threshold_flags_004552([], 5) == []", "assert threshold_flags_004552([-1, 0], 0) == [False, True]"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: rate_constant, number_of_steps.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"rate_constant\", \"number_of_steps\"]}", "dedupe_signature": "e7c3fe1f32cf43e4e227a3fb2ff935fb0e8bea881964e3cbbc431c2b8b87bc6c", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["rate_constant", "number_of_steps"]}, "id": "abstain_004553_rate_constant_number_of_steps", "license": "Apache-2.0", "prompt": "Use explicit Euler for dy/dt = -k y. The prompt gives y(0)=18 and h=0.9, but omits both k and the number of steps. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: rate_constant, number_of_steps.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["rate_constant", "number_of_steps"]}, "verifier": {"missing": ["rate_constant", "number_of_steps"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 4.85 kg and a = 0.2 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 0.97, \"unit\": \"N\"}", "dedupe_signature": "22be30037fd7fec72f2ccfa36459a8c2f5e352bbc4b3c90e38e500267bb6428e", "difficulty": "easy", "final_answer": {"answer": 0.97, "unit": "N"}, "id": "force_004554_4.85_0.2", "license": "Apache-2.0", "prompt": "A cart has mass 4.85 kg and measured acceleration 0.2 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 4.85 kg and a = 0.2 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 0.2, "mass": 4.85}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 29.65^2 and multiply by 0.5 * 27.4.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 12043.9782, \"unit\": \"J\"}", "dedupe_signature": "cb6bae67d6bde4b13e5cd60c6c3c86fed571fe3740f5513a683f15281b312250", "difficulty": "easy", "final_answer": {"answer": 12043.9782, "unit": "J"}, "id": "ke_004555_27.4_29.65", "license": "Apache-2.0", "prompt": "A body of mass 27.4 kg moves at 29.65 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 29.65^2 and multiply by 0.5 * 27.4.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 27.4, "velocity": 29.65}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=61 degrees through the sine of 2 theta.\n3. Substitute v=48.1 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 200.0054, \"unit\": \"m\"}", "dedupe_signature": "ce76555b09fbff56af178cb234d71fa704896d3d891df2ca91d6d306b3e93edf", "difficulty": "medium", "final_answer": {"answer": 200.0054, "unit": "m"}, "id": "projectile_range_004556_48.1_61", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 48.1 m/s and angle 61 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=61 degrees through the sine of 2 theta.\nSubstitute v=48.1 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 61, "gravity": 9.81, "speed": 48.1}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 555 * 2.44 * 74.\nFinal: {\"answer\": 100210.8, \"unit\": \"J\"}", "dedupe_signature": "7f0d0247e719db394f92b244b5292974ace676b4504743145f2a0baa45068251", "difficulty": "easy", "final_answer": {"answer": 100210.8, "unit": "J"}, "id": "heat_q_004558_555_2.44_74", "license": "Apache-2.0", "prompt": "A 555 g sample has specific heat 2.44 J/(g*K). How much heat is needed to raise its temperature by 74 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 555 * 2.44 * 74.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 74, "heat_capacity": 2.44, "mass_g": 555}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=17.9 V and R=126.5 ohm.\nFinal: {\"answer\": 2.5329, \"unit\": \"W\"}", "dedupe_signature": "0a3c6a2f39dc0ce3432f455ad8a3a702a6e324a6f1c237d841578bf50582317d", "difficulty": "easy", "final_answer": {"answer": 2.5329, "unit": "W"}, "id": "ohm_power_004559_17.9_126.5", "license": "Apache-2.0", "prompt": "A resistor has resistance 126.5 ohm and voltage 17.9 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=17.9 V and R=126.5 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 126.5, "voltage": 17.9}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=806 mg, t=276.5 h, and T_half=10.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 0.0, \"unit\": \"mg\"}", "dedupe_signature": "15076f566fa0a1c9b82c81d02f8f76ce8ac6c12c9a3e426a249e9d4df1b7b393", "difficulty": "medium", "final_answer": {"answer": 0.0, "unit": "mg"}, "id": "half_life_004560_806_10.5_276.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 806 mg. Its half-life is 10.5 hours. How many mg remain after 276.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=806 mg, t=276.5 h, and T_half=10.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 276.5, "half_life": 10.5, "initial_amount": 806.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 4.31 mol * 180.156 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 776.4724, \"unit\": \"g\"}", "dedupe_signature": "2d76fe95b75cba6c674b59d286bc7babd207dc108515b1ffccf753dad416a9a4", "difficulty": "medium", "final_answer": {"answer": 776.4724, "unit": "g"}, "id": "stoich_mass_004561_glucose_4.31", "license": "Apache-2.0", "prompt": "A sample contains 4.31 mol of glucose. Using molar mass 180.156 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 4.31 mol * 180.156 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "glucose", "molar_mass": 180.156, "moles": 4.31}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 3410 mL to 3.41 L.\n3. Compute M = 3.43 / 3.41.\nFinal: {\"answer\": 1.0059, \"unit\": \"mol/L\"}", "dedupe_signature": "a7cba1864239c1e3cd345e4b5d61cf07cce7956f4da6f2016d5e3e603f63783c", "difficulty": "medium", "final_answer": {"answer": 1.0059, "unit": "mol/L"}, "id": "molarity_004562_3.43_3410", "license": "Apache-2.0", "prompt": "A solution contains 3.43 mol of solute in 3410 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 3410 mL to 3.41 L.\nCompute M = 3.43 / 3.41.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 3.43, "volume_ml": 3410}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.22 y, so each step multiplies y by 1 - h*0.22.\n3. Apply that update for 11 steps and round the final state.\nFinal: {\"answer\": 21.4188, \"unit\": \"state_units\"}", "dedupe_signature": "32cda49a3615fc9c0c32aa7398d4721f1198af70fa657fa19def0e1bdc8f103b", "difficulty": "medium", "final_answer": {"answer": 21.4188, "unit": "state_units"}, "id": "euler_decay_004563_59_0.22_0.4_11", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.22 y with y(0)=59, step size h=0.4, for 11 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.22 y, so each step multiplies y by 1 - h*0.22.\nApply that update for 11 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 59.0, "rate": 0.22, "step": 0.4, "steps": 11}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(5.3)=0.75 and f(13.6)=13.2.\n3. The interval width is 8.3.\nFinal: {\"answer\": 57.8925, \"unit\": \"area_units\"}", "dedupe_signature": "335535727458a452015064c626c5f8ee42fb2d72c05cfe1c88c09df931ffe353", "difficulty": "medium", "final_answer": {"answer": 57.8925, "unit": "area_units"}, "id": "trapz_linear_004564_1.5_-7.2_5.3_13.6", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=1.5x+-7.2 from x=5.3 to x=13.6. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(5.3)=0.75 and f(13.6)=13.2.\nThe interval width is 8.3.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -7.2, "slope": 1.5, "x0": 5.3, "x1": 13.600000000000001}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.44 and add it to the current value.\nFinal: {\"answer\": [0.248, -0.796, -0.004], \"unit\": \"temperature_units\"}", "dedupe_signature": "eea5b1a79f54a2d00bc8943dec373485872f377c038b36f3dec36085e1cbd122", "difficulty": "hard", "final_answer": {"answer": [0.248, -0.796, -0.004], "unit": "temperature_units"}, "id": "heat_step_004565_0.44_0.15_-1.05_0.7_-0.95_-0.45", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=0.15, right=-0.45; current interior values are [-1.05, 0.7, -0.95]. Use r=0.44. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.44 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-1.05, 0.7, -0.95], "left": 0.15, "r": 0.44, "right": -0.45}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=306 degrees and keep the unit as newtons.\nFinal: {\"answer\": [217.7744, -299.7408], \"unit\": \"N\"}", "dedupe_signature": "6e5029f947651cccaf8319e32ae93c53ec86dd925d1c21da57f1c313c0761f2b", "difficulty": "medium", "final_answer": {"answer": [217.7744, -299.7408], "unit": "N"}, "id": "vector_components_004567_370.5_306", "license": "Apache-2.0", "prompt": "A vector has magnitude 370.5 N at 306 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=306 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 306, "magnitude": 370.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-7.95, -25.25], \"unit\": \"dimensionless\"}", "dedupe_signature": "7ad0cfa0555a3e7d857b64be584ae6e655b85ebc1ebcbe7cd5fdf98646770f8a", "difficulty": "medium", "final_answer": {"answer": [-7.95, -25.25], "unit": "dimensionless"}, "id": "line_two_point_004568_6_12.25_-7.95_-25.25", "license": "Apache-2.0", "prompt": "A line passes through points (6, -72.95) and (12.25, -122.638). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 6.0, "x2": 12.25, "y1": -72.95, "y2": -122.6375}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. mass times acceleration has newton dimensions\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "6ffda8f3f115889ecc7896de41c14b9448912fa804eb7c809ef5d03379435895", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_004569_consistent_03f5e041_559010", "license": "Apache-2.0", "prompt": "In lab notebook case 559010, check dimensional consistency for F = m * a. The left side has dimensions kg*m/s^2 and the right side has dimensions kg*m/s^2. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nmass times acceleration has newton dimensions\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "F = m * a"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef threshold_flags_004570(values, threshold):\n    return [value >= threshold for value in values]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"threshold_flags_004570\"}", "dedupe_signature": "2d1495223a9e42bb53cadc2ddf106a4a10d77589d99fc57c5a60c952885cb8e3", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "threshold_flags_004570"}, "id": "code_004570_threshold_flags_004570", "license": "Apache-2.0", "prompt": "Write a Python function threshold_flags_004570(values, threshold) that returns a list of booleans showing whether each value is greater than or equal to threshold. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "threshold_flags_004570"}, "verifier": {"function": "threshold_flags_004570", "tests": ["assert threshold_flags_004570([1, 2, 3], 2) == [False, True, True]", "assert threshold_flags_004570([], 5) == []", "assert threshold_flags_004570([-1, 0], 0) == [False, True]"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: recurrence, objective, tie_breaking_rule.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"recurrence\", \"objective\", \"tie_breaking_rule\"]}", "dedupe_signature": "9c550591e92e04b9349dc8660bdf1e36ba1883a71ae6abc040f2c1c945c4d886", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["recurrence", "objective", "tie_breaking_rule"]}, "id": "abstain_004571_recurrence_objective_tie_breaking_rule", "license": "Apache-2.0", "prompt": "Write a dynamic-programming solver for a routing scoring problem with 4634 items and budget 69250, but the recurrence, objective, and tie-breaking rule are all absent. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: recurrence, objective, tie_breaking_rule.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["recurrence", "objective", "tie_breaking_rule"]}, "verifier": {"missing": ["recurrence", "objective", "tie_breaking_rule"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 44.5^2 and multiply by 0.5 * 26.2.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 25941.275, \"unit\": \"J\"}", "dedupe_signature": "9e735e8d3a79dc4dbb2c504d201b9a7204fa84d81e022c679b21e6324b06af50", "difficulty": "easy", "final_answer": {"answer": 25941.275, "unit": "J"}, "id": "ke_004573_26.2_44.5", "license": "Apache-2.0", "prompt": "A body of mass 26.2 kg moves at 44.5 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 44.5^2 and multiply by 0.5 * 26.2.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 26.2, "velocity": 44.5}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=61 degrees through the sine of 2 theta.\n3. Substitute v=42.2 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 153.9488, \"unit\": \"m\"}", "dedupe_signature": "16c41ee253ba0e001f3121f686a9ab64ec0473bb24cf51046de2bb035afcab49", "difficulty": "medium", "final_answer": {"answer": 153.9488, "unit": "m"}, "id": "projectile_range_004574_42.2_61", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 42.2 m/s and angle 61 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=61 degrees through the sine of 2 theta.\nSubstitute v=42.2 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 61, "gravity": 9.81, "speed": 42.2}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 110 * 1.445 * 11.\nFinal: {\"answer\": 1748.45, \"unit\": \"J\"}", "dedupe_signature": "a042ead2cf0c32fd5cf7808dd1b907a3d1cd78ab8aa04126089c6003bdbbdd7c", "difficulty": "easy", "final_answer": {"answer": 1748.45, "unit": "J"}, "id": "heat_q_004576_110_1.445_11", "license": "Apache-2.0", "prompt": "A 110 g sample has specific heat 1.445 J/(g*K). How much heat is needed to raise its temperature by 11 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 110 * 1.445 * 11.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 11, "heat_capacity": 1.445, "mass_g": 110}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=226.5 V and R=95.2 ohm.\nFinal: {\"answer\": 538.8892, \"unit\": \"W\"}", "dedupe_signature": "48709525c73a07993ac02979b4b6e3b4eedbadec2d625946a78fab21546ef9c1", "difficulty": "easy", "final_answer": {"answer": 538.8892, "unit": "W"}, "id": "ohm_power_004577_226.5_95.2", "license": "Apache-2.0", "prompt": "A resistor has resistance 95.2 ohm and voltage 226.5 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=226.5 V and R=95.2 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 95.2, "voltage": 226.5}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=774 mg, t=72.5 h, and T_half=84 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 425.5234, \"unit\": \"mg\"}", "dedupe_signature": "ef6eb6807c954df64e9a30cc63137104f933add0bdfa1a1ff7015a20891765e4", "difficulty": "medium", "final_answer": {"answer": 425.5234, "unit": "mg"}, "id": "half_life_004578_774_84_72.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 774 mg. Its half-life is 84 hours. How many mg remain after 72.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=774 mg, t=72.5 h, and T_half=84 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 72.5, "half_life": 84.0, "initial_amount": 774.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 4.78 mol * 58.44 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 279.3432, \"unit\": \"g\"}", "dedupe_signature": "f777c6848f2e46a3b06d8c370a062ab675d661faa3a8169501fde1b01bf20ec9", "difficulty": "medium", "final_answer": {"answer": 279.3432, "unit": "g"}, "id": "stoich_mass_004579_sodium_chloride_4.78", "license": "Apache-2.0", "prompt": "A sample contains 4.78 mol of sodium chloride. Using molar mass 58.44 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 4.78 mol * 58.44 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "sodium chloride", "molar_mass": 58.44, "moles": 4.78}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 1615 mL to 1.615 L.\n3. Compute M = 3.075 / 1.615.\nFinal: {\"answer\": 1.904, \"unit\": \"mol/L\"}", "dedupe_signature": "c2d48e537f6271dc561d828c8dd41bed0780f2808f0af4336010b47c8431d795", "difficulty": "medium", "final_answer": {"answer": 1.904, "unit": "mol/L"}, "id": "molarity_004580_3.075_1615", "license": "Apache-2.0", "prompt": "A solution contains 3.075 mol of solute in 1615 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 1615 mL to 1.615 L.\nCompute M = 3.075 / 1.615.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 3.075, "volume_ml": 1615}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.03 y, so each step multiplies y by 1 - h*0.03.\n3. Apply that update for 5 steps and round the final state.\nFinal: {\"answer\": 49.935, \"unit\": \"state_units\"}", "dedupe_signature": "776a4a2641e1f366b1c49b1c45fc010dde4e2e432b0ca1d721b25a9f4108ee9c", "difficulty": "medium", "final_answer": {"answer": 49.935, "unit": "state_units"}, "id": "euler_decay_004581_67.5_0.03_1.95_5", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.03 y with y(0)=67.5, step size h=1.95, for 5 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.03 y, so each step multiplies y by 1 - h*0.03.\nApply that update for 5 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 67.5, "rate": 0.03, "step": 1.95, "steps": 5}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-1.7)=-2.49 and f(2.1)=19.17.\n3. The interval width is 3.8.\nFinal: {\"answer\": 31.692, \"unit\": \"area_units\"}", "dedupe_signature": "46fa4fb4a9a042cd3caff62fa1aaa01c1a0faead4537710b27b9b6a295f5dfc8", "difficulty": "medium", "final_answer": {"answer": 31.692, "unit": "area_units"}, "id": "trapz_linear_004582_5.7_7.2_-1.7_2.1", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=5.7x+7.2 from x=-1.7 to x=2.1. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-1.7)=-2.49 and f(2.1)=19.17.\nThe interval width is 3.8.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 7.2, "slope": 5.7, "x0": -1.7, "x1": 2.0999999999999996}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.06 and add it to the current value.\nFinal: {\"answer\": [-0.575, -1.68, 1.043], \"unit\": \"temperature_units\"}", "dedupe_signature": "a66489e2f49f4fb538f2202a27dc1bfc4d2dc52dd2a324b2fcaa1118fcde09e0", "difficulty": "hard", "final_answer": {"answer": [-0.575, -1.68, 1.043], "unit": "temperature_units"}, "id": "heat_step_004583_0.06_1.9_-0.65_-1.95_1.25_1.0", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.9, right=1; current interior values are [-0.65, -1.95, 1.25]. Use r=0.06. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.06 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-0.65, -1.95, 1.25], "left": 1.9, "r": 0.06, "right": 1.0}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=272 degrees and keep the unit as newtons.\nFinal: {\"answer\": [3.2631, -93.443], \"unit\": \"N\"}", "dedupe_signature": "9f04214cb1e2f9d04df5af9ad2858f069cc4a2493f3b6da73fd5e6e2cfd2c2d6", "difficulty": "medium", "final_answer": {"answer": [3.2631, -93.443], "unit": "N"}, "id": "vector_components_004585_93.5_272", "license": "Apache-2.0", "prompt": "A vector has magnitude 93.5 N at 272 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=272 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 272, "magnitude": 93.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [7.6, -14.5], \"unit\": \"dimensionless\"}", "dedupe_signature": "68477f3ef6f33129740fc4be1f208859810e20bd65379419897fa21754578922", "difficulty": "medium", "final_answer": {"answer": [7.6, -14.5], "unit": "dimensionless"}, "id": "line_two_point_004586_-17.75_-3_7.6_-14.5", "license": "Apache-2.0", "prompt": "A line passes through points (-17.75, -149.4) and (-3, -37.3). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -17.75, "x2": -3.0, "y1": -149.4, "y2": -37.3}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: rate_constant, number_of_steps.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"rate_constant\", \"number_of_steps\"]}", "dedupe_signature": "6c6d68eaff797d4c7371e37947dda862d1a7ae0ed30823362c0f917562228180", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["rate_constant", "number_of_steps"]}, "id": "abstain_004589_rate_constant_number_of_steps", "license": "Apache-2.0", "prompt": "Use explicit Euler for dy/dt = -k y. The prompt gives y(0)=11.5 and h=0.7, but omits both k and the number of steps. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: rate_constant, number_of_steps.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["rate_constant", "number_of_steps"]}, "verifier": {"missing": ["rate_constant", "number_of_steps"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 24.35 kg and a = 7.8 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 189.93, \"unit\": \"N\"}", "dedupe_signature": "58ceffc732f46d4dc24c08bef880d50d409b3a4c7cd3b91cee30e6aa2f1bad34", "difficulty": "easy", "final_answer": {"answer": 189.93, "unit": "N"}, "id": "force_004590_24.35_7.8", "license": "Apache-2.0", "prompt": "A cart has mass 24.35 kg and measured acceleration 7.8 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 24.35 kg and a = 7.8 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 7.8, "mass": 24.35}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 17.25^2 and multiply by 0.5 * 25.95.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 3860.8734, \"unit\": \"J\"}", "dedupe_signature": "5edf2238472e6c43d2d36ff87de545541e3185a0b5e187cb558f2c5a0318a158", "difficulty": "easy", "final_answer": {"answer": 3860.8734, "unit": "J"}, "id": "ke_004591_25.95_17.25", "license": "Apache-2.0", "prompt": "A body of mass 25.95 kg moves at 17.25 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 17.25^2 and multiply by 0.5 * 25.95.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 25.95, "velocity": 17.25}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=30 degrees through the sine of 2 theta.\n3. Substitute v=38.7 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 132.2159, \"unit\": \"m\"}", "dedupe_signature": "a6412c7c4a8cf32c729edbf03db120151e5fe432a9bf0e0af46c0b2ca961fdec", "difficulty": "medium", "final_answer": {"answer": 132.2159, "unit": "m"}, "id": "projectile_range_004592_38.7_30", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 38.7 m/s and angle 30 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=30 degrees through the sine of 2 theta.\nSubstitute v=38.7 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 30, "gravity": 9.81, "speed": 38.7}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 5.05 * 8.314 * 593 / 98.2.\nFinal: {\"answer\": 253.5389, \"unit\": \"kPa\"}", "dedupe_signature": "e4c9c3357ffbb3f70eaa4e72969574d73adf1df84a750c12e654aa3228d8fed2", "difficulty": "medium", "final_answer": {"answer": 253.5389, "unit": "kPa"}, "id": "ideal_gas_004593_5.05_593_98.2", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=5.05 mol, T=593 K, and V=98.2 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 5.05 * 8.314 * 593 / 98.2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 5.05, "temp_k": 593, "volume_l": 98.2}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 535 * 3.84 * 43.\nFinal: {\"answer\": 88339.2, \"unit\": \"J\"}", "dedupe_signature": "5677db28b73db7c0eacb81fbe8518a297999e3ce052debc61748ed1976f18ce9", "difficulty": "easy", "final_answer": {"answer": 88339.2, "unit": "J"}, "id": "heat_q_004594_535_3.84_43", "license": "Apache-2.0", "prompt": "A 535 g sample has specific heat 3.84 J/(g*K). How much heat is needed to raise its temperature by 43 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 535 * 3.84 * 43.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 43, "heat_capacity": 3.84, "mass_g": 535}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=728.5 mg, t=188.5 h, and T_half=51.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 57.6237, \"unit\": \"mg\"}", "dedupe_signature": "a86b2c7ab6164ebbd8e13f1c2b6ea2ba13206bb9f466a26aeade413153b7d623", "difficulty": "medium", "final_answer": {"answer": 57.6237, "unit": "mg"}, "id": "half_life_004596_728.5_51.5_188.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 728.5 mg. Its half-life is 51.5 hours. How many mg remain after 188.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=728.5 mg, t=188.5 h, and T_half=51.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 188.5, "half_life": 51.5, "initial_amount": 728.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 4.18 mol * 100.087 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 418.3637, \"unit\": \"g\"}", "dedupe_signature": "774f4a75c549d4bd5b728a25caf7331b4dc20870772f56a3feadfcdab2ed69f2", "difficulty": "medium", "final_answer": {"answer": 418.3637, "unit": "g"}, "id": "stoich_mass_004597_calcium_carbonate_4.18", "license": "Apache-2.0", "prompt": "A sample contains 4.18 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 4.18 mol * 100.087 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "calcium carbonate", "molar_mass": 100.087, "moles": 4.18}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 3805 mL to 3.805 L.\n3. Compute M = 4.185 / 3.805.\nFinal: {\"answer\": 1.0999, \"unit\": \"mol/L\"}", "dedupe_signature": "7137d3d60e2c40d33a1b760dd65fa9550a8ba7177b090464380a249ea5c2e5e9", "difficulty": "medium", "final_answer": {"answer": 1.0999, "unit": "mol/L"}, "id": "molarity_004598_4.185_3805", "license": "Apache-2.0", "prompt": "A solution contains 4.185 mol of solute in 3805 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 3805 mL to 3.805 L.\nCompute M = 4.185 / 3.805.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 4.185, "volume_ml": 3805}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.69 y, so each step multiplies y by 1 - h*0.69.\n3. Apply that update for 8 steps and round the final state.\nFinal: {\"answer\": 0.0, \"unit\": \"state_units\"}", "dedupe_signature": "c6f3c43ac316eed65330ea36c203d44fcb9234441dc5e58192857332c4e236af", "difficulty": "medium", "final_answer": {"answer": 0.0, "unit": "state_units"}, "id": "euler_decay_004599_47.5_0.69_1.3_8", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.69 y with y(0)=47.5, step size h=1.3, for 8 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.69 y, so each step multiplies y by 1 - h*0.69.\nApply that update for 8 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 47.5, "rate": 0.69, "step": 1.3, "steps": 8}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(9.5)=-63.8 and f(12.5)=-86.6.\n3. The interval width is 3.\nFinal: {\"answer\": -225.6, \"unit\": \"area_units\"}", "dedupe_signature": "23c584d008b17aa4113e5ea76d63c89195923862adf10c36b939082f322fc86a", "difficulty": "medium", "final_answer": {"answer": -225.6, "unit": "area_units"}, "id": "trapz_linear_004600_-7.6_8.4_9.5_12.5", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-7.6x+8.4 from x=9.5 to x=12.5. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(9.5)=-63.8 and f(12.5)=-86.6.\nThe interval width is 3.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 8.4, "slope": -7.6, "x0": 9.5, "x1": 12.5}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.08 and add it to the current value.\nFinal: {\"answer\": [0.948, 0.238, -0.06], \"unit\": \"temperature_units\"}", "dedupe_signature": "a18b9ed514559150e3e0f56e9555d3930f3d8bc1078d9f45f7c391e5adc7fc85", "difficulty": "hard", "final_answer": {"answer": [0.948, 0.238, -0.06], "unit": "temperature_units"}, "id": "heat_step_004601_0.08_-1.95_1.3_0.15_0.1_-1.95", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-1.95, right=-1.95; current interior values are [1.3, 0.15, 0.1]. Use r=0.08. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.08 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [1.3, 0.15, 0.1], "left": -1.95, "r": 0.08, "right": -1.95}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 37133.0 / 1000.\nFinal: {\"answer\": 37.133, \"unit\": \"kg\"}", "dedupe_signature": "42639829bc566675d9036e82c2b11ef8837b012bedca11cd90a9221e5c3f01d9", "difficulty": "easy", "final_answer": {"answer": 37.133, "unit": "kg"}, "id": "unit_convert_004602_g_to_kg_37133", "license": "Apache-2.0", "prompt": "Convert 37133 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 37133.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 37133.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=97 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-55.6334, 453.0973], \"unit\": \"N\"}", "dedupe_signature": "b74bf6a08bbc14f2c5a0ed658574b2acb0b40ddffddc55904052f5c63abc593d", "difficulty": "medium", "final_answer": {"answer": [-55.6334, 453.0973], "unit": "N"}, "id": "vector_components_004603_456.5_97", "license": "Apache-2.0", "prompt": "A vector has magnitude 456.5 N at 97 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=97 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 97, "magnitude": 456.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-6.2, 26.5], \"unit\": \"dimensionless\"}", "dedupe_signature": "d7d747cb90b01fb129b58982ce117bf66db9ad04db7fe41a1db20f42b215df17", "difficulty": "medium", "final_answer": {"answer": [-6.2, 26.5], "unit": "dimensionless"}, "id": "line_two_point_004604_8.25_22.5_-6.2_26.5", "license": "Apache-2.0", "prompt": "A line passes through points (8.25, -24.65) and (22.5, -113). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 8.25, "x2": 22.5, "y1": -24.65, "y2": -113.0}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef pairwise_ratios_004606(numerators, denominators):\n    if len(numerators) != len(denominators):\n        raise ValueError('length mismatch')\n    out = []\n    for numerator, denominator in zip(numerators, denominators):\n        if denominator == 0:\n            raise ValueError('zero denominator')\n        out.append(numerator / denominator)\n    return out\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"pairwise_ratios_004606\"}", "dedupe_signature": "04748093ecb2ba33b4692ba164908d50e1eba65ea080ffcf3713166e55de45a8", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "pairwise_ratios_004606"}, "id": "code_004606_pairwise_ratios_004606", "license": "Apache-2.0", "prompt": "Write a Python function pairwise_ratios_004606(numerators, denominators) that returns a list of n/d values. Raise ValueError if lengths differ or any denominator is zero. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "pairwise_ratios_004606"}, "verifier": {"function": "pairwise_ratios_004606", "tests": ["assert pairwise_ratios_004606([2, 9], [4, 3]) == [0.5, 3.0]", "try:\n    pairwise_ratios_004606([1], [0])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass", "try:\n    pairwise_ratios_004606([1, 2], [1])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: left_boundary, right_boundary.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"left_boundary\", \"right_boundary\"]}", "dedupe_signature": "3258a3356149447c5263f2f34872cab3ab6883010cfe91f09297f9c00f86723f", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["left_boundary", "right_boundary"]}, "id": "abstain_004607_left_boundary_right_boundary", "license": "Apache-2.0", "prompt": "Solve the 1D heat equation after one finite-difference step. The prompt gives r=0.12 and interior values [-1.8, 1.0, -0.2], but gives no boundary values. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: left_boundary, right_boundary.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["left_boundary", "right_boundary"]}, "verifier": {"missing": ["left_boundary", "right_boundary"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 39.8^2 and multiply by 0.5 * 20.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 15840.4, \"unit\": \"J\"}", "dedupe_signature": "28182b7e5c791908aa8050f5a8597baa36656eaec20c64e7b50cfc76c5d26272", "difficulty": "easy", "final_answer": {"answer": 15840.4, "unit": "J"}, "id": "ke_004609_20_39.8", "license": "Apache-2.0", "prompt": "A body of mass 20 kg moves at 39.8 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 39.8^2 and multiply by 0.5 * 20.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 20.0, "velocity": 39.8}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=48 degrees through the sine of 2 theta.\n3. Substitute v=48 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 233.5758, \"unit\": \"m\"}", "dedupe_signature": "828bd6cbf766dec700583034919b04a207dc477728941d8d4256e706456d5a5c", "difficulty": "medium", "final_answer": {"answer": 233.5758, "unit": "m"}, "id": "projectile_range_004610_48_48", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 48 m/s and angle 48 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=48 degrees through the sine of 2 theta.\nSubstitute v=48 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 48, "gravity": 9.81, "speed": 48.0}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 3.58 * 8.314 * 548 / 84.5.\nFinal: {\"answer\": 193.0265, \"unit\": \"kPa\"}", "dedupe_signature": "858366094e8ffa6f3125326e89df76b9fec38edb4c0c7d8cd3e135e44fbdc3a1", "difficulty": "medium", "final_answer": {"answer": 193.0265, "unit": "kPa"}, "id": "ideal_gas_004611_3.58_548_84.5", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=3.58 mol, T=548 K, and V=84.5 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 3.58 * 8.314 * 548 / 84.5.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 3.58, "temp_k": 548, "volume_l": 84.5}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 450 * 3.875 * 79.\nFinal: {\"answer\": 137756.25, \"unit\": \"J\"}", "dedupe_signature": "aa0dfa97eafffd8acdf385e2d27fd7282c3d253565e34a1c6573cd03bcc8f745", "difficulty": "easy", "final_answer": {"answer": 137756.25, "unit": "J"}, "id": "heat_q_004612_450_3.875_79", "license": "Apache-2.0", "prompt": "A 450 g sample has specific heat 3.875 J/(g*K). How much heat is needed to raise its temperature by 79 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 450 * 3.875 * 79.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 79, "heat_capacity": 3.875, "mass_g": 450}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=15.5 V and R=154.2 ohm.\nFinal: {\"answer\": 1.558, \"unit\": \"W\"}", "dedupe_signature": "57a9face33b28b2f188d6a17fb29df10e3162992ed8f0222dee8de01fa991ff3", "difficulty": "easy", "final_answer": {"answer": 1.558, "unit": "W"}, "id": "ohm_power_004613_15.5_154.2", "license": "Apache-2.0", "prompt": "A resistor has resistance 154.2 ohm and voltage 15.5 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=15.5 V and R=154.2 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 154.2, "voltage": 15.5}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=624.5 mg, t=76.5 h, and T_half=10 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 3.1092, \"unit\": \"mg\"}", "dedupe_signature": "ebbe24d77eb2ee81dbaa1ea0feec3f6fc7960d99107ab7fe312a96705a9897b7", "difficulty": "medium", "final_answer": {"answer": 3.1092, "unit": "mg"}, "id": "half_life_004614_624.5_10_76.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 624.5 mg. Its half-life is 10 hours. How many mg remain after 76.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=624.5 mg, t=76.5 h, and T_half=10 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 76.5, "half_life": 10.0, "initial_amount": 624.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 4.95 mol * 100.087 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 495.4307, \"unit\": \"g\"}", "dedupe_signature": "3bc907f5256164df5f9f7ccef2ea8b858628344336ae349f762dfc560df8f6e6", "difficulty": "medium", "final_answer": {"answer": 495.4307, "unit": "g"}, "id": "stoich_mass_004615_calcium_carbonate_4.95", "license": "Apache-2.0", "prompt": "A sample contains 4.95 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 4.95 mol * 100.087 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "calcium carbonate", "molar_mass": 100.087, "moles": 4.95}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 1415 mL to 1.415 L.\n3. Compute M = 3.05 / 1.415.\nFinal: {\"answer\": 2.1555, \"unit\": \"mol/L\"}", "dedupe_signature": "002805de7bbe4626eee9b08549c266046d503f4339372422f1b1744303c1c558", "difficulty": "medium", "final_answer": {"answer": 2.1555, "unit": "mol/L"}, "id": "molarity_004616_3.05_1415", "license": "Apache-2.0", "prompt": "A solution contains 3.05 mol of solute in 1415 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 1415 mL to 1.415 L.\nCompute M = 3.05 / 1.415.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 3.05, "volume_ml": 1415}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.42 y, so each step multiplies y by 1 - h*0.42.\n3. Apply that update for 3 steps and round the final state.\nFinal: {\"answer\": 14.3983, \"unit\": \"state_units\"}", "dedupe_signature": "837017bf1d81d297ecc8e097cfec559ca7fe326c5c4680c5529ac795cf8deb73", "difficulty": "medium", "final_answer": {"answer": 14.3983, "unit": "state_units"}, "id": "euler_decay_004617_25_0.42_0.4_3", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.42 y with y(0)=25, step size h=0.4, for 3 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.42 y, so each step multiplies y by 1 - h*0.42.\nApply that update for 3 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 25.0, "rate": 0.42, "step": 0.4, "steps": 3}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(9.5)=51.65 and f(15.5)=83.45.\n3. The interval width is 6.\nFinal: {\"answer\": 405.3, \"unit\": \"area_units\"}", "dedupe_signature": "3cb0f3616c88bdcf4300d76cb76e33de1a912448a6b372ae95c4db0c8a345bdf", "difficulty": "medium", "final_answer": {"answer": 405.3, "unit": "area_units"}, "id": "trapz_linear_004618_5.3_1.3_9.5_15.5", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=5.3x+1.3 from x=9.5 to x=15.5. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(9.5)=51.65 and f(15.5)=83.45.\nThe interval width is 6.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 1.3, "slope": 5.3, "x0": 9.5, "x1": 15.5}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.24 and add it to the current value.\nFinal: {\"answer\": [-0.228, 0.024, 0.496], \"unit\": \"temperature_units\"}", "dedupe_signature": "1a4d4b86e9f5df322e34560bde846ae261a6b76167fd6e8754b66cd8066460d8", "difficulty": "hard", "final_answer": {"answer": [-0.228, 0.024, 0.496], "unit": "temperature_units"}, "id": "heat_step_004619_0.24_1.65_-1.2_0.0_1.3_-0.75", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.65, right=-0.75; current interior values are [-1.2, 0.0, 1.3]. Use r=0.24. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.24 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-1.2, 0.0, 1.3], "left": 1.65, "r": 0.24, "right": -0.75}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 3464.0 / 1000.\nFinal: {\"answer\": 3.464, \"unit\": \"kg\"}", "dedupe_signature": "932bd4051ebd233457029834c4656f584a122209354a363e36ca88f49f2a7ad6", "difficulty": "easy", "final_answer": {"answer": 3.464, "unit": "kg"}, "id": "unit_convert_004620_g_to_kg_3464", "license": "Apache-2.0", "prompt": "Convert 3464 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 3464.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 3464.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=142 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-287.2299, 224.4086], \"unit\": \"N\"}", "dedupe_signature": "05292c5e2e3048584f19744307ec2b11b1bcf4b0a0fa492d55b50c8ca838024a", "difficulty": "medium", "final_answer": {"answer": [-287.2299, 224.4086], "unit": "N"}, "id": "vector_components_004621_364.5_142", "license": "Apache-2.0", "prompt": "A vector has magnitude 364.5 N at 142 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=142 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 142, "magnitude": 364.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [5.85, 28.25], \"unit\": \"dimensionless\"}", "dedupe_signature": "c22ea2bc319eb3640a630b5db218b306ee1f97b4e5259c8fdcdbda8a91960f09", "difficulty": "medium", "final_answer": {"answer": [5.85, 28.25], "unit": "dimensionless"}, "id": "line_two_point_004622_13_22.5_5.85_28.25", "license": "Apache-2.0", "prompt": "A line passes through points (13, 104.3) and (22.5, 159.875). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 13.0, "x2": 22.5, "y1": 104.3, "y2": 159.875}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. density times acceleration times height gives kg/(m*s^2), or pascal\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "9f368e010864ab0c426c6aff74c78e25db8b7810da50436777da2a6195617301", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_004623_consistent_b7d3eed1_409723", "license": "Apache-2.0", "prompt": "In simulation spec case 409723, check dimensional consistency for p = rho * g * h. The left side has dimensions Pa and the right side has dimensions Pa. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\ndensity times acceleration times height gives kg/(m*s^2), or pascal\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "p = rho * g * h"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef pairwise_ratios_004624(numerators, denominators):\n    if len(numerators) != len(denominators):\n        raise ValueError('length mismatch')\n    out = []\n    for numerator, denominator in zip(numerators, denominators):\n        if denominator == 0:\n            raise ValueError('zero denominator')\n        out.append(numerator / denominator)\n    return out\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"pairwise_ratios_004624\"}", "dedupe_signature": "13d0c9f13b0cbdfb33f644127a152dee2e217e565d7ae45647143be72549cd48", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "pairwise_ratios_004624"}, "id": "code_004624_pairwise_ratios_004624", "license": "Apache-2.0", "prompt": "Write a Python function pairwise_ratios_004624(numerators, denominators) that returns a list of n/d values. Raise ValueError if lengths differ or any denominator is zero. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "pairwise_ratios_004624"}, "verifier": {"function": "pairwise_ratios_004624", "tests": ["assert pairwise_ratios_004624([2, 9], [4, 3]) == [0.5, 3.0]", "try:\n    pairwise_ratios_004624([1], [0])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass", "try:\n    pairwise_ratios_004624([1, 2], [1])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 10.8 kg and a = 11.2 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 120.96, \"unit\": \"N\"}", "dedupe_signature": "79b613be2ea1f79b5bac33f652f8ba5d8035d3435e4ccdcd238f8c39ea95561c", "difficulty": "easy", "final_answer": {"answer": 120.96, "unit": "N"}, "id": "force_004626_10.8_11.2", "license": "Apache-2.0", "prompt": "A cart has mass 10.8 kg and measured acceleration 11.2 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 10.8 kg and a = 11.2 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 11.2, "mass": 10.8}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 44.65^2 and multiply by 0.5 * 27.25.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 27163.1066, \"unit\": \"J\"}", "dedupe_signature": "18979efc447e9671ff12178751735e34a43ba364c2b10200cd63ca687daeb073", "difficulty": "easy", "final_answer": {"answer": 27163.1066, "unit": "J"}, "id": "ke_004627_27.25_44.65", "license": "Apache-2.0", "prompt": "A body of mass 27.25 kg moves at 44.65 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 44.65^2 and multiply by 0.5 * 27.25.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 27.25, "velocity": 44.65}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 4.18 * 8.314 * 557 / 15.5.\nFinal: {\"answer\": 1248.8486, \"unit\": \"kPa\"}", "dedupe_signature": "5d416b3155689c90c4ab02bfee0b74c36d83f90eac9ffc69f7b0bff685d14ceb", "difficulty": "medium", "final_answer": {"answer": 1248.8486, "unit": "kPa"}, "id": "ideal_gas_004629_4.18_557_15.5", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=4.18 mol, T=557 K, and V=15.5 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 4.18 * 8.314 * 557 / 15.5.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 4.18, "temp_k": 557, "volume_l": 15.5}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 835 * 2.89 * 5.\nFinal: {\"answer\": 12065.75, \"unit\": \"J\"}", "dedupe_signature": "a985ba6478f52344fb2f3eb399f2d1fc97c1fa63835521990df70117d33960b1", "difficulty": "easy", "final_answer": {"answer": 12065.75, "unit": "J"}, "id": "heat_q_004630_835_2.89_5", "license": "Apache-2.0", "prompt": "A 835 g sample has specific heat 2.89 J/(g*K). How much heat is needed to raise its temperature by 5 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 835 * 2.89 * 5.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 5, "heat_capacity": 2.89, "mass_g": 835}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=581.5 mg, t=247 h, and T_half=41 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 8.9336, \"unit\": \"mg\"}", "dedupe_signature": "cf7fb35f425fd1e46070a0dbf9d12907e443cb60808397e6c1d21de74bdbd528", "difficulty": "medium", "final_answer": {"answer": 8.9336, "unit": "mg"}, "id": "half_life_004632_581.5_41_247", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 581.5 mg. Its half-life is 41 hours. How many mg remain after 247 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=581.5 mg, t=247 h, and T_half=41 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 247.0, "half_life": 41.0, "initial_amount": 581.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 0.8 mol * 58.44 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 46.752, \"unit\": \"g\"}", "dedupe_signature": "d513ef0ac2de58e3682ea99ff733d157d42df1f3d95811a318d503e7937a83fb", "difficulty": "medium", "final_answer": {"answer": 46.752, "unit": "g"}, "id": "stoich_mass_004633_sodium_chloride_0.8", "license": "Apache-2.0", "prompt": "A sample contains 0.8 mol of sodium chloride. Using molar mass 58.44 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 0.8 mol * 58.44 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "sodium chloride", "molar_mass": 58.44, "moles": 0.8}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 3025 mL to 3.025 L.\n3. Compute M = 0.325 / 3.025.\nFinal: {\"answer\": 0.1074, \"unit\": \"mol/L\"}", "dedupe_signature": "950c4d623599ef0a7f02d08414a2c4f956979555cb709ec8ad4a175bb41a4aad", "difficulty": "medium", "final_answer": {"answer": 0.1074, "unit": "mol/L"}, "id": "molarity_004634_0.325_3025", "license": "Apache-2.0", "prompt": "A solution contains 0.325 mol of solute in 3025 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 3025 mL to 3.025 L.\nCompute M = 0.325 / 3.025.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 0.325, "volume_ml": 3025}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.81 y, so each step multiplies y by 1 - h*0.81.\n3. Apply that update for 11 steps and round the final state.\nFinal: {\"answer\": 0.0, \"unit\": \"state_units\"}", "dedupe_signature": "52b4124e625fb2bbf9c7a85ed37a3134832ff1c87077465d30b40f69780ff357", "difficulty": "medium", "final_answer": {"answer": 0.0, "unit": "state_units"}, "id": "euler_decay_004635_78_0.81_1.45_11", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.81 y with y(0)=78, step size h=1.45, for 11 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.81 y, so each step multiplies y by 1 - h*0.81.\nApply that update for 11 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 78.0, "rate": 0.81, "step": 1.45, "steps": 11}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 100 centimeters in one meter.\n2. Apply the conversion factor directly to the given value.\n3. Compute 1394.0 / 100.\nFinal: {\"answer\": 13.94, \"unit\": \"m\"}", "dedupe_signature": "e6f74de78f03d9552195e71bb86b4fee67724e2df7133835ca272a080111895b", "difficulty": "easy", "final_answer": {"answer": 13.94, "unit": "m"}, "id": "unit_convert_004638_cm_to_m_1394", "license": "Apache-2.0", "prompt": "Convert 1394 cm to m. Return the converted value with unit.", "reasoning_trace": "There are 100 centimeters in one meter.\nApply the conversion factor directly to the given value.\nCompute 1394.0 / 100.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 1394.0}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-3.8, 27.25], \"unit\": \"dimensionless\"}", "dedupe_signature": "c9652585fed79a49a58782db8319f9c09c00c4a9358d3439c8d3abf87ac31d3b", "difficulty": "medium", "final_answer": {"answer": [-3.8, 27.25], "unit": "dimensionless"}, "id": "line_two_point_004640_-12.25_-10.25_-3.8_27.25", "license": "Apache-2.0", "prompt": "A line passes through points (-12.25, 73.8) and (-10.25, 66.2). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -12.25, "x2": -10.25, "y1": 73.8, "y2": 66.19999999999999}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. amount times volume is not concentration\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "458aa6fb08f762e14452fc61824c90b256e75d342560c22483b9e0142eb1fbbe", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_004641_inconsistent_74ac0b02_326065", "license": "Apache-2.0", "prompt": "In quality-control check case 326065, check dimensional consistency for C = n * V. The left side has dimensions mol/L and the right side has dimensions mol*L. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\namount times volume is not concentration\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "C = n * V"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef clamp_004642(x, lo, hi):\n    if lo > hi:\n        raise ValueError('lo must be <= hi')\n    return min(max(x, lo), hi)\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"clamp_004642\"}", "dedupe_signature": "d382acb608a6373cfd17dd744353cc3aaa3406275f2c7b58e51cdce32ea0d1d8", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "clamp_004642"}, "id": "code_004642_clamp_004642", "license": "Apache-2.0", "prompt": "Write a Python function clamp_004642(x, lo, hi) that clips x into the inclusive interval [lo, hi]. It must raise ValueError if lo > hi. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "clamp_004642"}, "verifier": {"function": "clamp_004642", "tests": ["assert clamp_004642(5, 0, 10) == 5", "assert clamp_004642(-2, 0, 10) == 0", "assert clamp_004642(12, 0, 10) == 10", "try:\n    clamp_004642(1, 3, 2)\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: target_schema, valid_examples.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"target_schema\", \"valid_examples\"]}", "dedupe_signature": "1335b0f206947d89d3fbaac95bef2d67b22583a5dd27f72d47639158636d5813", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["target_schema", "valid_examples"]}, "id": "abstain_004643_target_schema_valid_examples", "license": "Apache-2.0", "prompt": "Write a parser that converts each mobile survey record from batch 929960 into the correct schema, but the prompt does not include the target schema or examples. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: target_schema, valid_examples.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["target_schema", "valid_examples"]}, "verifier": {"missing": ["target_schema", "valid_examples"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 16.6 kg and a = 9.65 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 160.19, \"unit\": \"N\"}", "dedupe_signature": "541c6dd7a1247b2dac47e65ab270664c8d57024c9f6d0060d5c0c7ddd27fdf3b", "difficulty": "easy", "final_answer": {"answer": 160.19, "unit": "N"}, "id": "force_004644_16.6_9.65", "license": "Apache-2.0", "prompt": "A cart has mass 16.6 kg and measured acceleration 9.65 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 16.6 kg and a = 9.65 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 9.65, "mass": 16.6}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 19.95^2 and multiply by 0.5 * 26.8.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 5333.2335, \"unit\": \"J\"}", "dedupe_signature": "e1dcdff4fbffcf8cdaf5d5eb2b27a5f160c852c520433a8702bdf5264d3abf13", "difficulty": "easy", "final_answer": {"answer": 5333.2335, "unit": "J"}, "id": "ke_004645_26.8_19.95", "license": "Apache-2.0", "prompt": "A body of mass 26.8 kg moves at 19.95 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 19.95^2 and multiply by 0.5 * 26.8.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 26.8, "velocity": 19.95}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=31 degrees through the sine of 2 theta.\n3. Substitute v=60.9 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 333.8109, \"unit\": \"m\"}", "dedupe_signature": "51d98206b1d143710e756d7f70ac429790419110520b239bcfa69a84d781a500", "difficulty": "medium", "final_answer": {"answer": 333.8109, "unit": "m"}, "id": "projectile_range_004646_60.9_31", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 60.9 m/s and angle 31 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=31 degrees through the sine of 2 theta.\nSubstitute v=60.9 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 31, "gravity": 9.81, "speed": 60.9}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 1.84 * 8.314 * 268 / 79.2.\nFinal: {\"answer\": 51.7651, \"unit\": \"kPa\"}", "dedupe_signature": "c5704ce8e0c8d87b05bf699ed9fd10c4fafa7d855b972d74459351f170df045a", "difficulty": "medium", "final_answer": {"answer": 51.7651, "unit": "kPa"}, "id": "ideal_gas_004647_1.84_268_79.2", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=1.84 mol, T=268 K, and V=79.2 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 1.84 * 8.314 * 268 / 79.2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 1.84, "temp_k": 268, "volume_l": 79.2}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 615 * 2.035 * 27.\nFinal: {\"answer\": 33791.175, \"unit\": \"J\"}", "dedupe_signature": "1bf95aa01dc0bde523fbd8b3119cefbd3268bda730084231232aca68ef55e1b1", "difficulty": "easy", "final_answer": {"answer": 33791.175, "unit": "J"}, "id": "heat_q_004648_615_2.035_27", "license": "Apache-2.0", "prompt": "A 615 g sample has specific heat 2.035 J/(g*K). How much heat is needed to raise its temperature by 27 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 615 * 2.035 * 27.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 27, "heat_capacity": 2.035, "mass_g": 615}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=22.2 V and R=178.2 ohm.\nFinal: {\"answer\": 2.7657, \"unit\": \"W\"}", "dedupe_signature": "0c6a33e9a8ba33877e1c1c2f6042f0efd45f21ed7bc58feeb97a1e3b331e931b", "difficulty": "easy", "final_answer": {"answer": 2.7657, "unit": "W"}, "id": "ohm_power_004649_22.2_178.2", "license": "Apache-2.0", "prompt": "A resistor has resistance 178.2 ohm and voltage 22.2 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=22.2 V and R=178.2 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 178.2, "voltage": 22.2}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 3310 mL to 3.31 L.\n3. Compute M = 1.25 / 3.31.\nFinal: {\"answer\": 0.3776, \"unit\": \"mol/L\"}", "dedupe_signature": "4d1294c50eb3fcb5d64fb512929948632ce79397878edb206a73e3f682a65649", "difficulty": "medium", "final_answer": {"answer": 0.3776, "unit": "mol/L"}, "id": "molarity_004652_1.25_3310", "license": "Apache-2.0", "prompt": "A solution contains 1.25 mol of solute in 3310 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 3310 mL to 3.31 L.\nCompute M = 1.25 / 3.31.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 1.25, "volume_ml": 3310}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.85 y, so each step multiplies y by 1 - h*0.85.\n3. Apply that update for 9 steps and round the final state.\nFinal: {\"answer\": 0.0, \"unit\": \"state_units\"}", "dedupe_signature": "a496cb8e13ac7efc69631ba4cddc55f919850a8526d0d672568d3fed642d508e", "difficulty": "medium", "final_answer": {"answer": 0.0, "unit": "state_units"}, "id": "euler_decay_004653_19_0.85_1.05_9", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.85 y with y(0)=19, step size h=1.05, for 9 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.85 y, so each step multiplies y by 1 - h*0.85.\nApply that update for 9 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 19.0, "rate": 0.85, "step": 1.05, "steps": 9}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(6)=34.3 and f(13.4)=62.42.\n3. The interval width is 7.4.\nFinal: {\"answer\": 357.864, \"unit\": \"area_units\"}", "dedupe_signature": "c2de28640d2dfd2c65b61ad52a23ee802b10bb9dbb41034a1d34cbe64a885c02", "difficulty": "medium", "final_answer": {"answer": 357.864, "unit": "area_units"}, "id": "trapz_linear_004654_3.8_11.5_6_13.4", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=3.8x+11.5 from x=6 to x=13.4. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(6)=34.3 and f(13.4)=62.42.\nThe interval width is 7.4.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 11.5, "slope": 3.8, "x0": 6.0, "x1": 13.4}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.42 and add it to the current value.\nFinal: {\"answer\": [-1.122, 0.725, 0.338], \"unit\": \"temperature_units\"}", "dedupe_signature": "7655271cb5b8ffcce0ff9c16da08ca0c532569826365abac6e338364b0ded8a5", "difficulty": "hard", "final_answer": {"answer": [-1.122, 0.725, 0.338], "unit": "temperature_units"}, "id": "heat_step_004655_0.42_-1.4_1.65_-1.9_0.8_2.4", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-1.4, right=2.4; current interior values are [1.65, -1.9, 0.8]. Use r=0.42. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.42 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [1.65, -1.9, 0.8], "left": -1.4, "r": 0.42, "right": 2.4}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kelvin equals Celsius plus 273.15.\n2. Apply the conversion factor directly to the given value.\n3. Compute 5.5 + 273.15.\nFinal: {\"answer\": 278.65, \"unit\": \"K\"}", "dedupe_signature": "a4604b1d9bf700bba2e8a25540250fcf1c432a390f8fca1d2b9f7de8303ff929", "difficulty": "easy", "final_answer": {"answer": 278.65, "unit": "K"}, "id": "unit_convert_004656_c_to_k_5.5", "license": "Apache-2.0", "prompt": "Convert 5.5 degC to K. Return the converted value with unit.", "reasoning_trace": "Kelvin equals Celsius plus 273.15.\nApply the conversion factor directly to the given value.\nCompute 5.5 + 273.15.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 5.5}, "verifier": {"formula": "value + 273.15", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=107 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-50.2879, 164.4844], \"unit\": \"N\"}", "dedupe_signature": "2d6f0075d9738c2d2e986f77afd8d0a43b0c3ab96f5b6152a7f67b598c4caf44", "difficulty": "medium", "final_answer": {"answer": [-50.2879, 164.4844], "unit": "N"}, "id": "vector_components_004657_172_107", "license": "Apache-2.0", "prompt": "A vector has magnitude 172 N at 107 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=107 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 107, "magnitude": 172.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [9.8, -28.25], \"unit\": \"dimensionless\"}", "dedupe_signature": "91575f24181b38c4aa3edb094e28b2647676e8e7e4a0b7435141225c8585cfe8", "difficulty": "medium", "final_answer": {"answer": [9.8, -28.25], "unit": "dimensionless"}, "id": "line_two_point_004658_-10.25_-6.5_9.8_-28.25", "license": "Apache-2.0", "prompt": "A line passes through points (-10.25, -128.7) and (-6.5, -91.95). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -10.25, "x2": -6.5, "y1": -128.7, "y2": -91.95}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef center_values_004660(values):\n    if not values:\n        raise ValueError('center_values requires at least one value')\n    mean = sum(values) / len(values)\n    return [value - mean for value in values]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"center_values_004660\"}", "dedupe_signature": "1a4f8a86a94edc8dad13b7f9cb5ccc0dbbd63a9d04dedfe73a403f8705939c5c", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "center_values_004660"}, "id": "code_004660_center_values_004660", "license": "Apache-2.0", "prompt": "Write a Python function center_values_004660(values) that subtracts the arithmetic mean from each value and returns a new list. Raise ValueError for an empty input. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "center_values_004660"}, "verifier": {"function": "center_values_004660", "tests": ["out = center_values_004660([1, 2, 3]); assert out == [-1, 0, 1]", "assert center_values_004660([5]) == [0]", "try:\n    center_values_004660([])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: left_boundary, right_boundary.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"left_boundary\", \"right_boundary\"]}", "dedupe_signature": "ee8843d1eefb5a01c6eba8f032f2e20c8b38208ecbe0dba353c8e5278b236abf", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["left_boundary", "right_boundary"]}, "id": "abstain_004661_left_boundary_right_boundary", "license": "Apache-2.0", "prompt": "Solve the 1D heat equation after one finite-difference step. The prompt gives r=0.46 and interior values [-0.15, 0.2, 0.05], but gives no boundary values. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: left_boundary, right_boundary.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["left_boundary", "right_boundary"]}, "verifier": {"missing": ["left_boundary", "right_boundary"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 7.15 kg and a = 12.4 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 88.66, \"unit\": \"N\"}", "dedupe_signature": "9f8aa4e8cb8d744d0f0b0a241479289702459d5b8a6ec8a033f15bc29b87e8f8", "difficulty": "easy", "final_answer": {"answer": 88.66, "unit": "N"}, "id": "force_004662_7.15_12.4", "license": "Apache-2.0", "prompt": "A cart has mass 7.15 kg and measured acceleration 12.4 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 7.15 kg and a = 12.4 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 12.4, "mass": 7.15}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 22.1^2 and multiply by 0.5 * 5.05.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 1233.2353, \"unit\": \"J\"}", "dedupe_signature": "9316a614a03bae2418652c2c5e0b898711811d7703d69b48caad8d396cbb6bf2", "difficulty": "easy", "final_answer": {"answer": 1233.2353, "unit": "J"}, "id": "ke_004663_5.05_22.1", "license": "Apache-2.0", "prompt": "A body of mass 5.05 kg moves at 22.1 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 22.1^2 and multiply by 0.5 * 5.05.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 5.05, "velocity": 22.1}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 4.61 * 8.314 * 406 / 62.9.\nFinal: {\"answer\": 247.3924, \"unit\": \"kPa\"}", "dedupe_signature": "438a686240a321e9c4bfbd374d4a24eee552654a997f677220abc34587b01b3a", "difficulty": "medium", "final_answer": {"answer": 247.3924, "unit": "kPa"}, "id": "ideal_gas_004665_4.61_406_62.9", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=4.61 mol, T=406 K, and V=62.9 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 4.61 * 8.314 * 406 / 62.9.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 4.61, "temp_k": 406, "volume_l": 62.9}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1105 * 4.81 * 67.\nFinal: {\"answer\": 356108.35, \"unit\": \"J\"}", "dedupe_signature": "bebd754f1e1ed8d4cbec60ac69dec87c7f8df7b5857a8ec0d17a841b164669b7", "difficulty": "easy", "final_answer": {"answer": 356108.35, "unit": "J"}, "id": "heat_q_004666_1105_4.81_67", "license": "Apache-2.0", "prompt": "A 1105 g sample has specific heat 4.81 J/(g*K). How much heat is needed to raise its temperature by 67 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1105 * 4.81 * 67.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 67, "heat_capacity": 4.81, "mass_g": 1105}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=68.9 V and R=81.4 ohm.\nFinal: {\"answer\": 58.3195, \"unit\": \"W\"}", "dedupe_signature": "3ad3bad88f6a4b585164aec82398064ca282465c50485042db66cd84eb40331f", "difficulty": "easy", "final_answer": {"answer": 58.3195, "unit": "W"}, "id": "ohm_power_004667_68.9_81.4", "license": "Apache-2.0", "prompt": "A resistor has resistance 81.4 ohm and voltage 68.9 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=68.9 V and R=81.4 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 81.4, "voltage": 68.9}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=284 mg, t=249.5 h, and T_half=100 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 50.3789, \"unit\": \"mg\"}", "dedupe_signature": "e68a3b7d9e7c004e1a59d67643a1a7668caac9bc17b9aadc3d0e374fc6a63bab", "difficulty": "medium", "final_answer": {"answer": 50.3789, "unit": "mg"}, "id": "half_life_004668_284_100_249.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 284 mg. Its half-life is 100 hours. How many mg remain after 249.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=284 mg, t=249.5 h, and T_half=100 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 249.5, "half_life": 100.0, "initial_amount": 284.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 1.95 mol * 100.087 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 195.1696, \"unit\": \"g\"}", "dedupe_signature": "808f9ebd24f8ffd4289d6edea670ae1e97af2accc6d49766f5cc7d70d78e8297", "difficulty": "medium", "final_answer": {"answer": 195.1696, "unit": "g"}, "id": "stoich_mass_004669_calcium_carbonate_1.95", "license": "Apache-2.0", "prompt": "A sample contains 1.95 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 1.95 mol * 100.087 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "calcium carbonate", "molar_mass": 100.087, "moles": 1.95}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 60 mL to 0.06 L.\n3. Compute M = 3.175 / 0.06.\nFinal: {\"answer\": 52.9167, \"unit\": \"mol/L\"}", "dedupe_signature": "f0e96ed062461ce71ff87a1bce10a84be0e16b577f05e5961738c64163993068", "difficulty": "medium", "final_answer": {"answer": 52.9167, "unit": "mol/L"}, "id": "molarity_004670_3.175_60", "license": "Apache-2.0", "prompt": "A solution contains 3.175 mol of solute in 60 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 60 mL to 0.06 L.\nCompute M = 3.175 / 0.06.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 3.175, "volume_ml": 60}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.5 y, so each step multiplies y by 1 - h*0.5.\n3. Apply that update for 6 steps and round the final state.\nFinal: {\"answer\": 16.3223, \"unit\": \"state_units\"}", "dedupe_signature": "c1dfb917a48831afd9b74c004872d045f20fa798a04e6588167825388b1cba22", "difficulty": "medium", "final_answer": {"answer": 16.3223, "unit": "state_units"}, "id": "euler_decay_004671_19_0.5_0.05_6", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.5 y with y(0)=19, step size h=0.05, for 6 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.5 y, so each step multiplies y by 1 - h*0.5.\nApply that update for 6 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 19.0, "rate": 0.5, "step": 0.05, "steps": 6}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.02 and add it to the current value.\nFinal: {\"answer\": [-1.212, 0.575, -1.103], \"unit\": \"temperature_units\"}", "dedupe_signature": "320ae62245348901de5162dddba309954184021db41f2a4d2974f43d4cfd7a35", "difficulty": "hard", "final_answer": {"answer": [-1.212, 0.575, -1.103], "unit": "temperature_units"}, "id": "heat_step_004673_0.02_-1.25_-1.25_0.65_-1.2_1.8", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-1.25, right=1.8; current interior values are [-1.25, 0.65, -1.2]. Use r=0.02. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.02 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-1.25, 0.65, -1.2], "left": -1.25, "r": 0.02, "right": 1.8}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=248 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-187.3033, -463.5919], \"unit\": \"N\"}", "dedupe_signature": "903f9f1240ce5fdbe8f585267c887cadd6546a2f6f49e8120aeb0eb259ed8ed7", "difficulty": "medium", "final_answer": {"answer": [-187.3033, -463.5919], "unit": "N"}, "id": "vector_components_004675_500_248", "license": "Apache-2.0", "prompt": "A vector has magnitude 500 N at 248 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=248 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 248, "magnitude": 500.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [1.25, -28.25], \"unit\": \"dimensionless\"}", "dedupe_signature": "243af4cdc1e30fa2c24e042e14df6b4d8d71d2eef92dbfd8728df1f79eec6215", "difficulty": "medium", "final_answer": {"answer": [1.25, -28.25], "unit": "dimensionless"}, "id": "line_two_point_004676_13.25_14_1.25_-28.25", "license": "Apache-2.0", "prompt": "A line passes through points (13.25, -11.6875) and (14, -10.75). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 13.25, "x2": 14.0, "y1": -11.6875, "y2": -10.75}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. speed squared over acceleration has units of meters\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "c485a03f705c6d0a4136cc307f875d14af3400691d8d2243e66d64cd99d5ad26", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_004677_consistent_741d4e34_548733", "license": "Apache-2.0", "prompt": "In sensor calibration case 548733, check dimensional consistency for R = v^2 * sin(theta) / g. The left side has dimensions m and the right side has dimensions m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nspeed squared over acceleration has units of meters\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "R = v^2 * sin(theta) / g"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef threshold_flags_004678(values, threshold):\n    return [value >= threshold for value in values]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"threshold_flags_004678\"}", "dedupe_signature": "db97f62e2d2a2e4953d41af600fe14e1f7995b5cc1e6757ce49cb6a3833438c9", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "threshold_flags_004678"}, "id": "code_004678_threshold_flags_004678", "license": "Apache-2.0", "prompt": "Write a Python function threshold_flags_004678(values, threshold) that returns a list of booleans showing whether each value is greater than or equal to threshold. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "threshold_flags_004678"}, "verifier": {"function": "threshold_flags_004678", "tests": ["assert threshold_flags_004678([1, 2, 3], 2) == [False, True, True]", "assert threshold_flags_004678([], 5) == []", "assert threshold_flags_004678([-1, 0], 0) == [False, True]"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: required_fields, allowed_transformations.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"required_fields\", \"allowed_transformations\"]}", "dedupe_signature": "9387723f327087db80779060d9ad693ec9a0ac6864cd650333cbf36be9aed2df", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["required_fields", "allowed_transformations"]}, "id": "abstain_004679_required_fields_allowed_transformations", "license": "Apache-2.0", "prompt": "Write a sanitizer for valid billing sensor records in release 425325, but the prompt does not state which fields are required or which transformations are allowed. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: required_fields, allowed_transformations.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["required_fields", "allowed_transformations"]}, "verifier": {"missing": ["required_fields", "allowed_transformations"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 4.85 kg and a = 7.05 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 34.1925, \"unit\": \"N\"}", "dedupe_signature": "d173ea89ba9304d5dc88e623bdfdd023040866c233b3d4d261b383b9aaad0f7c", "difficulty": "easy", "final_answer": {"answer": 34.1925, "unit": "N"}, "id": "force_004680_4.85_7.05", "license": "Apache-2.0", "prompt": "A cart has mass 4.85 kg and measured acceleration 7.05 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 4.85 kg and a = 7.05 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 7.05, "mass": 4.85}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 40.2^2 and multiply by 0.5 * 11.55.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 9332.631, \"unit\": \"J\"}", "dedupe_signature": "8fcd9624e61402b4670d611b8665eb5c7e7d07079a38ca348457e043010f5e0a", "difficulty": "easy", "final_answer": {"answer": 9332.631, "unit": "J"}, "id": "ke_004681_11.55_40.2", "license": "Apache-2.0", "prompt": "A body of mass 11.55 kg moves at 40.2 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 40.2^2 and multiply by 0.5 * 11.55.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 11.55, "velocity": 40.2}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=27 degrees through the sine of 2 theta.\n3. Substitute v=70.4 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 408.7276, \"unit\": \"m\"}", "dedupe_signature": "74a33de3b67253270382c6b054f3ca89b0cac2d91da8dfb932fa98e515553b95", "difficulty": "medium", "final_answer": {"answer": 408.7276, "unit": "m"}, "id": "projectile_range_004682_70.4_27", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 70.4 m/s and angle 27 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=27 degrees through the sine of 2 theta.\nSubstitute v=70.4 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 27, "gravity": 9.81, "speed": 70.4}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 1.58 * 8.314 * 467 / 57.6.\nFinal: {\"answer\": 106.5029, \"unit\": \"kPa\"}", "dedupe_signature": "0881318045f93315cc1834441b249d83cb3bac554aa7afab198c51311eae394b", "difficulty": "medium", "final_answer": {"answer": 106.5029, "unit": "kPa"}, "id": "ideal_gas_004683_1.58_467_57.6", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=1.58 mol, T=467 K, and V=57.6 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 1.58 * 8.314 * 467 / 57.6.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 1.58, "temp_k": 467, "volume_l": 57.6}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1885 * 4.26 * 21.\nFinal: {\"answer\": 168632.1, \"unit\": \"J\"}", "dedupe_signature": "4f1f1a695862fe855c4794d25a2ee8266f7830611b775bea084f33d0669faebb", "difficulty": "easy", "final_answer": {"answer": 168632.1, "unit": "J"}, "id": "heat_q_004684_1885_4.26_21", "license": "Apache-2.0", "prompt": "A 1885 g sample has specific heat 4.26 J/(g*K). How much heat is needed to raise its temperature by 21 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1885 * 4.26 * 21.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 21, "heat_capacity": 4.26, "mass_g": 1885}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=129.9 V and R=125.9 ohm.\nFinal: {\"answer\": 134.0271, \"unit\": \"W\"}", "dedupe_signature": "222729e3c47ad99b841c8c45653f5c0328a71cbbf7ef9dbf2085a84d63a5ea30", "difficulty": "easy", "final_answer": {"answer": 134.0271, "unit": "W"}, "id": "ohm_power_004685_129.9_125.9", "license": "Apache-2.0", "prompt": "A resistor has resistance 125.9 ohm and voltage 129.9 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=129.9 V and R=125.9 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 125.9, "voltage": 129.9}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=540.5 mg, t=189.5 h, and T_half=35.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 13.3625, \"unit\": \"mg\"}", "dedupe_signature": "bee13b7873744411ec88149446c8e34b3b53274163f16387765fc35c23b63976", "difficulty": "medium", "final_answer": {"answer": 13.3625, "unit": "mg"}, "id": "half_life_004686_540.5_35.5_189.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 540.5 mg. Its half-life is 35.5 hours. How many mg remain after 189.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=540.5 mg, t=189.5 h, and T_half=35.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 189.5, "half_life": 35.5, "initial_amount": 540.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 1.17 mol * 44.01 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 51.4917, \"unit\": \"g\"}", "dedupe_signature": "89ed72c102a39322afb10d53ebbc3bcf8262a11628a56de65545b9f36e31b5e0", "difficulty": "medium", "final_answer": {"answer": 51.4917, "unit": "g"}, "id": "stoich_mass_004687_carbon_dioxide_1.17", "license": "Apache-2.0", "prompt": "A sample contains 1.17 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 1.17 mol * 44.01 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "carbon dioxide", "molar_mass": 44.01, "moles": 1.17}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.85 y, so each step multiplies y by 1 - h*0.85.\n3. Apply that update for 8 steps and round the final state.\nFinal: {\"answer\": 0.0219, \"unit\": \"state_units\"}", "dedupe_signature": "bcd560aacf89fb5b2f83735c08f21311a089b74184b9ee09d236794b4a8b632d", "difficulty": "medium", "final_answer": {"answer": 0.0219, "unit": "state_units"}, "id": "euler_decay_004689_73.5_0.85_0.75_8", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.85 y with y(0)=73.5, step size h=0.75, for 8 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.85 y, so each step multiplies y by 1 - h*0.85.\nApply that update for 8 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 73.5, "rate": 0.85, "step": 0.75, "steps": 8}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.38 and add it to the current value.\nFinal: {\"answer\": [0.388, 0.0, -0.746], \"unit\": \"temperature_units\"}", "dedupe_signature": "606cf782b7ae9c11b023a37accfdd45aa172460b301440ed83ec74aa44ddd1b0", "difficulty": "hard", "final_answer": {"answer": [0.388, 0.0, -0.746], "unit": "temperature_units"}, "id": "heat_step_004691_0.38_1.5_2.25_-1.9_-1.05_0.6", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.5, right=0.6; current interior values are [2.25, -1.9, -1.05]. Use r=0.38. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.38 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [2.25, -1.9, -1.05], "left": 1.5, "r": 0.38, "right": 0.6}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 100 centimeters in one meter.\n2. Apply the conversion factor directly to the given value.\n3. Compute 564.0 / 100.\nFinal: {\"answer\": 5.64, \"unit\": \"m\"}", "dedupe_signature": "be57cda17632f5c4619231f65d3353a586e17a60567f805f63ce0ac30255a695", "difficulty": "easy", "final_answer": {"answer": 5.64, "unit": "m"}, "id": "unit_convert_004692_cm_to_m_564", "license": "Apache-2.0", "prompt": "Convert 564 cm to m. Return the converted value with unit.", "reasoning_trace": "There are 100 centimeters in one meter.\nApply the conversion factor directly to the given value.\nCompute 564.0 / 100.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 564.0}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=222 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-202.1354, -182.0035], \"unit\": \"N\"}", "dedupe_signature": "ea067e97ebe4a3706748ed90a9008310032a725feeb007071ce2d59a30a38f40", "difficulty": "medium", "final_answer": {"answer": [-202.1354, -182.0035], "unit": "N"}, "id": "vector_components_004693_272_222", "license": "Apache-2.0", "prompt": "A vector has magnitude 272 N at 222 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=222 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 222, "magnitude": 272.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. velocity times time gives distance, not acceleration\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "da6d24c91586b2914ac7272dc6e4126b9a034ab2dea8c34b7eac8991602031dc", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_004695_inconsistent_7481c798_179575", "license": "Apache-2.0", "prompt": "In quality-control check case 179575, check dimensional consistency for a = v * t. The left side has dimensions m/s^2 and the right side has dimensions m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nvelocity times time gives distance, not acceleration\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "a = v * t"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef weighted_sum_004696(values, weights):\n    if len(values) != len(weights):\n        raise ValueError('length mismatch')\n    return sum(value * weight for value, weight in zip(values, weights))\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"weighted_sum_004696\"}", "dedupe_signature": "e4fe7746e65b648e0fd1cf5f37f93e92c4b78ed659a3851d89373b934087b8d1", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "weighted_sum_004696"}, "id": "code_004696_weighted_sum_004696", "license": "Apache-2.0", "prompt": "Write a Python function weighted_sum_004696(values, weights) that returns sum(value*weight). Raise ValueError when the two inputs have different lengths. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "weighted_sum_004696"}, "verifier": {"function": "weighted_sum_004696", "tests": ["assert weighted_sum_004696([2, 3], [4, 5]) == 23", "assert weighted_sum_004696([], []) == 0", "try:\n    weighted_sum_004696([1], [1, 2])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: launch_angle_or_vertical_velocity.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"launch_angle_or_vertical_velocity\"]}", "dedupe_signature": "24c2c3079b9a96554f413aca253b8935bd9a4b424d83b45c4883ad372a515ae6", "difficulty": "easy", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["launch_angle_or_vertical_velocity"]}, "id": "abstain_004697_launch_angle_or_vertical_velocity", "license": "Apache-2.0", "prompt": "Compute projectile range on level ground. The prompt gives initial speed 13.4 m/s but does not give launch angle or vertical velocity. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: launch_angle_or_vertical_velocity.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["launch_angle_or_vertical_velocity"]}, "verifier": {"missing": ["launch_angle_or_vertical_velocity"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 17.65 kg and a = 15.15 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 267.3975, \"unit\": \"N\"}", "dedupe_signature": "42567d3e8b5c9b4afecfcf9a6418d63b46091794be630813ec4bc00abe184a38", "difficulty": "easy", "final_answer": {"answer": 267.3975, "unit": "N"}, "id": "force_004698_17.65_15.15", "license": "Apache-2.0", "prompt": "A cart has mass 17.65 kg and measured acceleration 15.15 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 17.65 kg and a = 15.15 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 15.15, "mass": 17.65}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 16.7^2 and multiply by 0.5 * 15.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 2091.675, \"unit\": \"J\"}", "dedupe_signature": "dc73326fdf445dab9a7259f70100f301ed80cd1e0b81d708f7f8e4f54f5a6d26", "difficulty": "easy", "final_answer": {"answer": 2091.675, "unit": "J"}, "id": "ke_004699_15_16.7", "license": "Apache-2.0", "prompt": "A body of mass 15 kg moves at 16.7 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 16.7^2 and multiply by 0.5 * 15.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 15.0, "velocity": 16.7}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=38 degrees through the sine of 2 theta.\n3. Substitute v=69.5 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 477.7544, \"unit\": \"m\"}", "dedupe_signature": "a8ecad5ebcc8d49612b8e345fb26cdc410aa62e21134694cb563d5215c3b01b8", "difficulty": "medium", "final_answer": {"answer": 477.7544, "unit": "m"}, "id": "projectile_range_004700_69.5_38", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 69.5 m/s and angle 38 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=38 degrees through the sine of 2 theta.\nSubstitute v=69.5 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 38, "gravity": 9.81, "speed": 69.5}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1600 * 2.4 * 113.\nFinal: {\"answer\": 433920.0, \"unit\": \"J\"}", "dedupe_signature": "6d480d7544fbfe75f474a4e25f0cffd6f5da2caad3da87d5d598d2bac6f291f3", "difficulty": "easy", "final_answer": {"answer": 433920.0, "unit": "J"}, "id": "heat_q_004702_1600_2.4_113", "license": "Apache-2.0", "prompt": "A 1600 g sample has specific heat 2.4 J/(g*K). How much heat is needed to raise its temperature by 113 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1600 * 2.4 * 113.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 113, "heat_capacity": 2.4, "mass_g": 1600}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=983.5 mg, t=136 h, and T_half=9.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 0.0482, \"unit\": \"mg\"}", "dedupe_signature": "70ed679c076ee94153d0d8d3e6bf9f240bad64cbcb0be6370585a102adf69ae3", "difficulty": "medium", "final_answer": {"answer": 0.0482, "unit": "mg"}, "id": "half_life_004704_983.5_9.5_136", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 983.5 mg. Its half-life is 9.5 hours. How many mg remain after 136 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=983.5 mg, t=136 h, and T_half=9.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 136.0, "half_life": 9.5, "initial_amount": 983.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 7.87 mol * 58.44 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 459.9228, \"unit\": \"g\"}", "dedupe_signature": "69419e5d1279b61a37d49505c96a6439efb51ee06f268ad1806be2b81609f95a", "difficulty": "medium", "final_answer": {"answer": 459.9228, "unit": "g"}, "id": "stoich_mass_004705_sodium_chloride_7.87", "license": "Apache-2.0", "prompt": "A sample contains 7.87 mol of sodium chloride. Using molar mass 58.44 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 7.87 mol * 58.44 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "sodium chloride", "molar_mass": 58.44, "moles": 7.87}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.45 y, so each step multiplies y by 1 - h*0.45.\n3. Apply that update for 3 steps and round the final state.\nFinal: {\"answer\": 0.5245, \"unit\": \"state_units\"}", "dedupe_signature": "93d1172a29b80712351be7aa9f6f425bd921b6278c3105ef3fe3c13ce77bd2c6", "difficulty": "medium", "final_answer": {"answer": 0.5245, "unit": "state_units"}, "id": "euler_decay_004707_12.5_0.45_1.45_3", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.45 y with y(0)=12.5, step size h=1.45, for 3 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.45 y, so each step multiplies y by 1 - h*0.45.\nApply that update for 3 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 12.5, "rate": 0.45, "step": 1.45, "steps": 3}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(4)=-9.9 and f(9.5)=-32.45.\n3. The interval width is 5.5.\nFinal: {\"answer\": -116.4625, \"unit\": \"area_units\"}", "dedupe_signature": "ae31fd0b91a1f3adda642eb6c8d71dc59357506f0fb06fd86e847b7ba0b2495e", "difficulty": "medium", "final_answer": {"answer": -116.4625, "unit": "area_units"}, "id": "trapz_linear_004708_-4.1_6.5_4_9.5", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-4.1x+6.5 from x=4 to x=9.5. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(4)=-9.9 and f(9.5)=-32.45.\nThe interval width is 5.5.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 6.5, "slope": -4.1, "x0": 4.0, "x1": 9.5}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.44 and add it to the current value.\nFinal: {\"answer\": [0.28, -1.336, -1.116], \"unit\": \"temperature_units\"}", "dedupe_signature": "516115adf43b2ba751525c93fdb82074d1280be2a7a4dc8851c0c9ce6d41a1bd", "difficulty": "hard", "final_answer": {"answer": [0.28, -1.336, -1.116], "unit": "temperature_units"}, "id": "heat_step_004709_0.44_2.0_-1.15_-1.05_-1.6_-1.05", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=2, right=-1.05; current interior values are [-1.15, -1.05, -1.6]. Use r=0.44. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.44 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-1.15, -1.05, -1.6], "left": 2.0, "r": 0.44, "right": -1.05}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 32689.0 / 1000.\nFinal: {\"answer\": 32.689, \"unit\": \"kg\"}", "dedupe_signature": "e1c7da358d22942bede07240b8841631d2921593abc1ea24edb6c8b3169b5996", "difficulty": "easy", "final_answer": {"answer": 32.689, "unit": "kg"}, "id": "unit_convert_004710_g_to_kg_32689", "license": "Apache-2.0", "prompt": "Convert 32689 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 32689.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 32689.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=234 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-189.5607, -260.908], \"unit\": \"N\"}", "dedupe_signature": "8a38ad09d24d93c4ea216d97d464402db5c6a8c3657d3c6888a4c67a6105e879", "difficulty": "medium", "final_answer": {"answer": [-189.5607, -260.908], "unit": "N"}, "id": "vector_components_004711_322.5_234", "license": "Apache-2.0", "prompt": "A vector has magnitude 322.5 N at 234 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=234 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 234, "magnitude": 322.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [6.9, 9.5], \"unit\": \"dimensionless\"}", "dedupe_signature": "3eebd5ee4dbc3f7af1db7fe7acc6cb2037a567879f181c5f30285e44f4a46642", "difficulty": "medium", "final_answer": {"answer": [6.9, 9.5], "unit": "dimensionless"}, "id": "line_two_point_004712_2.5_15_6.9_9.5", "license": "Apache-2.0", "prompt": "A line passes through points (2.5, 26.75) and (15, 113). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 2.5, "x2": 15.0, "y1": 26.75, "y2": 113.0}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. grams cancel with J/(g*K), and kelvin cancels, leaving joules\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "5e6eaaea4cfcedad4ca674b09fce4ea5fa54ff954ec80b46f71462c05d664104", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_004713_consistent_4153435f_937225", "license": "Apache-2.0", "prompt": "In simulation spec case 937225, check dimensional consistency for Q = m * c * DeltaT. The left side has dimensions J and the right side has dimensions J. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\ngrams cancel with J/(g*K), and kelvin cancels, leaving joules\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "Q = m * c * DeltaT"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef safe_mean_004714(values):\n    if not values:\n        raise ValueError('safe_mean requires at least one value')\n    return sum(values) / len(values)\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"safe_mean_004714\"}", "dedupe_signature": "b02c98ef39352bcabd3cdc4ab5efa718162f3ebc8ac0d75614b06e1a3fd5de44", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "safe_mean_004714"}, "id": "code_004714_safe_mean_004714", "license": "Apache-2.0", "prompt": "Write a Python function safe_mean_004714(values) that returns the arithmetic mean. It must raise ValueError for an empty input and must not mutate the input list. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "safe_mean_004714"}, "verifier": {"function": "safe_mean_004714", "tests": ["assert safe_mean_004714([2, 4, 6]) == 4", "xs = [1, 2, 3]; assert safe_mean_004714(xs) == 2 and xs == [1, 2, 3]", "try:\n    safe_mean_004714([])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 13.7 kg and a = 4.5 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 61.65, \"unit\": \"N\"}", "dedupe_signature": "5e4564bdc9a3b8b3c478c15beb8f5609bb73002b969c1a31982a5fbac73fd3d8", "difficulty": "easy", "final_answer": {"answer": 61.65, "unit": "N"}, "id": "force_004716_13.7_4.5", "license": "Apache-2.0", "prompt": "A cart has mass 13.7 kg and measured acceleration 4.5 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 13.7 kg and a = 4.5 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 4.5, "mass": 13.7}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=7 degrees through the sine of 2 theta.\n3. Substitute v=17.3 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 7.3807, \"unit\": \"m\"}", "dedupe_signature": "71bbab89c28c691ab36a715f0d45b12ea0d1b78001e03284579ccb0e38979520", "difficulty": "medium", "final_answer": {"answer": 7.3807, "unit": "m"}, "id": "projectile_range_004718_17.3_7", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 17.3 m/s and angle 7 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=7 degrees through the sine of 2 theta.\nSubstitute v=17.3 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 7, "gravity": 9.81, "speed": 17.3}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 1.34 * 8.314 * 584 / 15.0.\nFinal: {\"answer\": 433.7469, \"unit\": \"kPa\"}", "dedupe_signature": "236fe1c021ef1a2621b4e4e7a2afe89afc360ec1bb2f54ba6f940753c2f61c82", "difficulty": "medium", "final_answer": {"answer": 433.7469, "unit": "kPa"}, "id": "ideal_gas_004719_1.34_584_15.0", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=1.34 mol, T=584 K, and V=15.0 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 1.34 * 8.314 * 584 / 15.0.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 1.34, "temp_k": 584, "volume_l": 15.0}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=150.4 V and R=66.3 ohm.\nFinal: {\"answer\": 341.1789, \"unit\": \"W\"}", "dedupe_signature": "5ee479514bef78465bf7483f5c90328d8ebef029dfddbb78a2e54c47d8d23424", "difficulty": "easy", "final_answer": {"answer": 341.1789, "unit": "W"}, "id": "ohm_power_004721_150.4_66.3", "license": "Apache-2.0", "prompt": "A resistor has resistance 66.3 ohm and voltage 150.4 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=150.4 V and R=66.3 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 66.3, "voltage": 150.4}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=681.5 mg, t=185.5 h, and T_half=15.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 0.1701, \"unit\": \"mg\"}", "dedupe_signature": "f40191a988106cb085d19ee47f8b8f1883acdb2716015d6ef157c4950a4a3a01", "difficulty": "medium", "final_answer": {"answer": 0.1701, "unit": "mg"}, "id": "half_life_004722_681.5_15.5_185.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 681.5 mg. Its half-life is 15.5 hours. How many mg remain after 185.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=681.5 mg, t=185.5 h, and T_half=15.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 185.5, "half_life": 15.5, "initial_amount": 681.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 3.44 mol * 18.015 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 61.9716, \"unit\": \"g\"}", "dedupe_signature": "45bec906ede8504c99e14f739243390e44bdf7c72ac4ce3025caade770d77057", "difficulty": "medium", "final_answer": {"answer": 61.9716, "unit": "g"}, "id": "stoich_mass_004723_water_3.44", "license": "Apache-2.0", "prompt": "A sample contains 3.44 mol of water. Using molar mass 18.015 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 3.44 mol * 18.015 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "water", "molar_mass": 18.015, "moles": 3.44}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(1.6)=29.08 and f(8)=69.4.\n3. The interval width is 6.4.\nFinal: {\"answer\": 315.136, \"unit\": \"area_units\"}", "dedupe_signature": "f05e3b4e9b0dfb68b2d174770021eda91d5d97a8f05223af8e9ea1b174d210da", "difficulty": "medium", "final_answer": {"answer": 315.136, "unit": "area_units"}, "id": "trapz_linear_004726_6.3_19_1.6_8", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=6.3x+19 from x=1.6 to x=8. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(1.6)=29.08 and f(8)=69.4.\nThe interval width is 6.4.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 19.0, "slope": 6.3, "x0": 1.6, "x1": 8.0}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.42 and add it to the current value.\nFinal: {\"answer\": [0.175, -0.523, 0.942], \"unit\": \"temperature_units\"}", "dedupe_signature": "f1db140dfeb07d3f079ad54b06e4c94ae528fd8589ccf378d7c4b38479e5337a", "difficulty": "hard", "final_answer": {"answer": [0.175, -0.523, 0.942], "unit": "temperature_units"}, "id": "heat_step_004727_0.42_-0.25_-0.35_0.8_-1.2_1.9", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-0.25, right=1.9; current interior values are [-0.35, 0.8, -1.2]. Use r=0.42. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.42 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-0.35, 0.8, -1.2], "left": -0.25, "r": 0.42, "right": 1.9}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=6 degrees and keep the unit as newtons.\nFinal: {\"answer\": [130.7796, 13.7455], \"unit\": \"N\"}", "dedupe_signature": "d720a4aafebbd70c5a8d0d3ee2d85e7ac73cddd03397bbc3af5839ec02cda96b", "difficulty": "medium", "final_answer": {"answer": [130.7796, 13.7455], "unit": "N"}, "id": "vector_components_004729_131.5_6", "license": "Apache-2.0", "prompt": "A vector has magnitude 131.5 N at 6 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=6 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 6, "magnitude": 131.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-5.65, -16.75], \"unit\": \"dimensionless\"}", "dedupe_signature": "edb72668b925214165c2e4dbcfbcf4a41b954d57a185a77e62506019acccd9a4", "difficulty": "medium", "final_answer": {"answer": [-5.65, -16.75], "unit": "dimensionless"}, "id": "line_two_point_004730_3.25_15.75_-5.65_-16.75", "license": "Apache-2.0", "prompt": "A line passes through points (3.25, -35.1125) and (15.75, -105.738). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 3.25, "x2": 15.75, "y1": -35.1125, "y2": -105.73750000000001}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. speed squared over acceleration has units of meters\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "0407c5f25d63be042d446d549b98fe9e63992b6294ef0032636a66776f071447", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_004731_consistent_741d4e34_744926", "license": "Apache-2.0", "prompt": "In lab notebook case 744926, check dimensional consistency for R = v^2 * sin(theta) / g. The left side has dimensions m and the right side has dimensions m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nspeed squared over acceleration has units of meters\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "R = v^2 * sin(theta) / g"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef running_total_004732(values):\n    total = 0\n    out = []\n    for value in values:\n        total += value\n        out.append(total)\n    return out\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"running_total_004732\"}", "dedupe_signature": "ed61caa1cc11899a0c441b8794adbee8f734e9e914daee7507a5dd5db6f37920", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "running_total_004732"}, "id": "code_004732_running_total_004732", "license": "Apache-2.0", "prompt": "Write a Python function running_total_004732(values) that returns cumulative sums as a new list. It must not mutate the input list. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "running_total_004732"}, "verifier": {"function": "running_total_004732", "tests": ["assert running_total_004732([1, 2, 3]) == [1, 3, 6]", "xs = [4, -1, 2]; assert running_total_004732(xs) == [4, 3, 5] and xs == [4, -1, 2]", "assert running_total_004732([]) == []"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: rate_constant, number_of_steps.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"rate_constant\", \"number_of_steps\"]}", "dedupe_signature": "6d593ef83ac999cf12476faaaf0fcc130a73df7e9cc7ea6a669ea4271d392cbb", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["rate_constant", "number_of_steps"]}, "id": "abstain_004733_rate_constant_number_of_steps", "license": "Apache-2.0", "prompt": "Use explicit Euler for dy/dt = -k y. The prompt gives y(0)=58.5 and h=1.65, but omits both k and the number of steps. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: rate_constant, number_of_steps.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["rate_constant", "number_of_steps"]}, "verifier": {"missing": ["rate_constant", "number_of_steps"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 16.6 kg and a = 3.45 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 57.27, \"unit\": \"N\"}", "dedupe_signature": "b5d1a047ccd6b7e6437db1c1c4a36ccc9ddfcb996afd6a0294faa0320a35b3a8", "difficulty": "easy", "final_answer": {"answer": 57.27, "unit": "N"}, "id": "force_004734_16.6_3.45", "license": "Apache-2.0", "prompt": "A cart has mass 16.6 kg and measured acceleration 3.45 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 16.6 kg and a = 3.45 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 3.45, "mass": 16.6}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 14.35^2 and multiply by 0.5 * 5.85.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 602.3233, \"unit\": \"J\"}", "dedupe_signature": "7723bb68f9a016884d53ae3126a860bb80beed8d8ddbc9920af9ad0fa9908003", "difficulty": "easy", "final_answer": {"answer": 602.3233, "unit": "J"}, "id": "ke_004735_5.85_14.35", "license": "Apache-2.0", "prompt": "A body of mass 5.85 kg moves at 14.35 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 14.35^2 and multiply by 0.5 * 5.85.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 5.85, "velocity": 14.35}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=21 degrees through the sine of 2 theta.\n3. Substitute v=12.1 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 9.9865, \"unit\": \"m\"}", "dedupe_signature": "2e840a2b9bea504a40c799b3a46563912923f229d3f1f74739658ba99b335b27", "difficulty": "medium", "final_answer": {"answer": 9.9865, "unit": "m"}, "id": "projectile_range_004736_12.1_21", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 12.1 m/s and angle 21 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=21 degrees through the sine of 2 theta.\nSubstitute v=12.1 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 21, "gravity": 9.81, "speed": 12.1}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 4.46 * 8.314 * 317 / 89.6.\nFinal: {\"answer\": 131.1886, \"unit\": \"kPa\"}", "dedupe_signature": "842e3a7d6d7865593a5c39a2baaca94c00c88f980a76e6688a1fb80f51ba88eb", "difficulty": "medium", "final_answer": {"answer": 131.1886, "unit": "kPa"}, "id": "ideal_gas_004737_4.46_317_89.6", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=4.46 mol, T=317 K, and V=89.6 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 4.46 * 8.314 * 317 / 89.6.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 4.46, "temp_k": 317, "volume_l": 89.6}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1295 * 1.535 * 102.\nFinal: {\"answer\": 202758.15, \"unit\": \"J\"}", "dedupe_signature": "9563c7247e4dd6cf098eb0b2d354f7836c9c3f613e4d6ef055c3148600d79fde", "difficulty": "easy", "final_answer": {"answer": 202758.15, "unit": "J"}, "id": "heat_q_004738_1295_1.535_102", "license": "Apache-2.0", "prompt": "A 1295 g sample has specific heat 1.535 J/(g*K). How much heat is needed to raise its temperature by 102 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1295 * 1.535 * 102.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 102, "heat_capacity": 1.535, "mass_g": 1295}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 0.86 mol * 44.01 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 37.8486, \"unit\": \"g\"}", "dedupe_signature": "22c25600c1b380267e94e2f45464951123335441459870ac4773937022eab9e2", "difficulty": "medium", "final_answer": {"answer": 37.8486, "unit": "g"}, "id": "stoich_mass_004741_carbon_dioxide_0.86", "license": "Apache-2.0", "prompt": "A sample contains 0.86 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 0.86 mol * 44.01 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "carbon dioxide", "molar_mass": 44.01, "moles": 0.86}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 2905 mL to 2.905 L.\n3. Compute M = 4.74 / 2.905.\nFinal: {\"answer\": 1.6317, \"unit\": \"mol/L\"}", "dedupe_signature": "97c46a9cd3efcadff16ff25bb7c1c5da8d1a279a6231ddbdc83ef0a4f10163c1", "difficulty": "medium", "final_answer": {"answer": 1.6317, "unit": "mol/L"}, "id": "molarity_004742_4.74_2905", "license": "Apache-2.0", "prompt": "A solution contains 4.74 mol of solute in 2905 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 2905 mL to 2.905 L.\nCompute M = 4.74 / 2.905.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 4.74, "volume_ml": 2905}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.59 y, so each step multiplies y by 1 - h*0.59.\n3. Apply that update for 5 steps and round the final state.\nFinal: {\"answer\": 0.0038, \"unit\": \"state_units\"}", "dedupe_signature": "3026d01d639e2021656a8f4fe510848fe3527c686e414caf95dd110cbed0d543", "difficulty": "medium", "final_answer": {"answer": 0.0038, "unit": "state_units"}, "id": "euler_decay_004743_24_0.59_1.4_5", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.59 y with y(0)=24, step size h=1.4, for 5 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.59 y, so each step multiplies y by 1 - h*0.59.\nApply that update for 5 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 24.0, "rate": 0.59, "step": 1.4, "steps": 5}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-3.9)=7.03 and f(3.4)=31.12.\n3. The interval width is 7.3.\nFinal: {\"answer\": 139.2475, \"unit\": \"area_units\"}", "dedupe_signature": "024bc45718e1e096763aa986c8610ab17516a6d8bb575186c55b763c44563b0e", "difficulty": "medium", "final_answer": {"answer": 139.2475, "unit": "area_units"}, "id": "trapz_linear_004744_3.3_19.9_-3.9_3.4", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=3.3x+19.9 from x=-3.9 to x=3.4. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-3.9)=7.03 and f(3.4)=31.12.\nThe interval width is 7.3.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 19.9, "slope": 3.3, "x0": -3.9, "x1": 3.4}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.16 and add it to the current value.\nFinal: {\"answer\": [1.304, 1.1, 0.728], \"unit\": \"temperature_units\"}", "dedupe_signature": "c32563e0e665388d282e25cb750bd43f5ea96b1d84794d8de1c8e6c2c42ff555", "difficulty": "hard", "final_answer": {"answer": [1.304, 1.1, 0.728], "unit": "temperature_units"}, "id": "heat_step_004745_0.16_-1.45_2.0_1.1_0.2_2.6", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-1.45, right=2.6; current interior values are [2.0, 1.1, 0.2]. Use r=0.16. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.16 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [2.0, 1.1, 0.2], "left": -1.45, "r": 0.16, "right": 2.6}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 6732.0 / 1000.\nFinal: {\"answer\": 6.732, \"unit\": \"kg\"}", "dedupe_signature": "f3e07454a753252a5f37b0712bfc4c607582ac3ecdb982b2cf674309075c511a", "difficulty": "easy", "final_answer": {"answer": 6.732, "unit": "kg"}, "id": "unit_convert_004746_g_to_kg_6732", "license": "Apache-2.0", "prompt": "Convert 6732 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 6732.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 6732.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=55 degrees and keep the unit as newtons.\nFinal: {\"answer\": [143.1073, 204.3784], \"unit\": \"N\"}", "dedupe_signature": "c5c498726d1e640399d952924eddc6cbda9928f8bf5f01b69001588ac33430be", "difficulty": "medium", "final_answer": {"answer": [143.1073, 204.3784], "unit": "N"}, "id": "vector_components_004747_249.5_55", "license": "Apache-2.0", "prompt": "A vector has magnitude 249.5 N at 55 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=55 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 55, "magnitude": 249.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [7.65, 7.25], \"unit\": \"dimensionless\"}", "dedupe_signature": "86ddd66375b20d2beaa64253574e0ff4e896e6629137e92612237cbeccfad6bf", "difficulty": "medium", "final_answer": {"answer": [7.65, 7.25], "unit": "dimensionless"}, "id": "line_two_point_004748_-11.75_-3.75_7.65_7.25", "license": "Apache-2.0", "prompt": "A line passes through points (-11.75, -82.6375) and (-3.75, -21.4375). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -11.75, "x2": -3.75, "y1": -82.6375, "y2": -21.4375}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. amount times volume is not concentration\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "0d159b06abf81b3ac8ddcd9128569584b35c3f80d75bf4ee03dc8d379cc96c20", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_004749_inconsistent_74ac0b02_482226", "license": "Apache-2.0", "prompt": "In lab notebook case 482226, check dimensional consistency for C = n * V. The left side has dimensions mol/L and the right side has dimensions mol*L. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\namount times volume is not concentration\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "C = n * V"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: target_schema, valid_examples.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"target_schema\", \"valid_examples\"]}", "dedupe_signature": "b1aa508e641b2d6a9700d8ab84dcfed380cbbeeb4c16321dfee2f1a9be91dcbb", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["target_schema", "valid_examples"]}, "id": "abstain_004751_target_schema_valid_examples", "license": "Apache-2.0", "prompt": "Write a parser that converts each mobile invoice record from batch 473955 into the correct schema, but the prompt does not include the target schema or examples. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: target_schema, valid_examples.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["target_schema", "valid_examples"]}, "verifier": {"missing": ["target_schema", "valid_examples"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 7.8 kg and a = 14.6 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 113.88, \"unit\": \"N\"}", "dedupe_signature": "65323535303895b1f4434aabb56f0e641ea4ac0b9a540137494311e35f494e2f", "difficulty": "easy", "final_answer": {"answer": 113.88, "unit": "N"}, "id": "force_004752_7.8_14.6", "license": "Apache-2.0", "prompt": "A cart has mass 7.8 kg and measured acceleration 14.6 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 7.8 kg and a = 14.6 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 14.6, "mass": 7.8}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 36.45^2 and multiply by 0.5 * 21.2.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 14083.1865, \"unit\": \"J\"}", "dedupe_signature": "056d480d7927de24d1c33c487a81acdcc7d77e352196471dce3f1697d5e57d0c", "difficulty": "easy", "final_answer": {"answer": 14083.1865, "unit": "J"}, "id": "ke_004753_21.2_36.45", "license": "Apache-2.0", "prompt": "A body of mass 21.2 kg moves at 36.45 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 36.45^2 and multiply by 0.5 * 21.2.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 21.2, "velocity": 36.45}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 3.5 * 8.314 * 320 / 46.7.\nFinal: {\"answer\": 199.3936, \"unit\": \"kPa\"}", "dedupe_signature": "0b5e9529de2efe68503941142ebcedde9e8ba91e807b2b21171ee6f575d1e045", "difficulty": "medium", "final_answer": {"answer": 199.3936, "unit": "kPa"}, "id": "ideal_gas_004755_3.5_320_46.7", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=3.5 mol, T=320 K, and V=46.7 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 3.5 * 8.314 * 320 / 46.7.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 3.5, "temp_k": 320, "volume_l": 46.7}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=25.4 V and R=66.4 ohm.\nFinal: {\"answer\": 9.7163, \"unit\": \"W\"}", "dedupe_signature": "6ba3f654352d14077bbb128affb8def75968d3e008f984e99d98f8143ec2f45a", "difficulty": "easy", "final_answer": {"answer": 9.7163, "unit": "W"}, "id": "ohm_power_004757_25.4_66.4", "license": "Apache-2.0", "prompt": "A resistor has resistance 66.4 ohm and voltage 25.4 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=25.4 V and R=66.4 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 66.4, "voltage": 25.4}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 0.88 mol * 58.44 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 51.4272, \"unit\": \"g\"}", "dedupe_signature": "f9d93590dfc132968441c21a1735ce22bff7773b2163adc3695b8ff486b67860", "difficulty": "medium", "final_answer": {"answer": 51.4272, "unit": "g"}, "id": "stoich_mass_004759_sodium_chloride_0.88", "license": "Apache-2.0", "prompt": "A sample contains 0.88 mol of sodium chloride. Using molar mass 58.44 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 0.88 mol * 58.44 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "sodium chloride", "molar_mass": 58.44, "moles": 0.88}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(1.3)=5.85 and f(6.3)=-21.65.\n3. The interval width is 5.\nFinal: {\"answer\": -39.5, \"unit\": \"area_units\"}", "dedupe_signature": "7cc965a8e2d4eb95eaf50ed147e730c35b1a88ec9642614199b460a83bf04637", "difficulty": "medium", "final_answer": {"answer": -39.5, "unit": "area_units"}, "id": "trapz_linear_004762_-5.5_13_1.3_6.3", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-5.5x+13 from x=1.3 to x=6.3. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(1.3)=5.85 and f(6.3)=-21.65.\nThe interval width is 5.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 13.0, "slope": -5.5, "x0": 1.3, "x1": 6.3}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kelvin equals Celsius plus 273.15.\n2. Apply the conversion factor directly to the given value.\n3. Compute 54.5 + 273.15.\nFinal: {\"answer\": 327.65, \"unit\": \"K\"}", "dedupe_signature": "3a1f7ede864d6ee38703a3f65ae2469b22016b894521d677f3e278f645ddb9ea", "difficulty": "easy", "final_answer": {"answer": 327.65, "unit": "K"}, "id": "unit_convert_004764_c_to_k_54.5", "license": "Apache-2.0", "prompt": "Convert 54.5 degC to K. Return the converted value with unit.", "reasoning_trace": "Kelvin equals Celsius plus 273.15.\nApply the conversion factor directly to the given value.\nCompute 54.5 + 273.15.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 54.5}, "verifier": {"formula": "value + 273.15", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=110 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-137.4921, 377.7564], \"unit\": \"N\"}", "dedupe_signature": "9dc80474e6304f45ce634add5e854fa5506aea4e52753560cb7dd1873650fe03", "difficulty": "medium", "final_answer": {"answer": [-137.4921, 377.7564], "unit": "N"}, "id": "vector_components_004765_402_110", "license": "Apache-2.0", "prompt": "A vector has magnitude 402 N at 110 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=110 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 110, "magnitude": 402.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [5.65, -19.25], \"unit\": \"dimensionless\"}", "dedupe_signature": "f6ba6ca6920d1340d5aa53f4861c7e72de73afce301a636fd1dd2ad9582c5faa", "difficulty": "medium", "final_answer": {"answer": [5.65, -19.25], "unit": "dimensionless"}, "id": "line_two_point_004766_8.5_11.25_5.65_-19.25", "license": "Apache-2.0", "prompt": "A line passes through points (8.5, 28.775) and (11.25, 44.3125). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 8.5, "x2": 11.25, "y1": 28.775000000000006, "y2": 44.31250000000001}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. volt squared divided by ohm is watt\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "2fc05497d82d89a4f0c6e9c5af3d96729319623c1fa12831306c5085692c1761", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_004767_consistent_82e93f3d_36008", "license": "Apache-2.0", "prompt": "In model card equation case 36008, check dimensional consistency for P = V^2 / R. The left side has dimensions W and the right side has dimensions W. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nvolt squared divided by ohm is watt\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "P = V^2 / R"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: rate_constant, number_of_steps.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"rate_constant\", \"number_of_steps\"]}", "dedupe_signature": "aef3422fd430e7433a79d1f7564cc4028fc9f2c16e000544e491681ab2581386", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["rate_constant", "number_of_steps"]}, "id": "abstain_004769_rate_constant_number_of_steps", "license": "Apache-2.0", "prompt": "Use explicit Euler for dy/dt = -k y. The prompt gives y(0)=78 and h=0.3, but omits both k and the number of steps. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: rate_constant, number_of_steps.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["rate_constant", "number_of_steps"]}, "verifier": {"missing": ["rate_constant", "number_of_steps"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 19.55 kg and a = 6 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 117.3, \"unit\": \"N\"}", "dedupe_signature": "fafdc90a35dc0795cb4dbdc975e34cd746161709a1d86049208c198cc21a50fb", "difficulty": "easy", "final_answer": {"answer": 117.3, "unit": "N"}, "id": "force_004770_19.55_6", "license": "Apache-2.0", "prompt": "A cart has mass 19.55 kg and measured acceleration 6 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 19.55 kg and a = 6 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 6.0, "mass": 19.55}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 7.55^2 and multiply by 0.5 * 25.2.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 718.2315, \"unit\": \"J\"}", "dedupe_signature": "7ebc07fbdce2519f752aa4dc64844eb7da698093733496b4f1ad7aebbcbc67d8", "difficulty": "easy", "final_answer": {"answer": 718.2315, "unit": "J"}, "id": "ke_004771_25.2_7.55", "license": "Apache-2.0", "prompt": "A body of mass 25.2 kg moves at 7.55 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 7.55^2 and multiply by 0.5 * 25.2.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 25.2, "velocity": 7.55}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=16 degrees through the sine of 2 theta.\n3. Substitute v=49.6 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 132.8936, \"unit\": \"m\"}", "dedupe_signature": "243d70af2143b7fca179442312dab8a167a3263f5edabeef9477351de91b5b6c", "difficulty": "medium", "final_answer": {"answer": 132.8936, "unit": "m"}, "id": "projectile_range_004772_49.6_16", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 49.6 m/s and angle 16 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=16 degrees through the sine of 2 theta.\nSubstitute v=49.6 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 16, "gravity": 9.81, "speed": 49.6}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 730 * 3.375 * 109.\nFinal: {\"answer\": 268548.75, \"unit\": \"J\"}", "dedupe_signature": "ab9953dffe5943c60f0af9188ed8952824e455126639f3481ab40dd801faa093", "difficulty": "easy", "final_answer": {"answer": 268548.75, "unit": "J"}, "id": "heat_q_004774_730_3.375_109", "license": "Apache-2.0", "prompt": "A 730 g sample has specific heat 3.375 J/(g*K). How much heat is needed to raise its temperature by 109 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 730 * 3.375 * 109.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 109, "heat_capacity": 3.375, "mass_g": 730}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=231.6 V and R=186.2 ohm.\nFinal: {\"answer\": 288.0696, \"unit\": \"W\"}", "dedupe_signature": "f33ae6aa0d6ad7946e400fdf40ae1ceaa778cab04831f080018bdacd5b9e8ac4", "difficulty": "easy", "final_answer": {"answer": 288.0696, "unit": "W"}, "id": "ohm_power_004775_231.6_186.2", "license": "Apache-2.0", "prompt": "A resistor has resistance 186.2 ohm and voltage 231.6 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=231.6 V and R=186.2 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 186.2, "voltage": 231.6}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.93 y, so each step multiplies y by 1 - h*0.93.\n3. Apply that update for 8 steps and round the final state.\nFinal: {\"answer\": 0.0122, \"unit\": \"state_units\"}", "dedupe_signature": "55a3c30d67c3d37e623155cb9a8a0fb8c72c54575bc98ecd68d3d90a85c0214f", "difficulty": "medium", "final_answer": {"answer": 0.0122, "unit": "state_units"}, "id": "euler_decay_004779_56_0.93_1.45_8", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.93 y with y(0)=56, step size h=1.45, for 8 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.93 y, so each step multiplies y by 1 - h*0.93.\nApply that update for 8 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 56.0, "rate": 0.93, "step": 1.45, "steps": 8}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-2)=6.6 and f(0.9)=8.34.\n3. The interval width is 2.9.\nFinal: {\"answer\": 21.663, \"unit\": \"area_units\"}", "dedupe_signature": "377ff6f6fd4ba02566d4f8d34c77d4b256f44f58c525128c578bedc7b789ec62", "difficulty": "medium", "final_answer": {"answer": 21.663, "unit": "area_units"}, "id": "trapz_linear_004780_0.6_7.8_-2_0.9", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=0.6x+7.8 from x=-2 to x=0.9. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-2)=6.6 and f(0.9)=8.34.\nThe interval width is 2.9.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 7.8, "slope": 0.6, "x0": -2.0, "x1": 0.8999999999999999}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kelvin equals Celsius plus 273.15.\n2. Apply the conversion factor directly to the given value.\n3. Compute -19.0 + 273.15.\nFinal: {\"answer\": 254.15, \"unit\": \"K\"}", "dedupe_signature": "9027ddef9cd6aa88f5ea62f1b08a04ed6ed8b6eb3815a2aaab0573cc27d9837c", "difficulty": "easy", "final_answer": {"answer": 254.15, "unit": "K"}, "id": "unit_convert_004782_c_to_k_-19", "license": "Apache-2.0", "prompt": "Convert -19 degC to K. Return the converted value with unit.", "reasoning_trace": "Kelvin equals Celsius plus 273.15.\nApply the conversion factor directly to the given value.\nCompute -19.0 + 273.15.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": -19.0}, "verifier": {"formula": "value + 273.15", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=36 degrees and keep the unit as newtons.\nFinal: {\"answer\": [292.8642, 212.7783], \"unit\": \"N\"}", "dedupe_signature": "f415038d5a9629d5ca3ef4daa665e204570e3fa0d961de8e10a29dd237bcc055", "difficulty": "medium", "final_answer": {"answer": [292.8642, 212.7783], "unit": "N"}, "id": "vector_components_004783_362_36", "license": "Apache-2.0", "prompt": "A vector has magnitude 362 N at 36 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=36 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 36, "magnitude": 362.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-9.95, -17.75], \"unit\": \"dimensionless\"}", "dedupe_signature": "90f4991e07e2d03c3a26930ca70117e9ab61cd5f2b1e02899e3e1fd8f969be4c", "difficulty": "medium", "final_answer": {"answer": [-9.95, -17.75], "unit": "dimensionless"}, "id": "line_two_point_004784_13.25_17.5_-9.95_-17.75", "license": "Apache-2.0", "prompt": "A line passes through points (13.25, -149.587) and (17.5, -191.875). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 13.25, "x2": 17.5, "y1": -149.58749999999998, "y2": -191.875}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. volt squared divided by ohm is watt\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "0ff5b0afd5b7c2ccfe370aa4a3e894ba04d0e7d84127a3a7bee02ce229392106", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_004785_consistent_82e93f3d_589744", "license": "Apache-2.0", "prompt": "In field worksheet case 589744, check dimensional consistency for P = V^2 / R. The left side has dimensions W and the right side has dimensions W. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nvolt squared divided by ohm is watt\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "P = V^2 / R"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: volume.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"volume\"]}", "dedupe_signature": "757c88a56e4cac60d93eb1280d6e894b38962729a0281a56123571cdac4e71f4", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["volume"]}, "id": "abstain_004787_volume", "license": "Apache-2.0", "prompt": "Compute pressure from the ideal gas law. The prompt gives n=4.34 mol and T=423 K, but does not give volume. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: volume.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["volume"]}, "verifier": {"missing": ["volume"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 9.75 kg and a = 2.7 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 26.325, \"unit\": \"N\"}", "dedupe_signature": "9c874b6d4bcf1e103582e9f545d91cb250c33e3fd8f40359e103d3ebfa58c456", "difficulty": "easy", "final_answer": {"answer": 26.325, "unit": "N"}, "id": "force_004788_9.75_2.7", "license": "Apache-2.0", "prompt": "A cart has mass 9.75 kg and measured acceleration 2.7 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 9.75 kg and a = 2.7 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 2.7, "mass": 9.75}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 44.1^2 and multiply by 0.5 * 21.05.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 20469.1253, \"unit\": \"J\"}", "dedupe_signature": "95caa1b905e3e869d4d00b191b5f8444c760a7e55562dd82d8034d7e507f84e1", "difficulty": "easy", "final_answer": {"answer": 20469.1253, "unit": "J"}, "id": "ke_004789_21.05_44.1", "license": "Apache-2.0", "prompt": "A body of mass 21.05 kg moves at 44.1 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 44.1^2 and multiply by 0.5 * 21.05.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 21.05, "velocity": 44.1}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=17 degrees through the sine of 2 theta.\n3. Substitute v=71.6 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 292.2259, \"unit\": \"m\"}", "dedupe_signature": "dd9a7cb1e0556970763c7e2f25f654d8bb1cce476f495dbbd4d46b8032297b3e", "difficulty": "medium", "final_answer": {"answer": 292.2259, "unit": "m"}, "id": "projectile_range_004790_71.6_17", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 71.6 m/s and angle 17 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=17 degrees through the sine of 2 theta.\nSubstitute v=71.6 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 17, "gravity": 9.81, "speed": 71.6}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 1.08 * 8.314 * 599 / 53.2.\nFinal: {\"answer\": 101.0995, \"unit\": \"kPa\"}", "dedupe_signature": "00b90a401579dcfb0fba069076fe6ca5a43c1a47ec2553560562e34afaf274b8", "difficulty": "medium", "final_answer": {"answer": 101.0995, "unit": "kPa"}, "id": "ideal_gas_004791_1.08_599_53.2", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=1.08 mol, T=599 K, and V=53.2 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 1.08 * 8.314 * 599 / 53.2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 1.08, "temp_k": 599, "volume_l": 53.2}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 275 * 0.61 * 41.\nFinal: {\"answer\": 6877.75, \"unit\": \"J\"}", "dedupe_signature": "43791a8232d9d66b1e5d9a059369d7127a067c3f2a9ec9d524f31dd1b6dbb68a", "difficulty": "easy", "final_answer": {"answer": 6877.75, "unit": "J"}, "id": "heat_q_004792_275_0.61_41", "license": "Apache-2.0", "prompt": "A 275 g sample has specific heat 0.61 J/(g*K). How much heat is needed to raise its temperature by 41 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 275 * 0.61 * 41.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 41, "heat_capacity": 0.61, "mass_g": 275}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=90.4 V and R=181.4 ohm.\nFinal: {\"answer\": 45.0505, \"unit\": \"W\"}", "dedupe_signature": "86b2071926e82055973eb6f951523d166ce731d41c22576cc0abb9b5f258e6ac", "difficulty": "easy", "final_answer": {"answer": 45.0505, "unit": "W"}, "id": "ohm_power_004793_90.4_181.4", "license": "Apache-2.0", "prompt": "A resistor has resistance 181.4 ohm and voltage 90.4 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=90.4 V and R=181.4 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 181.4, "voltage": 90.4}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=78 mg, t=253.5 h, and T_half=32 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 0.3216, \"unit\": \"mg\"}", "dedupe_signature": "2decd45b6e5f27d2e347496510e7542bb64083177f3d15edc3842837199348c5", "difficulty": "medium", "final_answer": {"answer": 0.3216, "unit": "mg"}, "id": "half_life_004794_78_32_253.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 78 mg. Its half-life is 32 hours. How many mg remain after 253.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=78 mg, t=253.5 h, and T_half=32 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 253.5, "half_life": 32.0, "initial_amount": 78.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 2430 mL to 2.43 L.\n3. Compute M = 0.55 / 2.43.\nFinal: {\"answer\": 0.2263, \"unit\": \"mol/L\"}", "dedupe_signature": "d1c5d6769fe94e0bc97b3fd13c0c38175b1aa7790cff558965384cc39cb7e696", "difficulty": "medium", "final_answer": {"answer": 0.2263, "unit": "mol/L"}, "id": "molarity_004796_0.55_2430", "license": "Apache-2.0", "prompt": "A solution contains 0.55 mol of solute in 2430 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 2430 mL to 2.43 L.\nCompute M = 0.55 / 2.43.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 0.55, "volume_ml": 2430}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.42 y, so each step multiplies y by 1 - h*0.42.\n3. Apply that update for 10 steps and round the final state.\nFinal: {\"answer\": 0.0313, \"unit\": \"state_units\"}", "dedupe_signature": "3b602c1330565255ac8dc8fff19382d07ae7025fa8584dcebdf510ab8faf180b", "difficulty": "medium", "final_answer": {"answer": 0.0313, "unit": "state_units"}, "id": "euler_decay_004797_10.5_0.42_1.05_10", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.42 y with y(0)=10.5, step size h=1.05, for 10 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.42 y, so each step multiplies y by 1 - h*0.42.\nApply that update for 10 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 10.5, "rate": 0.42, "step": 1.05, "steps": 10}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(7.3)=50.44 and f(8.9)=58.12.\n3. The interval width is 1.6.\nFinal: {\"answer\": 86.848, \"unit\": \"area_units\"}", "dedupe_signature": "c8205c68c200b9c223479fba95597a598390667adeaa875547443025738c0f52", "difficulty": "medium", "final_answer": {"answer": 86.848, "unit": "area_units"}, "id": "trapz_linear_004798_4.8_15.4_7.3_8.9", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=4.8x+15.4 from x=7.3 to x=8.9. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(7.3)=50.44 and f(8.9)=58.12.\nThe interval width is 1.6.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 15.4, "slope": 4.8, "x0": 7.3, "x1": 8.9}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.44 and add it to the current value.\nFinal: {\"answer\": [1.426, 0.06, 1.112], \"unit\": \"temperature_units\"}", "dedupe_signature": "97a6312061476158f696319f112f09374a3190c6869516a63bed0ab93ccd029e", "difficulty": "hard", "final_answer": {"answer": [1.426, 0.06, 1.112], "unit": "temperature_units"}, "id": "heat_step_004799_0.44_2.05_-1.5_1.6_1.2_0.6", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=2.05, right=0.6; current interior values are [-1.5, 1.6, 1.2]. Use r=0.44. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.44 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-1.5, 1.6, 1.2], "left": 2.05, "r": 0.44, "right": 0.6}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 100 centimeters in one meter.\n2. Apply the conversion factor directly to the given value.\n3. Compute 4268.0 / 100.\nFinal: {\"answer\": 42.68, \"unit\": \"m\"}", "dedupe_signature": "524387c48b4a2a7df587d2bca30f3d4c77b224cf52e18d2fa8676f4f914bf843", "difficulty": "easy", "final_answer": {"answer": 42.68, "unit": "m"}, "id": "unit_convert_004800_cm_to_m_4268", "license": "Apache-2.0", "prompt": "Convert 4268 cm to m. Return the converted value with unit.", "reasoning_trace": "There are 100 centimeters in one meter.\nApply the conversion factor directly to the given value.\nCompute 4268.0 / 100.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 4268.0}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [7.45, 6.75], \"unit\": \"dimensionless\"}", "dedupe_signature": "6e89e6d4b2bd6a9f92f4d064a94fa1a22e1ba69e28c3143bb0358c39161bada0", "difficulty": "medium", "final_answer": {"answer": [7.45, 6.75], "unit": "dimensionless"}, "id": "line_two_point_004802_-2.25_0.5_7.45_6.75", "license": "Apache-2.0", "prompt": "A line passes through points (-2.25, -10.0125) and (0.5, 10.475). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -2.25, "x2": 0.5, "y1": -10.0125, "y2": 10.475}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: rate_constant, number_of_steps.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"rate_constant\", \"number_of_steps\"]}", "dedupe_signature": "dbc54bc872ad3403b4b35f4f4f2e3a050f4463f7d807140560af4c6cca70eeb7", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["rate_constant", "number_of_steps"]}, "id": "abstain_004805_rate_constant_number_of_steps", "license": "Apache-2.0", "prompt": "Use explicit Euler for dy/dt = -k y. The prompt gives y(0)=54 and h=0.6, but omits both k and the number of steps. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: rate_constant, number_of_steps.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["rate_constant", "number_of_steps"]}, "verifier": {"missing": ["rate_constant", "number_of_steps"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 21.05 kg and a = 6.8 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 143.14, \"unit\": \"N\"}", "dedupe_signature": "cd0754679ffe4424b05cbee3f292612794d25a360b055f31632499550a835bd1", "difficulty": "easy", "final_answer": {"answer": 143.14, "unit": "N"}, "id": "force_004806_21.05_6.8", "license": "Apache-2.0", "prompt": "A cart has mass 21.05 kg and measured acceleration 6.8 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 21.05 kg and a = 6.8 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 6.8, "mass": 21.05}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=8 degrees through the sine of 2 theta.\n3. Substitute v=80.2 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 180.7248, \"unit\": \"m\"}", "dedupe_signature": "92168e349a18acf806ebdecfc244c11dd95548586e5313c53dedf30e7715b2a2", "difficulty": "medium", "final_answer": {"answer": 180.7248, "unit": "m"}, "id": "projectile_range_004808_80.2_8", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 80.2 m/s and angle 8 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=8 degrees through the sine of 2 theta.\nSubstitute v=80.2 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 8, "gravity": 9.81, "speed": 80.2}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 4.02 * 8.314 * 263 / 89.4.\nFinal: {\"answer\": 98.3228, \"unit\": \"kPa\"}", "dedupe_signature": "0d47b5634716a48926192d8ffd23716a86c65c8d34dd93e8c228af7d0aff1eb9", "difficulty": "medium", "final_answer": {"answer": 98.3228, "unit": "kPa"}, "id": "ideal_gas_004809_4.02_263_89.4", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=4.02 mol, T=263 K, and V=89.4 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 4.02 * 8.314 * 263 / 89.4.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 4.02, "temp_k": 263, "volume_l": 89.4}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 385 * 4.945 * 68.\nFinal: {\"answer\": 129460.1, \"unit\": \"J\"}", "dedupe_signature": "4c26cd666b2a930c37f25151be7747599ed87f498a021c04ad8105e4ddf4a309", "difficulty": "easy", "final_answer": {"answer": 129460.1, "unit": "J"}, "id": "heat_q_004810_385_4.945_68", "license": "Apache-2.0", "prompt": "A 385 g sample has specific heat 4.945 J/(g*K). How much heat is needed to raise its temperature by 68 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 385 * 4.945 * 68.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 68, "heat_capacity": 4.945, "mass_g": 385}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=121.6 V and R=199.9 ohm.\nFinal: {\"answer\": 73.9698, \"unit\": \"W\"}", "dedupe_signature": "a7b46ecbb0a66b78dd71121362cc7fbfe639b2de5ca487292908684abd783444", "difficulty": "easy", "final_answer": {"answer": 73.9698, "unit": "W"}, "id": "ohm_power_004811_121.6_199.9", "license": "Apache-2.0", "prompt": "A resistor has resistance 199.9 ohm and voltage 121.6 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=121.6 V and R=199.9 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 199.9, "voltage": 121.6}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=52.5 mg, t=96.5 h, and T_half=66.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 19.2011, \"unit\": \"mg\"}", "dedupe_signature": "7a8cc3d09f033918d2134b2f08a2f9010aba6f53f0ffca02e7ce4c1951822acb", "difficulty": "medium", "final_answer": {"answer": 19.2011, "unit": "mg"}, "id": "half_life_004812_52.5_66.5_96.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 52.5 mg. Its half-life is 66.5 hours. How many mg remain after 96.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=52.5 mg, t=96.5 h, and T_half=66.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 96.5, "half_life": 66.5, "initial_amount": 52.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 5.66 mol * 58.44 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 330.7704, \"unit\": \"g\"}", "dedupe_signature": "9b95fe9dd6e299ed5099ddbc813581c9981904727815e20887b367bf3e0727a5", "difficulty": "medium", "final_answer": {"answer": 330.7704, "unit": "g"}, "id": "stoich_mass_004813_sodium_chloride_5.66", "license": "Apache-2.0", "prompt": "A sample contains 5.66 mol of sodium chloride. Using molar mass 58.44 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 5.66 mol * 58.44 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "sodium chloride", "molar_mass": 58.44, "moles": 5.66}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 3895 mL to 3.895 L.\n3. Compute M = 4.015 / 3.895.\nFinal: {\"answer\": 1.0308, \"unit\": \"mol/L\"}", "dedupe_signature": "0dd0493ef69ec32a32366410e9a50d1888b588da2b86efe2c5521d5a0a9d5673", "difficulty": "medium", "final_answer": {"answer": 1.0308, "unit": "mol/L"}, "id": "molarity_004814_4.015_3895", "license": "Apache-2.0", "prompt": "A solution contains 4.015 mol of solute in 3895 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 3895 mL to 3.895 L.\nCompute M = 4.015 / 3.895.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 4.015, "volume_ml": 3895}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.03 y, so each step multiplies y by 1 - h*0.03.\n3. Apply that update for 3 steps and round the final state.\nFinal: {\"answer\": 62.1752, \"unit\": \"state_units\"}", "dedupe_signature": "358862900e6654747b12dfebb467b9027ac0ab42ca5358a990d47567993b7a30", "difficulty": "medium", "final_answer": {"answer": 62.1752, "unit": "state_units"}, "id": "euler_decay_004815_74.5_0.03_1.95_3", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.03 y with y(0)=74.5, step size h=1.95, for 3 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.03 y, so each step multiplies y by 1 - h*0.03.\nApply that update for 3 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 74.5, "rate": 0.03, "step": 1.95, "steps": 3}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.08 and add it to the current value.\nFinal: {\"answer\": [1.236, 1.82, 2.534], \"unit\": \"temperature_units\"}", "dedupe_signature": "113867830cfb94c5938721d153a5bbe2167dfa5108c887388ad075ba0290e3e6", "difficulty": "hard", "final_answer": {"answer": [1.236, 1.82, 2.534], "unit": "temperature_units"}, "id": "heat_step_004817_0.08_1.05_1.2_1.8_2.65_2.05", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.05, right=2.05; current interior values are [1.2, 1.8, 2.65]. Use r=0.08. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.08 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [1.2, 1.8, 2.65], "left": 1.05, "r": 0.08, "right": 2.05}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 744.0 / 1000.\nFinal: {\"answer\": 0.744, \"unit\": \"kg\"}", "dedupe_signature": "2ef83612af13fd2c39ef78bfaafb19e169d5689412f44db6a72c5983a40b5853", "difficulty": "easy", "final_answer": {"answer": 0.744, "unit": "kg"}, "id": "unit_convert_004818_g_to_kg_744", "license": "Apache-2.0", "prompt": "Convert 744 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 744.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 744.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=9 degrees and keep the unit as newtons.\nFinal: {\"answer\": [56.7921, 8.995], \"unit\": \"N\"}", "dedupe_signature": "42a4bcc39160ec88c1d0f913fc16a0d8b33b8a78d172a2fe89c45923aaf812a2", "difficulty": "medium", "final_answer": {"answer": [56.7921, 8.995], "unit": "N"}, "id": "vector_components_004819_57.5_9", "license": "Apache-2.0", "prompt": "A vector has magnitude 57.5 N at 9 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=9 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 9, "magnitude": 57.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [2.05, 12.0], \"unit\": \"dimensionless\"}", "dedupe_signature": "b89035c4bb9605c9e09ab0ecdce4493f5e7531c61449898d777a5ace9c08d516", "difficulty": "medium", "final_answer": {"answer": [2.05, 12.0], "unit": "dimensionless"}, "id": "line_two_point_004820_-7.25_6.25_2.05_12", "license": "Apache-2.0", "prompt": "A line passes through points (-7.25, -2.8625) and (6.25, 24.8125). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -7.25, "x2": 6.25, "y1": -2.862499999999999, "y2": 24.8125}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. mass times acceleration has newton dimensions\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "ac82dc12b5db5246fda389929156365cf61203f3fb2828db884734054ba0ff6a", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_004821_consistent_03f5e041_559878", "license": "Apache-2.0", "prompt": "In model card equation case 559878, check dimensional consistency for F = m * a. The left side has dimensions kg*m/s^2 and the right side has dimensions kg*m/s^2. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nmass times acceleration has newton dimensions\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "F = m * a"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 23.85 kg and a = 6.5 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 155.025, \"unit\": \"N\"}", "dedupe_signature": "f9ab8152ad8d036c31a545f8e7c28875a876275fdc8233b6595e8e169d3e9442", "difficulty": "easy", "final_answer": {"answer": 155.025, "unit": "N"}, "id": "force_004824_23.85_6.5", "license": "Apache-2.0", "prompt": "A cart has mass 23.85 kg and measured acceleration 6.5 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 23.85 kg and a = 6.5 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 6.5, "mass": 23.85}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 16.1^2 and multiply by 0.5 * 8.1.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 1049.8005, \"unit\": \"J\"}", "dedupe_signature": "cedf887219e38bcad1bbf2cacd38f719466bb1a5ab3f8dddc299d75c9e78e727", "difficulty": "easy", "final_answer": {"answer": 1049.8005, "unit": "J"}, "id": "ke_004825_8.1_16.1", "license": "Apache-2.0", "prompt": "A body of mass 8.1 kg moves at 16.1 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 16.1^2 and multiply by 0.5 * 8.1.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 8.1, "velocity": 16.1}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=82 degrees through the sine of 2 theta.\n3. Substitute v=7.1 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 1.4164, \"unit\": \"m\"}", "dedupe_signature": "feba3ff18e9b83198be40f56d9f027fc307110d80a7cf8dd216f6d03e3e2920c", "difficulty": "medium", "final_answer": {"answer": 1.4164, "unit": "m"}, "id": "projectile_range_004826_7.1_82", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 7.1 m/s and angle 82 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=82 degrees through the sine of 2 theta.\nSubstitute v=7.1 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 82, "gravity": 9.81, "speed": 7.1}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1465 * 3.945 * 78.\nFinal: {\"answer\": 450795.15, \"unit\": \"J\"}", "dedupe_signature": "1189d3d332dd0d7288a7d22fbd57d9f67eebeb16ee899a3164d5999b3c281ba0", "difficulty": "easy", "final_answer": {"answer": 450795.15, "unit": "J"}, "id": "heat_q_004828_1465_3.945_78", "license": "Apache-2.0", "prompt": "A 1465 g sample has specific heat 3.945 J/(g*K). How much heat is needed to raise its temperature by 78 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1465 * 3.945 * 78.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 78, "heat_capacity": 3.945, "mass_g": 1465}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=203.5 V and R=80.2 ohm.\nFinal: {\"answer\": 516.3622, \"unit\": \"W\"}", "dedupe_signature": "3a2576bd8181245e93a93b2d7adb4299a19fa5c79fe05c7ecd62ec3cf0ece15b", "difficulty": "easy", "final_answer": {"answer": 516.3622, "unit": "W"}, "id": "ohm_power_004829_203.5_80.2", "license": "Apache-2.0", "prompt": "A resistor has resistance 80.2 ohm and voltage 203.5 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=203.5 V and R=80.2 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 80.2, "voltage": 203.5}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=826 mg, t=36 h, and T_half=14.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 147.773, \"unit\": \"mg\"}", "dedupe_signature": "5076af1c538952c376adb8ec4023d65aa66c06bd57d839c78facba2f14fdb145", "difficulty": "medium", "final_answer": {"answer": 147.773, "unit": "mg"}, "id": "half_life_004830_826_14.5_36", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 826 mg. Its half-life is 14.5 hours. How many mg remain after 36 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=826 mg, t=36 h, and T_half=14.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 36.0, "half_life": 14.5, "initial_amount": 826.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 7.1 mol * 58.44 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 414.924, \"unit\": \"g\"}", "dedupe_signature": "c10c7c6f060510c2443b7388ac56330d276802cc99301cae91dc78867ab04112", "difficulty": "medium", "final_answer": {"answer": 414.924, "unit": "g"}, "id": "stoich_mass_004831_sodium_chloride_7.1", "license": "Apache-2.0", "prompt": "A sample contains 7.1 mol of sodium chloride. Using molar mass 58.44 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 7.1 mol * 58.44 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "sodium chloride", "molar_mass": 58.44, "moles": 7.1}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 2820 mL to 2.82 L.\n3. Compute M = 1.34 / 2.82.\nFinal: {\"answer\": 0.4752, \"unit\": \"mol/L\"}", "dedupe_signature": "0dabc9980ed4cd8b23d609644313effc6314db3e900546a84977cde79edac9ff", "difficulty": "medium", "final_answer": {"answer": 0.4752, "unit": "mol/L"}, "id": "molarity_004832_1.34_2820", "license": "Apache-2.0", "prompt": "A solution contains 1.34 mol of solute in 2820 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 2820 mL to 2.82 L.\nCompute M = 1.34 / 2.82.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 1.34, "volume_ml": 2820}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.83 y, so each step multiplies y by 1 - h*0.83.\n3. Apply that update for 10 steps and round the final state.\nFinal: {\"answer\": 1.6647, \"unit\": \"state_units\"}", "dedupe_signature": "a7c0b6b1c5e7a4ea4cd6e15fa3148ea1e5498363975c4b4a1716b01b3eb6aa99", "difficulty": "medium", "final_answer": {"answer": 1.6647, "unit": "state_units"}, "id": "euler_decay_004833_51.5_0.83_0.35_10", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.83 y with y(0)=51.5, step size h=0.35, for 10 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.83 y, so each step multiplies y by 1 - h*0.83.\nApply that update for 10 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 51.5, "rate": 0.83, "step": 0.35, "steps": 10}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(8.5)=3.25 and f(18.4)=22.06.\n3. The interval width is 9.9.\nFinal: {\"answer\": 125.2845, \"unit\": \"area_units\"}", "dedupe_signature": "209e1f9ab6793e0ddd6e36342577d1462eed23c3f4bf0acdb89f435943024e6e", "difficulty": "medium", "final_answer": {"answer": 125.2845, "unit": "area_units"}, "id": "trapz_linear_004834_1.9_-12.9_8.5_18.4", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=1.9x+-12.9 from x=8.5 to x=18.4. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(8.5)=3.25 and f(18.4)=22.06.\nThe interval width is 9.9.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -12.9, "slope": 1.9, "x0": 8.5, "x1": 18.4}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.38 and add it to the current value.\nFinal: {\"answer\": [-0.112, -0.25, -0.551], \"unit\": \"temperature_units\"}", "dedupe_signature": "8b3ef5b537c16fc52abccccab376519f51e2d750f4165741ef3962a0d8bb2da6", "difficulty": "hard", "final_answer": {"answer": [-0.112, -0.25, -0.551], "unit": "temperature_units"}, "id": "heat_step_004835_0.38_-0.9_-0.15_0.7_-0.95_-1.55", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-0.9, right=-1.55; current interior values are [-0.15, 0.7, -0.95]. Use r=0.38. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.38 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-0.15, 0.7, -0.95], "left": -0.9, "r": 0.38, "right": -1.55}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 49262.0 / 1000.\nFinal: {\"answer\": 49.262, \"unit\": \"kg\"}", "dedupe_signature": "d4c2aa7276f86b18b40ff93d7650e1f9f0e99d250a7271c0afec7c7a411c8ba5", "difficulty": "easy", "final_answer": {"answer": 49.262, "unit": "kg"}, "id": "unit_convert_004836_g_to_kg_49262", "license": "Apache-2.0", "prompt": "Convert 49262 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 49262.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 49262.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=215 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-348.1396, -243.77], \"unit\": \"N\"}", "dedupe_signature": "cfa569cb903cf231206bcfb4f57d9d537fdb452a5070b83d29af4475745d1ddb", "difficulty": "medium", "final_answer": {"answer": [-348.1396, -243.77], "unit": "N"}, "id": "vector_components_004837_425_215", "license": "Apache-2.0", "prompt": "A vector has magnitude 425 N at 215 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=215 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 215, "magnitude": 425.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-0.4, -20.25], \"unit\": \"dimensionless\"}", "dedupe_signature": "f0847f67d0a1f67def5b76add837128257d8edcf853f31eb0699f017d88fd3d5", "difficulty": "medium", "final_answer": {"answer": [-0.4, -20.25], "unit": "dimensionless"}, "id": "line_two_point_004838_-8.5_5_-0.4_-20.25", "license": "Apache-2.0", "prompt": "A line passes through points (-8.5, -16.85) and (5, -22.25). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -8.5, "x2": 5.0, "y1": -16.85, "y2": -22.25}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef finite_differences_004840(values):\n    return [values[i + 1] - values[i] for i in range(len(values) - 1)]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"finite_differences_004840\"}", "dedupe_signature": "cfe07e020ef57b3337f9f41467f8ea217a3a4739694dd75dbeef8e44f8dc3531", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "finite_differences_004840"}, "id": "code_004840_finite_differences_004840", "license": "Apache-2.0", "prompt": "Write a Python function finite_differences_004840(values) that returns the list of successive differences values[i+1] - values[i]. It must return [] for fewer than two values. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "finite_differences_004840"}, "verifier": {"function": "finite_differences_004840", "tests": ["assert finite_differences_004840([1, 4, 9, 16]) == [3, 5, 7]", "assert finite_differences_004840([5]) == []", "assert finite_differences_004840([]) == []"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: volume.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"volume\"]}", "dedupe_signature": "0290add245d1a001903a3fdc3bb5ea1b48bbfc646cb5aa615b215c988361eade", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["volume"]}, "id": "abstain_004841_volume", "license": "Apache-2.0", "prompt": "Compute pressure from the ideal gas law. The prompt gives n=4.54 mol and T=504 K, but does not give volume. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: volume.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["volume"]}, "verifier": {"missing": ["volume"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 5.55 kg and a = 1.55 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 8.6025, \"unit\": \"N\"}", "dedupe_signature": "226ff921dc5d5fe64ac5f6ca8c8de7d19e0f4e297dea082beb10f840bf854b03", "difficulty": "easy", "final_answer": {"answer": 8.6025, "unit": "N"}, "id": "force_004842_5.55_1.55", "license": "Apache-2.0", "prompt": "A cart has mass 5.55 kg and measured acceleration 1.55 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 5.55 kg and a = 1.55 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 1.55, "mass": 5.55}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 10.85^2 and multiply by 0.5 * 17.9.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 1053.6164, \"unit\": \"J\"}", "dedupe_signature": "d9246205bd3c86f829c37d00fe54c3ca058488831b36d01a3d5cb93f4f1b9fde", "difficulty": "easy", "final_answer": {"answer": 1053.6164, "unit": "J"}, "id": "ke_004843_17.9_10.85", "license": "Apache-2.0", "prompt": "A body of mass 17.9 kg moves at 10.85 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 10.85^2 and multiply by 0.5 * 17.9.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 17.9, "velocity": 10.85}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=52 degrees through the sine of 2 theta.\n3. Substitute v=72.6 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 521.3248, \"unit\": \"m\"}", "dedupe_signature": "f66ec15cbdb3d002b6c15096a55531db7e41d6dec92e0646e1a3be3b5eb5c0c4", "difficulty": "medium", "final_answer": {"answer": 521.3248, "unit": "m"}, "id": "projectile_range_004844_72.6_52", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 72.6 m/s and angle 52 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=52 degrees through the sine of 2 theta.\nSubstitute v=72.6 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 52, "gravity": 9.81, "speed": 72.6}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 3.48 * 8.314 * 516 / 8.7.\nFinal: {\"answer\": 1716.0096, \"unit\": \"kPa\"}", "dedupe_signature": "574e355eff1337e8027eee9d24a8f6f0d5d06a16ba01e71cb1ac24e35a24c9ce", "difficulty": "medium", "final_answer": {"answer": 1716.0096, "unit": "kPa"}, "id": "ideal_gas_004845_3.48_516_8.7", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=3.48 mol, T=516 K, and V=8.7 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 3.48 * 8.314 * 516 / 8.7.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 3.48, "temp_k": 516, "volume_l": 8.7}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 755 * 1.53 * 8.\nFinal: {\"answer\": 9241.2, \"unit\": \"J\"}", "dedupe_signature": "97ea7da43a4c5d66493c7ff1344758d8928b9577022038e104726f9879762dcc", "difficulty": "easy", "final_answer": {"answer": 9241.2, "unit": "J"}, "id": "heat_q_004846_755_1.53_8", "license": "Apache-2.0", "prompt": "A 755 g sample has specific heat 1.53 J/(g*K). How much heat is needed to raise its temperature by 8 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 755 * 1.53 * 8.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 8, "heat_capacity": 1.53, "mass_g": 755}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=14 V and R=128.5 ohm.\nFinal: {\"answer\": 1.5253, \"unit\": \"W\"}", "dedupe_signature": "541eb29d1c37842caf0ff08929be8f821e3963dd9c841824db7f914af4fb8632", "difficulty": "easy", "final_answer": {"answer": 1.5253, "unit": "W"}, "id": "ohm_power_004847_14_128.5", "license": "Apache-2.0", "prompt": "A resistor has resistance 128.5 ohm and voltage 14 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=14 V and R=128.5 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 128.5, "voltage": 14.0}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 6.78 mol * 180.156 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 1221.4577, \"unit\": \"g\"}", "dedupe_signature": "9de563fd0cd11693086f369f7757a50e13147a5896b0c6380d6dfd487fd550d4", "difficulty": "medium", "final_answer": {"answer": 1221.4577, "unit": "g"}, "id": "stoich_mass_004849_glucose_6.78", "license": "Apache-2.0", "prompt": "A sample contains 6.78 mol of glucose. Using molar mass 180.156 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 6.78 mol * 180.156 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "glucose", "molar_mass": 180.156, "moles": 6.78}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 3750 mL to 3.75 L.\n3. Compute M = 4.495 / 3.75.\nFinal: {\"answer\": 1.1987, \"unit\": \"mol/L\"}", "dedupe_signature": "13ba6154ef7b6f1bc0a575613b73f860bf49b66c92cc3dfd838e5df6af4d1e6c", "difficulty": "medium", "final_answer": {"answer": 1.1987, "unit": "mol/L"}, "id": "molarity_004850_4.495_3750", "license": "Apache-2.0", "prompt": "A solution contains 4.495 mol of solute in 3750 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 3750 mL to 3.75 L.\nCompute M = 4.495 / 3.75.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 4.495, "volume_ml": 3750}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.85 y, so each step multiplies y by 1 - h*0.85.\n3. Apply that update for 2 steps and round the final state.\nFinal: {\"answer\": 1.28, \"unit\": \"state_units\"}", "dedupe_signature": "042ddf7c543ab54115de2b644ece233dfae324fcc28f827208ed4e9a9e4b1e72", "difficulty": "medium", "final_answer": {"answer": 1.28, "unit": "state_units"}, "id": "euler_decay_004851_12.5_0.85_0.8_2", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.85 y with y(0)=12.5, step size h=0.8, for 2 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.85 y, so each step multiplies y by 1 - h*0.85.\nApply that update for 2 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 12.5, "rate": 0.85, "step": 0.8, "steps": 2}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.18 and add it to the current value.\nFinal: {\"answer\": [2.248, 0.66, -0.458], \"unit\": \"temperature_units\"}", "dedupe_signature": "1fea39aa8c9e101f60d20f5d942d2c0bbf59cc67694307a481f7db4767982968", "difficulty": "hard", "final_answer": {"answer": [2.248, 0.66, -0.458], "unit": "temperature_units"}, "id": "heat_step_004853_0.18_1.7_2.95_0.3_-0.35_-1.6", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.7, right=-1.6; current interior values are [2.95, 0.3, -0.35]. Use r=0.18. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.18 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [2.95, 0.3, -0.35], "left": 1.7, "r": 0.18, "right": -1.6}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kelvin equals Celsius plus 273.15.\n2. Apply the conversion factor directly to the given value.\n3. Compute 157.5 + 273.15.\nFinal: {\"answer\": 430.65, \"unit\": \"K\"}", "dedupe_signature": "5840f73b8a6db9baecbd6c051fa12e80ad033cc9e42fb1ed345253306cc8671b", "difficulty": "easy", "final_answer": {"answer": 430.65, "unit": "K"}, "id": "unit_convert_004854_c_to_k_157.5", "license": "Apache-2.0", "prompt": "Convert 157.5 degC to K. Return the converted value with unit.", "reasoning_trace": "Kelvin equals Celsius plus 273.15.\nApply the conversion factor directly to the given value.\nCompute 157.5 + 273.15.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 157.5}, "verifier": {"formula": "value + 273.15", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=229 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-244.71, -281.5067], \"unit\": \"N\"}", "dedupe_signature": "1ccce490e063b174ae1ddcc7b7c9b7cab4839c61598ea345f9bc3e2947fdee10", "difficulty": "medium", "final_answer": {"answer": [-244.71, -281.5067], "unit": "N"}, "id": "vector_components_004855_373_229", "license": "Apache-2.0", "prompt": "A vector has magnitude 373 N at 229 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=229 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 229, "magnitude": 373.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-1.25, 30.0], \"unit\": \"dimensionless\"}", "dedupe_signature": "775aad5b90e211dd3860b1020e1bc803e9f71117cd0998fe8c744e17f1b59560", "difficulty": "medium", "final_answer": {"answer": [-1.25, 30.0], "unit": "dimensionless"}, "id": "line_two_point_004856_-9.75_0.5_-1.25_30", "license": "Apache-2.0", "prompt": "A line passes through points (-9.75, 42.1875) and (0.5, 29.375). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -9.75, "x2": 0.5, "y1": 42.1875, "y2": 29.375}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. volt squared divided by ohm is watt\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "b95bbd7dc54a8855eeb5e902ee7ab830cca69804e5c8e3b9d8951ee26222fa36", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_004857_consistent_82e93f3d_508014", "license": "Apache-2.0", "prompt": "In quality-control check case 508014, check dimensional consistency for P = V^2 / R. The left side has dimensions W and the right side has dimensions W. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nvolt squared divided by ohm is watt\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "P = V^2 / R"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef threshold_flags_004858(values, threshold):\n    return [value >= threshold for value in values]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"threshold_flags_004858\"}", "dedupe_signature": "94ed20a96b7a5e6704f7e3fabe1196506a350d140aa42ef3f3faba3c0386abe5", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "threshold_flags_004858"}, "id": "code_004858_threshold_flags_004858", "license": "Apache-2.0", "prompt": "Write a Python function threshold_flags_004858(values, threshold) that returns a list of booleans showing whether each value is greater than or equal to threshold. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "threshold_flags_004858"}, "verifier": {"function": "threshold_flags_004858", "tests": ["assert threshold_flags_004858([1, 2, 3], 2) == [False, True, True]", "assert threshold_flags_004858([], 5) == []", "assert threshold_flags_004858([-1, 0], 0) == [False, True]"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 3.45 kg and a = 10.75 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 37.0875, \"unit\": \"N\"}", "dedupe_signature": "91d2fa78ff18ba49f30f001c02ff2cc4d93c2ca02442ae4eedde108274516baa", "difficulty": "easy", "final_answer": {"answer": 37.0875, "unit": "N"}, "id": "force_004860_3.45_10.75", "license": "Apache-2.0", "prompt": "A cart has mass 3.45 kg and measured acceleration 10.75 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 3.45 kg and a = 10.75 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 10.75, "mass": 3.45}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=10 degrees through the sine of 2 theta.\n3. Substitute v=42.9 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 64.1649, \"unit\": \"m\"}", "dedupe_signature": "65246cb3ac9df13fecf1fbc7964fb26e8865d39dc51b04f58321dcd8bda06aba", "difficulty": "medium", "final_answer": {"answer": 64.1649, "unit": "m"}, "id": "projectile_range_004862_42.9_10", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 42.9 m/s and angle 10 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=10 degrees through the sine of 2 theta.\nSubstitute v=42.9 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 10, "gravity": 9.81, "speed": 42.9}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 885 * 2.465 * 55.\nFinal: {\"answer\": 119983.875, \"unit\": \"J\"}", "dedupe_signature": "5b6da49d3ee063e2b2de24729923cee89fb98596c8aad6210fa992bd8c5eff2e", "difficulty": "easy", "final_answer": {"answer": 119983.875, "unit": "J"}, "id": "heat_q_004864_885_2.465_55", "license": "Apache-2.0", "prompt": "A 885 g sample has specific heat 2.465 J/(g*K). How much heat is needed to raise its temperature by 55 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 885 * 2.465 * 55.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 55, "heat_capacity": 2.465, "mass_g": 885}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=25.5 V and R=189.3 ohm.\nFinal: {\"answer\": 3.435, \"unit\": \"W\"}", "dedupe_signature": "812f8dde5998ef4db86006f4e57e2ffc1c4a5b408ead2cdbaa71146867c35e81", "difficulty": "easy", "final_answer": {"answer": 3.435, "unit": "W"}, "id": "ohm_power_004865_25.5_189.3", "license": "Apache-2.0", "prompt": "A resistor has resistance 189.3 ohm and voltage 25.5 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=25.5 V and R=189.3 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 189.3, "voltage": 25.5}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=229 mg, t=137 h, and T_half=67 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 55.5005, \"unit\": \"mg\"}", "dedupe_signature": "67e789c536ae0169fe6dd3eb8d068971769bdfe3adf2fe95afdad6eff3e15bbd", "difficulty": "medium", "final_answer": {"answer": 55.5005, "unit": "mg"}, "id": "half_life_004866_229_67_137", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 229 mg. Its half-life is 67 hours. How many mg remain after 137 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=229 mg, t=137 h, and T_half=67 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 137.0, "half_life": 67.0, "initial_amount": 229.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 1.46 mol * 44.01 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 64.2546, \"unit\": \"g\"}", "dedupe_signature": "3782583e2721eeb6727ab90868a616861483d28a56cb2d9fb7e15d2d527d3a5b", "difficulty": "medium", "final_answer": {"answer": 64.2546, "unit": "g"}, "id": "stoich_mass_004867_carbon_dioxide_1.46", "license": "Apache-2.0", "prompt": "A sample contains 1.46 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 1.46 mol * 44.01 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "carbon dioxide", "molar_mass": 44.01, "moles": 1.46}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 3955 mL to 3.955 L.\n3. Compute M = 3.355 / 3.955.\nFinal: {\"answer\": 0.8483, \"unit\": \"mol/L\"}", "dedupe_signature": "0d024990357f5339ac79f12328d88d10d0610e1405c09fe5d6e5cdf1c88f6de9", "difficulty": "medium", "final_answer": {"answer": 0.8483, "unit": "mol/L"}, "id": "molarity_004868_3.355_3955", "license": "Apache-2.0", "prompt": "A solution contains 3.355 mol of solute in 3955 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 3955 mL to 3.955 L.\nCompute M = 3.355 / 3.955.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 3.355, "volume_ml": 3955}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.64 y, so each step multiplies y by 1 - h*0.64.\n3. Apply that update for 9 steps and round the final state.\nFinal: {\"answer\": 0.0, \"unit\": \"state_units\"}", "dedupe_signature": "a51a3558d45175c5704c7e43e81b004fe7fe8a248047ca6844f702bef5724ce0", "difficulty": "medium", "final_answer": {"answer": 0.0, "unit": "state_units"}, "id": "euler_decay_004869_1_0.64_1.65_9", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.64 y with y(0)=1, step size h=1.65, for 9 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.64 y, so each step multiplies y by 1 - h*0.64.\nApply that update for 9 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 1.0, "rate": 0.64, "step": 1.65, "steps": 9}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-3.1)=1.91 and f(-0.3)=-12.37.\n3. The interval width is 2.8.\nFinal: {\"answer\": -14.644, \"unit\": \"area_units\"}", "dedupe_signature": "0673e9e3b6e056a1ed2aa56a4d93fa3fdf6ed5b5077219caf001474742695b91", "difficulty": "medium", "final_answer": {"answer": -14.644, "unit": "area_units"}, "id": "trapz_linear_004870_-5.1_-13.9_-3.1_-0.3", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-5.1x+-13.9 from x=-3.1 to x=-0.3. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-3.1)=1.91 and f(-0.3)=-12.37.\nThe interval width is 2.8.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -13.9, "slope": -5.1, "x0": -3.1, "x1": -0.30000000000000027}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.44 and add it to the current value.\nFinal: {\"answer\": [0.434, 2.216, -0.606], \"unit\": \"temperature_units\"}", "dedupe_signature": "e416bbe40bc81e3cf03bf51eff98d3f2c85184dbafadf7623284fdce4ee88073", "difficulty": "hard", "final_answer": {"answer": [0.434, 2.216, -0.606], "unit": "temperature_units"}, "id": "heat_step_004871_0.44_1.4_2.7_-1.15_2.65_-0.95", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.4, right=-0.95; current interior values are [2.7, -1.15, 2.65]. Use r=0.44. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.44 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [2.7, -1.15, 2.65], "left": 1.4, "r": 0.44, "right": -0.95}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kelvin equals Celsius plus 273.15.\n2. Apply the conversion factor directly to the given value.\n3. Compute -68.0 + 273.15.\nFinal: {\"answer\": 205.15, \"unit\": \"K\"}", "dedupe_signature": "556f087e08397b03de5a47c06be10b88bd60499f81c4fc02416639b52ea0886e", "difficulty": "easy", "final_answer": {"answer": 205.15, "unit": "K"}, "id": "unit_convert_004872_c_to_k_-68", "license": "Apache-2.0", "prompt": "Convert -68 degC to K. Return the converted value with unit.", "reasoning_trace": "Kelvin equals Celsius plus 273.15.\nApply the conversion factor directly to the given value.\nCompute -68.0 + 273.15.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": -68.0}, "verifier": {"formula": "value + 273.15", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=157 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-430.7963, 182.8622], \"unit\": \"N\"}", "dedupe_signature": "c8a7e6a66ba5ad33013ceff7dd6d226dfb6d9a560af2fbd7e3380e86f4d5b7f8", "difficulty": "medium", "final_answer": {"answer": [-430.7963, 182.8622], "unit": "N"}, "id": "vector_components_004873_468_157", "license": "Apache-2.0", "prompt": "A vector has magnitude 468 N at 157 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=157 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 157, "magnitude": 468.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-0.05, -29.5], \"unit\": \"dimensionless\"}", "dedupe_signature": "548336b73cd8852d42b32611c3ae02d427862ce50bd2c9aadf48c83da240600d", "difficulty": "medium", "final_answer": {"answer": [-0.05, -29.5], "unit": "dimensionless"}, "id": "line_two_point_004874_-1_3.5_-0.05_-29.5", "license": "Apache-2.0", "prompt": "A line passes through points (-1, -29.45) and (3.5, -29.675). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -1.0, "x2": 3.5, "y1": -29.45, "y2": -29.675}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. speed squared over acceleration has units of meters\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "7fd58c7dbecb18d79af6dec9acfb1242046685d634fdf9594ec773689efdc66e", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_004875_consistent_741d4e34_728805", "license": "Apache-2.0", "prompt": "In field worksheet case 728805, check dimensional consistency for R = v^2 * sin(theta) / g. The left side has dimensions m and the right side has dimensions m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nspeed squared over acceleration has units of meters\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "R = v^2 * sin(theta) / g"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef center_values_004876(values):\n    if not values:\n        raise ValueError('center_values requires at least one value')\n    mean = sum(values) / len(values)\n    return [value - mean for value in values]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"center_values_004876\"}", "dedupe_signature": "d50255d9d4b8116def7225bbc095942477a3e2898875f1dbc5f0a3911f7bb992", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "center_values_004876"}, "id": "code_004876_center_values_004876", "license": "Apache-2.0", "prompt": "Write a Python function center_values_004876(values) that subtracts the arithmetic mean from each value and returns a new list. Raise ValueError for an empty input. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "center_values_004876"}, "verifier": {"function": "center_values_004876", "tests": ["out = center_values_004876([1, 2, 3]); assert out == [-1, 0, 1]", "assert center_values_004876([5]) == [0]", "try:\n    center_values_004876([])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: launch_angle_or_vertical_velocity.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"launch_angle_or_vertical_velocity\"]}", "dedupe_signature": "db08c2399007d5d66702a95c1bdb7d9907d4c668ae4a920eca0a91e160278ec8", "difficulty": "easy", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["launch_angle_or_vertical_velocity"]}, "id": "abstain_004877_launch_angle_or_vertical_velocity", "license": "Apache-2.0", "prompt": "Compute projectile range on level ground. The prompt gives initial speed 30 m/s but does not give launch angle or vertical velocity. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: launch_angle_or_vertical_velocity.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["launch_angle_or_vertical_velocity"]}, "verifier": {"missing": ["launch_angle_or_vertical_velocity"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 23.3 kg and a = 7.2 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 167.76, \"unit\": \"N\"}", "dedupe_signature": "e742d47b31fd1efcb6da790844e3ead63a4447292d2df6d9db339a8477c78de7", "difficulty": "easy", "final_answer": {"answer": 167.76, "unit": "N"}, "id": "force_004878_23.3_7.2", "license": "Apache-2.0", "prompt": "A cart has mass 23.3 kg and measured acceleration 7.2 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 23.3 kg and a = 7.2 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 7.2, "mass": 23.3}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 45^2 and multiply by 0.5 * 22.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 22275.0, \"unit\": \"J\"}", "dedupe_signature": "c7bb8b99b4902bbf1cf06f9f2b67241697494763253e8ee57862ef89bc1710db", "difficulty": "easy", "final_answer": {"answer": 22275.0, "unit": "J"}, "id": "ke_004879_22_45", "license": "Apache-2.0", "prompt": "A body of mass 22 kg moves at 45 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 45^2 and multiply by 0.5 * 22.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 22.0, "velocity": 45.0}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=78 degrees through the sine of 2 theta.\n3. Substitute v=57.6 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 137.5591, \"unit\": \"m\"}", "dedupe_signature": "e805d977fe20f791ade0153eeb0b7c806cd3876f344dc68bee8e78dd7238ae8d", "difficulty": "medium", "final_answer": {"answer": 137.5591, "unit": "m"}, "id": "projectile_range_004880_57.6_78", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 57.6 m/s and angle 78 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=78 degrees through the sine of 2 theta.\nSubstitute v=57.6 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 78, "gravity": 9.81, "speed": 57.6}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 2.9 * 8.314 * 434 / 113.1.\nFinal: {\"answer\": 92.5199, \"unit\": \"kPa\"}", "dedupe_signature": "2aa7567dfa3f003c57547ff2556326cc8626ab5ade861c01f27f573425a4c85c", "difficulty": "medium", "final_answer": {"answer": 92.5199, "unit": "kPa"}, "id": "ideal_gas_004881_2.9_434_113.1", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=2.9 mol, T=434 K, and V=113.1 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 2.9 * 8.314 * 434 / 113.1.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 2.9, "temp_k": 434, "volume_l": 113.1}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=79.2 V and R=22.9 ohm.\nFinal: {\"answer\": 273.9144, \"unit\": \"W\"}", "dedupe_signature": "6fba87d0b68e9ea153a5f8541a1e9f3f5502b0ae1c6928865528c4b67dc9b72e", "difficulty": "easy", "final_answer": {"answer": 273.9144, "unit": "W"}, "id": "ohm_power_004883_79.2_22.9", "license": "Apache-2.0", "prompt": "A resistor has resistance 22.9 ohm and voltage 79.2 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=79.2 V and R=22.9 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 22.9, "voltage": 79.2}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=511.5 mg, t=56.5 h, and T_half=35.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 169.7233, \"unit\": \"mg\"}", "dedupe_signature": "f98b63af0e4aa77088b09ee359abff499881d41e98e2140ef5af886b9d18ec50", "difficulty": "medium", "final_answer": {"answer": 169.7233, "unit": "mg"}, "id": "half_life_004884_511.5_35.5_56.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 511.5 mg. Its half-life is 35.5 hours. How many mg remain after 56.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=511.5 mg, t=56.5 h, and T_half=35.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 56.5, "half_life": 35.5, "initial_amount": 511.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 2.58 mol * 100.087 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 258.2245, \"unit\": \"g\"}", "dedupe_signature": "f61f5c8943ff6de8feb8d81ddf7932ad4488cbd7e28c62be7752d158cdf2525c", "difficulty": "medium", "final_answer": {"answer": 258.2245, "unit": "g"}, "id": "stoich_mass_004885_calcium_carbonate_2.58", "license": "Apache-2.0", "prompt": "A sample contains 2.58 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 2.58 mol * 100.087 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "calcium carbonate", "molar_mass": 100.087, "moles": 2.58}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 2265 mL to 2.265 L.\n3. Compute M = 4.31 / 2.265.\nFinal: {\"answer\": 1.9029, \"unit\": \"mol/L\"}", "dedupe_signature": "bd2d8dbe7445ec0d4253a87536ddaf43f9d926149c5086ffee3b87db89fb974e", "difficulty": "medium", "final_answer": {"answer": 1.9029, "unit": "mol/L"}, "id": "molarity_004886_4.31_2265", "license": "Apache-2.0", "prompt": "A solution contains 4.31 mol of solute in 2265 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 2265 mL to 2.265 L.\nCompute M = 4.31 / 2.265.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 4.31, "volume_ml": 2265}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.41 y, so each step multiplies y by 1 - h*0.41.\n3. Apply that update for 6 steps and round the final state.\nFinal: {\"answer\": 0.5887, \"unit\": \"state_units\"}", "dedupe_signature": "0a2eb3ad05e58ddf5f3f760564e78ae028eec14752413042254d95c3aeaf6b3e", "difficulty": "medium", "final_answer": {"answer": 0.5887, "unit": "state_units"}, "id": "euler_decay_004887_21.5_0.41_1.1_6", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.41 y with y(0)=21.5, step size h=1.1, for 6 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.41 y, so each step multiplies y by 1 - h*0.41.\nApply that update for 6 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 21.5, "rate": 0.41, "step": 1.1, "steps": 6}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-1.9)=12.03 and f(1.7)=-15.69.\n3. The interval width is 3.6.\nFinal: {\"answer\": -6.588, \"unit\": \"area_units\"}", "dedupe_signature": "667f68765854847603975574c37209da9e9e15acc7bed7cca81bcde7152a6b18", "difficulty": "medium", "final_answer": {"answer": -6.588, "unit": "area_units"}, "id": "trapz_linear_004888_-7.7_-2.6_-1.9_1.7", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-7.7x+-2.6 from x=-1.9 to x=1.7. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-1.9)=12.03 and f(1.7)=-15.69.\nThe interval width is 3.6.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -2.6, "slope": -7.7, "x0": -1.9, "x1": 1.7000000000000002}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.4 and add it to the current value.\nFinal: {\"answer\": [-1.01, -0.6, -0.13], \"unit\": \"temperature_units\"}", "dedupe_signature": "2066e91f4a1c02c016a3b48767faa14a765820a15059eb4e6e7f9d83d694f8f3", "difficulty": "hard", "final_answer": {"answer": [-1.01, -0.6, -0.13], "unit": "temperature_units"}, "id": "heat_step_004889_0.4_-1.85_-1.35_0.0_-0.15_-0.25", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-1.85, right=-0.25; current interior values are [-1.35, 0.0, -0.15]. Use r=0.4. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.4 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-1.35, 0.0, -0.15], "left": -1.85, "r": 0.4, "right": -0.25}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=149 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-9.0003, 5.4079], \"unit\": \"N\"}", "dedupe_signature": "b4f8363a2f0d8031c2ec01fbe5991bbdaf72cfcb002b517e71f918bd789769cd", "difficulty": "medium", "final_answer": {"answer": [-9.0003, 5.4079], "unit": "N"}, "id": "vector_components_004891_10.5_149", "license": "Apache-2.0", "prompt": "A vector has magnitude 10.5 N at 149 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=149 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 149, "magnitude": 10.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-6.85, -24.5], \"unit\": \"dimensionless\"}", "dedupe_signature": "0a6f33b63d31d8de62e798ca0db636ad8d814bd2fbe8a16b4449b66f69987d7f", "difficulty": "medium", "final_answer": {"answer": [-6.85, -24.5], "unit": "dimensionless"}, "id": "line_two_point_004892_5.5_19_-6.85_-24.5", "license": "Apache-2.0", "prompt": "A line passes through points (5.5, -62.175) and (19, -154.65). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 5.5, "x2": 19.0, "y1": -62.175, "y2": -154.65}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. m*v is momentum, not energy\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "b556c7fbe1d5eed9b059062018746f18c0ff74af1ef8670b753b4f4280d6842c", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_004893_inconsistent_1e14b074_45398", "license": "Apache-2.0", "prompt": "In instrument manual case 45398, check dimensional consistency for E = m * v. The left side has dimensions kg*m^2/s^2 and the right side has dimensions kg*m/s. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nm*v is momentum, not energy\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "E = m * v"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 16.1 kg and a = 13.55 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 218.155, \"unit\": \"N\"}", "dedupe_signature": "44a2fd8cfc7f34d4a723166c7849fe05564853eb452db40b708f085196b7089c", "difficulty": "easy", "final_answer": {"answer": 218.155, "unit": "N"}, "id": "force_004896_16.1_13.55", "license": "Apache-2.0", "prompt": "A cart has mass 16.1 kg and measured acceleration 13.55 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 16.1 kg and a = 13.55 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 13.55, "mass": 16.1}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 32.35^2 and multiply by 0.5 * 27.05.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 14154.2168, \"unit\": \"J\"}", "dedupe_signature": "21f55ed66d30d7987740306c694bddb3fcaf2cc45ba160dbdaf4355831d43900", "difficulty": "easy", "final_answer": {"answer": 14154.2168, "unit": "J"}, "id": "ke_004897_27.05_32.35", "license": "Apache-2.0", "prompt": "A body of mass 27.05 kg moves at 32.35 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 32.35^2 and multiply by 0.5 * 27.05.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 27.05, "velocity": 32.35}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=50 degrees through the sine of 2 theta.\n3. Substitute v=31 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 96.473, \"unit\": \"m\"}", "dedupe_signature": "67d28917d061927bf6ea1a64d6f31b7ca67e6dcd657d17882d08ac45df08d2b0", "difficulty": "medium", "final_answer": {"answer": 96.473, "unit": "m"}, "id": "projectile_range_004898_31_50", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 31 m/s and angle 50 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=50 degrees through the sine of 2 theta.\nSubstitute v=31 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 50, "gravity": 9.81, "speed": 31.0}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 3.02 * 8.314 * 530 / 65.8.\nFinal: {\"answer\": 202.2399, \"unit\": \"kPa\"}", "dedupe_signature": "cb4da2a4093384dde1d4fa2d8860144211aaef4a1df0a8ffa234247bc81ef256", "difficulty": "medium", "final_answer": {"answer": 202.2399, "unit": "kPa"}, "id": "ideal_gas_004899_3.02_530_65.8", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=3.02 mol, T=530 K, and V=65.8 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 3.02 * 8.314 * 530 / 65.8.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 3.02, "temp_k": 530, "volume_l": 65.8}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 890 * 3.125 * 16.\nFinal: {\"answer\": 44500.0, \"unit\": \"J\"}", "dedupe_signature": "9e836295bbcc84805d9ef58e6e1311db97c1f43d0dcd47fb9bea88c8da6bd6c1", "difficulty": "easy", "final_answer": {"answer": 44500.0, "unit": "J"}, "id": "heat_q_004900_890_3.125_16", "license": "Apache-2.0", "prompt": "A 890 g sample has specific heat 3.125 J/(g*K). How much heat is needed to raise its temperature by 16 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 890 * 3.125 * 16.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 16, "heat_capacity": 3.125, "mass_g": 890}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=141.2 V and R=57.5 ohm.\nFinal: {\"answer\": 346.7381, \"unit\": \"W\"}", "dedupe_signature": "10cb5ba1492e5a866363d6f115d3a8e709c2588dd12383bd6c2d35cffb99370b", "difficulty": "easy", "final_answer": {"answer": 346.7381, "unit": "W"}, "id": "ohm_power_004901_141.2_57.5", "license": "Apache-2.0", "prompt": "A resistor has resistance 57.5 ohm and voltage 141.2 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=141.2 V and R=57.5 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 57.5, "voltage": 141.2}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=433.5 mg, t=3 h, and T_half=92.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 423.8634, \"unit\": \"mg\"}", "dedupe_signature": "10175ae25c5fb73e8e367c39fec10e8cf7badfad6bbd80e5d38bbdb8c302ba4c", "difficulty": "medium", "final_answer": {"answer": 423.8634, "unit": "mg"}, "id": "half_life_004902_433.5_92.5_3", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 433.5 mg. Its half-life is 92.5 hours. How many mg remain after 3 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=433.5 mg, t=3 h, and T_half=92.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 3.0, "half_life": 92.5, "initial_amount": 433.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 6.51 mol * 44.01 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 286.5051, \"unit\": \"g\"}", "dedupe_signature": "e50ae1b0cdeae9c16b15df8c648fed2c5fa44211c3c0cafb367fdba774aa68e8", "difficulty": "medium", "final_answer": {"answer": 286.5051, "unit": "g"}, "id": "stoich_mass_004903_carbon_dioxide_6.51", "license": "Apache-2.0", "prompt": "A sample contains 6.51 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 6.51 mol * 44.01 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "carbon dioxide", "molar_mass": 44.01, "moles": 6.51}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.17 y, so each step multiplies y by 1 - h*0.17.\n3. Apply that update for 6 steps and round the final state.\nFinal: {\"answer\": 8.2298, \"unit\": \"state_units\"}", "dedupe_signature": "299f86b8308df0aefefa93f80d9ec90a5ca9fe7d37e7edc5018706cd4df92a36", "difficulty": "medium", "final_answer": {"answer": 8.2298, "unit": "state_units"}, "id": "euler_decay_004905_28.5_0.17_1.1_6", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.17 y with y(0)=28.5, step size h=1.1, for 6 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.17 y, so each step multiplies y by 1 - h*0.17.\nApply that update for 6 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 28.5, "rate": 0.17, "step": 1.1, "steps": 6}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(7.3)=28.39 and f(15.7)=81.31.\n3. The interval width is 8.4.\nFinal: {\"answer\": 460.74, \"unit\": \"area_units\"}", "dedupe_signature": "4c56b92707762ff56a5d7c09d502e084db48aa2cac9e55eddb1c52b9d6888f17", "difficulty": "medium", "final_answer": {"answer": 460.74, "unit": "area_units"}, "id": "trapz_linear_004906_6.3_-17.6_7.3_15.7", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=6.3x+-17.6 from x=7.3 to x=15.7. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(7.3)=28.39 and f(15.7)=81.31.\nThe interval width is 8.4.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -17.6, "slope": 6.3, "x0": 7.3, "x1": 15.7}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.04 and add it to the current value.\nFinal: {\"answer\": [-0.734, 0.566, 2.164], \"unit\": \"temperature_units\"}", "dedupe_signature": "ce10db8b4f1b341ba24f50f19e9a042895e371535306296b94e1a88448f96b35", "difficulty": "hard", "final_answer": {"answer": [-0.734, 0.566, 2.164], "unit": "temperature_units"}, "id": "heat_step_004907_0.04_-1.65_-0.75_0.55_2.25_1.8", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-1.65, right=1.8; current interior values are [-0.75, 0.55, 2.25]. Use r=0.04. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.04 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-0.75, 0.55, 2.25], "left": -1.65, "r": 0.04, "right": 1.8}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 19360.0 / 1000.\nFinal: {\"answer\": 19.36, \"unit\": \"kg\"}", "dedupe_signature": "be8e56795a7d1b098cfa45a79bb3ede87a354c29c9f66d9ce1ab6e144e3fc516", "difficulty": "easy", "final_answer": {"answer": 19.36, "unit": "kg"}, "id": "unit_convert_004908_g_to_kg_19360", "license": "Apache-2.0", "prompt": "Convert 19360 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 19360.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 19360.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=210 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-153.7195, -88.75], \"unit\": \"N\"}", "dedupe_signature": "d6c04c74b15d713f25d3d978dd104e13eba903f703fe9728b2ec99a7ce492b5a", "difficulty": "medium", "final_answer": {"answer": [-153.7195, -88.75], "unit": "N"}, "id": "vector_components_004909_177.5_210", "license": "Apache-2.0", "prompt": "A vector has magnitude 177.5 N at 210 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=210 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 210, "magnitude": 177.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [2.1, 28.75], \"unit\": \"dimensionless\"}", "dedupe_signature": "65d761a992cbf008a7e4d83151de89e87e0a9dd0752419bc87114a46cfdca382", "difficulty": "medium", "final_answer": {"answer": [2.1, 28.75], "unit": "dimensionless"}, "id": "line_two_point_004910_19.75_28_2.1_28.75", "license": "Apache-2.0", "prompt": "A line passes through points (19.75, 70.225) and (28, 87.55). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 19.75, "x2": 28.0, "y1": 70.225, "y2": 87.55000000000001}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. velocity times time gives distance, not acceleration\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "3d55e8b98b75857b27a1c90410a6401f16d5d7078d709a54020459cf402fd9e1", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_004911_inconsistent_7481c798_96329", "license": "Apache-2.0", "prompt": "In sensor calibration case 96329, check dimensional consistency for a = v * t. The left side has dimensions m/s^2 and the right side has dimensions m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nvelocity times time gives distance, not acceleration\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "a = v * t"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef threshold_flags_004912(values, threshold):\n    return [value >= threshold for value in values]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"threshold_flags_004912\"}", "dedupe_signature": "bb54211b274047ce133ece28645e487d95f1fad5ecd010f3eb6403d6f09649b8", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "threshold_flags_004912"}, "id": "code_004912_threshold_flags_004912", "license": "Apache-2.0", "prompt": "Write a Python function threshold_flags_004912(values, threshold) that returns a list of booleans showing whether each value is greater than or equal to threshold. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "threshold_flags_004912"}, "verifier": {"function": "threshold_flags_004912", "tests": ["assert threshold_flags_004912([1, 2, 3], 2) == [False, True, True]", "assert threshold_flags_004912([], 5) == []", "assert threshold_flags_004912([-1, 0], 0) == [False, True]"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: launch_angle_or_vertical_velocity.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"launch_angle_or_vertical_velocity\"]}", "dedupe_signature": "027101ffdc4b86a0ec0e04754ff71d5281a7cbad974dfb132edf98d2758ee610", "difficulty": "easy", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["launch_angle_or_vertical_velocity"]}, "id": "abstain_004913_launch_angle_or_vertical_velocity", "license": "Apache-2.0", "prompt": "Compute projectile range on level ground. The prompt gives initial speed 42.5 m/s but does not give launch angle or vertical velocity. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: launch_angle_or_vertical_velocity.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["launch_angle_or_vertical_velocity"]}, "verifier": {"missing": ["launch_angle_or_vertical_velocity"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 5.6 kg and a = 14.3 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 80.08, \"unit\": \"N\"}", "dedupe_signature": "0cde2380f16242f1ab25bd9351ea345d7ebba767a9d20c4a15c5362af0dd324d", "difficulty": "easy", "final_answer": {"answer": 80.08, "unit": "N"}, "id": "force_004914_5.6_14.3", "license": "Apache-2.0", "prompt": "A cart has mass 5.6 kg and measured acceleration 14.3 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 5.6 kg and a = 14.3 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 14.3, "mass": 5.6}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 23.25^2 and multiply by 0.5 * 16.2.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 4378.5562, \"unit\": \"J\"}", "dedupe_signature": "7669082036f21ab9c47f7d9afbf5e50464b462a1077161f16cf777408c88f647", "difficulty": "easy", "final_answer": {"answer": 4378.5562, "unit": "J"}, "id": "ke_004915_16.2_23.25", "license": "Apache-2.0", "prompt": "A body of mass 16.2 kg moves at 23.25 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 23.25^2 and multiply by 0.5 * 16.2.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 16.2, "velocity": 23.25}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 3.2 * 8.314 * 268 / 22.1.\nFinal: {\"answer\": 322.6283, \"unit\": \"kPa\"}", "dedupe_signature": "19bac945ba732027287bb7114d073eb6b295418adbba317cda321e2aa7efb788", "difficulty": "medium", "final_answer": {"answer": 322.6283, "unit": "kPa"}, "id": "ideal_gas_004917_3.2_268_22.1", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=3.2 mol, T=268 K, and V=22.1 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 3.2 * 8.314 * 268 / 22.1.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 3.2, "temp_k": 268, "volume_l": 22.1}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 405 * 4.28 * 73.\nFinal: {\"answer\": 126538.2, \"unit\": \"J\"}", "dedupe_signature": "c9c574a4929ac5c33f4974eebe7bcdb00f7ba6e353505979732b2c3f3312be70", "difficulty": "easy", "final_answer": {"answer": 126538.2, "unit": "J"}, "id": "heat_q_004918_405_4.28_73", "license": "Apache-2.0", "prompt": "A 405 g sample has specific heat 4.28 J/(g*K). How much heat is needed to raise its temperature by 73 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 405 * 4.28 * 73.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 73, "heat_capacity": 4.28, "mass_g": 405}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=237.6 V and R=135.2 ohm.\nFinal: {\"answer\": 417.5574, \"unit\": \"W\"}", "dedupe_signature": "59d0994694a9344422a5ba1cf74d4d291eea256597af620b7155ba29fcb2bc7f", "difficulty": "easy", "final_answer": {"answer": 417.5574, "unit": "W"}, "id": "ohm_power_004919_237.6_135.2", "license": "Apache-2.0", "prompt": "A resistor has resistance 135.2 ohm and voltage 237.6 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=237.6 V and R=135.2 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 135.2, "voltage": 237.6}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=73.5 mg, t=293 h, and T_half=46 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 0.8889, \"unit\": \"mg\"}", "dedupe_signature": "24c1d286e4c6a514f01be01f58fbe9d67b474c3d3c292dfa7f8e96c5b05d760f", "difficulty": "medium", "final_answer": {"answer": 0.8889, "unit": "mg"}, "id": "half_life_004920_73.5_46_293", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 73.5 mg. Its half-life is 46 hours. How many mg remain after 293 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=73.5 mg, t=293 h, and T_half=46 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 293.0, "half_life": 46.0, "initial_amount": 73.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 0.34 mol * 18.015 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 6.1251, \"unit\": \"g\"}", "dedupe_signature": "96ef24b50417651f9e49a3202689138509f333b87f10221cdc8bc96bd782fc6c", "difficulty": "medium", "final_answer": {"answer": 6.1251, "unit": "g"}, "id": "stoich_mass_004921_water_0.34", "license": "Apache-2.0", "prompt": "A sample contains 0.34 mol of water. Using molar mass 18.015 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 0.34 mol * 18.015 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "water", "molar_mass": 18.015, "moles": 0.34}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 2960 mL to 2.96 L.\n3. Compute M = 1.85 / 2.96.\nFinal: {\"answer\": 0.625, \"unit\": \"mol/L\"}", "dedupe_signature": "5b5076f5d69abbf1ba3b15ebb22b7189fe1da3d4cbdac4aab4a0f6edf332f5e8", "difficulty": "medium", "final_answer": {"answer": 0.625, "unit": "mol/L"}, "id": "molarity_004922_1.85_2960", "license": "Apache-2.0", "prompt": "A solution contains 1.85 mol of solute in 2960 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 2960 mL to 2.96 L.\nCompute M = 1.85 / 2.96.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 1.85, "volume_ml": 2960}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(7.5)=-8.5 and f(14.4)=-5.74.\n3. The interval width is 6.9.\nFinal: {\"answer\": -49.128, \"unit\": \"area_units\"}", "dedupe_signature": "e81e4a2c23d8d2f8b2ecc68176b393929ce0c8d738e710178c99531dcacffff0", "difficulty": "medium", "final_answer": {"answer": -49.128, "unit": "area_units"}, "id": "trapz_linear_004924_0.4_-11.5_7.5_14.4", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=0.4x+-11.5 from x=7.5 to x=14.4. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(7.5)=-8.5 and f(14.4)=-5.74.\nThe interval width is 6.9.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -11.5, "slope": 0.4, "x0": 7.5, "x1": 14.4}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.1 and add it to the current value.\nFinal: {\"answer\": [0.785, 0.755, 1.32], \"unit\": \"temperature_units\"}", "dedupe_signature": "9cb6b73881295c1dec9db6545d4442e7e8fdb3fdd3c4db5fdab55d2eacf92bba", "difficulty": "hard", "final_answer": {"answer": [0.785, 0.755, 1.32], "unit": "temperature_units"}, "id": "heat_step_004925_0.1_1.55_0.7_0.7_1.25_2.5", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.55, right=2.5; current interior values are [0.7, 0.7, 1.25]. Use r=0.1. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.1 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [0.7, 0.7, 1.25], "left": 1.55, "r": 0.1, "right": 2.5}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kelvin equals Celsius plus 273.15.\n2. Apply the conversion factor directly to the given value.\n3. Compute 192.0 + 273.15.\nFinal: {\"answer\": 465.15, \"unit\": \"K\"}", "dedupe_signature": "229df9594daf7cdc11318dae1306278974580dab55a732fbd4a902ab85f1e7cb", "difficulty": "easy", "final_answer": {"answer": 465.15, "unit": "K"}, "id": "unit_convert_004926_c_to_k_192", "license": "Apache-2.0", "prompt": "Convert 192 degC to K. Return the converted value with unit.", "reasoning_trace": "Kelvin equals Celsius plus 273.15.\nApply the conversion factor directly to the given value.\nCompute 192.0 + 273.15.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 192.0}, "verifier": {"formula": "value + 273.15", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=182 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-268.3364, -9.3705], \"unit\": \"N\"}", "dedupe_signature": "684f1fd1e081d3a8597a1ae3f23489c9d1d4e8c5a5e30a6a0ce833a33bedede8", "difficulty": "medium", "final_answer": {"answer": [-268.3364, -9.3705], "unit": "N"}, "id": "vector_components_004927_268.5_182", "license": "Apache-2.0", "prompt": "A vector has magnitude 268.5 N at 182 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=182 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 182, "magnitude": 268.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [3.75, -18.5], \"unit\": \"dimensionless\"}", "dedupe_signature": "104d0347a3511064618b991a0773b195732f0f03bb360a29ca70c638ee7275d0", "difficulty": "medium", "final_answer": {"answer": [3.75, -18.5], "unit": "dimensionless"}, "id": "line_two_point_004928_-5_7.75_3.75_-18.5", "license": "Apache-2.0", "prompt": "A line passes through points (-5, -37.25) and (7.75, 10.5625). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -5.0, "x2": 7.75, "y1": -37.25, "y2": 10.5625}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. velocity times time gives distance, not acceleration\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "ef11894842cf26c77862f70ea9866c27f00afbe180979c764bf179114506a7c3", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_004929_inconsistent_7481c798_733265", "license": "Apache-2.0", "prompt": "In instrument manual case 733265, check dimensional consistency for a = v * t. The left side has dimensions m/s^2 and the right side has dimensions m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nvelocity times time gives distance, not acceleration\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "a = v * t"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: left_boundary, right_boundary.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"left_boundary\", \"right_boundary\"]}", "dedupe_signature": "223684e47224c06940185d06dfaa44650c6f747639f458485ac257ab52f2d755", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["left_boundary", "right_boundary"]}, "id": "abstain_004931_left_boundary_right_boundary", "license": "Apache-2.0", "prompt": "Solve the 1D heat equation after one finite-difference step. The prompt gives r=0.22 and interior values [-1.85, -1.3, -0.25], but gives no boundary values. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: left_boundary, right_boundary.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["left_boundary", "right_boundary"]}, "verifier": {"missing": ["left_boundary", "right_boundary"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 3.9 kg and a = 2.25 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 8.775, \"unit\": \"N\"}", "dedupe_signature": "72f390cdab38cb5abdc3be406d7b637d018efb908a50e09d4e8886ae29916412", "difficulty": "easy", "final_answer": {"answer": 8.775, "unit": "N"}, "id": "force_004932_3.9_2.25", "license": "Apache-2.0", "prompt": "A cart has mass 3.9 kg and measured acceleration 2.25 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 3.9 kg and a = 2.25 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 2.25, "mass": 3.9}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 15.7^2 and multiply by 0.5 * 4.7.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 579.2515, \"unit\": \"J\"}", "dedupe_signature": "b58cce1cc323e79a90ae0e08974f8b86c87510ccea043f0cedbb9cfdd3253de3", "difficulty": "easy", "final_answer": {"answer": 579.2515, "unit": "J"}, "id": "ke_004933_4.7_15.7", "license": "Apache-2.0", "prompt": "A body of mass 4.7 kg moves at 15.7 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 15.7^2 and multiply by 0.5 * 4.7.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 4.7, "velocity": 15.7}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=16 degrees through the sine of 2 theta.\n3. Substitute v=66 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 235.3036, \"unit\": \"m\"}", "dedupe_signature": "df0f6c1b9a8dc28d1ef0f6c78c97f66fd53e58c02a303d94fca1ae35effe48f0", "difficulty": "medium", "final_answer": {"answer": 235.3036, "unit": "m"}, "id": "projectile_range_004934_66_16", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 66 m/s and angle 16 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=16 degrees through the sine of 2 theta.\nSubstitute v=66 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 16, "gravity": 9.81, "speed": 66.0}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 5.09 * 8.314 * 474 / 114.5.\nFinal: {\"answer\": 175.1865, \"unit\": \"kPa\"}", "dedupe_signature": "6e7011a5c48627159bdfa05f6c69681b548cff704a5dbc91ceb69da04a998453", "difficulty": "medium", "final_answer": {"answer": 175.1865, "unit": "kPa"}, "id": "ideal_gas_004935_5.09_474_114.5", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=5.09 mol, T=474 K, and V=114.5 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 5.09 * 8.314 * 474 / 114.5.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 5.09, "temp_k": 474, "volume_l": 114.5}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=185.6 V and R=83.4 ohm.\nFinal: {\"answer\": 413.0379, \"unit\": \"W\"}", "dedupe_signature": "e2beef8e3364479c5ca448d69505c3664c1a92780a24ec6130d88677c722cb47", "difficulty": "easy", "final_answer": {"answer": 413.0379, "unit": "W"}, "id": "ohm_power_004937_185.6_83.4", "license": "Apache-2.0", "prompt": "A resistor has resistance 83.4 ohm and voltage 185.6 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=185.6 V and R=83.4 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 83.4, "voltage": 185.6}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 0.8 mol * 100.087 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 80.0696, \"unit\": \"g\"}", "dedupe_signature": "d53773221323058f5ba0da9458dbadc19abf4a5ebee801b531dd74f14e82a9fd", "difficulty": "medium", "final_answer": {"answer": 80.0696, "unit": "g"}, "id": "stoich_mass_004939_calcium_carbonate_0.8", "license": "Apache-2.0", "prompt": "A sample contains 0.8 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 0.8 mol * 100.087 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "calcium carbonate", "molar_mass": 100.087, "moles": 0.8}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.07 y, so each step multiplies y by 1 - h*0.07.\n3. Apply that update for 5 steps and round the final state.\nFinal: {\"answer\": 15.6567, \"unit\": \"state_units\"}", "dedupe_signature": "62f7ae4a7fa30a53281fd5d5e655f1ce79b2b529fe22d7ac5d80640e67ccf5f9", "difficulty": "medium", "final_answer": {"answer": 15.6567, "unit": "state_units"}, "id": "euler_decay_004941_29.5_0.07_1.7_5", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.07 y with y(0)=29.5, step size h=1.7, for 5 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.07 y, so each step multiplies y by 1 - h*0.07.\nApply that update for 5 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 29.5, "rate": 0.07, "step": 1.7, "steps": 5}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-3)=-4.9 and f(3)=18.5.\n3. The interval width is 6.\nFinal: {\"answer\": 40.8, \"unit\": \"area_units\"}", "dedupe_signature": "1d1fcb892928e41f44f243abf79a154cca3dbe78b4a0ce0438991aa6a592466f", "difficulty": "medium", "final_answer": {"answer": 40.8, "unit": "area_units"}, "id": "trapz_linear_004942_3.9_6.8_-3_3", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=3.9x+6.8 from x=-3 to x=3. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-3)=-4.9 and f(3)=18.5.\nThe interval width is 6.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 6.8, "slope": 3.9, "x0": -3.0, "x1": 3.0}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.3 and add it to the current value.\nFinal: {\"answer\": [0.385, 0.87, 0.495], \"unit\": \"temperature_units\"}", "dedupe_signature": "9f1b8fe9c5c088910ef462b6643b0a0e16825565d2c1d54ece09b890eaef4adf", "difficulty": "hard", "final_answer": {"answer": [0.385, 0.87, 0.495], "unit": "temperature_units"}, "id": "heat_step_004943_0.3_-0.6_-0.5_2.55_0.0_-0.9", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-0.6, right=-0.9; current interior values are [-0.5, 2.55, 0.0]. Use r=0.3. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.3 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-0.5, 2.55, 0.0], "left": -0.6, "r": 0.3, "right": -0.9}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 100 centimeters in one meter.\n2. Apply the conversion factor directly to the given value.\n3. Compute 4628.5 / 100.\nFinal: {\"answer\": 46.285, \"unit\": \"m\"}", "dedupe_signature": "3f46998ea51cc20ad19c3998616d8d0e9273d757ba01e990dbc4ab15b5c47f89", "difficulty": "easy", "final_answer": {"answer": 46.285, "unit": "m"}, "id": "unit_convert_004944_cm_to_m_4628.5", "license": "Apache-2.0", "prompt": "Convert 4628.5 cm to m. Return the converted value with unit.", "reasoning_trace": "There are 100 centimeters in one meter.\nApply the conversion factor directly to the given value.\nCompute 4628.5 / 100.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 4628.5}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=85 degrees and keep the unit as newtons.\nFinal: {\"answer\": [2.1789, 24.9049], \"unit\": \"N\"}", "dedupe_signature": "5059c16f56144239cffa55541391ea51f7d8fc77aed9b18b21df36c13eb1dd34", "difficulty": "medium", "final_answer": {"answer": [2.1789, 24.9049], "unit": "N"}, "id": "vector_components_004945_25_85", "license": "Apache-2.0", "prompt": "A vector has magnitude 25 N at 85 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=85 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 85, "magnitude": 25.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-4.95, 16.75], \"unit\": \"dimensionless\"}", "dedupe_signature": "0c9d3ec45c817c8497d38a705b24daa83df3bb005664ccb0ebc9e27b813b8cd0", "difficulty": "medium", "final_answer": {"answer": [-4.95, 16.75], "unit": "dimensionless"}, "id": "line_two_point_004946_-6.5_-1_-4.95_16.75", "license": "Apache-2.0", "prompt": "A line passes through points (-6.5, 48.925) and (-1, 21.7). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -6.5, "x2": -1.0, "y1": 48.925000000000004, "y2": 21.7}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. lever arm times force has torque dimensions\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "c6bbe10c0d8a83b3fa33c56281325dff6e37048a30873dd0dd2ec939040c1f4e", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_004947_consistent_5ca82cb9_123424", "license": "Apache-2.0", "prompt": "In quality-control check case 123424, check dimensional consistency for tau = r * F. The left side has dimensions N*m and the right side has dimensions N*m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nlever arm times force has torque dimensions\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "tau = r * F"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef threshold_flags_004948(values, threshold):\n    return [value >= threshold for value in values]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"threshold_flags_004948\"}", "dedupe_signature": "593cf92365b10c5de5113d5bf89ee3fd41736c3258a378cc884ff844446b2740", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "threshold_flags_004948"}, "id": "code_004948_threshold_flags_004948", "license": "Apache-2.0", "prompt": "Write a Python function threshold_flags_004948(values, threshold) that returns a list of booleans showing whether each value is greater than or equal to threshold. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "threshold_flags_004948"}, "verifier": {"function": "threshold_flags_004948", "tests": ["assert threshold_flags_004948([1, 2, 3], 2) == [False, True, True]", "assert threshold_flags_004948([], 5) == []", "assert threshold_flags_004948([-1, 0], 0) == [False, True]"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: launch_angle_or_vertical_velocity.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"launch_angle_or_vertical_velocity\"]}", "dedupe_signature": "145b28408aeefd96f274865de3961f1dc3b801248f8eeacce2557e2269124ad0", "difficulty": "easy", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["launch_angle_or_vertical_velocity"]}, "id": "abstain_004949_launch_angle_or_vertical_velocity", "license": "Apache-2.0", "prompt": "Compute projectile range on level ground. The prompt gives initial speed 67 m/s but does not give launch angle or vertical velocity. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: launch_angle_or_vertical_velocity.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["launch_angle_or_vertical_velocity"]}, "verifier": {"missing": ["launch_angle_or_vertical_velocity"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 10.1 kg and a = 13.7 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 138.37, \"unit\": \"N\"}", "dedupe_signature": "1eb3b8767212ba5f8d801c28e5758c3028d7b186f341ba89b4e4fac79fb8c5c9", "difficulty": "easy", "final_answer": {"answer": 138.37, "unit": "N"}, "id": "force_004950_10.1_13.7", "license": "Apache-2.0", "prompt": "A cart has mass 10.1 kg and measured acceleration 13.7 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 10.1 kg and a = 13.7 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 13.7, "mass": 10.1}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 3.45^2 and multiply by 0.5 * 24.25.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 144.3178, \"unit\": \"J\"}", "dedupe_signature": "d739c1fbaebb04b722dbf27bea7d12a79f2ade6bb0bcb3196b7c1c93c43ccaf6", "difficulty": "easy", "final_answer": {"answer": 144.3178, "unit": "J"}, "id": "ke_004951_24.25_3.45", "license": "Apache-2.0", "prompt": "A body of mass 24.25 kg moves at 3.45 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 3.45^2 and multiply by 0.5 * 24.25.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 24.25, "velocity": 3.45}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=65 degrees through the sine of 2 theta.\n3. Substitute v=69.8 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 380.4484, \"unit\": \"m\"}", "dedupe_signature": "1edb5c0cb711154527c18504f1b172b25234be7820cd461697e6d2a6e442ff63", "difficulty": "medium", "final_answer": {"answer": 380.4484, "unit": "m"}, "id": "projectile_range_004952_69.8_65", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 69.8 m/s and angle 65 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=65 degrees through the sine of 2 theta.\nSubstitute v=69.8 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 65, "gravity": 9.81, "speed": 69.8}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 0.18 * 8.314 * 546 / 35.6.\nFinal: {\"answer\": 22.9522, \"unit\": \"kPa\"}", "dedupe_signature": "cfed931cee4c2d8035404303f72ab1d406675d32c77ae53f2b832b672bb28d66", "difficulty": "medium", "final_answer": {"answer": 22.9522, "unit": "kPa"}, "id": "ideal_gas_004953_0.18_546_35.6", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=0.18 mol, T=546 K, and V=35.6 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 0.18 * 8.314 * 546 / 35.6.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 0.18, "temp_k": 546, "volume_l": 35.6}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1435 * 2.51 * 19.\nFinal: {\"answer\": 68435.15, \"unit\": \"J\"}", "dedupe_signature": "2adbadd1b25433ef13d4efda1f0b5c55f20616ce2652d85063057cc33af933b0", "difficulty": "easy", "final_answer": {"answer": 68435.15, "unit": "J"}, "id": "heat_q_004954_1435_2.51_19", "license": "Apache-2.0", "prompt": "A 1435 g sample has specific heat 2.51 J/(g*K). How much heat is needed to raise its temperature by 19 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1435 * 2.51 * 19.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 19, "heat_capacity": 2.51, "mass_g": 1435}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=162.8 V and R=19.3 ohm.\nFinal: {\"answer\": 1373.256, \"unit\": \"W\"}", "dedupe_signature": "ac7bf13a560a2bdb0bba77f4882254e6a25ebc2949ff934a1a6a255973c8451d", "difficulty": "easy", "final_answer": {"answer": 1373.256, "unit": "W"}, "id": "ohm_power_004955_162.8_19.3", "license": "Apache-2.0", "prompt": "A resistor has resistance 19.3 ohm and voltage 162.8 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=162.8 V and R=19.3 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 19.3, "voltage": 162.8}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=793 mg, t=334.5 h, and T_half=27.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 0.1728, \"unit\": \"mg\"}", "dedupe_signature": "d660a9f19aa3524e28f88dacf4d7f863f9318db050a452b37212beb280441512", "difficulty": "medium", "final_answer": {"answer": 0.1728, "unit": "mg"}, "id": "half_life_004956_793_27.5_334.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 793 mg. Its half-life is 27.5 hours. How many mg remain after 334.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=793 mg, t=334.5 h, and T_half=27.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 334.5, "half_life": 27.5, "initial_amount": 793.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 0.25 mol * 18.015 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 4.5038, \"unit\": \"g\"}", "dedupe_signature": "2d86d7ea792dbefeac44544fc0ef051241cb86a5df0adfeafaac2562dec8bb64", "difficulty": "medium", "final_answer": {"answer": 4.5038, "unit": "g"}, "id": "stoich_mass_004957_water_0.25", "license": "Apache-2.0", "prompt": "A sample contains 0.25 mol of water. Using molar mass 18.015 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 0.25 mol * 18.015 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "water", "molar_mass": 18.015, "moles": 0.25}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 1460 mL to 1.46 L.\n3. Compute M = 1.075 / 1.46.\nFinal: {\"answer\": 0.7363, \"unit\": \"mol/L\"}", "dedupe_signature": "f61b3cb554d9f64f02e3b0252da817be3c8ecafcedea902f769071479e6eecb2", "difficulty": "medium", "final_answer": {"answer": 0.7363, "unit": "mol/L"}, "id": "molarity_004958_1.075_1460", "license": "Apache-2.0", "prompt": "A solution contains 1.075 mol of solute in 1460 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 1460 mL to 1.46 L.\nCompute M = 1.075 / 1.46.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 1.075, "volume_ml": 1460}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.21 y, so each step multiplies y by 1 - h*0.21.\n3. Apply that update for 10 steps and round the final state.\nFinal: {\"answer\": 0.212, \"unit\": \"state_units\"}", "dedupe_signature": "2ea8839adef8cce3221bebe64ad72f59d6eeeff5ac72832c2d7f35ecc8f271fa", "difficulty": "medium", "final_answer": {"answer": 0.212, "unit": "state_units"}, "id": "euler_decay_004959_29_0.21_1.85_10", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.21 y with y(0)=29, step size h=1.85, for 10 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.21 y, so each step multiplies y by 1 - h*0.21.\nApply that update for 10 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 29.0, "rate": 0.21, "step": 1.85, "steps": 10}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(9.5)=5.3 and f(12.2)=4.76.\n3. The interval width is 2.7.\nFinal: {\"answer\": 13.581, \"unit\": \"area_units\"}", "dedupe_signature": "aa82d026b28cb31c93e79c19a93ae75d20c9b2deb6ad2ba9b797a4d63868a2b1", "difficulty": "medium", "final_answer": {"answer": 13.581, "unit": "area_units"}, "id": "trapz_linear_004960_-0.2_7.2_9.5_12.2", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-0.2x+7.2 from x=9.5 to x=12.2. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(9.5)=5.3 and f(12.2)=4.76.\nThe interval width is 2.7.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 7.2, "slope": -0.2, "x0": 9.5, "x1": 12.2}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.22 and add it to the current value.\nFinal: {\"answer\": [-0.557, 0.781, 1.23], \"unit\": \"temperature_units\"}", "dedupe_signature": "e08d09d11ce34ad1a13dad4400c2cd28de665aae0e30381763e8bcd249a39df7", "difficulty": "hard", "final_answer": {"answer": [-0.557, 0.781, 1.23], "unit": "temperature_units"}, "id": "heat_step_004961_0.22_-1.85_-0.7_1.1_1.45_0.8", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-1.85, right=0.8; current interior values are [-0.7, 1.1, 1.45]. Use r=0.22. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.22 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-0.7, 1.1, 1.45], "left": -1.85, "r": 0.22, "right": 0.8}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 40467.0 / 1000.\nFinal: {\"answer\": 40.467, \"unit\": \"kg\"}", "dedupe_signature": "41565ae9052141d426a036e2ab2c5be22f8afd8d4afeb92884b0914b31630f4f", "difficulty": "easy", "final_answer": {"answer": 40.467, "unit": "kg"}, "id": "unit_convert_004962_g_to_kg_40467", "license": "Apache-2.0", "prompt": "Convert 40467 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 40467.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 40467.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=306 degrees and keep the unit as newtons.\nFinal: {\"answer\": [28.2137, -38.8328], \"unit\": \"N\"}", "dedupe_signature": "966d11cd45f960b967176948ca76a2e89590ad452b987465a6c06be38819fdd6", "difficulty": "medium", "final_answer": {"answer": [28.2137, -38.8328], "unit": "N"}, "id": "vector_components_004963_48_306", "license": "Apache-2.0", "prompt": "A vector has magnitude 48 N at 306 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=306 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 306, "magnitude": 48.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-0.5, 21.25], \"unit\": \"dimensionless\"}", "dedupe_signature": "345e561f8060d724f16c38a78a14764cbe94094f2d2be0ff870ebe47183a2f63", "difficulty": "medium", "final_answer": {"answer": [-0.5, 21.25], "unit": "dimensionless"}, "id": "line_two_point_004964_-4_0.25_-0.5_21.25", "license": "Apache-2.0", "prompt": "A line passes through points (-4, 23.25) and (0.25, 21.125). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -4.0, "x2": 0.25, "y1": 23.25, "y2": 21.125}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. mass times acceleration has newton dimensions\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "7a3481a5d64695504e148fe6d1937b47344fc22c0522ad2b695daece9d326710", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_004965_consistent_03f5e041_301797", "license": "Apache-2.0", "prompt": "In simulation spec case 301797, check dimensional consistency for F = m * a. The left side has dimensions kg*m/s^2 and the right side has dimensions kg*m/s^2. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nmass times acceleration has newton dimensions\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "F = m * a"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef safe_mean_004966(values):\n    if not values:\n        raise ValueError('safe_mean requires at least one value')\n    return sum(values) / len(values)\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"safe_mean_004966\"}", "dedupe_signature": "ccdc68b922b2e054cd9b1fcc39269d67d40cf849009a63d375714f3b215dc5fb", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "safe_mean_004966"}, "id": "code_004966_safe_mean_004966", "license": "Apache-2.0", "prompt": "Write a Python function safe_mean_004966(values) that returns the arithmetic mean. It must raise ValueError for an empty input and must not mutate the input list. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "safe_mean_004966"}, "verifier": {"function": "safe_mean_004966", "tests": ["assert safe_mean_004966([2, 4, 6]) == 4", "xs = [1, 2, 3]; assert safe_mean_004966(xs) == 2 and xs == [1, 2, 3]", "try:\n    safe_mean_004966([])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 6.2 kg and a = 12.1 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 75.02, \"unit\": \"N\"}", "dedupe_signature": "638a4b7c3f0be4aa38802543cae4918d7659aec96e376be93c187ecbbac23e43", "difficulty": "easy", "final_answer": {"answer": 75.02, "unit": "N"}, "id": "force_004968_6.2_12.1", "license": "Apache-2.0", "prompt": "A cart has mass 6.2 kg and measured acceleration 12.1 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 6.2 kg and a = 12.1 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 12.1, "mass": 6.2}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 29.2^2 and multiply by 0.5 * 11.4.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 4860.048, \"unit\": \"J\"}", "dedupe_signature": "045d5cb285adae57dd1f28ee7ce8349f8a676ba30f276820eaa795aec2a8aab3", "difficulty": "easy", "final_answer": {"answer": 4860.048, "unit": "J"}, "id": "ke_004969_11.4_29.2", "license": "Apache-2.0", "prompt": "A body of mass 11.4 kg moves at 29.2 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 29.2^2 and multiply by 0.5 * 11.4.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 11.4, "velocity": 29.2}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=65 degrees through the sine of 2 theta.\n3. Substitute v=43.1 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 145.0573, \"unit\": \"m\"}", "dedupe_signature": "8d22c48204f4319750c6c569dc6a882f8b3cdf93fac61dc32221e12f8556840f", "difficulty": "medium", "final_answer": {"answer": 145.0573, "unit": "m"}, "id": "projectile_range_004970_43.1_65", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 43.1 m/s and angle 65 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=65 degrees through the sine of 2 theta.\nSubstitute v=43.1 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 65, "gravity": 9.81, "speed": 43.1}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 0.42 * 8.314 * 465 / 91.1.\nFinal: {\"answer\": 17.8235, \"unit\": \"kPa\"}", "dedupe_signature": "fe8e94d73c445bbd080168925943def6c594ce5354a4ebfc9933f57cddc26efc", "difficulty": "medium", "final_answer": {"answer": 17.8235, "unit": "kPa"}, "id": "ideal_gas_004971_0.42_465_91.1", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=0.42 mol, T=465 K, and V=91.1 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 0.42 * 8.314 * 465 / 91.1.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 0.42, "temp_k": 465, "volume_l": 91.1}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1960 * 4.58 * 39.\nFinal: {\"answer\": 350095.2, \"unit\": \"J\"}", "dedupe_signature": "bb00db5cbde4a543bd17ae9a208a3d25027cce49ec2f1e6bf94ff5e8cba2afdc", "difficulty": "easy", "final_answer": {"answer": 350095.2, "unit": "J"}, "id": "heat_q_004972_1960_4.58_39", "license": "Apache-2.0", "prompt": "A 1960 g sample has specific heat 4.58 J/(g*K). How much heat is needed to raise its temperature by 39 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1960 * 4.58 * 39.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 39, "heat_capacity": 4.58, "mass_g": 1960}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=135.1 V and R=100.9 ohm.\nFinal: {\"answer\": 180.8921, \"unit\": \"W\"}", "dedupe_signature": "bbd636a283b2ebb86dc75d86ea6fcac2f8158864860d1ec4ec18988ad7490493", "difficulty": "easy", "final_answer": {"answer": 180.8921, "unit": "W"}, "id": "ohm_power_004973_135.1_100.9", "license": "Apache-2.0", "prompt": "A resistor has resistance 100.9 ohm and voltage 135.1 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=135.1 V and R=100.9 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 100.9, "voltage": 135.1}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=796.5 mg, t=359.5 h, and T_half=84 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 41.0062, \"unit\": \"mg\"}", "dedupe_signature": "5747b54aa5a0e43df366d6b3ac76553bf7a04efe35c8734b37bc7f1d57dbf26c", "difficulty": "medium", "final_answer": {"answer": 41.0062, "unit": "mg"}, "id": "half_life_004974_796.5_84_359.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 796.5 mg. Its half-life is 84 hours. How many mg remain after 359.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=796.5 mg, t=359.5 h, and T_half=84 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 359.5, "half_life": 84.0, "initial_amount": 796.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 4.46 mol * 180.156 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 803.4958, \"unit\": \"g\"}", "dedupe_signature": "785d4a33ba8c3576f51a732b2347aa3e43bf5173e60daf1e8d08d80c4e3690fc", "difficulty": "medium", "final_answer": {"answer": 803.4958, "unit": "g"}, "id": "stoich_mass_004975_glucose_4.46", "license": "Apache-2.0", "prompt": "A sample contains 4.46 mol of glucose. Using molar mass 180.156 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 4.46 mol * 180.156 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "glucose", "molar_mass": 180.156, "moles": 4.46}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-0.6)=-1.66 and f(7.4)=11.14.\n3. The interval width is 8.\nFinal: {\"answer\": 37.92, \"unit\": \"area_units\"}", "dedupe_signature": "404282e310ff887f45177a68be4d5ca6d29b581fdf6fcb5d563d3649aa4fb2a7", "difficulty": "medium", "final_answer": {"answer": 37.92, "unit": "area_units"}, "id": "trapz_linear_004978_1.6_-0.7_-0.6_7.4", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=1.6x+-0.7 from x=-0.6 to x=7.4. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-0.6)=-1.66 and f(7.4)=11.14.\nThe interval width is 8.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -0.7, "slope": 1.6, "x0": -0.6, "x1": 7.4}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kelvin equals Celsius plus 273.15.\n2. Apply the conversion factor directly to the given value.\n3. Compute 131.5 + 273.15.\nFinal: {\"answer\": 404.65, \"unit\": \"K\"}", "dedupe_signature": "c163cf45b068b3666021057afcb8fea55071a260cbcfc46a133ba15fc914aff6", "difficulty": "easy", "final_answer": {"answer": 404.65, "unit": "K"}, "id": "unit_convert_004980_c_to_k_131.5", "license": "Apache-2.0", "prompt": "Convert 131.5 degC to K. Return the converted value with unit.", "reasoning_trace": "Kelvin equals Celsius plus 273.15.\nApply the conversion factor directly to the given value.\nCompute 131.5 + 273.15.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 131.5}, "verifier": {"formula": "value + 273.15", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=194 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-208.1284, -51.8922], \"unit\": \"N\"}", "dedupe_signature": "cf39383b175525888fc783b5d417a869f1dacc34499d61b7788cdd9fceff438d", "difficulty": "medium", "final_answer": {"answer": [-208.1284, -51.8922], "unit": "N"}, "id": "vector_components_004981_214.5_194", "license": "Apache-2.0", "prompt": "A vector has magnitude 214.5 N at 194 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=194 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 194, "magnitude": 214.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-5.8, -22.25], \"unit\": \"dimensionless\"}", "dedupe_signature": "8904933d2753fefd9f7335120722de7be4a38736e6daf226658d63727e42d849", "difficulty": "medium", "final_answer": {"answer": [-5.8, -22.25], "unit": "dimensionless"}, "id": "line_two_point_004982_-11_-2.75_-5.8_-22.25", "license": "Apache-2.0", "prompt": "A line passes through points (-11, 41.55) and (-2.75, -6.3). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -11.0, "x2": -2.75, "y1": 41.55, "y2": -6.300000000000001}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. coulomb per second is ampere\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "da12f081a7e5090055e874ec5a2efb7c759dbce2c79a5959e840deaab2cff155", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_004983_consistent_8b38953d_914390", "license": "Apache-2.0", "prompt": "In quality-control check case 914390, check dimensional consistency for I = Q / t. The left side has dimensions A and the right side has dimensions A. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\ncoulomb per second is ampere\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "I = Q / t"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 2 kg and a = 2.85 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 5.7, \"unit\": \"N\"}", "dedupe_signature": "274234c8290902add8f8d19e8b4eebef7af00c86dc951080b4ff05365a6f25a0", "difficulty": "easy", "final_answer": {"answer": 5.7, "unit": "N"}, "id": "force_004986_2_2.85", "license": "Apache-2.0", "prompt": "A cart has mass 2 kg and measured acceleration 2.85 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 2 kg and a = 2.85 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 2.85, "mass": 2.0}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 17.15^2 and multiply by 0.5 * 28.6.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 4205.9517, \"unit\": \"J\"}", "dedupe_signature": "2170bb3349d31cbbd66e3e6afb656b0d5954f11d9e6bba05324f2535677b41b1", "difficulty": "easy", "final_answer": {"answer": 4205.9517, "unit": "J"}, "id": "ke_004987_28.6_17.15", "license": "Apache-2.0", "prompt": "A body of mass 28.6 kg moves at 17.15 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 17.15^2 and multiply by 0.5 * 28.6.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 28.6, "velocity": 17.15}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 4.92 * 8.314 * 305 / 13.6.\nFinal: {\"answer\": 917.3521, \"unit\": \"kPa\"}", "dedupe_signature": "7052c12331d0853b95ba901798e77c3752764359a5b34011234d417be3f56525", "difficulty": "medium", "final_answer": {"answer": 917.3521, "unit": "kPa"}, "id": "ideal_gas_004989_4.92_305_13.6", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=4.92 mol, T=305 K, and V=13.6 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 4.92 * 8.314 * 305 / 13.6.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 4.92, "temp_k": 305, "volume_l": 13.6}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 745 * 1.17 * 31.\nFinal: {\"answer\": 27021.15, \"unit\": \"J\"}", "dedupe_signature": "05c6e960b527426b21587d3eacc4b45477fdb8c92723dfee9c60ba92d1e4b177", "difficulty": "easy", "final_answer": {"answer": 27021.15, "unit": "J"}, "id": "heat_q_004990_745_1.17_31", "license": "Apache-2.0", "prompt": "A 745 g sample has specific heat 1.17 J/(g*K). How much heat is needed to raise its temperature by 31 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 745 * 1.17 * 31.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 31, "heat_capacity": 1.17, "mass_g": 745}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=176.9 V and R=136.5 ohm.\nFinal: {\"answer\": 229.2572, \"unit\": \"W\"}", "dedupe_signature": "c339728fb438f62e7a8771d34d20d9eb65be355c1b3e9a84dca3ab1ef6f3a1d7", "difficulty": "easy", "final_answer": {"answer": 229.2572, "unit": "W"}, "id": "ohm_power_004991_176.9_136.5", "license": "Apache-2.0", "prompt": "A resistor has resistance 136.5 ohm and voltage 176.9 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=176.9 V and R=136.5 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 136.5, "voltage": 176.9}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=794 mg, t=255 h, and T_half=97 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 128.3669, \"unit\": \"mg\"}", "dedupe_signature": "e5d2f7f3f58b7dcd3142baa456be6164e85f1b2c92ea97cbe8ae81cb7269bcdb", "difficulty": "medium", "final_answer": {"answer": 128.3669, "unit": "mg"}, "id": "half_life_004992_794_97_255", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 794 mg. Its half-life is 97 hours. How many mg remain after 255 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=794 mg, t=255 h, and T_half=97 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 255.0, "half_life": 97.0, "initial_amount": 794.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 1 mol * 44.01 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 44.01, \"unit\": \"g\"}", "dedupe_signature": "567dbc6a58c84db094a519822109b6eeca6336a37e008178e018dd5c061cfe11", "difficulty": "medium", "final_answer": {"answer": 44.01, "unit": "g"}, "id": "stoich_mass_004993_carbon_dioxide_1", "license": "Apache-2.0", "prompt": "A sample contains 1 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 1 mol * 44.01 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "carbon dioxide", "molar_mass": 44.01, "moles": 1.0}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(4.2)=22.56 and f(10.3)=70.14.\n3. The interval width is 6.1.\nFinal: {\"answer\": 282.735, \"unit\": \"area_units\"}", "dedupe_signature": "06d3a6a43c233bc16a75193da03ddcebab8aa0f99db1954b62bc5a01863dda98", "difficulty": "medium", "final_answer": {"answer": 282.735, "unit": "area_units"}, "id": "trapz_linear_004996_7.8_-10.2_4.2_10.3", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=7.8x+-10.2 from x=4.2 to x=10.3. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(4.2)=22.56 and f(10.3)=70.14.\nThe interval width is 6.1.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -10.2, "slope": 7.8, "x0": 4.2, "x1": 10.3}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.44 and add it to the current value.\nFinal: {\"answer\": [0.7, 1.622, -0.34], \"unit\": \"temperature_units\"}", "dedupe_signature": "c2de6167fd46ec6fa7251f7b88a50a12d8c542a4421ccc997c355c8c635b9ed6", "difficulty": "hard", "final_answer": {"answer": [0.7, 1.622, -0.34], "unit": "temperature_units"}, "id": "heat_step_004997_0.44_0.6_1.8_0.5_1.75_-1.75", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=0.6, right=-1.75; current interior values are [1.8, 0.5, 1.75]. Use r=0.44. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.44 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [1.8, 0.5, 1.75], "left": 0.6, "r": 0.44, "right": -1.75}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=300 degrees and keep the unit as newtons.\nFinal: {\"answer\": [41.0, -71.0141], \"unit\": \"N\"}", "dedupe_signature": "67c8d331ffbdb4349eda4c61d51687c047199b022a8908d9285680dc70777947", "difficulty": "medium", "final_answer": {"answer": [41.0, -71.0141], "unit": "N"}, "id": "vector_components_004999_82_300", "license": "Apache-2.0", "prompt": "A vector has magnitude 82 N at 300 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=300 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 300, "magnitude": 82.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [0.95, -16.25], \"unit\": \"dimensionless\"}", "dedupe_signature": "824f83cb0166579170379fa1c9646854cb2bd9df9049d327c0434d6b5c8fceb0", "difficulty": "medium", "final_answer": {"answer": [0.95, -16.25], "unit": "dimensionless"}, "id": "line_two_point_005000_16_23.5_0.95_-16.25", "license": "Apache-2.0", "prompt": "A line passes through points (16, -1.05) and (23.5, 6.075). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 16.0, "x2": 23.5, "y1": -1.0500000000000007, "y2": 6.074999999999999}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. mass times acceleration has newton dimensions\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "0be3615baa21ef6ff657f8d21cffa8a216272abf173888f3f965a184cfb90948", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_005001_consistent_03f5e041_340462", "license": "Apache-2.0", "prompt": "In quality-control check case 340462, check dimensional consistency for F = m * a. The left side has dimensions kg*m/s^2 and the right side has dimensions kg*m/s^2. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nmass times acceleration has newton dimensions\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "F = m * a"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef clamp_005002(x, lo, hi):\n    if lo > hi:\n        raise ValueError('lo must be <= hi')\n    return min(max(x, lo), hi)\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"clamp_005002\"}", "dedupe_signature": "e58f2440cd50c20c225e7ecdfdb63043cb6488aa78c5fa9874a4d6ecdbabaa37", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "clamp_005002"}, "id": "code_005002_clamp_005002", "license": "Apache-2.0", "prompt": "Write a Python function clamp_005002(x, lo, hi) that clips x into the inclusive interval [lo, hi]. It must raise ValueError if lo > hi. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "clamp_005002"}, "verifier": {"function": "clamp_005002", "tests": ["assert clamp_005002(5, 0, 10) == 5", "assert clamp_005002(-2, 0, 10) == 0", "assert clamp_005002(12, 0, 10) == 10", "try:\n    clamp_005002(1, 3, 2)\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 24.2 kg and a = 9.5 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 229.9, \"unit\": \"N\"}", "dedupe_signature": "14e8e294f6fa9abd1896ddb72ab652414ecdda425173afa49979f2a89c749580", "difficulty": "easy", "final_answer": {"answer": 229.9, "unit": "N"}, "id": "force_005004_24.2_9.5", "license": "Apache-2.0", "prompt": "A cart has mass 24.2 kg and measured acceleration 9.5 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 24.2 kg and a = 9.5 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 9.5, "mass": 24.2}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 40.1^2 and multiply by 0.5 * 26.1.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 20984.5305, \"unit\": \"J\"}", "dedupe_signature": "6f724892ef855d3ab663f42970ea487d2a04ce790318597367714ffdc3a68306", "difficulty": "easy", "final_answer": {"answer": 20984.5305, "unit": "J"}, "id": "ke_005005_26.1_40.1", "license": "Apache-2.0", "prompt": "A body of mass 26.1 kg moves at 40.1 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 40.1^2 and multiply by 0.5 * 26.1.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 26.1, "velocity": 40.1}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=84 degrees through the sine of 2 theta.\n3. Substitute v=7.2 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 1.0987, \"unit\": \"m\"}", "dedupe_signature": "02f505cde9da6b22bb866e6c1c9ddf71220301f144547fa7d2d8a6061aeb1216", "difficulty": "medium", "final_answer": {"answer": 1.0987, "unit": "m"}, "id": "projectile_range_005006_7.2_84", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 7.2 m/s and angle 84 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=84 degrees through the sine of 2 theta.\nSubstitute v=7.2 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 84, "gravity": 9.81, "speed": 7.2}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1975 * 2.92 * 87.\nFinal: {\"answer\": 501729.0, \"unit\": \"J\"}", "dedupe_signature": "e01410e08d8f3ed3442e99da1f4a44118eab654fc696c0c3892f2a1990d9de61", "difficulty": "easy", "final_answer": {"answer": 501729.0, "unit": "J"}, "id": "heat_q_005008_1975_2.92_87", "license": "Apache-2.0", "prompt": "A 1975 g sample has specific heat 2.92 J/(g*K). How much heat is needed to raise its temperature by 87 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1975 * 2.92 * 87.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 87, "heat_capacity": 2.92, "mass_g": 1975}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=200.2 V and R=155.8 ohm.\nFinal: {\"answer\": 257.2531, \"unit\": \"W\"}", "dedupe_signature": "4a7497b65d4b779b8cd53b859f956971bb71c531d8b378ff54e54e5079e56625", "difficulty": "easy", "final_answer": {"answer": 257.2531, "unit": "W"}, "id": "ohm_power_005009_200.2_155.8", "license": "Apache-2.0", "prompt": "A resistor has resistance 155.8 ohm and voltage 200.2 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=200.2 V and R=155.8 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 155.8, "voltage": 200.2}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=809.5 mg, t=110 h, and T_half=101.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 381.9244, \"unit\": \"mg\"}", "dedupe_signature": "c88cc59ce6067ea3f441ba2a7f3ad303b0c0cd500c68f7e09e6e858e30a21fa2", "difficulty": "medium", "final_answer": {"answer": 381.9244, "unit": "mg"}, "id": "half_life_005010_809.5_101.5_110", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 809.5 mg. Its half-life is 101.5 hours. How many mg remain after 110 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=809.5 mg, t=110 h, and T_half=101.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 110.0, "half_life": 101.5, "initial_amount": 809.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 2.35 mol * 180.156 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 423.3666, \"unit\": \"g\"}", "dedupe_signature": "b1cd177d71b1e461c0b2907a00b398c6145513f249d0c2486530dd40ca5bcecd", "difficulty": "medium", "final_answer": {"answer": 423.3666, "unit": "g"}, "id": "stoich_mass_005011_glucose_2.35", "license": "Apache-2.0", "prompt": "A sample contains 2.35 mol of glucose. Using molar mass 180.156 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 2.35 mol * 180.156 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "glucose", "molar_mass": 180.156, "moles": 2.35}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 1910 mL to 1.91 L.\n3. Compute M = 0.22 / 1.91.\nFinal: {\"answer\": 0.1152, \"unit\": \"mol/L\"}", "dedupe_signature": "791e9704c4937243628bd004ba6de6e05c0bb08257ed8be214b23742028d2f97", "difficulty": "medium", "final_answer": {"answer": 0.1152, "unit": "mol/L"}, "id": "molarity_005012_0.22_1910", "license": "Apache-2.0", "prompt": "A solution contains 0.22 mol of solute in 1910 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 1910 mL to 1.91 L.\nCompute M = 0.22 / 1.91.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 0.22, "volume_ml": 1910}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.05 y, so each step multiplies y by 1 - h*0.05.\n3. Apply that update for 5 steps and round the final state.\nFinal: {\"answer\": 30.2331, \"unit\": \"state_units\"}", "dedupe_signature": "60588140a30ce227bcf0371794c6a4c9cc96679c6af6fe1d1471620944ea746c", "difficulty": "medium", "final_answer": {"answer": 30.2331, "unit": "state_units"}, "id": "euler_decay_005013_46.5_0.05_1.65_5", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.05 y with y(0)=46.5, step size h=1.65, for 5 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.05 y, so each step multiplies y by 1 - h*0.05.\nApply that update for 5 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 46.5, "rate": 0.05, "step": 1.65, "steps": 5}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(1.4)=6.4 and f(2.4)=4.9.\n3. The interval width is 1.\nFinal: {\"answer\": 5.65, \"unit\": \"area_units\"}", "dedupe_signature": "088160a99e3e026f5889dc6c3d5e50d0ccc15ab6b32c8e5d1733664d03fc97fd", "difficulty": "medium", "final_answer": {"answer": 5.65, "unit": "area_units"}, "id": "trapz_linear_005014_-1.5_8.5_1.4_2.4", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-1.5x+8.5 from x=1.4 to x=2.4. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(1.4)=6.4 and f(2.4)=4.9.\nThe interval width is 1.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 8.5, "slope": -1.5, "x0": 1.4, "x1": 2.4}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kelvin equals Celsius plus 273.15.\n2. Apply the conversion factor directly to the given value.\n3. Compute 133.0 + 273.15.\nFinal: {\"answer\": 406.15, \"unit\": \"K\"}", "dedupe_signature": "fe7dbc89c182bb49174a6f7e9da3b4fc65ccd7e8c43cc2e3b3055ef556aef03c", "difficulty": "easy", "final_answer": {"answer": 406.15, "unit": "K"}, "id": "unit_convert_005016_c_to_k_133", "license": "Apache-2.0", "prompt": "Convert 133 degC to K. Return the converted value with unit.", "reasoning_trace": "Kelvin equals Celsius plus 273.15.\nApply the conversion factor directly to the given value.\nCompute 133.0 + 273.15.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 133.0}, "verifier": {"formula": "value + 273.15", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. mass times acceleration has newton dimensions\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "bf98f1ac85eb56e320e496e5f4143da5760c023b31912e64d19b6f2b6aed032a", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_005019_consistent_03f5e041_467480", "license": "Apache-2.0", "prompt": "In simulation spec case 467480, check dimensional consistency for F = m * a. The left side has dimensions kg*m/s^2 and the right side has dimensions kg*m/s^2. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nmass times acceleration has newton dimensions\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "F = m * a"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef running_total_005020(values):\n    total = 0\n    out = []\n    for value in values:\n        total += value\n        out.append(total)\n    return out\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"running_total_005020\"}", "dedupe_signature": "0807ec8c35cffb81479744c025cee9112a85a5ecbd83cc2b66dd73a998756570", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "running_total_005020"}, "id": "code_005020_running_total_005020", "license": "Apache-2.0", "prompt": "Write a Python function running_total_005020(values) that returns cumulative sums as a new list. It must not mutate the input list. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "running_total_005020"}, "verifier": {"function": "running_total_005020", "tests": ["assert running_total_005020([1, 2, 3]) == [1, 3, 6]", "xs = [4, -1, 2]; assert running_total_005020(xs) == [4, 3, 5] and xs == [4, -1, 2]", "assert running_total_005020([]) == []"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: volume.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"volume\"]}", "dedupe_signature": "051cd6185af6d4bc84dc4b2dc1f350262cc45c1e7cbf7c5f1ed91391872390f9", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["volume"]}, "id": "abstain_005021_volume", "license": "Apache-2.0", "prompt": "Compute pressure from the ideal gas law. The prompt gives n=2.47 mol and T=518 K, but does not give volume. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: volume.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["volume"]}, "verifier": {"missing": ["volume"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 5.55 kg and a = 14.5 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 80.475, \"unit\": \"N\"}", "dedupe_signature": "babb1ad8425df8812fab4cbf01396af4cf95eb74893674dc2a97181ae7986e40", "difficulty": "easy", "final_answer": {"answer": 80.475, "unit": "N"}, "id": "force_005022_5.55_14.5", "license": "Apache-2.0", "prompt": "A cart has mass 5.55 kg and measured acceleration 14.5 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 5.55 kg and a = 14.5 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 14.5, "mass": 5.55}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 23.5^2 and multiply by 0.5 * 5.4.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 1491.075, \"unit\": \"J\"}", "dedupe_signature": "34c771d74cc14f0220958b33cb484d45af1cb1adb65907cb5a2e4936fa5a7074", "difficulty": "easy", "final_answer": {"answer": 1491.075, "unit": "J"}, "id": "ke_005023_5.4_23.5", "license": "Apache-2.0", "prompt": "A body of mass 5.4 kg moves at 23.5 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 23.5^2 and multiply by 0.5 * 5.4.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 5.4, "velocity": 23.5}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=51 degrees through the sine of 2 theta.\n3. Substitute v=23.6 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 55.5341, \"unit\": \"m\"}", "dedupe_signature": "abac75e80fbcf3281add94d58ab2fb306283ac523440abf7967fdd538e4d91ee", "difficulty": "medium", "final_answer": {"answer": 55.5341, "unit": "m"}, "id": "projectile_range_005024_23.6_51", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 23.6 m/s and angle 51 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=51 degrees through the sine of 2 theta.\nSubstitute v=23.6 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 51, "gravity": 9.81, "speed": 23.6}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 5.93 * 8.314 * 309 / 3.1.\nFinal: {\"answer\": 4914.2981, \"unit\": \"kPa\"}", "dedupe_signature": "8085495f364ec967ee0ba2f0fe3e526e58ca996ee24fe743796a8cde3eee3ece", "difficulty": "medium", "final_answer": {"answer": 4914.2981, "unit": "kPa"}, "id": "ideal_gas_005025_5.93_309_3.1", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=5.93 mol, T=309 K, and V=3.1 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 5.93 * 8.314 * 309 / 3.1.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 5.93, "temp_k": 309, "volume_l": 3.1}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=216.6 V and R=18.2 ohm.\nFinal: {\"answer\": 2577.778, \"unit\": \"W\"}", "dedupe_signature": "f0b008bb7824b3d94e3590e818a5d2f95184964e4a2fcd3866dc4655b176838e", "difficulty": "easy", "final_answer": {"answer": 2577.778, "unit": "W"}, "id": "ohm_power_005027_216.6_18.2", "license": "Apache-2.0", "prompt": "A resistor has resistance 18.2 ohm and voltage 216.6 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=216.6 V and R=18.2 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 18.2, "voltage": 216.6}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 2.93 mol * 180.156 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 527.8571, \"unit\": \"g\"}", "dedupe_signature": "754e803921dcfa22bca353cdec3971632c08303ecfc5bc24072b745666ae2c56", "difficulty": "medium", "final_answer": {"answer": 527.8571, "unit": "g"}, "id": "stoich_mass_005029_glucose_2.93", "license": "Apache-2.0", "prompt": "A sample contains 2.93 mol of glucose. Using molar mass 180.156 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 2.93 mol * 180.156 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "glucose", "molar_mass": 180.156, "moles": 2.93}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 2070 mL to 2.07 L.\n3. Compute M = 1.305 / 2.07.\nFinal: {\"answer\": 0.6304, \"unit\": \"mol/L\"}", "dedupe_signature": "e34e9a418cdb95af78bdcc3754fc78c7283f34e276374be310c29aad02ae2357", "difficulty": "medium", "final_answer": {"answer": 0.6304, "unit": "mol/L"}, "id": "molarity_005030_1.305_2070", "license": "Apache-2.0", "prompt": "A solution contains 1.305 mol of solute in 2070 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 2070 mL to 2.07 L.\nCompute M = 1.305 / 2.07.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 1.305, "volume_ml": 2070}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.41 y, so each step multiplies y by 1 - h*0.41.\n3. Apply that update for 7 steps and round the final state.\nFinal: {\"answer\": 5.5949, \"unit\": \"state_units\"}", "dedupe_signature": "1405a83ca9eacadd8d909b75f877771d770ed4d56b87bd2105c648ed5ed53d72", "difficulty": "medium", "final_answer": {"answer": 5.5949, "unit": "state_units"}, "id": "euler_decay_005031_7.5_0.41_0.1_7", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.41 y with y(0)=7.5, step size h=0.1, for 7 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.41 y, so each step multiplies y by 1 - h*0.41.\nApply that update for 7 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 7.5, "rate": 0.41, "step": 0.1, "steps": 7}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-6.7)=10.76 and f(-6.5)=10.2.\n3. The interval width is 0.2.\nFinal: {\"answer\": 2.096, \"unit\": \"area_units\"}", "dedupe_signature": "6dc8b23e20dba82ce22dd2c2bb481cb67019d39c30891df5dd813e0605398468", "difficulty": "medium", "final_answer": {"answer": 2.096, "unit": "area_units"}, "id": "trapz_linear_005032_-2.8_-8_-6.7_-6.5", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-2.8x+-8 from x=-6.7 to x=-6.5. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-6.7)=10.76 and f(-6.5)=10.2.\nThe interval width is 0.2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -8.0, "slope": -2.8, "x0": -6.7, "x1": -6.5}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.04 and add it to the current value.\nFinal: {\"answer\": [-1.186, 0.644, 1.152], \"unit\": \"temperature_units\"}", "dedupe_signature": "224096b98d66b22318e6843ff177516af2de5ab3defaba71c0b62fbbb70dc4f1", "difficulty": "hard", "final_answer": {"answer": [-1.186, 0.644, 1.152], "unit": "temperature_units"}, "id": "heat_step_005033_0.04_-0.45_-1.3_0.7_1.3_-1.8", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-0.45, right=-1.8; current interior values are [-1.3, 0.7, 1.3]. Use r=0.04. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.04 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-1.3, 0.7, 1.3], "left": -0.45, "r": 0.04, "right": -1.8}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kelvin equals Celsius plus 273.15.\n2. Apply the conversion factor directly to the given value.\n3. Compute 142.0 + 273.15.\nFinal: {\"answer\": 415.15, \"unit\": \"K\"}", "dedupe_signature": "ca0392a6002e8beff30ad7a5c047322a59cea6dc5915d6da823c0fcca7607a55", "difficulty": "easy", "final_answer": {"answer": 415.15, "unit": "K"}, "id": "unit_convert_005034_c_to_k_142", "license": "Apache-2.0", "prompt": "Convert 142 degC to K. Return the converted value with unit.", "reasoning_trace": "Kelvin equals Celsius plus 273.15.\nApply the conversion factor directly to the given value.\nCompute 142.0 + 273.15.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 142.0}, "verifier": {"formula": "value + 273.15", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-1.6, 11.25], \"unit\": \"dimensionless\"}", "dedupe_signature": "18f664e84f5fa36d5ea3c1c93b6c9a05979213c43c7a59ebfd03534c92a40008", "difficulty": "medium", "final_answer": {"answer": [-1.6, 11.25], "unit": "dimensionless"}, "id": "line_two_point_005036_16_19_-1.6_11.25", "license": "Apache-2.0", "prompt": "A line passes through points (16, -14.35) and (19, -19.15). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 16.0, "x2": 19.0, "y1": -14.350000000000001, "y2": -19.150000000000002}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. energy divided by length is force, not spring constant\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "8be88e6ba312445011ca4830a9849c8ce8afce100da4db7f8b1661980a39e810", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_005037_inconsistent_56040f5d_313709", "license": "Apache-2.0", "prompt": "In lab notebook case 313709, check dimensional consistency for k = E / x. The left side has dimensions N/m and the right side has dimensions J/m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nenergy divided by length is force, not spring constant\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "k = E / x"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef threshold_flags_005038(values, threshold):\n    return [value >= threshold for value in values]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"threshold_flags_005038\"}", "dedupe_signature": "9d08c926327bf23b438c458ba41f5b21fb4bd3f116ee21f15b6aac3a0d73993c", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "threshold_flags_005038"}, "id": "code_005038_threshold_flags_005038", "license": "Apache-2.0", "prompt": "Write a Python function threshold_flags_005038(values, threshold) that returns a list of booleans showing whether each value is greater than or equal to threshold. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "threshold_flags_005038"}, "verifier": {"function": "threshold_flags_005038", "tests": ["assert threshold_flags_005038([1, 2, 3], 2) == [False, True, True]", "assert threshold_flags_005038([], 5) == []", "assert threshold_flags_005038([-1, 0], 0) == [False, True]"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: required_fields, allowed_transformations.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"required_fields\", \"allowed_transformations\"]}", "dedupe_signature": "55d52d1fc684d58468aaf8071e892e36a3e95e8b2d34b616243addbc2e50e6ed", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["required_fields", "allowed_transformations"]}, "id": "abstain_005039_required_fields_allowed_transformations", "license": "Apache-2.0", "prompt": "Write a sanitizer for valid billing crop records in release 676777, but the prompt does not state which fields are required or which transformations are allowed. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: required_fields, allowed_transformations.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["required_fields", "allowed_transformations"]}, "verifier": {"missing": ["required_fields", "allowed_transformations"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 10.1 kg and a = 14.65 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 147.965, \"unit\": \"N\"}", "dedupe_signature": "28b019f21e22342db116fcbfbb281c26a56edb482814c57f5b7aeb5e5c618e50", "difficulty": "easy", "final_answer": {"answer": 147.965, "unit": "N"}, "id": "force_005040_10.1_14.65", "license": "Apache-2.0", "prompt": "A cart has mass 10.1 kg and measured acceleration 14.65 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 10.1 kg and a = 14.65 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 14.65, "mass": 10.1}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 35.8^2 and multiply by 0.5 * 2.75.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 1762.255, \"unit\": \"J\"}", "dedupe_signature": "978f1f735cd3e6424d365b42cd8dad9bc1310ce43c033a75d3758a5280fe9886", "difficulty": "easy", "final_answer": {"answer": 1762.255, "unit": "J"}, "id": "ke_005041_2.75_35.8", "license": "Apache-2.0", "prompt": "A body of mass 2.75 kg moves at 35.8 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 35.8^2 and multiply by 0.5 * 2.75.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 2.75, "velocity": 35.8}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 2.01 * 8.314 * 303 / 42.8.\nFinal: {\"answer\": 118.3055, \"unit\": \"kPa\"}", "dedupe_signature": "742873626b9ec53df29c53203eeb59b299e65a7c197a3ec2a340056ec8c4246d", "difficulty": "medium", "final_answer": {"answer": 118.3055, "unit": "kPa"}, "id": "ideal_gas_005043_2.01_303_42.8", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=2.01 mol, T=303 K, and V=42.8 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 2.01 * 8.314 * 303 / 42.8.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 2.01, "temp_k": 303, "volume_l": 42.8}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1195 * 2.115 * 79.\nFinal: {\"answer\": 199666.575, \"unit\": \"J\"}", "dedupe_signature": "b55751c527404c0116ad6089e34bc1af73acb2a547904a0973fd3b4f9e152332", "difficulty": "easy", "final_answer": {"answer": 199666.575, "unit": "J"}, "id": "heat_q_005044_1195_2.115_79", "license": "Apache-2.0", "prompt": "A 1195 g sample has specific heat 2.115 J/(g*K). How much heat is needed to raise its temperature by 79 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1195 * 2.115 * 79.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 79, "heat_capacity": 2.115, "mass_g": 1195}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=280.5 mg, t=113 h, and T_half=65.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 84.8396, \"unit\": \"mg\"}", "dedupe_signature": "21f2583c71252ad67745a3fa8f4463f1002cec1b7e04740fa44e112a6b7e4b73", "difficulty": "medium", "final_answer": {"answer": 84.8396, "unit": "mg"}, "id": "half_life_005046_280.5_65.5_113", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 280.5 mg. Its half-life is 65.5 hours. How many mg remain after 113 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=280.5 mg, t=113 h, and T_half=65.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 113.0, "half_life": 65.5, "initial_amount": 280.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 4.81 mol * 58.44 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 281.0964, \"unit\": \"g\"}", "dedupe_signature": "b6acb52016c32b0064cef58eee80e9894f67b65c53aed5051f4b5b8f77769472", "difficulty": "medium", "final_answer": {"answer": 281.0964, "unit": "g"}, "id": "stoich_mass_005047_sodium_chloride_4.81", "license": "Apache-2.0", "prompt": "A sample contains 4.81 mol of sodium chloride. Using molar mass 58.44 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 4.81 mol * 58.44 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "sodium chloride", "molar_mass": 58.44, "moles": 4.81}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 2175 mL to 2.175 L.\n3. Compute M = 1.46 / 2.175.\nFinal: {\"answer\": 0.6713, \"unit\": \"mol/L\"}", "dedupe_signature": "206ae85023e7c8170b1fb787870268b092d0ca958fb20fda0e1c2553b144a6a4", "difficulty": "medium", "final_answer": {"answer": 0.6713, "unit": "mol/L"}, "id": "molarity_005048_1.46_2175", "license": "Apache-2.0", "prompt": "A solution contains 1.46 mol of solute in 2175 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 2175 mL to 2.175 L.\nCompute M = 1.46 / 2.175.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 1.46, "volume_ml": 2175}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.05 y, so each step multiplies y by 1 - h*0.05.\n3. Apply that update for 10 steps and round the final state.\nFinal: {\"answer\": 9.6553, \"unit\": \"state_units\"}", "dedupe_signature": "6561cd63cf88a6185e7c88aa8981dfafcad23bc7feee0102c75dd0269f6ef33c", "difficulty": "medium", "final_answer": {"answer": 9.6553, "unit": "state_units"}, "id": "euler_decay_005049_17_0.05_1.1_10", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.05 y with y(0)=17, step size h=1.1, for 10 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.05 y, so each step multiplies y by 1 - h*0.05.\nApply that update for 10 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 17.0, "rate": 0.05, "step": 1.1, "steps": 10}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(9.4)=62.28 and f(19.1)=132.12.\n3. The interval width is 9.7.\nFinal: {\"answer\": 942.84, \"unit\": \"area_units\"}", "dedupe_signature": "a913b44fff1461080a50c420fb0290d9fc29c0f18d62077ea68a3b0d79eed4bb", "difficulty": "medium", "final_answer": {"answer": 942.84, "unit": "area_units"}, "id": "trapz_linear_005050_7.2_-5.4_9.4_19.1", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=7.2x+-5.4 from x=9.4 to x=19.1. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(9.4)=62.28 and f(19.1)=132.12.\nThe interval width is 9.7.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -5.4, "slope": 7.2, "x0": 9.4, "x1": 19.1}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.22 and add it to the current value.\nFinal: {\"answer\": [-0.641, 1.366, 1.698], \"unit\": \"temperature_units\"}", "dedupe_signature": "54b67295e72994abdb6d307d0f9d57cc0f3a2c7e47b0f2515a48681480ca97b2", "difficulty": "hard", "final_answer": {"answer": [-0.641, 1.366, 1.698], "unit": "temperature_units"}, "id": "heat_step_005051_0.22_-1.75_-1.4_2.4_1.5_1.5", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-1.75, right=1.5; current interior values are [-1.4, 2.4, 1.5]. Use r=0.22. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.22 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-1.4, 2.4, 1.5], "left": -1.75, "r": 0.22, "right": 1.5}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 9388.0 / 1000.\nFinal: {\"answer\": 9.388, \"unit\": \"kg\"}", "dedupe_signature": "8918ad4c9cffb139807fd93425a26e6451dd77579573e77946fa93f6553ce6f2", "difficulty": "easy", "final_answer": {"answer": 9.388, "unit": "kg"}, "id": "unit_convert_005052_g_to_kg_9388", "license": "Apache-2.0", "prompt": "Convert 9388 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 9388.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 9388.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=115 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-192.9252, 413.7295], \"unit\": \"N\"}", "dedupe_signature": "fc7af73945a3ca127a5d391a2634a23102424eaebbb23c7f67f56ee1fbfbe9a0", "difficulty": "medium", "final_answer": {"answer": [-192.9252, 413.7295], "unit": "N"}, "id": "vector_components_005053_456.5_115", "license": "Apache-2.0", "prompt": "A vector has magnitude 456.5 N at 115 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=115 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 115, "magnitude": 456.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. lever arm times force has torque dimensions\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "a2bfc1aa3a9fe36b69f1b8278ac962be22179d7dbbb890c64fb8a8b3cc168bb0", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_005055_consistent_5ca82cb9_147153", "license": "Apache-2.0", "prompt": "In model card equation case 147153, check dimensional consistency for tau = r * F. The left side has dimensions N*m and the right side has dimensions N*m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nlever arm times force has torque dimensions\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "tau = r * F"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: target_schema, valid_examples.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"target_schema\", \"valid_examples\"]}", "dedupe_signature": "7d2c861e2ca8b922d2d26d0d2a0fefb9e8973d3e5aed07e443bba19af04f9d62", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["target_schema", "valid_examples"]}, "id": "abstain_005057_target_schema_valid_examples", "license": "Apache-2.0", "prompt": "Write a parser that converts each billing sensor record from batch 327655 into the correct schema, but the prompt does not include the target schema or examples. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: target_schema, valid_examples.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["target_schema", "valid_examples"]}, "verifier": {"missing": ["target_schema", "valid_examples"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 2.25 kg and a = 11.05 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 24.8625, \"unit\": \"N\"}", "dedupe_signature": "221cbf7ca8b3d8e542ca66b9a351a64246e8758d7385001bdf2b92131ec81d08", "difficulty": "easy", "final_answer": {"answer": 24.8625, "unit": "N"}, "id": "force_005058_2.25_11.05", "license": "Apache-2.0", "prompt": "A cart has mass 2.25 kg and measured acceleration 11.05 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 2.25 kg and a = 11.05 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 11.05, "mass": 2.25}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=6 degrees through the sine of 2 theta.\n3. Substitute v=61.3 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 79.6399, \"unit\": \"m\"}", "dedupe_signature": "ddec6657427fc6b8d54aa5f3357d3a13ade523e2d9af8ba865bd2bddd7bc1ba7", "difficulty": "medium", "final_answer": {"answer": 79.6399, "unit": "m"}, "id": "projectile_range_005060_61.3_6", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 61.3 m/s and angle 6 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=6 degrees through the sine of 2 theta.\nSubstitute v=61.3 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 6, "gravity": 9.81, "speed": 61.3}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 3.56 * 8.314 * 400 / 109.0.\nFinal: {\"answer\": 108.6159, \"unit\": \"kPa\"}", "dedupe_signature": "96beeb944f65662129c740ba8dbc70e3496de2acbf22764fb03ec9a88c6ae413", "difficulty": "medium", "final_answer": {"answer": 108.6159, "unit": "kPa"}, "id": "ideal_gas_005061_3.56_400_109.0", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=3.56 mol, T=400 K, and V=109.0 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 3.56 * 8.314 * 400 / 109.0.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 3.56, "temp_k": 400, "volume_l": 109.0}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 620 * 4.74 * 111.\nFinal: {\"answer\": 326206.8, \"unit\": \"J\"}", "dedupe_signature": "78b06e290518c0164dd9bc535f59ae003b31d61a8f62bf8dfb4433be4c9b1408", "difficulty": "easy", "final_answer": {"answer": 326206.8, "unit": "J"}, "id": "heat_q_005062_620_4.74_111", "license": "Apache-2.0", "prompt": "A 620 g sample has specific heat 4.74 J/(g*K). How much heat is needed to raise its temperature by 111 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 620 * 4.74 * 111.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 111, "heat_capacity": 4.74, "mass_g": 620}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=174.1 V and R=99.5 ohm.\nFinal: {\"answer\": 304.6313, \"unit\": \"W\"}", "dedupe_signature": "5719c235d19f1826d8cf452a385d8878f05eea56a1684063e5a45bf466e635bc", "difficulty": "easy", "final_answer": {"answer": 304.6313, "unit": "W"}, "id": "ohm_power_005063_174.1_99.5", "license": "Apache-2.0", "prompt": "A resistor has resistance 99.5 ohm and voltage 174.1 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=174.1 V and R=99.5 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 99.5, "voltage": 174.1}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=910.5 mg, t=90.5 h, and T_half=4 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 0.0001, \"unit\": \"mg\"}", "dedupe_signature": "691c0c4ba3bfa0d72256c90516fd95fb4305eae34b48db0ddeae5b42d08d712f", "difficulty": "medium", "final_answer": {"answer": 0.0001, "unit": "mg"}, "id": "half_life_005064_910.5_4_90.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 910.5 mg. Its half-life is 4 hours. How many mg remain after 90.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=910.5 mg, t=90.5 h, and T_half=4 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 90.5, "half_life": 4.0, "initial_amount": 910.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 1.6 mol * 44.01 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 70.416, \"unit\": \"g\"}", "dedupe_signature": "2acc114d52e83036267b2ab4835145943bd9a42bccc1fb5d5cd2a831a977f417", "difficulty": "medium", "final_answer": {"answer": 70.416, "unit": "g"}, "id": "stoich_mass_005065_carbon_dioxide_1.6", "license": "Apache-2.0", "prompt": "A sample contains 1.6 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 1.6 mol * 44.01 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "carbon dioxide", "molar_mass": 44.01, "moles": 1.6}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 4760 mL to 4.76 L.\n3. Compute M = 1.805 / 4.76.\nFinal: {\"answer\": 0.3792, \"unit\": \"mol/L\"}", "dedupe_signature": "3a10c6ecccd31299456aa17a7cf901685b9b5ad85a1580ae7ac7101c9a5be021", "difficulty": "medium", "final_answer": {"answer": 0.3792, "unit": "mol/L"}, "id": "molarity_005066_1.805_4760", "license": "Apache-2.0", "prompt": "A solution contains 1.805 mol of solute in 4760 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 4760 mL to 4.76 L.\nCompute M = 1.805 / 4.76.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 1.805, "volume_ml": 4760}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.65 y, so each step multiplies y by 1 - h*0.65.\n3. Apply that update for 2 steps and round the final state.\nFinal: {\"answer\": 32.7864, \"unit\": \"state_units\"}", "dedupe_signature": "b42ac392b41a03e518fffa7b05bbc585bbb3449d9d0d2b6729dbaaad7a54cc2e", "difficulty": "medium", "final_answer": {"answer": 32.7864, "unit": "state_units"}, "id": "euler_decay_005067_65.5_0.65_0.45_2", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.65 y with y(0)=65.5, step size h=0.45, for 2 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.65 y, so each step multiplies y by 1 - h*0.65.\nApply that update for 2 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 65.5, "rate": 0.65, "step": 0.45, "steps": 2}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-3.7)=32.66 and f(5.4)=-38.32.\n3. The interval width is 9.1.\nFinal: {\"answer\": -25.753, \"unit\": \"area_units\"}", "dedupe_signature": "975af754343baba79d7a892ead7b09ed462b5582356ce6ab8b8fd0baa84f4e56", "difficulty": "medium", "final_answer": {"answer": -25.753, "unit": "area_units"}, "id": "trapz_linear_005068_-7.8_3.8_-3.7_5.4", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-7.8x+3.8 from x=-3.7 to x=5.4. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-3.7)=32.66 and f(5.4)=-38.32.\nThe interval width is 9.1.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 3.8, "slope": -7.8, "x0": -3.7, "x1": 5.3999999999999995}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.4 and add it to the current value.\nFinal: {\"answer\": [0.51, -0.66, -1.8], \"unit\": \"temperature_units\"}", "dedupe_signature": "f93a57e6c92980d3b2377938590e3d68865f8e27893afd9fd0837e68b8819b5d", "difficulty": "hard", "final_answer": {"answer": [0.51, -0.66, -1.8], "unit": "temperature_units"}, "id": "heat_step_005069_0.4_2.7_0.75_-1.8_-1.5_-1.95", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=2.7, right=-1.95; current interior values are [0.75, -1.8, -1.5]. Use r=0.4. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.4 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [0.75, -1.8, -1.5], "left": 2.7, "r": 0.4, "right": -1.95}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kelvin equals Celsius plus 273.15.\n2. Apply the conversion factor directly to the given value.\n3. Compute 36.5 + 273.15.\nFinal: {\"answer\": 309.65, \"unit\": \"K\"}", "dedupe_signature": "b24b896abf8387a39b29260f0fbf79adb0bf53e76535464064b442c1ce7f41b5", "difficulty": "easy", "final_answer": {"answer": 309.65, "unit": "K"}, "id": "unit_convert_005070_c_to_k_36.5", "license": "Apache-2.0", "prompt": "Convert 36.5 degC to K. Return the converted value with unit.", "reasoning_trace": "Kelvin equals Celsius plus 273.15.\nApply the conversion factor directly to the given value.\nCompute 36.5 + 273.15.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 36.5}, "verifier": {"formula": "value + 273.15", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=47 degrees and keep the unit as newtons.\nFinal: {\"answer\": [162.3156, 174.0622], \"unit\": \"N\"}", "dedupe_signature": "d6900f78aca7b7dede46dbb6ea6bba42f5975f6872972defeb24cf8834674c17", "difficulty": "medium", "final_answer": {"answer": [162.3156, 174.0622], "unit": "N"}, "id": "vector_components_005071_238_47", "license": "Apache-2.0", "prompt": "A vector has magnitude 238 N at 47 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=47 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 47, "magnitude": 238.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [0.05, -1.0], \"unit\": \"dimensionless\"}", "dedupe_signature": "d54f1e071d23d6b73010d39d441aa3e064fce251367b1e8ec33858fbc2dd4dc1", "difficulty": "medium", "final_answer": {"answer": [0.05, -1.0], "unit": "dimensionless"}, "id": "line_two_point_005072_-1.75_-1.25_0.05_-1", "license": "Apache-2.0", "prompt": "A line passes through points (-1.75, -1.0875) and (-1.25, -1.0625). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -1.75, "x2": -1.25, "y1": -1.0875, "y2": -1.0625}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. speed squared over acceleration has units of meters\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "c17b735700d020e0bf0577e6061b667309d8c45f29f2ce4d59abdfe486fc5e82", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_005073_consistent_741d4e34_181073", "license": "Apache-2.0", "prompt": "In lab notebook case 181073, check dimensional consistency for R = v^2 * sin(theta) / g. The left side has dimensions m and the right side has dimensions m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nspeed squared over acceleration has units of meters\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "R = v^2 * sin(theta) / g"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: volume.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"volume\"]}", "dedupe_signature": "01106b3a19053dd2c193ab451d9a8eac83835279a955a0ed2d25ed856229f087", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["volume"]}, "id": "abstain_005075_volume", "license": "Apache-2.0", "prompt": "Compute pressure from the ideal gas law. The prompt gives n=5.86 mol and T=571 K, but does not give volume. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: volume.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["volume"]}, "verifier": {"missing": ["volume"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 6.35 kg and a = 2.75 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 17.4625, \"unit\": \"N\"}", "dedupe_signature": "05d08c23bf66808b088f472833a227e2054183e915104584003169b2756a18d2", "difficulty": "easy", "final_answer": {"answer": 17.4625, "unit": "N"}, "id": "force_005076_6.35_2.75", "license": "Apache-2.0", "prompt": "A cart has mass 6.35 kg and measured acceleration 2.75 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 6.35 kg and a = 2.75 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 2.75, "mass": 6.35}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 9.75^2 and multiply by 0.5 * 12.6.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 598.8937, \"unit\": \"J\"}", "dedupe_signature": "9123926e5688de19ae4462c7e3d869e8c5cada881016a811d38155d702b19b1a", "difficulty": "easy", "final_answer": {"answer": 598.8937, "unit": "J"}, "id": "ke_005077_12.6_9.75", "license": "Apache-2.0", "prompt": "A body of mass 12.6 kg moves at 9.75 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 9.75^2 and multiply by 0.5 * 12.6.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 12.6, "velocity": 9.75}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=27 degrees through the sine of 2 theta.\n3. Substitute v=63.3 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 330.4426, \"unit\": \"m\"}", "dedupe_signature": "f9eb149cceec7a020e6cb5ded7fd937f195706143563ebf293ac539c547c2a3f", "difficulty": "medium", "final_answer": {"answer": 330.4426, "unit": "m"}, "id": "projectile_range_005078_63.3_27", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 63.3 m/s and angle 27 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=27 degrees through the sine of 2 theta.\nSubstitute v=63.3 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 27, "gravity": 9.81, "speed": 63.3}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 1.72 * 8.314 * 272 / 52.8.\nFinal: {\"answer\": 73.6671, \"unit\": \"kPa\"}", "dedupe_signature": "a8c28328bb3158259c84f8cf868bc14b216e32601193fdc15b4ca7fc11284d9f", "difficulty": "medium", "final_answer": {"answer": 73.6671, "unit": "kPa"}, "id": "ideal_gas_005079_1.72_272_52.8", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=1.72 mol, T=272 K, and V=52.8 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 1.72 * 8.314 * 272 / 52.8.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 1.72, "temp_k": 272, "volume_l": 52.8}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1125 * 2.03 * 101.\nFinal: {\"answer\": 230658.75, \"unit\": \"J\"}", "dedupe_signature": "64481e77b64853bcb909da1731fad1a5cb882b6f5e7caa3d1e9e6ba5590412d4", "difficulty": "easy", "final_answer": {"answer": 230658.75, "unit": "J"}, "id": "heat_q_005080_1125_2.03_101", "license": "Apache-2.0", "prompt": "A 1125 g sample has specific heat 2.03 J/(g*K). How much heat is needed to raise its temperature by 101 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1125 * 2.03 * 101.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 101, "heat_capacity": 2.03, "mass_g": 1125}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=10.5 V and R=149.9 ohm.\nFinal: {\"answer\": 0.7355, \"unit\": \"W\"}", "dedupe_signature": "11e3c7b6fc462e2cceefdc583d264c3c9e8e8bea198009898e38e2f5f8cac652", "difficulty": "easy", "final_answer": {"answer": 0.7355, "unit": "W"}, "id": "ohm_power_005081_10.5_149.9", "license": "Apache-2.0", "prompt": "A resistor has resistance 149.9 ohm and voltage 10.5 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=10.5 V and R=149.9 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 149.9, "voltage": 10.5}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=442.5 mg, t=198.5 h, and T_half=106 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 120.8348, \"unit\": \"mg\"}", "dedupe_signature": "bcaca4e1b62940cee738d070bf0c3d58d5df6834940d211db20e2ee22e58efbe", "difficulty": "medium", "final_answer": {"answer": 120.8348, "unit": "mg"}, "id": "half_life_005082_442.5_106_198.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 442.5 mg. Its half-life is 106 hours. How many mg remain after 198.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=442.5 mg, t=198.5 h, and T_half=106 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 198.5, "half_life": 106.0, "initial_amount": 442.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 900 mL to 0.9 L.\n3. Compute M = 4.325 / 0.9.\nFinal: {\"answer\": 4.8056, \"unit\": \"mol/L\"}", "dedupe_signature": "d81a4393921718992db3d1090440fcf4d3e088acbe3861ad0fead22163dac2b4", "difficulty": "medium", "final_answer": {"answer": 4.8056, "unit": "mol/L"}, "id": "molarity_005084_4.325_900", "license": "Apache-2.0", "prompt": "A solution contains 4.325 mol of solute in 900 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 900 mL to 0.9 L.\nCompute M = 4.325 / 0.9.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 4.325, "volume_ml": 900}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.11 y, so each step multiplies y by 1 - h*0.11.\n3. Apply that update for 3 steps and round the final state.\nFinal: {\"answer\": 7.1252, \"unit\": \"state_units\"}", "dedupe_signature": "87de67f0f7456f30c4a852f277846454618c0467d43f7a094d65ca53e029d6de", "difficulty": "medium", "final_answer": {"answer": 7.1252, "unit": "state_units"}, "id": "euler_decay_005085_12_0.11_1.45_3", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.11 y with y(0)=12, step size h=1.45, for 3 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.11 y, so each step multiplies y by 1 - h*0.11.\nApply that update for 3 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 12.0, "rate": 0.11, "step": 1.45, "steps": 3}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-2)=23.8 and f(0.7)=6.52.\n3. The interval width is 2.7.\nFinal: {\"answer\": 40.932, \"unit\": \"area_units\"}", "dedupe_signature": "c5a3855bf0dba4c2748e87f08d468dd9f0d5227c5e9270ff26bd1e178513803a", "difficulty": "medium", "final_answer": {"answer": 40.932, "unit": "area_units"}, "id": "trapz_linear_005086_-6.4_11_-2_0.7", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-6.4x+11 from x=-2 to x=0.7. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-2)=23.8 and f(0.7)=6.52.\nThe interval width is 2.7.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 11.0, "slope": -6.4, "x0": -2.0, "x1": 0.7000000000000002}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 49210.0 / 1000.\nFinal: {\"answer\": 49.21, \"unit\": \"kg\"}", "dedupe_signature": "a6efa7537ebb49c68afcd518f1a3fb53f22e03d19d9a2a77bd412092724d68a8", "difficulty": "easy", "final_answer": {"answer": 49.21, "unit": "kg"}, "id": "unit_convert_005088_g_to_kg_49210", "license": "Apache-2.0", "prompt": "Convert 49210 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 49210.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 49210.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. grams cancel with J/(g*K), and kelvin cancels, leaving joules\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "ac116de5877eeb797ce8fa0d93c83248ee687679e55864f3ab35fa798da0010f", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_005091_consistent_4153435f_801030", "license": "Apache-2.0", "prompt": "In field worksheet case 801030, check dimensional consistency for Q = m * c * DeltaT. The left side has dimensions J and the right side has dimensions J. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\ngrams cancel with J/(g*K), and kelvin cancels, leaving joules\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "Q = m * c * DeltaT"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef clamp_005092(x, lo, hi):\n    if lo > hi:\n        raise ValueError('lo must be <= hi')\n    return min(max(x, lo), hi)\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"clamp_005092\"}", "dedupe_signature": "59bba5bec088988b533e54110432bf7e503072805131e51c4f78d33098e342b1", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "clamp_005092"}, "id": "code_005092_clamp_005092", "license": "Apache-2.0", "prompt": "Write a Python function clamp_005092(x, lo, hi) that clips x into the inclusive interval [lo, hi]. It must raise ValueError if lo > hi. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "clamp_005092"}, "verifier": {"function": "clamp_005092", "tests": ["assert clamp_005092(5, 0, 10) == 5", "assert clamp_005092(-2, 0, 10) == 0", "assert clamp_005092(12, 0, 10) == 10", "try:\n    clamp_005092(1, 3, 2)\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: recurrence, objective, tie_breaking_rule.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"recurrence\", \"objective\", \"tie_breaking_rule\"]}", "dedupe_signature": "22f4a56af2479a3b42f88892401a63c16fdb60ddd2835db21adc0c14da84dde9", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["recurrence", "objective", "tie_breaking_rule"]}, "id": "abstain_005093_recurrence_objective_tie_breaking_rule", "license": "Apache-2.0", "prompt": "Write a dynamic-programming solver for a alignment scoring problem with 4519 items and budget 65025, but the recurrence, objective, and tie-breaking rule are all absent. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: recurrence, objective, tie_breaking_rule.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["recurrence", "objective", "tie_breaking_rule"]}, "verifier": {"missing": ["recurrence", "objective", "tie_breaking_rule"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 8.4 kg and a = 4.75 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 39.9, \"unit\": \"N\"}", "dedupe_signature": "6b49b713ab361f71ec142271d63a4216d08e5c856b2c6ce443cee97613647306", "difficulty": "easy", "final_answer": {"answer": 39.9, "unit": "N"}, "id": "force_005094_8.4_4.75", "license": "Apache-2.0", "prompt": "A cart has mass 8.4 kg and measured acceleration 4.75 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 8.4 kg and a = 4.75 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 4.75, "mass": 8.4}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 41.2^2 and multiply by 0.5 * 27.85.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 23636.852, \"unit\": \"J\"}", "dedupe_signature": "6f84ea41178c9d08c08123015568065ba0251175704988bc5fcb4aa3a43d4a12", "difficulty": "easy", "final_answer": {"answer": 23636.852, "unit": "J"}, "id": "ke_005095_27.85_41.2", "license": "Apache-2.0", "prompt": "A body of mass 27.85 kg moves at 41.2 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 41.2^2 and multiply by 0.5 * 27.85.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 27.85, "velocity": 41.2}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=61 degrees through the sine of 2 theta.\n3. Substitute v=25.8 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 57.5428, \"unit\": \"m\"}", "dedupe_signature": "8035e975bb5419f04318d6834e85e1acc37bd5fbd8fb705e6e924361d7703552", "difficulty": "medium", "final_answer": {"answer": 57.5428, "unit": "m"}, "id": "projectile_range_005096_25.8_61", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 25.8 m/s and angle 61 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=61 degrees through the sine of 2 theta.\nSubstitute v=25.8 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 61, "gravity": 9.81, "speed": 25.8}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 2.07 * 8.314 * 270 / 119.0.\nFinal: {\"answer\": 39.0479, \"unit\": \"kPa\"}", "dedupe_signature": "23b3e2c4e758d752a319eb4292008d5f39be356b404184e9d72741fcc958997c", "difficulty": "medium", "final_answer": {"answer": 39.0479, "unit": "kPa"}, "id": "ideal_gas_005097_2.07_270_119.0", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=2.07 mol, T=270 K, and V=119.0 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 2.07 * 8.314 * 270 / 119.0.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 2.07, "temp_k": 270, "volume_l": 119.0}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1250 * 0.755 * 116.\nFinal: {\"answer\": 109475.0, \"unit\": \"J\"}", "dedupe_signature": "7345136999511a30fac6cc2bf686e69cbe295ec2f3e0ba081b7ef886e78a60c2", "difficulty": "easy", "final_answer": {"answer": 109475.0, "unit": "J"}, "id": "heat_q_005098_1250_0.755_116", "license": "Apache-2.0", "prompt": "A 1250 g sample has specific heat 0.755 J/(g*K). How much heat is needed to raise its temperature by 116 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1250 * 0.755 * 116.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 116, "heat_capacity": 0.755, "mass_g": 1250}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=71.6 V and R=84.4 ohm.\nFinal: {\"answer\": 60.7412, \"unit\": \"W\"}", "dedupe_signature": "c48bb2cafcea432701471038739fc3f4222f6a8a62168375c5a017d39608a790", "difficulty": "easy", "final_answer": {"answer": 60.7412, "unit": "W"}, "id": "ohm_power_005099_71.6_84.4", "license": "Apache-2.0", "prompt": "A resistor has resistance 84.4 ohm and voltage 71.6 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=71.6 V and R=84.4 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 84.4, "voltage": 71.6}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=622 mg, t=50.5 h, and T_half=1.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 0.0, \"unit\": \"mg\"}", "dedupe_signature": "0babbb89ab1f5c546842a5af8f4b3bf00130270d82ccc0092f5784c1af86a058", "difficulty": "medium", "final_answer": {"answer": 0.0, "unit": "mg"}, "id": "half_life_005100_622_1.5_50.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 622 mg. Its half-life is 1.5 hours. How many mg remain after 50.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=622 mg, t=50.5 h, and T_half=1.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 50.5, "half_life": 1.5, "initial_amount": 622.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 4.13 mol * 180.156 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 744.0443, \"unit\": \"g\"}", "dedupe_signature": "fd8dcf5dcc0b6251f27c26f023600af5d0bbfc5ae920da1bc2a163e739c3f845", "difficulty": "medium", "final_answer": {"answer": 744.0443, "unit": "g"}, "id": "stoich_mass_005101_glucose_4.13", "license": "Apache-2.0", "prompt": "A sample contains 4.13 mol of glucose. Using molar mass 180.156 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 4.13 mol * 180.156 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "glucose", "molar_mass": 180.156, "moles": 4.13}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.88 y, so each step multiplies y by 1 - h*0.88.\n3. Apply that update for 11 steps and round the final state.\nFinal: {\"answer\": 0.0, \"unit\": \"state_units\"}", "dedupe_signature": "2c3716de89090900fb708c5f62f4dc82cebb500c4a4036ce0de0a36688d2285b", "difficulty": "medium", "final_answer": {"answer": 0.0, "unit": "state_units"}, "id": "euler_decay_005103_64.5_0.88_0.85_11", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.88 y with y(0)=64.5, step size h=0.85, for 11 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.88 y, so each step multiplies y by 1 - h*0.88.\nApply that update for 11 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 64.5, "rate": 0.88, "step": 0.85, "steps": 11}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(6.4)=-45.66 and f(7.6)=-53.34.\n3. The interval width is 1.2.\nFinal: {\"answer\": -59.4, \"unit\": \"area_units\"}", "dedupe_signature": "2e6e4e606bf2050e67a32dba7f9ca01f4b8a2727a794f61ffcfc8e747a41f3fd", "difficulty": "medium", "final_answer": {"answer": -59.4, "unit": "area_units"}, "id": "trapz_linear_005104_-6.4_-4.7_6.4_7.6", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-6.4x+-4.7 from x=6.4 to x=7.6. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(6.4)=-45.66 and f(7.6)=-53.34.\nThe interval width is 1.2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -4.7, "slope": -6.4, "x0": 6.4, "x1": 7.6000000000000005}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.14 and add it to the current value.\nFinal: {\"answer\": [-1.258, 0.351, 1.904], \"unit\": \"temperature_units\"}", "dedupe_signature": "af5453e792d20da1122bad5dd4ead18f37785f28f84e1a34d3c9cbee56d63d6e", "difficulty": "hard", "final_answer": {"answer": [-1.258, 0.351, 1.904], "unit": "temperature_units"}, "id": "heat_step_005105_0.14_-0.9_-1.65_0.4_2.1_2.4", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-0.9, right=2.4; current interior values are [-1.65, 0.4, 2.1]. Use r=0.14. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.14 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-1.65, 0.4, 2.1], "left": -0.9, "r": 0.14, "right": 2.4}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kelvin equals Celsius plus 273.15.\n2. Apply the conversion factor directly to the given value.\n3. Compute 108.5 + 273.15.\nFinal: {\"answer\": 381.65, \"unit\": \"K\"}", "dedupe_signature": "cc5cf8cce35deff0055e7b726e9069405b14725afa7c8a69ce53b296dd4cb12c", "difficulty": "easy", "final_answer": {"answer": 381.65, "unit": "K"}, "id": "unit_convert_005106_c_to_k_108.5", "license": "Apache-2.0", "prompt": "Convert 108.5 degC to K. Return the converted value with unit.", "reasoning_trace": "Kelvin equals Celsius plus 273.15.\nApply the conversion factor directly to the given value.\nCompute 108.5 + 273.15.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 108.5}, "verifier": {"formula": "value + 273.15", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=234 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-291.2476, -400.8679], \"unit\": \"N\"}", "dedupe_signature": "21ae678a3b202eaf7d2d5cedb829acff5f6cb987aa9df17aeecc760f0fd25c25", "difficulty": "medium", "final_answer": {"answer": [-291.2476, -400.8679], "unit": "N"}, "id": "vector_components_005107_495.5_234", "license": "Apache-2.0", "prompt": "A vector has magnitude 495.5 N at 234 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=234 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 234, "magnitude": 495.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [8.45, -22.5], \"unit\": \"dimensionless\"}", "dedupe_signature": "48284752a0364d6a433f03ee55e8ce9113276a1adec8f9b4a8bdab241dea0592", "difficulty": "medium", "final_answer": {"answer": [8.45, -22.5], "unit": "dimensionless"}, "id": "line_two_point_005108_5.75_10_8.45_-22.5", "license": "Apache-2.0", "prompt": "A line passes through points (5.75, 26.0875) and (10, 62). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 5.75, "x2": 10.0, "y1": 26.0875, "y2": 62.0}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. lever arm times force has torque dimensions\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "81438931bb60f23095a7e48f1f9eecb74a6fa91b58a7a0eb678afac1d9893990", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_005109_consistent_5ca82cb9_491384", "license": "Apache-2.0", "prompt": "In model card equation case 491384, check dimensional consistency for tau = r * F. The left side has dimensions N*m and the right side has dimensions N*m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nlever arm times force has torque dimensions\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "tau = r * F"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef running_total_005110(values):\n    total = 0\n    out = []\n    for value in values:\n        total += value\n        out.append(total)\n    return out\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"running_total_005110\"}", "dedupe_signature": "568e7e00e246b3a41bda9a95d7e4f777a489b6b3cc5410c73a7dc15348c77f2c", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "running_total_005110"}, "id": "code_005110_running_total_005110", "license": "Apache-2.0", "prompt": "Write a Python function running_total_005110(values) that returns cumulative sums as a new list. It must not mutate the input list. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "running_total_005110"}, "verifier": {"function": "running_total_005110", "tests": ["assert running_total_005110([1, 2, 3]) == [1, 3, 6]", "xs = [4, -1, 2]; assert running_total_005110(xs) == [4, 3, 5] and xs == [4, -1, 2]", "assert running_total_005110([]) == []"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 1.7 kg and a = 14.3 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 24.31, \"unit\": \"N\"}", "dedupe_signature": "dfb378a6ce64c77d0d97061b40a9da625d9fac57b8a499e378bd86556defab93", "difficulty": "easy", "final_answer": {"answer": 24.31, "unit": "N"}, "id": "force_005112_1.7_14.3", "license": "Apache-2.0", "prompt": "A cart has mass 1.7 kg and measured acceleration 14.3 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 1.7 kg and a = 14.3 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 14.3, "mass": 1.7}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 39.05^2 and multiply by 0.5 * 28.4.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 21653.6155, \"unit\": \"J\"}", "dedupe_signature": "2ea2634e6fdcb828d022591e99a2d694f424ac42ea21369c58db6a3ca1ca1ba0", "difficulty": "easy", "final_answer": {"answer": 21653.6155, "unit": "J"}, "id": "ke_005113_28.4_39.05", "license": "Apache-2.0", "prompt": "A body of mass 28.4 kg moves at 39.05 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 39.05^2 and multiply by 0.5 * 28.4.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 28.4, "velocity": 39.05}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1670 * 0.565 * 106.\nFinal: {\"answer\": 100016.3, \"unit\": \"J\"}", "dedupe_signature": "f174a421127e09b0e38b29e880e1208983fbd20010569a1649bfc3fc6c2aaa65", "difficulty": "easy", "final_answer": {"answer": 100016.3, "unit": "J"}, "id": "heat_q_005116_1670_0.565_106", "license": "Apache-2.0", "prompt": "A 1670 g sample has specific heat 0.565 J/(g*K). How much heat is needed to raise its temperature by 106 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1670 * 0.565 * 106.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 106, "heat_capacity": 0.565, "mass_g": 1670}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=218.4 V and R=2.6 ohm.\nFinal: {\"answer\": 18345.6, \"unit\": \"W\"}", "dedupe_signature": "8e07c82ea3429c14096f01abff1edad78ded85a30c96f1fdb766f6e30ec95097", "difficulty": "easy", "final_answer": {"answer": 18345.6, "unit": "W"}, "id": "ohm_power_005117_218.4_2.6", "license": "Apache-2.0", "prompt": "A resistor has resistance 2.6 ohm and voltage 218.4 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=218.4 V and R=2.6 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 2.6, "voltage": 218.4}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=496 mg, t=121 h, and T_half=107.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 227.3254, \"unit\": \"mg\"}", "dedupe_signature": "278bc03b2c02d062bc9c645d6f8120e7badc33fcbc1406a83a926dc4c6d5480a", "difficulty": "medium", "final_answer": {"answer": 227.3254, "unit": "mg"}, "id": "half_life_005118_496_107.5_121", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 496 mg. Its half-life is 107.5 hours. How many mg remain after 121 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=496 mg, t=121 h, and T_half=107.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 121.0, "half_life": 107.5, "initial_amount": 496.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.11 y, so each step multiplies y by 1 - h*0.11.\n3. Apply that update for 7 steps and round the final state.\nFinal: {\"answer\": 2.4327, \"unit\": \"state_units\"}", "dedupe_signature": "23d3697f94e7bca4c6c984b280c9ef5f6162002d4abbec2a83fed449ccaa4cf7", "difficulty": "medium", "final_answer": {"answer": 2.4327, "unit": "state_units"}, "id": "euler_decay_005121_5.5_0.11_1_7", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.11 y with y(0)=5.5, step size h=1, for 7 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.11 y, so each step multiplies y by 1 - h*0.11.\nApply that update for 7 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 5.5, "rate": 0.11, "step": 1.0, "steps": 7}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-2.7)=-11.65 and f(1.7)=-13.85.\n3. The interval width is 4.4.\nFinal: {\"answer\": -56.1, \"unit\": \"area_units\"}", "dedupe_signature": "f5450068880b1b97d591553842334896b835204c0ab6a9a6b3f8f09a460a0967", "difficulty": "medium", "final_answer": {"answer": -56.1, "unit": "area_units"}, "id": "trapz_linear_005122_-0.5_-13_-2.7_1.7", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-0.5x+-13 from x=-2.7 to x=1.7. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-2.7)=-11.65 and f(1.7)=-13.85.\nThe interval width is 4.4.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -13.0, "slope": -0.5, "x0": -2.7, "x1": 1.7000000000000002}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.02 and add it to the current value.\nFinal: {\"answer\": [-1.762, 2.192, -1.172], \"unit\": \"temperature_units\"}", "dedupe_signature": "459d8eee063d0b3ade019205504c2ac7516a45e288e159c495e7a22242249adf", "difficulty": "hard", "final_answer": {"answer": [-1.762, 2.192, -1.172], "unit": "temperature_units"}, "id": "heat_step_005123_0.02_0.75_-1.9_2.35_-1.3_1.45", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=0.75, right=1.45; current interior values are [-1.9, 2.35, -1.3]. Use r=0.02. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.02 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-1.9, 2.35, -1.3], "left": 0.75, "r": 0.02, "right": 1.45}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=210 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-177.9682, -102.75], \"unit\": \"N\"}", "dedupe_signature": "5a017667043e91df342831e756292fee6fce5235469122a7c5c10f65f127eaa6", "difficulty": "medium", "final_answer": {"answer": [-177.9682, -102.75], "unit": "N"}, "id": "vector_components_005125_205.5_210", "license": "Apache-2.0", "prompt": "A vector has magnitude 205.5 N at 210 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=210 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 210, "magnitude": 205.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. velocity divided by time is acceleration\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "4177d0d38536fcd34866c46c89d8aa68eacaf1a9eb99523f645dd6897a4fda80", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_005127_inconsistent_c1271127_526151", "license": "Apache-2.0", "prompt": "In simulation spec case 526151, check dimensional consistency for x = v / t. The left side has dimensions m and the right side has dimensions m/s^2. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nvelocity divided by time is acceleration\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "x = v / t"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef finite_differences_005128(values):\n    return [values[i + 1] - values[i] for i in range(len(values) - 1)]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"finite_differences_005128\"}", "dedupe_signature": "8c26f49a1fe1c0d619ad090ad345250b6f8a1a09f4941a6fefb38b0644254d16", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "finite_differences_005128"}, "id": "code_005128_finite_differences_005128", "license": "Apache-2.0", "prompt": "Write a Python function finite_differences_005128(values) that returns the list of successive differences values[i+1] - values[i]. It must return [] for fewer than two values. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "finite_differences_005128"}, "verifier": {"function": "finite_differences_005128", "tests": ["assert finite_differences_005128([1, 4, 9, 16]) == [3, 5, 7]", "assert finite_differences_005128([5]) == []", "assert finite_differences_005128([]) == []"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: recurrence, objective, tie_breaking_rule.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"recurrence\", \"objective\", \"tie_breaking_rule\"]}", "dedupe_signature": "71d48ffc944d931e407f37d447abab246d281056a2d3eb016d1aea1176176f5b", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["recurrence", "objective", "tie_breaking_rule"]}, "id": "abstain_005129_recurrence_objective_tie_breaking_rule", "license": "Apache-2.0", "prompt": "Write a dynamic-programming solver for a segmentation scoring problem with 3615 items and budget 43515, but the recurrence, objective, and tie-breaking rule are all absent. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: recurrence, objective, tie_breaking_rule.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["recurrence", "objective", "tie_breaking_rule"]}, "verifier": {"missing": ["recurrence", "objective", "tie_breaking_rule"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 15.1 kg and a = 11.45 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 172.895, \"unit\": \"N\"}", "dedupe_signature": "e5ddbab45b55c899c3f0b46b26540e6ba8e70a48b5c50429881f389cd8372bf5", "difficulty": "easy", "final_answer": {"answer": 172.895, "unit": "N"}, "id": "force_005130_15.1_11.45", "license": "Apache-2.0", "prompt": "A cart has mass 15.1 kg and measured acceleration 11.45 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 15.1 kg and a = 11.45 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 11.45, "mass": 15.1}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 13.05^2 and multiply by 0.5 * 18.1.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 1541.2376, \"unit\": \"J\"}", "dedupe_signature": "6677c1b444d81678f3b2b0f160a07b7ce11c91503e7d4ccbc0f0a118fe31f42a", "difficulty": "easy", "final_answer": {"answer": 1541.2376, "unit": "J"}, "id": "ke_005131_18.1_13.05", "license": "Apache-2.0", "prompt": "A body of mass 18.1 kg moves at 13.05 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 13.05^2 and multiply by 0.5 * 18.1.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 18.1, "velocity": 13.05}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=42 degrees through the sine of 2 theta.\n3. Substitute v=84.9 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 730.7364, \"unit\": \"m\"}", "dedupe_signature": "de72324f2f220b029151227bac661426711d622c470e10724f01221cb86915ba", "difficulty": "medium", "final_answer": {"answer": 730.7364, "unit": "m"}, "id": "projectile_range_005132_84.9_42", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 84.9 m/s and angle 42 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=42 degrees through the sine of 2 theta.\nSubstitute v=84.9 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 42, "gravity": 9.81, "speed": 84.9}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 4.6 * 8.314 * 552 / 2.9.\nFinal: {\"answer\": 7279.6237, \"unit\": \"kPa\"}", "dedupe_signature": "e773a8292f7cb9da6742543524d09ddf9ac1f3e3c0b13891dbd9a3aa9581f622", "difficulty": "medium", "final_answer": {"answer": 7279.6237, "unit": "kPa"}, "id": "ideal_gas_005133_4.6_552_2.9", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=4.6 mol, T=552 K, and V=2.9 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 4.6 * 8.314 * 552 / 2.9.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 4.6, "temp_k": 552, "volume_l": 2.9}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1305 * 3.585 * 46.\nFinal: {\"answer\": 215207.55, \"unit\": \"J\"}", "dedupe_signature": "beb4d1645fe1bc324aae2e6931fc5b13edf57880678862e0b6a09d0d2b1e9d85", "difficulty": "easy", "final_answer": {"answer": 215207.55, "unit": "J"}, "id": "heat_q_005134_1305_3.585_46", "license": "Apache-2.0", "prompt": "A 1305 g sample has specific heat 3.585 J/(g*K). How much heat is needed to raise its temperature by 46 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1305 * 3.585 * 46.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 46, "heat_capacity": 3.585, "mass_g": 1305}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=104.9 V and R=122.4 ohm.\nFinal: {\"answer\": 89.902, \"unit\": \"W\"}", "dedupe_signature": "d6657bbc9bcd26b3133b28564afde9aa542659a23c3c44b8a7fd227ea646e17c", "difficulty": "easy", "final_answer": {"answer": 89.902, "unit": "W"}, "id": "ohm_power_005135_104.9_122.4", "license": "Apache-2.0", "prompt": "A resistor has resistance 122.4 ohm and voltage 104.9 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=104.9 V and R=122.4 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 122.4, "voltage": 104.9}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=22 mg, t=218.5 h, and T_half=15.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 0.0013, \"unit\": \"mg\"}", "dedupe_signature": "b27b728d59f5dabfa0279b10331a6c7598b49bd0b1f89eeceed94789c93f7501", "difficulty": "medium", "final_answer": {"answer": 0.0013, "unit": "mg"}, "id": "half_life_005136_22_15.5_218.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 22 mg. Its half-life is 15.5 hours. How many mg remain after 218.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=22 mg, t=218.5 h, and T_half=15.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 218.5, "half_life": 15.5, "initial_amount": 22.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 6.05 mol * 100.087 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 605.5263, \"unit\": \"g\"}", "dedupe_signature": "0fd18dec761cddea19433f72320526572ee0355e1478fc672815686d20c94253", "difficulty": "medium", "final_answer": {"answer": 605.5263, "unit": "g"}, "id": "stoich_mass_005137_calcium_carbonate_6.05", "license": "Apache-2.0", "prompt": "A sample contains 6.05 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 6.05 mol * 100.087 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "calcium carbonate", "molar_mass": 100.087, "moles": 6.05}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 4985 mL to 4.985 L.\n3. Compute M = 1.335 / 4.985.\nFinal: {\"answer\": 0.2678, \"unit\": \"mol/L\"}", "dedupe_signature": "571633871617fff6a1bcc585901726a4fa4ebb9ec759ba26f157a62864476be8", "difficulty": "medium", "final_answer": {"answer": 0.2678, "unit": "mol/L"}, "id": "molarity_005138_1.335_4985", "license": "Apache-2.0", "prompt": "A solution contains 1.335 mol of solute in 4985 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 4985 mL to 4.985 L.\nCompute M = 1.335 / 4.985.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 1.335, "volume_ml": 4985}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.38 y, so each step multiplies y by 1 - h*0.38.\n3. Apply that update for 9 steps and round the final state.\nFinal: {\"answer\": 0.2074, \"unit\": \"state_units\"}", "dedupe_signature": "aca24c5c47d909c2fc4ec4120785a3dd040cdbb8c2790502d1ca2bbc776c0b17", "difficulty": "medium", "final_answer": {"answer": 0.2074, "unit": "state_units"}, "id": "euler_decay_005139_36.5_0.38_1.15_9", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.38 y with y(0)=36.5, step size h=1.15, for 9 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.38 y, so each step multiplies y by 1 - h*0.38.\nApply that update for 9 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 36.5, "rate": 0.38, "step": 1.15, "steps": 9}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(9.8)=-44.56 and f(14.6)=-62.32.\n3. The interval width is 4.8.\nFinal: {\"answer\": -256.512, \"unit\": \"area_units\"}", "dedupe_signature": "0a3b56da0cdd64d8f5f9752d781b240f060f3726e48ef5272c3bd929b27965c8", "difficulty": "medium", "final_answer": {"answer": -256.512, "unit": "area_units"}, "id": "trapz_linear_005140_-3.7_-8.3_9.8_14.6", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-3.7x+-8.3 from x=9.8 to x=14.6. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(9.8)=-44.56 and f(14.6)=-62.32.\nThe interval width is 4.8.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -8.3, "slope": -3.7, "x0": 9.8, "x1": 14.600000000000001}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.22 and add it to the current value.\nFinal: {\"answer\": [-0.685, 0.551, 1.158], \"unit\": \"temperature_units\"}", "dedupe_signature": "9cfd9bb1e36a259d7678b322cea4b7cc9358703eee27285f9540f13d730d158d", "difficulty": "hard", "final_answer": {"answer": [-0.685, 0.551, 1.158], "unit": "temperature_units"}, "id": "heat_step_005141_0.22_-0.75_-1.4_1.2_0.85_1.9", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-0.75, right=1.9; current interior values are [-1.4, 1.2, 0.85]. Use r=0.22. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.22 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-1.4, 1.2, 0.85], "left": -0.75, "r": 0.22, "right": 1.9}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kelvin equals Celsius plus 273.15.\n2. Apply the conversion factor directly to the given value.\n3. Compute 83.5 + 273.15.\nFinal: {\"answer\": 356.65, \"unit\": \"K\"}", "dedupe_signature": "1a353e011e7d6e3d8c6011b5197c219ab2698455476928fe1cbda9b1aafab10c", "difficulty": "easy", "final_answer": {"answer": 356.65, "unit": "K"}, "id": "unit_convert_005142_c_to_k_83.5", "license": "Apache-2.0", "prompt": "Convert 83.5 degC to K. Return the converted value with unit.", "reasoning_trace": "Kelvin equals Celsius plus 273.15.\nApply the conversion factor directly to the given value.\nCompute 83.5 + 273.15.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 83.5}, "verifier": {"formula": "value + 273.15", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [3.1, 9.75], \"unit\": \"dimensionless\"}", "dedupe_signature": "0a6130c4fffa7bdcfb973e4b1c02a4fd4a1fc45c76132b178ad34a5ada692d05", "difficulty": "medium", "final_answer": {"answer": [3.1, 9.75], "unit": "dimensionless"}, "id": "line_two_point_005144_-6.5_-0.25_3.1_9.75", "license": "Apache-2.0", "prompt": "A line passes through points (-6.5, -10.4) and (-0.25, 8.975). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -6.5, "x2": -0.25, "y1": -10.400000000000002, "y2": 8.975}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. grams cancel with J/(g*K), and kelvin cancels, leaving joules\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "68c480e4b9acce2487d0e5f964d9143caa1faa5dcd094afba9610b5cd9789d59", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_005145_consistent_4153435f_373948", "license": "Apache-2.0", "prompt": "In quality-control check case 373948, check dimensional consistency for Q = m * c * DeltaT. The left side has dimensions J and the right side has dimensions J. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\ngrams cancel with J/(g*K), and kelvin cancels, leaving joules\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "Q = m * c * DeltaT"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef center_values_005146(values):\n    if not values:\n        raise ValueError('center_values requires at least one value')\n    mean = sum(values) / len(values)\n    return [value - mean for value in values]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"center_values_005146\"}", "dedupe_signature": "bdbec915101c6274cab574b9df11357e385ac3b61c38cc35ac8b22899e8ba9cf", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "center_values_005146"}, "id": "code_005146_center_values_005146", "license": "Apache-2.0", "prompt": "Write a Python function center_values_005146(values) that subtracts the arithmetic mean from each value and returns a new list. Raise ValueError for an empty input. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "center_values_005146"}, "verifier": {"function": "center_values_005146", "tests": ["out = center_values_005146([1, 2, 3]); assert out == [-1, 0, 1]", "assert center_values_005146([5]) == [0]", "try:\n    center_values_005146([])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: rate_constant, number_of_steps.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"rate_constant\", \"number_of_steps\"]}", "dedupe_signature": "1c84959c7a8ed6dafd13a7c5ab0db3efbda426fa7eaf2d5f6b63baab5962fce0", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["rate_constant", "number_of_steps"]}, "id": "abstain_005147_rate_constant_number_of_steps", "license": "Apache-2.0", "prompt": "Use explicit Euler for dy/dt = -k y. The prompt gives y(0)=71.5 and h=0.5, but omits both k and the number of steps. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: rate_constant, number_of_steps.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["rate_constant", "number_of_steps"]}, "verifier": {"missing": ["rate_constant", "number_of_steps"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 19.2 kg and a = 10.5 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 201.6, \"unit\": \"N\"}", "dedupe_signature": "280959b5692f833046b1c151d49b71672741d8c47e31b97e2cfd0ed33611f09b", "difficulty": "easy", "final_answer": {"answer": 201.6, "unit": "N"}, "id": "force_005148_19.2_10.5", "license": "Apache-2.0", "prompt": "A cart has mass 19.2 kg and measured acceleration 10.5 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 19.2 kg and a = 10.5 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 10.5, "mass": 19.2}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 1.6 * 8.314 * 360 / 106.0.\nFinal: {\"answer\": 45.178, \"unit\": \"kPa\"}", "dedupe_signature": "515010a375753bb59bff1c03a810bc1f31e25342aced6899bdecebc6a74721e6", "difficulty": "medium", "final_answer": {"answer": 45.178, "unit": "kPa"}, "id": "ideal_gas_005151_1.6_360_106.0", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=1.6 mol, T=360 K, and V=106.0 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 1.6 * 8.314 * 360 / 106.0.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 1.6, "temp_k": 360, "volume_l": 106.0}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1095 * 2.245 * 78.\nFinal: {\"answer\": 191745.45, \"unit\": \"J\"}", "dedupe_signature": "7e0be4f018522873a8d0d6899660478783467b12b8cf3c05ee534ee402903eff", "difficulty": "easy", "final_answer": {"answer": 191745.45, "unit": "J"}, "id": "heat_q_005152_1095_2.245_78", "license": "Apache-2.0", "prompt": "A 1095 g sample has specific heat 2.245 J/(g*K). How much heat is needed to raise its temperature by 78 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1095 * 2.245 * 78.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 78, "heat_capacity": 2.245, "mass_g": 1095}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=143.2 V and R=92.9 ohm.\nFinal: {\"answer\": 220.7346, \"unit\": \"W\"}", "dedupe_signature": "94b96e844a50481dc90ee9020fc313236c949d536c7cdac734aa60b7d131b077", "difficulty": "easy", "final_answer": {"answer": 220.7346, "unit": "W"}, "id": "ohm_power_005153_143.2_92.9", "license": "Apache-2.0", "prompt": "A resistor has resistance 92.9 ohm and voltage 143.2 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=143.2 V and R=92.9 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 92.9, "voltage": 143.2}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=879 mg, t=128.5 h, and T_half=103.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 371.746, \"unit\": \"mg\"}", "dedupe_signature": "93e6ae8d675c4e81b40e1c273231c743066377ce4553db9e11482b47bfaae9be", "difficulty": "medium", "final_answer": {"answer": 371.746, "unit": "mg"}, "id": "half_life_005154_879_103.5_128.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 879 mg. Its half-life is 103.5 hours. How many mg remain after 128.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=879 mg, t=128.5 h, and T_half=103.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 128.5, "half_life": 103.5, "initial_amount": 879.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 2.82 mol * 180.156 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 508.0399, \"unit\": \"g\"}", "dedupe_signature": "cf4b1c888721f2ff61b43c3b7768983352d797c6e551f5d2b7b0d66bc454613a", "difficulty": "medium", "final_answer": {"answer": 508.0399, "unit": "g"}, "id": "stoich_mass_005155_glucose_2.82", "license": "Apache-2.0", "prompt": "A sample contains 2.82 mol of glucose. Using molar mass 180.156 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 2.82 mol * 180.156 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "glucose", "molar_mass": 180.156, "moles": 2.82}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 4560 mL to 4.56 L.\n3. Compute M = 2.495 / 4.56.\nFinal: {\"answer\": 0.5471, \"unit\": \"mol/L\"}", "dedupe_signature": "44537e1f3bd704a1e491a5a8d632fb947827d2725f9af230ded5f10bfb62b6d4", "difficulty": "medium", "final_answer": {"answer": 0.5471, "unit": "mol/L"}, "id": "molarity_005156_2.495_4560", "license": "Apache-2.0", "prompt": "A solution contains 2.495 mol of solute in 4560 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 4560 mL to 4.56 L.\nCompute M = 2.495 / 4.56.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 2.495, "volume_ml": 4560}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 27968.0 / 1000.\nFinal: {\"answer\": 27.968, \"unit\": \"kg\"}", "dedupe_signature": "b793fc404397105d3106ee40cabc6b0e222336337f1ff21767e8b07e241ea3ff", "difficulty": "easy", "final_answer": {"answer": 27.968, "unit": "kg"}, "id": "unit_convert_005160_g_to_kg_27968", "license": "Apache-2.0", "prompt": "Convert 27968 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 27968.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 27968.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=293 degrees and keep the unit as newtons.\nFinal: {\"answer\": [165.8654, -390.7543], \"unit\": \"N\"}", "dedupe_signature": "cb68c1122bbc591410002fb0bf1032140681f634d9970fab26a15fdf1b7e17d5", "difficulty": "medium", "final_answer": {"answer": [165.8654, -390.7543], "unit": "N"}, "id": "vector_components_005161_424.5_293", "license": "Apache-2.0", "prompt": "A vector has magnitude 424.5 N at 293 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=293 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 293, "magnitude": 424.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [1.4, 12.75], \"unit\": \"dimensionless\"}", "dedupe_signature": "8a1d93bfbb0b85f6650812b8c850815df4c428d2ebcd9e802d6ee48cfe254489", "difficulty": "medium", "final_answer": {"answer": [1.4, 12.75], "unit": "dimensionless"}, "id": "line_two_point_005162_-6_3.5_1.4_12.75", "license": "Apache-2.0", "prompt": "A line passes through points (-6, 4.35) and (3.5, 17.65). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -6.0, "x2": 3.5, "y1": 4.350000000000001, "y2": 17.65}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. lever arm times force has torque dimensions\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "95eab38f479a286253d40bf58bf9bcd9738d9f1d137492ff8d8fafb698eef66a", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_005163_consistent_5ca82cb9_44857", "license": "Apache-2.0", "prompt": "In quality-control check case 44857, check dimensional consistency for tau = r * F. The left side has dimensions N*m and the right side has dimensions N*m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nlever arm times force has torque dimensions\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "tau = r * F"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef threshold_flags_005164(values, threshold):\n    return [value >= threshold for value in values]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"threshold_flags_005164\"}", "dedupe_signature": "81753a6894da96bad5ea1461b96ffd34b42f6be616d256e5484ff100fee4b041", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "threshold_flags_005164"}, "id": "code_005164_threshold_flags_005164", "license": "Apache-2.0", "prompt": "Write a Python function threshold_flags_005164(values, threshold) that returns a list of booleans showing whether each value is greater than or equal to threshold. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "threshold_flags_005164"}, "verifier": {"function": "threshold_flags_005164", "tests": ["assert threshold_flags_005164([1, 2, 3], 2) == [False, True, True]", "assert threshold_flags_005164([], 5) == []", "assert threshold_flags_005164([-1, 0], 0) == [False, True]"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: rate_constant, number_of_steps.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"rate_constant\", \"number_of_steps\"]}", "dedupe_signature": "46bff368cdf68cc8b4b0728d46798b298a96ee465c53b28c8f311bc415c04e4d", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["rate_constant", "number_of_steps"]}, "id": "abstain_005165_rate_constant_number_of_steps", "license": "Apache-2.0", "prompt": "Use explicit Euler for dy/dt = -k y. The prompt gives y(0)=8.5 and h=1.5, but omits both k and the number of steps. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: rate_constant, number_of_steps.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["rate_constant", "number_of_steps"]}, "verifier": {"missing": ["rate_constant", "number_of_steps"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 8.05 kg and a = 7.85 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 63.1925, \"unit\": \"N\"}", "dedupe_signature": "7bbc9349bd98a8b314eb28eb2f0accef8d867b78d779aebe4c40389f40cb9e19", "difficulty": "easy", "final_answer": {"answer": 63.1925, "unit": "N"}, "id": "force_005166_8.05_7.85", "license": "Apache-2.0", "prompt": "A cart has mass 8.05 kg and measured acceleration 7.85 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 8.05 kg and a = 7.85 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 7.85, "mass": 8.05}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=27 degrees through the sine of 2 theta.\n3. Substitute v=31.9 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 83.9209, \"unit\": \"m\"}", "dedupe_signature": "be15abf8bb53d43b70600fef28a39a3f475392758c047aafadcf0d2b4bd2f139", "difficulty": "medium", "final_answer": {"answer": 83.9209, "unit": "m"}, "id": "projectile_range_005168_31.9_27", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 31.9 m/s and angle 27 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=27 degrees through the sine of 2 theta.\nSubstitute v=31.9 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 27, "gravity": 9.81, "speed": 31.9}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=124 V and R=190.2 ohm.\nFinal: {\"answer\": 80.8412, \"unit\": \"W\"}", "dedupe_signature": "48f4ad9e4c3eecaf99bf092ff1bdf75f4b89eeca6fafceda6f2d9c5f1d7143a5", "difficulty": "easy", "final_answer": {"answer": 80.8412, "unit": "W"}, "id": "ohm_power_005171_124_190.2", "license": "Apache-2.0", "prompt": "A resistor has resistance 190.2 ohm and voltage 124 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=124 V and R=190.2 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 190.2, "voltage": 124.0}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=262.5 mg, t=128.5 h, and T_half=80 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 86.2184, \"unit\": \"mg\"}", "dedupe_signature": "840676bbcc60e936873560c91e618a0acb49b7004bede2ce4eac839e47b73668", "difficulty": "medium", "final_answer": {"answer": 86.2184, "unit": "mg"}, "id": "half_life_005172_262.5_80_128.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 262.5 mg. Its half-life is 80 hours. How many mg remain after 128.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=262.5 mg, t=128.5 h, and T_half=80 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 128.5, "half_life": 80.0, "initial_amount": 262.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 2985 mL to 2.985 L.\n3. Compute M = 2.965 / 2.985.\nFinal: {\"answer\": 0.9933, \"unit\": \"mol/L\"}", "dedupe_signature": "d9835c336a976e2221da396ccb37975b6d4c24f1b69ec80f4dae0e0fb1adf662", "difficulty": "medium", "final_answer": {"answer": 0.9933, "unit": "mol/L"}, "id": "molarity_005174_2.965_2985", "license": "Apache-2.0", "prompt": "A solution contains 2.965 mol of solute in 2985 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 2985 mL to 2.985 L.\nCompute M = 2.965 / 2.985.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 2.965, "volume_ml": 2985}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.39 y, so each step multiplies y by 1 - h*0.39.\n3. Apply that update for 5 steps and round the final state.\nFinal: {\"answer\": 7.7836, \"unit\": \"state_units\"}", "dedupe_signature": "d7796446a151e780b46062ed6c0fa77a6166b736e31615d7bb04ec36b9b5db4a", "difficulty": "medium", "final_answer": {"answer": 7.7836, "unit": "state_units"}, "id": "euler_decay_005175_13_0.39_0.25_5", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.39 y with y(0)=13, step size h=0.25, for 5 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.39 y, so each step multiplies y by 1 - h*0.39.\nApply that update for 5 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 13.0, "rate": 0.39, "step": 0.25, "steps": 5}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-2)=-22.5 and f(-0.1)=-7.87.\n3. The interval width is 1.9.\nFinal: {\"answer\": -28.8515, \"unit\": \"area_units\"}", "dedupe_signature": "d871f687c264ad56c7cbc037e803b10d3c0c37898dd35f044261f3950fdd5c1c", "difficulty": "medium", "final_answer": {"answer": -28.8515, "unit": "area_units"}, "id": "trapz_linear_005176_7.7_-7.1_-2_-0.1", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=7.7x+-7.1 from x=-2 to x=-0.1. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-2)=-22.5 and f(-0.1)=-7.87.\nThe interval width is 1.9.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -7.1, "slope": 7.7, "x0": -2.0, "x1": -0.10000000000000009}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.28 and add it to the current value.\nFinal: {\"answer\": [-0.088, -0.57, 0.164], \"unit\": \"temperature_units\"}", "dedupe_signature": "6b418b1aa491d9c7eb5484c6d7b2b213d5a0291d39c353b7ba316b48cd29610d", "difficulty": "hard", "final_answer": {"answer": [-0.088, -0.57, 0.164], "unit": "temperature_units"}, "id": "heat_step_005177_0.28_1.25_-0.9_-0.15_-0.9_2.15", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.25, right=2.15; current interior values are [-0.9, -0.15, -0.9]. Use r=0.28. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.28 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-0.9, -0.15, -0.9], "left": 1.25, "r": 0.28, "right": 2.15}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 13587.0 / 1000.\nFinal: {\"answer\": 13.587, \"unit\": \"kg\"}", "dedupe_signature": "eecc27114d13d488af5d606a899de88818ba5e17d8045bbf2f56dc166e0b66e5", "difficulty": "easy", "final_answer": {"answer": 13.587, "unit": "kg"}, "id": "unit_convert_005178_g_to_kg_13587", "license": "Apache-2.0", "prompt": "Convert 13587 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 13587.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 13587.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=85 degrees and keep the unit as newtons.\nFinal: {\"answer\": [11.766, 134.4863], \"unit\": \"N\"}", "dedupe_signature": "d189ea7ba2287823b385b76c1b732de2a9b2b1f3e48305814976c26edbdef344", "difficulty": "medium", "final_answer": {"answer": [11.766, 134.4863], "unit": "N"}, "id": "vector_components_005179_135_85", "license": "Apache-2.0", "prompt": "A vector has magnitude 135 N at 85 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=85 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 85, "magnitude": 135.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. velocity divided by time is acceleration\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "a56509f27c458962f94c725b0de17a70d58dba79acaadfd8754cb994dd338e69", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_005181_inconsistent_c1271127_383789", "license": "Apache-2.0", "prompt": "In student derivation case 383789, check dimensional consistency for x = v / t. The left side has dimensions m and the right side has dimensions m/s^2. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nvelocity divided by time is acceleration\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "x = v / t"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef threshold_flags_005182(values, threshold):\n    return [value >= threshold for value in values]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"threshold_flags_005182\"}", "dedupe_signature": "aed13a8890ae0f98522c0deb519d0b104f9e98efe05815a0494895dbc5351da5", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "threshold_flags_005182"}, "id": "code_005182_threshold_flags_005182", "license": "Apache-2.0", "prompt": "Write a Python function threshold_flags_005182(values, threshold) that returns a list of booleans showing whether each value is greater than or equal to threshold. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "threshold_flags_005182"}, "verifier": {"function": "threshold_flags_005182", "tests": ["assert threshold_flags_005182([1, 2, 3], 2) == [False, True, True]", "assert threshold_flags_005182([], 5) == []", "assert threshold_flags_005182([-1, 0], 0) == [False, True]"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 14.15 kg and a = 8 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 113.2, \"unit\": \"N\"}", "dedupe_signature": "628271667d569864b18c580212f9dbccde2a8324a3de2149a779c1cbfc1f445d", "difficulty": "easy", "final_answer": {"answer": 113.2, "unit": "N"}, "id": "force_005184_14.15_8", "license": "Apache-2.0", "prompt": "A cart has mass 14.15 kg and measured acceleration 8 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 14.15 kg and a = 8 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 8.0, "mass": 14.15}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 35.65^2 and multiply by 0.5 * 17.15.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 10898.1604, \"unit\": \"J\"}", "dedupe_signature": "584fbd69466b7e66756aff504a0056b76fb005de6dc129be475cd2959d3205ed", "difficulty": "easy", "final_answer": {"answer": 10898.1604, "unit": "J"}, "id": "ke_005185_17.15_35.65", "license": "Apache-2.0", "prompt": "A body of mass 17.15 kg moves at 35.65 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 35.65^2 and multiply by 0.5 * 17.15.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 17.15, "velocity": 35.65}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=67 degrees through the sine of 2 theta.\n3. Substitute v=54.5 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 217.8001, \"unit\": \"m\"}", "dedupe_signature": "110eeb97ecdb96df147a0e8cf108797025c43713fde136fe879eb0c919a5e211", "difficulty": "medium", "final_answer": {"answer": 217.8001, "unit": "m"}, "id": "projectile_range_005186_54.5_67", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 54.5 m/s and angle 67 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=67 degrees through the sine of 2 theta.\nSubstitute v=54.5 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 67, "gravity": 9.81, "speed": 54.5}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 2.02 * 8.314 * 593 / 84.8.\nFinal: {\"answer\": 117.4411, \"unit\": \"kPa\"}", "dedupe_signature": "6dcfc0c02dabf1493a03ab81a42e1fe703d69dc7b96eb65ac71d5293ece7e824", "difficulty": "medium", "final_answer": {"answer": 117.4411, "unit": "kPa"}, "id": "ideal_gas_005187_2.02_593_84.8", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=2.02 mol, T=593 K, and V=84.8 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 2.02 * 8.314 * 593 / 84.8.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 2.02, "temp_k": 593, "volume_l": 84.8}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1100 * 2.565 * 92.\nFinal: {\"answer\": 259578.0, \"unit\": \"J\"}", "dedupe_signature": "34a7fb187fbc1bb47fe91ea091c0ee234cc89138221aca6737687b60954e64cd", "difficulty": "easy", "final_answer": {"answer": 259578.0, "unit": "J"}, "id": "heat_q_005188_1100_2.565_92", "license": "Apache-2.0", "prompt": "A 1100 g sample has specific heat 2.565 J/(g*K). How much heat is needed to raise its temperature by 92 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1100 * 2.565 * 92.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 92, "heat_capacity": 2.565, "mass_g": 1100}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=169.7 V and R=34.6 ohm.\nFinal: {\"answer\": 832.3147, \"unit\": \"W\"}", "dedupe_signature": "d2a096dc8c21668fdc549e8f573f7c449cce8d7acf9ba3e8a0fba4ed5973642a", "difficulty": "easy", "final_answer": {"answer": 832.3147, "unit": "W"}, "id": "ohm_power_005189_169.7_34.6", "license": "Apache-2.0", "prompt": "A resistor has resistance 34.6 ohm and voltage 169.7 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=169.7 V and R=34.6 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 34.6, "voltage": 169.7}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=31.5 mg, t=254.5 h, and T_half=56 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 1.3497, \"unit\": \"mg\"}", "dedupe_signature": "3e965cdf04bfdc9daee9bcbc5474b8b945553a9d948e72b924cb539c0ca500de", "difficulty": "medium", "final_answer": {"answer": 1.3497, "unit": "mg"}, "id": "half_life_005190_31.5_56_254.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 31.5 mg. Its half-life is 56 hours. How many mg remain after 254.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=31.5 mg, t=254.5 h, and T_half=56 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 254.5, "half_life": 56.0, "initial_amount": 31.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 7.2 mol * 44.01 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 316.872, \"unit\": \"g\"}", "dedupe_signature": "56b9f21d83bbcb3f852b0f76d7d5a5f24d35c17e491ae4d168e78c7757105500", "difficulty": "medium", "final_answer": {"answer": 316.872, "unit": "g"}, "id": "stoich_mass_005191_carbon_dioxide_7.2", "license": "Apache-2.0", "prompt": "A sample contains 7.2 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 7.2 mol * 44.01 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "carbon dioxide", "molar_mass": 44.01, "moles": 7.2}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 3145 mL to 3.145 L.\n3. Compute M = 2.86 / 3.145.\nFinal: {\"answer\": 0.9094, \"unit\": \"mol/L\"}", "dedupe_signature": "5a599ba7384735844c0659d0c2a18f12db04d72ba7a252e254e817e7831c8c91", "difficulty": "medium", "final_answer": {"answer": 0.9094, "unit": "mol/L"}, "id": "molarity_005192_2.86_3145", "license": "Apache-2.0", "prompt": "A solution contains 2.86 mol of solute in 3145 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 3145 mL to 3.145 L.\nCompute M = 2.86 / 3.145.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 2.86, "volume_ml": 3145}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.12 and add it to the current value.\nFinal: {\"answer\": [-0.69, -0.282, -0.616], \"unit\": \"temperature_units\"}", "dedupe_signature": "452bc03347c4506fe9aeb5a109084c301607037890ed4200cac771437363ac87", "difficulty": "hard", "final_answer": {"answer": [-0.69, -0.282, -0.616], "unit": "temperature_units"}, "id": "heat_step_005195_0.12_1.85_-1.2_0.0_-1.15_2.15", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.85, right=2.15; current interior values are [-1.2, 0.0, -1.15]. Use r=0.12. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.12 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-1.2, 0.0, -1.15], "left": 1.85, "r": 0.12, "right": 2.15}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 100 centimeters in one meter.\n2. Apply the conversion factor directly to the given value.\n3. Compute 4929.5 / 100.\nFinal: {\"answer\": 49.295, \"unit\": \"m\"}", "dedupe_signature": "1a6c9b37967be87c6759b89f6b9ec2670d6f58cd7adc570ec8729c2464a7895d", "difficulty": "easy", "final_answer": {"answer": 49.295, "unit": "m"}, "id": "unit_convert_005196_cm_to_m_4929.5", "license": "Apache-2.0", "prompt": "Convert 4929.5 cm to m. Return the converted value with unit.", "reasoning_trace": "There are 100 centimeters in one meter.\nApply the conversion factor directly to the given value.\nCompute 4929.5 / 100.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 4929.5}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=213 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-261.6652, -169.9274], \"unit\": \"N\"}", "dedupe_signature": "ce751cc05091e87f895fc770f71f5908f5c5a12d1d50afdeedbcc50ee99cd163", "difficulty": "medium", "final_answer": {"answer": [-261.6652, -169.9274], "unit": "N"}, "id": "vector_components_005197_312_213", "license": "Apache-2.0", "prompt": "A vector has magnitude 312 N at 213 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=213 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 213, "magnitude": 312.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [2.9, 23.25], \"unit\": \"dimensionless\"}", "dedupe_signature": "4822981a8b0e8e46952c59754dd328dd33ee883c6047ab946b8b5968f72dd958", "difficulty": "medium", "final_answer": {"answer": [2.9, 23.25], "unit": "dimensionless"}, "id": "line_two_point_005198_-17_-16.5_2.9_23.25", "license": "Apache-2.0", "prompt": "A line passes through points (-17, -26.05) and (-16.5, -24.6). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -17.0, "x2": -16.5, "y1": -26.049999999999997, "y2": -24.6}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 19.8^2 and multiply by 0.5 * 2.8.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 548.856, \"unit\": \"J\"}", "dedupe_signature": "a86c0f63dd8293623af773c87c49fdd8bb0ee8850008e5941a7aa26a77cfe95e", "difficulty": "easy", "final_answer": {"answer": 548.856, "unit": "J"}, "id": "ke_005203_2.8_19.8", "license": "Apache-2.0", "prompt": "A body of mass 2.8 kg moves at 19.8 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 19.8^2 and multiply by 0.5 * 2.8.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 2.8, "velocity": 19.8}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=60 degrees through the sine of 2 theta.\n3. Substitute v=59.8 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 315.6923, \"unit\": \"m\"}", "dedupe_signature": "718789f3d3b8c56db1cd84098e08f4faf120714163aa94713230967f8b03d609", "difficulty": "medium", "final_answer": {"answer": 315.6923, "unit": "m"}, "id": "projectile_range_005204_59.8_60", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 59.8 m/s and angle 60 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=60 degrees through the sine of 2 theta.\nSubstitute v=59.8 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 60, "gravity": 9.81, "speed": 59.8}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=146.1 V and R=82.3 ohm.\nFinal: {\"answer\": 259.3586, \"unit\": \"W\"}", "dedupe_signature": "709d46ac9f0f603b39d3c91437ed735f3b5b0c49614172978aafee6adbe1f8a0", "difficulty": "easy", "final_answer": {"answer": 259.3586, "unit": "W"}, "id": "ohm_power_005207_146.1_82.3", "license": "Apache-2.0", "prompt": "A resistor has resistance 82.3 ohm and voltage 146.1 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=146.1 V and R=82.3 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 82.3, "voltage": 146.1}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=52.5 mg, t=151.5 h, and T_half=105 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 19.3115, \"unit\": \"mg\"}", "dedupe_signature": "8496d80b499fe7e652c1fc2d3c53ae6c2829cac69fec57f6f7080d5998717ada", "difficulty": "medium", "final_answer": {"answer": 19.3115, "unit": "mg"}, "id": "half_life_005208_52.5_105_151.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 52.5 mg. Its half-life is 105 hours. How many mg remain after 151.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=52.5 mg, t=151.5 h, and T_half=105 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 151.5, "half_life": 105.0, "initial_amount": 52.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 4.57 mol * 18.015 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 82.3286, \"unit\": \"g\"}", "dedupe_signature": "1379769de7f2864d7f39398ec468fcf41220d31b91a3e23a8bec2e1c83883574", "difficulty": "medium", "final_answer": {"answer": 82.3286, "unit": "g"}, "id": "stoich_mass_005209_water_4.57", "license": "Apache-2.0", "prompt": "A sample contains 4.57 mol of water. Using molar mass 18.015 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 4.57 mol * 18.015 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "water", "molar_mass": 18.015, "moles": 4.57}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 2135 mL to 2.135 L.\n3. Compute M = 4.26 / 2.135.\nFinal: {\"answer\": 1.9953, \"unit\": \"mol/L\"}", "dedupe_signature": "855ae7ab3b194ac6490b4e240103eb70c640eab3127ae9266cc55cb75351d3b7", "difficulty": "medium", "final_answer": {"answer": 1.9953, "unit": "mol/L"}, "id": "molarity_005210_4.26_2135", "license": "Apache-2.0", "prompt": "A solution contains 4.26 mol of solute in 2135 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 2135 mL to 2.135 L.\nCompute M = 4.26 / 2.135.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 4.26, "volume_ml": 2135}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(2.8)=-2.9 and f(9)=-2.9.\n3. The interval width is 6.2.\nFinal: {\"answer\": -17.98, \"unit\": \"area_units\"}", "dedupe_signature": "36ba6fb87dfcec1ac813c5bb01f1c4a7e28d2cc10577b4812964d8fed9b288bb", "difficulty": "medium", "final_answer": {"answer": -17.98, "unit": "area_units"}, "id": "trapz_linear_005212_0_-2.9_2.8_9", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=0x+-2.9 from x=2.8 to x=9. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(2.8)=-2.9 and f(9)=-2.9.\nThe interval width is 6.2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -2.9, "slope": 0.0, "x0": 2.8, "x1": 9.0}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 100 centimeters in one meter.\n2. Apply the conversion factor directly to the given value.\n3. Compute 4309.0 / 100.\nFinal: {\"answer\": 43.09, \"unit\": \"m\"}", "dedupe_signature": "0ba5641fff07b7aea12831afd3202814a537a2e08c47b676b707ea0d642c660c", "difficulty": "easy", "final_answer": {"answer": 43.09, "unit": "m"}, "id": "unit_convert_005214_cm_to_m_4309", "license": "Apache-2.0", "prompt": "Convert 4309 cm to m. Return the converted value with unit.", "reasoning_trace": "There are 100 centimeters in one meter.\nApply the conversion factor directly to the given value.\nCompute 4309.0 / 100.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 4309.0}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=75 degrees and keep the unit as newtons.\nFinal: {\"answer\": [107.7981, 402.3081], \"unit\": \"N\"}", "dedupe_signature": "1c7cee1b8665e11215e40e2c15d59d506caf290d423be47f0408874b2e5e818b", "difficulty": "medium", "final_answer": {"answer": [107.7981, 402.3081], "unit": "N"}, "id": "vector_components_005215_416.5_75", "license": "Apache-2.0", "prompt": "A vector has magnitude 416.5 N at 75 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=75 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 75, "magnitude": 416.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [8.65, 29.0], \"unit\": \"dimensionless\"}", "dedupe_signature": "80e16fefa208f9da88388fd0150ddcdf8dd4b9cd066161186588bec7f5a279d4", "difficulty": "medium", "final_answer": {"answer": [8.65, 29.0], "unit": "dimensionless"}, "id": "line_two_point_005216_1.75_15.5_8.65_29", "license": "Apache-2.0", "prompt": "A line passes through points (1.75, 44.1375) and (15.5, 163.075). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 1.75, "x2": 15.5, "y1": 44.1375, "y2": 163.07500000000002}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. volt squared divided by ohm is watt\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "c6cce61facda6739ff7cd87828405b322c2849fb3a9caa313d6186a92f1c4415", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_005217_consistent_82e93f3d_57058", "license": "Apache-2.0", "prompt": "In instrument manual case 57058, check dimensional consistency for P = V^2 / R. The left side has dimensions W and the right side has dimensions W. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nvolt squared divided by ohm is watt\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "P = V^2 / R"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: recurrence, objective, tie_breaking_rule.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"recurrence\", \"objective\", \"tie_breaking_rule\"]}", "dedupe_signature": "e1d12c5ac18fad054de0402fc42afb419f465a409f7c01628cec8558d0c97316", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["recurrence", "objective", "tie_breaking_rule"]}, "id": "abstain_005219_recurrence_objective_tie_breaking_rule", "license": "Apache-2.0", "prompt": "Write a dynamic-programming solver for a routing scoring problem with 1521 items and budget 17985, but the recurrence, objective, and tie-breaking rule are all absent. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: recurrence, objective, tie_breaking_rule.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["recurrence", "objective", "tie_breaking_rule"]}, "verifier": {"missing": ["recurrence", "objective", "tie_breaking_rule"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 18 kg and a = 11.85 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 213.3, \"unit\": \"N\"}", "dedupe_signature": "67d8bbb4d634ceca3c63184648c30ae8402717fa6ab8fa8c5e412e26396180e2", "difficulty": "easy", "final_answer": {"answer": 213.3, "unit": "N"}, "id": "force_005220_18_11.85", "license": "Apache-2.0", "prompt": "A cart has mass 18 kg and measured acceleration 11.85 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 18 kg and a = 11.85 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 11.85, "mass": 18.0}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 36.5^2 and multiply by 0.5 * 20.25.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 13489.0312, \"unit\": \"J\"}", "dedupe_signature": "781bf5ed95b28c42b4fd464cbce82171cbb0f08d1215530e496b1568942c97c2", "difficulty": "easy", "final_answer": {"answer": 13489.0312, "unit": "J"}, "id": "ke_005221_20.25_36.5", "license": "Apache-2.0", "prompt": "A body of mass 20.25 kg moves at 36.5 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 36.5^2 and multiply by 0.5 * 20.25.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 20.25, "velocity": 36.5}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=26 degrees through the sine of 2 theta.\n3. Substitute v=79.4 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 506.4122, \"unit\": \"m\"}", "dedupe_signature": "5b3830fa8a414dd620e9e7e4c0f13ef6858bfa8e4c55357f4f4accf00bc76ccd", "difficulty": "medium", "final_answer": {"answer": 506.4122, "unit": "m"}, "id": "projectile_range_005222_79.4_26", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 79.4 m/s and angle 26 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=26 degrees through the sine of 2 theta.\nSubstitute v=79.4 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 26, "gravity": 9.81, "speed": 79.4}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 2.76 * 8.314 * 387 / 13.4.\nFinal: {\"answer\": 662.7127, \"unit\": \"kPa\"}", "dedupe_signature": "278bfc31a2f2efbebf352063008b6b419c1a0a8767a28a6fe1e4a63d8869b35e", "difficulty": "medium", "final_answer": {"answer": 662.7127, "unit": "kPa"}, "id": "ideal_gas_005223_2.76_387_13.4", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=2.76 mol, T=387 K, and V=13.4 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 2.76 * 8.314 * 387 / 13.4.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 2.76, "temp_k": 387, "volume_l": 13.4}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1225 * 4.195 * 1.\nFinal: {\"answer\": 5138.875, \"unit\": \"J\"}", "dedupe_signature": "bfede5951258b61adcff84d771e793fb1ca34c2080c63eef2e68196ea3c9f151", "difficulty": "easy", "final_answer": {"answer": 5138.875, "unit": "J"}, "id": "heat_q_005224_1225_4.195_1", "license": "Apache-2.0", "prompt": "A 1225 g sample has specific heat 4.195 J/(g*K). How much heat is needed to raise its temperature by 1 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1225 * 4.195 * 1.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 1, "heat_capacity": 4.195, "mass_g": 1225}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=13.9 V and R=165.3 ohm.\nFinal: {\"answer\": 1.1688, \"unit\": \"W\"}", "dedupe_signature": "137b8867024e3041b6d8ecb0995671318c634f09f7b872fbad4c2f916904fde6", "difficulty": "easy", "final_answer": {"answer": 1.1688, "unit": "W"}, "id": "ohm_power_005225_13.9_165.3", "license": "Apache-2.0", "prompt": "A resistor has resistance 165.3 ohm and voltage 13.9 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=13.9 V and R=165.3 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 165.3, "voltage": 13.9}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=556 mg, t=53.5 h, and T_half=104 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 389.2405, \"unit\": \"mg\"}", "dedupe_signature": "7cd0eb332b1e3eba7040fea3486fbb46a05a3175470411adadd75ef920347eef", "difficulty": "medium", "final_answer": {"answer": 389.2405, "unit": "mg"}, "id": "half_life_005226_556_104_53.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 556 mg. Its half-life is 104 hours. How many mg remain after 53.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=556 mg, t=53.5 h, and T_half=104 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 53.5, "half_life": 104.0, "initial_amount": 556.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 1920 mL to 1.92 L.\n3. Compute M = 0.495 / 1.92.\nFinal: {\"answer\": 0.2578, \"unit\": \"mol/L\"}", "dedupe_signature": "0cce097652ab9cd8a3dbd9ef6748b5b4ba1d80ce3b7cc4a5cd475c8e861af7a5", "difficulty": "medium", "final_answer": {"answer": 0.2578, "unit": "mol/L"}, "id": "molarity_005228_0.495_1920", "license": "Apache-2.0", "prompt": "A solution contains 0.495 mol of solute in 1920 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 1920 mL to 1.92 L.\nCompute M = 0.495 / 1.92.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 0.495, "volume_ml": 1920}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.18 and add it to the current value.\nFinal: {\"answer\": [1.346, 1.723, 2.065], \"unit\": \"temperature_units\"}", "dedupe_signature": "d9f4833332c8a5685768bc5bd0a007b91bff9166643f90ff8f4ca2c861ca0c01", "difficulty": "hard", "final_answer": {"answer": [1.346, 1.723, 2.065], "unit": "temperature_units"}, "id": "heat_step_005231_0.18_-2.0_2.3_1.3_2.65_0.75", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-2, right=0.75; current interior values are [2.3, 1.3, 2.65]. Use r=0.18. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.18 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [2.3, 1.3, 2.65], "left": -2.0, "r": 0.18, "right": 0.75}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 100 centimeters in one meter.\n2. Apply the conversion factor directly to the given value.\n3. Compute 4295.0 / 100.\nFinal: {\"answer\": 42.95, \"unit\": \"m\"}", "dedupe_signature": "187c3ff54220dbb6e3f81d3abe26f0fd1a621912a04addc69b83628fb44e7b2f", "difficulty": "easy", "final_answer": {"answer": 42.95, "unit": "m"}, "id": "unit_convert_005232_cm_to_m_4295", "license": "Apache-2.0", "prompt": "Convert 4295 cm to m. Return the converted value with unit.", "reasoning_trace": "There are 100 centimeters in one meter.\nApply the conversion factor directly to the given value.\nCompute 4295.0 / 100.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 4295.0}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-9.05, 26.25], \"unit\": \"dimensionless\"}", "dedupe_signature": "7f44910a53d82924a3745af5df09e47c8b2d6ada76d5305331252f29bfde3bd9", "difficulty": "medium", "final_answer": {"answer": [-9.05, 26.25], "unit": "dimensionless"}, "id": "line_two_point_005234_-13.75_-6.75_-9.05_26.25", "license": "Apache-2.0", "prompt": "A line passes through points (-13.75, 150.688) and (-6.75, 87.3375). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -13.75, "x2": -6.75, "y1": 150.6875, "y2": 87.3375}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. speed squared over acceleration has units of meters\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "58f01df7da97a0ff59180679a751ff0809aecbe6ce88649bc87857156180daab", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_005235_consistent_741d4e34_563286", "license": "Apache-2.0", "prompt": "In sensor calibration case 563286, check dimensional consistency for R = v^2 * sin(theta) / g. The left side has dimensions m and the right side has dimensions m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nspeed squared over acceleration has units of meters\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "R = v^2 * sin(theta) / g"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: volume.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"volume\"]}", "dedupe_signature": "6087dfbe2a375380366777352a45fcd76efa6c6e1184433932e4a54911836b41", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["volume"]}, "id": "abstain_005237_volume", "license": "Apache-2.0", "prompt": "Compute pressure from the ideal gas law. The prompt gives n=0.72 mol and T=274 K, but does not give volume. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: volume.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["volume"]}, "verifier": {"missing": ["volume"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 6.65 kg and a = 14.75 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 98.0875, \"unit\": \"N\"}", "dedupe_signature": "e834610da4997a2806aae0fa8ca13569c8087f485e983612aa33102edf0ddfec", "difficulty": "easy", "final_answer": {"answer": 98.0875, "unit": "N"}, "id": "force_005238_6.65_14.75", "license": "Apache-2.0", "prompt": "A cart has mass 6.65 kg and measured acceleration 14.75 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 6.65 kg and a = 14.75 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 14.75, "mass": 6.65}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 1.35^2 and multiply by 0.5 * 7.75.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 7.0622, \"unit\": \"J\"}", "dedupe_signature": "22ff0d2a3b71421058d8dae25501c98069c3fe4bd884e34865e2fd2c7ae71122", "difficulty": "easy", "final_answer": {"answer": 7.0622, "unit": "J"}, "id": "ke_005239_7.75_1.35", "license": "Apache-2.0", "prompt": "A body of mass 7.75 kg moves at 1.35 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 1.35^2 and multiply by 0.5 * 7.75.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 7.75, "velocity": 1.35}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=47 degrees through the sine of 2 theta.\n3. Substitute v=46.8 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 222.7222, \"unit\": \"m\"}", "dedupe_signature": "ed5e03090e77fcfdb77e237e49862f61985ef98c64dc8c9a619f6e70fe197a5a", "difficulty": "medium", "final_answer": {"answer": 222.7222, "unit": "m"}, "id": "projectile_range_005240_46.8_47", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 46.8 m/s and angle 47 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=47 degrees through the sine of 2 theta.\nSubstitute v=46.8 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 47, "gravity": 9.81, "speed": 46.8}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 4.3 * 8.314 * 568 / 89.7.\nFinal: {\"answer\": 226.3781, \"unit\": \"kPa\"}", "dedupe_signature": "16ea2fd893bfbba3f2fcbd0cc65ff447108f6472c456ff472bea92553a0b569a", "difficulty": "medium", "final_answer": {"answer": 226.3781, "unit": "kPa"}, "id": "ideal_gas_005241_4.3_568_89.7", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=4.3 mol, T=568 K, and V=89.7 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 4.3 * 8.314 * 568 / 89.7.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 4.3, "temp_k": 568, "volume_l": 89.7}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 475 * 2.425 * 68.\nFinal: {\"answer\": 78327.5, \"unit\": \"J\"}", "dedupe_signature": "0dd2946ec9675c4e8d031bb74522f4d01f5e09de816c5868d3f18a4f2c1002da", "difficulty": "easy", "final_answer": {"answer": 78327.5, "unit": "J"}, "id": "heat_q_005242_475_2.425_68", "license": "Apache-2.0", "prompt": "A 475 g sample has specific heat 2.425 J/(g*K). How much heat is needed to raise its temperature by 68 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 475 * 2.425 * 68.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 68, "heat_capacity": 2.425, "mass_g": 475}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=125.5 V and R=137.5 ohm.\nFinal: {\"answer\": 114.5473, \"unit\": \"W\"}", "dedupe_signature": "de18de9e8e5b03700009352c585bc6cad8249153375a441a079fbcf48542db42", "difficulty": "easy", "final_answer": {"answer": 114.5473, "unit": "W"}, "id": "ohm_power_005243_125.5_137.5", "license": "Apache-2.0", "prompt": "A resistor has resistance 137.5 ohm and voltage 125.5 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=125.5 V and R=137.5 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 137.5, "voltage": 125.5}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=546.5 mg, t=35.5 h, and T_half=83 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 406.2902, \"unit\": \"mg\"}", "dedupe_signature": "55054da7a0fa0e03ac05436060007bda517df274ce42bb60cbd202607e94056c", "difficulty": "medium", "final_answer": {"answer": 406.2902, "unit": "mg"}, "id": "half_life_005244_546.5_83_35.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 546.5 mg. Its half-life is 83 hours. How many mg remain after 35.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=546.5 mg, t=35.5 h, and T_half=83 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 35.5, "half_life": 83.0, "initial_amount": 546.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 6.02 mol * 44.01 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 264.9402, \"unit\": \"g\"}", "dedupe_signature": "5e703a1b3f91c9141098b2821a5fac31612b6071864242b64b53d24ba3cbc071", "difficulty": "medium", "final_answer": {"answer": 264.9402, "unit": "g"}, "id": "stoich_mass_005245_carbon_dioxide_6.02", "license": "Apache-2.0", "prompt": "A sample contains 6.02 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 6.02 mol * 44.01 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "carbon dioxide", "molar_mass": 44.01, "moles": 6.02}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 1605 mL to 1.605 L.\n3. Compute M = 2.13 / 1.605.\nFinal: {\"answer\": 1.3271, \"unit\": \"mol/L\"}", "dedupe_signature": "e920a8a4a93773e55e1b8f93a534c6622fa3b5d8508e8e9f96fbb5932abd0e8d", "difficulty": "medium", "final_answer": {"answer": 1.3271, "unit": "mol/L"}, "id": "molarity_005246_2.13_1605", "license": "Apache-2.0", "prompt": "A solution contains 2.13 mol of solute in 1605 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 1605 mL to 1.605 L.\nCompute M = 2.13 / 1.605.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 2.13, "volume_ml": 1605}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.35 y, so each step multiplies y by 1 - h*0.35.\n3. Apply that update for 3 steps and round the final state.\nFinal: {\"answer\": 1.7923, \"unit\": \"state_units\"}", "dedupe_signature": "a8164a69903618601f35c1e9e9c72c51072a297382b94b7326f19fc297cab6e8", "difficulty": "medium", "final_answer": {"answer": 1.7923, "unit": "state_units"}, "id": "euler_decay_005247_56_0.35_1.95_3", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.35 y with y(0)=56, step size h=1.95, for 3 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.35 y, so each step multiplies y by 1 - h*0.35.\nApply that update for 3 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 56.0, "rate": 0.35, "step": 1.95, "steps": 3}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-2.8)=9.62 and f(0.2)=3.92.\n3. The interval width is 3.\nFinal: {\"answer\": 20.31, \"unit\": \"area_units\"}", "dedupe_signature": "b872d843880a1827ffe7aad58fe0be2c87281e9ee74e04d2d4b9380a8f7f0b8f", "difficulty": "medium", "final_answer": {"answer": 20.31, "unit": "area_units"}, "id": "trapz_linear_005248_-1.9_4.3_-2.8_0.2", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-1.9x+4.3 from x=-2.8 to x=0.2. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-2.8)=9.62 and f(0.2)=3.92.\nThe interval width is 3.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 4.3, "slope": -1.9, "x0": -2.8, "x1": 0.20000000000000018}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kelvin equals Celsius plus 273.15.\n2. Apply the conversion factor directly to the given value.\n3. Compute 167.5 + 273.15.\nFinal: {\"answer\": 440.65, \"unit\": \"K\"}", "dedupe_signature": "75dafd8a5b95ba290d68f82dbfef311af90f6f612acb56876c3da06a4320d56f", "difficulty": "easy", "final_answer": {"answer": 440.65, "unit": "K"}, "id": "unit_convert_005250_c_to_k_167.5", "license": "Apache-2.0", "prompt": "Convert 167.5 degC to K. Return the converted value with unit.", "reasoning_trace": "Kelvin equals Celsius plus 273.15.\nApply the conversion factor directly to the given value.\nCompute 167.5 + 273.15.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 167.5}, "verifier": {"formula": "value + 273.15", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=223 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-300.952, -280.6423], \"unit\": \"N\"}", "dedupe_signature": "d5018fa3f1d5ebc3779e91491b78eba448923f3adab1a2f6bf63d6aca0184513", "difficulty": "medium", "final_answer": {"answer": [-300.952, -280.6423], "unit": "N"}, "id": "vector_components_005251_411.5_223", "license": "Apache-2.0", "prompt": "A vector has magnitude 411.5 N at 223 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=223 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 223, "magnitude": 411.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [1.8, 20.25], \"unit\": \"dimensionless\"}", "dedupe_signature": "dfef87c47b9f917289956b6527a394af46856bdc2fe97f11bcff5b353c55213c", "difficulty": "medium", "final_answer": {"answer": [1.8, 20.25], "unit": "dimensionless"}, "id": "line_two_point_005252_-10.75_4.25_1.8_20.25", "license": "Apache-2.0", "prompt": "A line passes through points (-10.75, 0.9) and (4.25, 27.9). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -10.75, "x2": 4.25, "y1": 0.8999999999999986, "y2": 27.9}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. speed squared over acceleration has units of meters\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "4f094d273cfd40cf475830d37e567c660905d2ddfe973b6632450650f6cf45ab", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_005253_consistent_741d4e34_741078", "license": "Apache-2.0", "prompt": "In field worksheet case 741078, check dimensional consistency for R = v^2 * sin(theta) / g. The left side has dimensions m and the right side has dimensions m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nspeed squared over acceleration has units of meters\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "R = v^2 * sin(theta) / g"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef normalize_005254(values):\n    total = sum(values)\n    if total == 0:\n        raise ValueError('cannot normalize zero-sum values')\n    return [v / total for v in values]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"normalize_005254\"}", "dedupe_signature": "adccbb6834dc2798ba52de9b61fe2950a47b3db69a4c311468e1e9553f583556", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "normalize_005254"}, "id": "code_005254_normalize_005254", "license": "Apache-2.0", "prompt": "Write a Python function normalize_005254(values) that returns a new list whose values sum to 1. Raise ValueError if the sum is zero. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "normalize_005254"}, "verifier": {"function": "normalize_005254", "tests": ["out = normalize_005254([2, 3, 5]); assert len(out) == 3", "assert abs(sum(normalize_005254([2, 3, 5])) - 1.0) < 1e-12", "assert normalize_005254([1, 1]) == [0.5, 0.5]", "try:\n    normalize_005254([1, -1])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: recurrence, objective, tie_breaking_rule.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"recurrence\", \"objective\", \"tie_breaking_rule\"]}", "dedupe_signature": "014737e985bf13e02b6ab723c4e8979c048ca13d65f8cc704f9b31b890a4e1e4", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["recurrence", "objective", "tie_breaking_rule"]}, "id": "abstain_005255_recurrence_objective_tie_breaking_rule", "license": "Apache-2.0", "prompt": "Write a dynamic-programming solver for a knapsack scoring problem with 4808 items and budget 28680, but the recurrence, objective, and tie-breaking rule are all absent. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: recurrence, objective, tie_breaking_rule.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["recurrence", "objective", "tie_breaking_rule"]}, "verifier": {"missing": ["recurrence", "objective", "tie_breaking_rule"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 4.15^2 and multiply by 0.5 * 17.3.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 148.9746, \"unit\": \"J\"}", "dedupe_signature": "da4d6d03f34c61070644ca5915b0ebaa65ce444b0ac501daba812c7fd33b7d8c", "difficulty": "easy", "final_answer": {"answer": 148.9746, "unit": "J"}, "id": "ke_005257_17.3_4.15", "license": "Apache-2.0", "prompt": "A body of mass 17.3 kg moves at 4.15 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 4.15^2 and multiply by 0.5 * 17.3.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 17.3, "velocity": 4.15}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=20 degrees through the sine of 2 theta.\n3. Substitute v=46.1 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 139.2516, \"unit\": \"m\"}", "dedupe_signature": "fb0e53a446c0703d061c85beaa8d37ad736dd5c2792e92e5318e43b6ccb0675c", "difficulty": "medium", "final_answer": {"answer": 139.2516, "unit": "m"}, "id": "projectile_range_005258_46.1_20", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 46.1 m/s and angle 20 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=20 degrees through the sine of 2 theta.\nSubstitute v=46.1 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 20, "gravity": 9.81, "speed": 46.1}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 0.76 * 8.314 * 612 / 41.6.\nFinal: {\"answer\": 92.9569, \"unit\": \"kPa\"}", "dedupe_signature": "2f33a3d9aaa53c4d5522a52326670d290052d5205b276108faaef4fafa683d5b", "difficulty": "medium", "final_answer": {"answer": 92.9569, "unit": "kPa"}, "id": "ideal_gas_005259_0.76_612_41.6", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=0.76 mol, T=612 K, and V=41.6 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 0.76 * 8.314 * 612 / 41.6.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 0.76, "temp_k": 612, "volume_l": 41.6}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1650 * 4.09 * 114.\nFinal: {\"answer\": 769329.0, \"unit\": \"J\"}", "dedupe_signature": "5f5bec89fdcd70c7ce76d050d507e6d006f73af09db5aa3b356f0a2a56d669e4", "difficulty": "easy", "final_answer": {"answer": 769329.0, "unit": "J"}, "id": "heat_q_005260_1650_4.09_114", "license": "Apache-2.0", "prompt": "A 1650 g sample has specific heat 4.09 J/(g*K). How much heat is needed to raise its temperature by 114 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1650 * 4.09 * 114.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 114, "heat_capacity": 4.09, "mass_g": 1650}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=20.3 V and R=15.6 ohm.\nFinal: {\"answer\": 26.416, \"unit\": \"W\"}", "dedupe_signature": "f32af5ae534ce2c669b1bfd78b4e8e56efbd7c37de7a2e3777bddc4a3eff02bc", "difficulty": "easy", "final_answer": {"answer": 26.416, "unit": "W"}, "id": "ohm_power_005261_20.3_15.6", "license": "Apache-2.0", "prompt": "A resistor has resistance 15.6 ohm and voltage 20.3 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=20.3 V and R=15.6 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 15.6, "voltage": 20.3}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=429 mg, t=218 h, and T_half=54 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 26.1329, \"unit\": \"mg\"}", "dedupe_signature": "aa8c94b2464ae979cbd4359b6c597a07029315cffc63d4734d158090c4cb34a0", "difficulty": "medium", "final_answer": {"answer": 26.1329, "unit": "mg"}, "id": "half_life_005262_429_54_218", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 429 mg. Its half-life is 54 hours. How many mg remain after 218 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=429 mg, t=218 h, and T_half=54 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 218.0, "half_life": 54.0, "initial_amount": 429.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 0.76 mol * 18.015 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 13.6914, \"unit\": \"g\"}", "dedupe_signature": "b95eaec642ff5c1f3313a2cdd34cf7d67ac7eaddfa9346fdb0b7cafe0d9975e7", "difficulty": "medium", "final_answer": {"answer": 13.6914, "unit": "g"}, "id": "stoich_mass_005263_water_0.76", "license": "Apache-2.0", "prompt": "A sample contains 0.76 mol of water. Using molar mass 18.015 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 0.76 mol * 18.015 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "water", "molar_mass": 18.015, "moles": 0.76}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 2105 mL to 2.105 L.\n3. Compute M = 4.41 / 2.105.\nFinal: {\"answer\": 2.095, \"unit\": \"mol/L\"}", "dedupe_signature": "9f2edcef8db87b6b1aba2ac06582d506a90496e136be4492272f8d52a77d2e4c", "difficulty": "medium", "final_answer": {"answer": 2.095, "unit": "mol/L"}, "id": "molarity_005264_4.41_2105", "license": "Apache-2.0", "prompt": "A solution contains 4.41 mol of solute in 2105 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 2105 mL to 2.105 L.\nCompute M = 4.41 / 2.105.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 4.41, "volume_ml": 2105}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.49 y, so each step multiplies y by 1 - h*0.49.\n3. Apply that update for 9 steps and round the final state.\nFinal: {\"answer\": 0.0064, \"unit\": \"state_units\"}", "dedupe_signature": "5adc9f058cad3d7c3e16165ace8481a92cf9465d670fe5f75a5e9e07234874d5", "difficulty": "medium", "final_answer": {"answer": 0.0064, "unit": "state_units"}, "id": "euler_decay_005265_58.5_0.49_1.3_9", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.49 y with y(0)=58.5, step size h=1.3, for 9 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.49 y, so each step multiplies y by 1 - h*0.49.\nApply that update for 9 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 58.5, "rate": 0.49, "step": 1.3, "steps": 9}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 37100.0 / 1000.\nFinal: {\"answer\": 37.1, \"unit\": \"kg\"}", "dedupe_signature": "079a7eafb3450c2180476596bbe762ab38ef0d4e12b6f2c051a25a6916655b16", "difficulty": "easy", "final_answer": {"answer": 37.1, "unit": "kg"}, "id": "unit_convert_005268_g_to_kg_37100", "license": "Apache-2.0", "prompt": "Convert 37100 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 37100.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 37100.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=328 degrees and keep the unit as newtons.\nFinal: {\"answer\": [64.0276, -40.0089], \"unit\": \"N\"}", "dedupe_signature": "bed10349a37e541ebb4d1a7080bd1eee3d50ba30d5ff9bbb1a1f650a2d0891f0", "difficulty": "medium", "final_answer": {"answer": [64.0276, -40.0089], "unit": "N"}, "id": "vector_components_005269_75.5_328", "license": "Apache-2.0", "prompt": "A vector has magnitude 75.5 N at 328 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=328 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 328, "magnitude": 75.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [9.0, 18.25], \"unit\": \"dimensionless\"}", "dedupe_signature": "503f13feeb83ad2bfd12ccb529a49bdffe0710d2ad3eed1a7f615c7c613a52a9", "difficulty": "medium", "final_answer": {"answer": [9.0, 18.25], "unit": "dimensionless"}, "id": "line_two_point_005270_19.5_21.75_9_18.25", "license": "Apache-2.0", "prompt": "A line passes through points (19.5, 193.75) and (21.75, 214). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 19.5, "x2": 21.75, "y1": 193.75, "y2": 214.0}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. lever arm times force has torque dimensions\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "a9986e673f294d47229847da8ee1a6be826fc4f57da913508552c1f1c66d268c", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_005271_consistent_5ca82cb9_44036", "license": "Apache-2.0", "prompt": "In model card equation case 44036, check dimensional consistency for tau = r * F. The left side has dimensions N*m and the right side has dimensions N*m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nlever arm times force has torque dimensions\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "tau = r * F"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef normalize_005272(values):\n    total = sum(values)\n    if total == 0:\n        raise ValueError('cannot normalize zero-sum values')\n    return [v / total for v in values]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"normalize_005272\"}", "dedupe_signature": "c7e68bb8a673bcf0b616b403036451ecbcbdc23d6dfa7dd60e654d99da86e84c", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "normalize_005272"}, "id": "code_005272_normalize_005272", "license": "Apache-2.0", "prompt": "Write a Python function normalize_005272(values) that returns a new list whose values sum to 1. Raise ValueError if the sum is zero. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "normalize_005272"}, "verifier": {"function": "normalize_005272", "tests": ["out = normalize_005272([2, 3, 5]); assert len(out) == 3", "assert abs(sum(normalize_005272([2, 3, 5])) - 1.0) < 1e-12", "assert normalize_005272([1, 1]) == [0.5, 0.5]", "try:\n    normalize_005272([1, -1])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: target_schema, valid_examples.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"target_schema\", \"valid_examples\"]}", "dedupe_signature": "7f3fe7776d7a70aedc4674cd60e3c3bb82d55975061e5d6af7781212aaed25eb", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["target_schema", "valid_examples"]}, "id": "abstain_005273_target_schema_valid_examples", "license": "Apache-2.0", "prompt": "Write a parser that converts each registry clinical record from batch 711772 into the correct schema, but the prompt does not include the target schema or examples. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: target_schema, valid_examples.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["target_schema", "valid_examples"]}, "verifier": {"missing": ["target_schema", "valid_examples"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 29.1^2 and multiply by 0.5 * 6.5.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 2752.1325, \"unit\": \"J\"}", "dedupe_signature": "9b240cb9d906e3234a25971d771e61102de9f24bcc1f555d44ff98c30e880fa7", "difficulty": "easy", "final_answer": {"answer": 2752.1325, "unit": "J"}, "id": "ke_005275_6.5_29.1", "license": "Apache-2.0", "prompt": "A body of mass 6.5 kg moves at 29.1 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 29.1^2 and multiply by 0.5 * 6.5.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 6.5, "velocity": 29.1}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=66 degrees through the sine of 2 theta.\n3. Substitute v=76.3 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 441.0152, \"unit\": \"m\"}", "dedupe_signature": "feb4797088e6d9bf2c15904abbc40090542b27cf2e2a05cf2d1d9e23a5f8f138", "difficulty": "medium", "final_answer": {"answer": 441.0152, "unit": "m"}, "id": "projectile_range_005276_76.3_66", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 76.3 m/s and angle 66 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=66 degrees through the sine of 2 theta.\nSubstitute v=76.3 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 66, "gravity": 9.81, "speed": 76.3}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 115 * 1.69 * 6.\nFinal: {\"answer\": 1166.1, \"unit\": \"J\"}", "dedupe_signature": "814c540829926e067fea44c626fd3f072f1a403573f0330553e1fc522d01b0a9", "difficulty": "easy", "final_answer": {"answer": 1166.1, "unit": "J"}, "id": "heat_q_005278_115_1.69_6", "license": "Apache-2.0", "prompt": "A 115 g sample has specific heat 1.69 J/(g*K). How much heat is needed to raise its temperature by 6 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 115 * 1.69 * 6.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 6, "heat_capacity": 1.69, "mass_g": 115}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=47.4 V and R=43 ohm.\nFinal: {\"answer\": 52.2502, \"unit\": \"W\"}", "dedupe_signature": "2ce9da8b7fc272d8cf995ad8b4d9f60bfbae936ebab4d269ac60918fbfaa4e72", "difficulty": "easy", "final_answer": {"answer": 52.2502, "unit": "W"}, "id": "ohm_power_005279_47.4_43", "license": "Apache-2.0", "prompt": "A resistor has resistance 43 ohm and voltage 47.4 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=47.4 V and R=43 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 43.0, "voltage": 47.4}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=195 mg, t=356.5 h, and T_half=71.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 6.1531, \"unit\": \"mg\"}", "dedupe_signature": "58d8506f1fc47a5b695a77e601069e076e7301b179e127d5513fd08b8c2f2967", "difficulty": "medium", "final_answer": {"answer": 6.1531, "unit": "mg"}, "id": "half_life_005280_195_71.5_356.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 195 mg. Its half-life is 71.5 hours. How many mg remain after 356.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=195 mg, t=356.5 h, and T_half=71.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 356.5, "half_life": 71.5, "initial_amount": 195.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 7.87 mol * 180.156 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 1417.8277, \"unit\": \"g\"}", "dedupe_signature": "3393cc54b7cac4a18f0b7b07b31c2aae7335c2301a627be0b3803e021d82183e", "difficulty": "medium", "final_answer": {"answer": 1417.8277, "unit": "g"}, "id": "stoich_mass_005281_glucose_7.87", "license": "Apache-2.0", "prompt": "A sample contains 7.87 mol of glucose. Using molar mass 180.156 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 7.87 mol * 180.156 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "glucose", "molar_mass": 180.156, "moles": 7.87}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.61 y, so each step multiplies y by 1 - h*0.61.\n3. Apply that update for 4 steps and round the final state.\nFinal: {\"answer\": 12.8103, \"unit\": \"state_units\"}", "dedupe_signature": "2f513a1a80078186c14736803aeb4223f59f2120758f41bacaa402a6f82fdd67", "difficulty": "medium", "final_answer": {"answer": 12.8103, "unit": "state_units"}, "id": "euler_decay_005283_14.5_0.61_0.05_4", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.61 y with y(0)=14.5, step size h=0.05, for 4 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.61 y, so each step multiplies y by 1 - h*0.61.\nApply that update for 4 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 14.5, "rate": 0.61, "step": 0.05, "steps": 4}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-4.2)=-15.46 and f(0.9)=-8.83.\n3. The interval width is 5.1.\nFinal: {\"answer\": -61.9395, \"unit\": \"area_units\"}", "dedupe_signature": "4d786aefcff054dcc15c1ac3664f722f183ee13504096bd50dc59fd5f412c9ba", "difficulty": "medium", "final_answer": {"answer": -61.9395, "unit": "area_units"}, "id": "trapz_linear_005284_1.3_-10_-4.2_0.9", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=1.3x+-10 from x=-4.2 to x=0.9. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-4.2)=-15.46 and f(0.9)=-8.83.\nThe interval width is 5.1.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -10.0, "slope": 1.3, "x0": -4.2, "x1": 0.8999999999999995}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.28 and add it to the current value.\nFinal: {\"answer\": [0.54, 0.512, 0.542], \"unit\": \"temperature_units\"}", "dedupe_signature": "c7bd8a836f0b17871239f33a772b430c8fd5873996e95bfd7da60b54f72fe37f", "difficulty": "hard", "final_answer": {"answer": [0.54, 0.512, 0.542], "unit": "temperature_units"}, "id": "heat_step_005285_0.28_-1.15_2.15_-0.3_0.15_2.0", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-1.15, right=2; current interior values are [2.15, -0.3, 0.15]. Use r=0.28. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.28 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [2.15, -0.3, 0.15], "left": -1.15, "r": 0.28, "right": 2.0}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 47206.0 / 1000.\nFinal: {\"answer\": 47.206, \"unit\": \"kg\"}", "dedupe_signature": "4a14de7ad84b9aed43d91c0aa846fc2314c036b610dd036d0d20ed7933ee32dd", "difficulty": "easy", "final_answer": {"answer": 47.206, "unit": "kg"}, "id": "unit_convert_005286_g_to_kg_47206", "license": "Apache-2.0", "prompt": "Convert 47206 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 47206.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 47206.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=353 degrees and keep the unit as newtons.\nFinal: {\"answer\": [391.5595, -48.0775], \"unit\": \"N\"}", "dedupe_signature": "b75863bf6a10b6eafa27607e9dc1a75dae7d65950071d524ca47e88861e33f87", "difficulty": "medium", "final_answer": {"answer": [391.5595, -48.0775], "unit": "N"}, "id": "vector_components_005287_394.5_353", "license": "Apache-2.0", "prompt": "A vector has magnitude 394.5 N at 353 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=353 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 353, "magnitude": 394.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. m*v is momentum, not energy\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "5b87921b36b423124f529be09f6ab5d8f2fbe40e49f118ca997f5f0ca0f67fed", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_005289_inconsistent_1e14b074_863758", "license": "Apache-2.0", "prompt": "In sensor calibration case 863758, check dimensional consistency for E = m * v. The left side has dimensions kg*m^2/s^2 and the right side has dimensions kg*m/s. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nm*v is momentum, not energy\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "E = m * v"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 12.5 kg and a = 8.55 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 106.875, \"unit\": \"N\"}", "dedupe_signature": "58810b90648c1f585180e4fc95b896ed102fb679e5c691bc6d94cdd49caf3538", "difficulty": "easy", "final_answer": {"answer": 106.875, "unit": "N"}, "id": "force_005292_12.5_8.55", "license": "Apache-2.0", "prompt": "A cart has mass 12.5 kg and measured acceleration 8.55 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 12.5 kg and a = 8.55 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 8.55, "mass": 12.5}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 23.25^2 and multiply by 0.5 * 14.75.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 3986.6484, \"unit\": \"J\"}", "dedupe_signature": "5137b62405211e2b556e23b31edfd61b1fbdf340fb5ede6d70d6b3ba826b0508", "difficulty": "easy", "final_answer": {"answer": 3986.6484, "unit": "J"}, "id": "ke_005293_14.75_23.25", "license": "Apache-2.0", "prompt": "A body of mass 14.75 kg moves at 23.25 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 23.25^2 and multiply by 0.5 * 14.75.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 14.75, "velocity": 23.25}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=33 degrees through the sine of 2 theta.\n3. Substitute v=45.1 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 189.4149, \"unit\": \"m\"}", "dedupe_signature": "e83935c0bd5f09018cc03a432c53780c8bdb51b7821913e8592e20f21d3c4520", "difficulty": "medium", "final_answer": {"answer": 189.4149, "unit": "m"}, "id": "projectile_range_005294_45.1_33", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 45.1 m/s and angle 33 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=33 degrees through the sine of 2 theta.\nSubstitute v=45.1 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 33, "gravity": 9.81, "speed": 45.1}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 5.22 * 8.314 * 438 / 40.2.\nFinal: {\"answer\": 472.8556, \"unit\": \"kPa\"}", "dedupe_signature": "7b8ec3f541865259d62a296fde8798a31a0a392c59decdd69611646674bb81a4", "difficulty": "medium", "final_answer": {"answer": 472.8556, "unit": "kPa"}, "id": "ideal_gas_005295_5.22_438_40.2", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=5.22 mol, T=438 K, and V=40.2 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 5.22 * 8.314 * 438 / 40.2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 5.22, "temp_k": 438, "volume_l": 40.2}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 715 * 2.59 * 115.\nFinal: {\"answer\": 212962.75, \"unit\": \"J\"}", "dedupe_signature": "8bb71b6b50974ff6ad0741adc20114b151176c9640e58afbc12afe2def0cf0d5", "difficulty": "easy", "final_answer": {"answer": 212962.75, "unit": "J"}, "id": "heat_q_005296_715_2.59_115", "license": "Apache-2.0", "prompt": "A 715 g sample has specific heat 2.59 J/(g*K). How much heat is needed to raise its temperature by 115 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 715 * 2.59 * 115.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 115, "heat_capacity": 2.59, "mass_g": 715}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=73.1 V and R=29.4 ohm.\nFinal: {\"answer\": 181.7554, \"unit\": \"W\"}", "dedupe_signature": "26aa9b7d3f4d827f0f30be4b197c74b827b4b3986abbb93d691ecdea6f1593e8", "difficulty": "easy", "final_answer": {"answer": 181.7554, "unit": "W"}, "id": "ohm_power_005297_73.1_29.4", "license": "Apache-2.0", "prompt": "A resistor has resistance 29.4 ohm and voltage 73.1 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=73.1 V and R=29.4 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 29.4, "voltage": 73.1}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=51 mg, t=26.5 h, and T_half=42.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 33.1031, \"unit\": \"mg\"}", "dedupe_signature": "7f65890971f35a759d81b4b8a9409ed6daa0ecf71c91093085166c1eb7fbaf74", "difficulty": "medium", "final_answer": {"answer": 33.1031, "unit": "mg"}, "id": "half_life_005298_51_42.5_26.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 51 mg. Its half-life is 42.5 hours. How many mg remain after 26.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=51 mg, t=26.5 h, and T_half=42.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 26.5, "half_life": 42.5, "initial_amount": 51.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 0.78 mol * 100.087 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 78.0679, \"unit\": \"g\"}", "dedupe_signature": "25af91b8ac1e84f8ac45e0515ab367465e4496ef881c435e2d70c48b68d30956", "difficulty": "medium", "final_answer": {"answer": 78.0679, "unit": "g"}, "id": "stoich_mass_005299_calcium_carbonate_0.78", "license": "Apache-2.0", "prompt": "A sample contains 0.78 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 0.78 mol * 100.087 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "calcium carbonate", "molar_mass": 100.087, "moles": 0.78}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 3995 mL to 3.995 L.\n3. Compute M = 3.07 / 3.995.\nFinal: {\"answer\": 0.7685, \"unit\": \"mol/L\"}", "dedupe_signature": "bcbcdebacebb01a4ff2abb74a1a589f8b5c3ff31614b0ab028f9f27c289c4289", "difficulty": "medium", "final_answer": {"answer": 0.7685, "unit": "mol/L"}, "id": "molarity_005300_3.07_3995", "license": "Apache-2.0", "prompt": "A solution contains 3.07 mol of solute in 3995 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 3995 mL to 3.995 L.\nCompute M = 3.07 / 3.995.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 3.07, "volume_ml": 3995}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.61 y, so each step multiplies y by 1 - h*0.61.\n3. Apply that update for 7 steps and round the final state.\nFinal: {\"answer\": -0.0001, \"unit\": \"state_units\"}", "dedupe_signature": "7285e314466649ef043defa7bcc943daf5b3b78b66a614b47ea09aeabad63b47", "difficulty": "medium", "final_answer": {"answer": -0.0001, "unit": "state_units"}, "id": "euler_decay_005301_20_0.61_1.9_7", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.61 y with y(0)=20, step size h=1.9, for 7 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.61 y, so each step multiplies y by 1 - h*0.61.\nApply that update for 7 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 20.0, "rate": 0.61, "step": 1.9, "steps": 7}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(0.6)=9.72 and f(7.8)=-6.84.\n3. The interval width is 7.2.\nFinal: {\"answer\": 10.368, \"unit\": \"area_units\"}", "dedupe_signature": "5da8b90b16d3c2a5db7d2ac63630ac32a6c7447cbc51b08209a3ccb1e008c0d7", "difficulty": "medium", "final_answer": {"answer": 10.368, "unit": "area_units"}, "id": "trapz_linear_005302_-2.3_11.1_0.6_7.8", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-2.3x+11.1 from x=0.6 to x=7.8. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(0.6)=9.72 and f(7.8)=-6.84.\nThe interval width is 7.2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 11.1, "slope": -2.3, "x0": 0.6, "x1": 7.8}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.3 and add it to the current value.\nFinal: {\"answer\": [1.075, 0.355, -0.035], \"unit\": \"temperature_units\"}", "dedupe_signature": "9a5414502a0dbe4bd60c300679301776a32d146fc3fc54e7ee9ef5cd36fbee1c", "difficulty": "hard", "final_answer": {"answer": [1.075, 0.355, -0.035], "unit": "temperature_units"}, "id": "heat_step_005303_0.3_1.75_0.4_1.3_-0.95_-0.15", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.75, right=-0.15; current interior values are [0.4, 1.3, -0.95]. Use r=0.3. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.3 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [0.4, 1.3, -0.95], "left": 1.75, "r": 0.3, "right": -0.15}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 100 centimeters in one meter.\n2. Apply the conversion factor directly to the given value.\n3. Compute 995.5 / 100.\nFinal: {\"answer\": 9.955, \"unit\": \"m\"}", "dedupe_signature": "bd565766faabfb9b758fc2ec74912b745939ac984e4136d8f31ba7f0df6d15ef", "difficulty": "easy", "final_answer": {"answer": 9.955, "unit": "m"}, "id": "unit_convert_005304_cm_to_m_995.5", "license": "Apache-2.0", "prompt": "Convert 995.5 cm to m. Return the converted value with unit.", "reasoning_trace": "There are 100 centimeters in one meter.\nApply the conversion factor directly to the given value.\nCompute 995.5 / 100.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 995.5}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-0.8, 0.5], \"unit\": \"dimensionless\"}", "dedupe_signature": "f92fb5fb6dedbae76886da0a86c8211c096513886a40098ef440e8931b81dbc3", "difficulty": "medium", "final_answer": {"answer": [-0.8, 0.5], "unit": "dimensionless"}, "id": "line_two_point_005306_-18.75_-4.25_-0.8_0.5", "license": "Apache-2.0", "prompt": "A line passes through points (-18.75, 15.5) and (-4.25, 3.9). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -18.75, "x2": -4.25, "y1": 15.5, "y2": 3.9000000000000004}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. amount times volume is not concentration\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "4399563a08075bc0566382b9849f080caa1e575378fe59ffbbb103d5fe27d1ee", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_005307_inconsistent_74ac0b02_701523", "license": "Apache-2.0", "prompt": "In model card equation case 701523, check dimensional consistency for C = n * V. The left side has dimensions mol/L and the right side has dimensions mol*L. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\namount times volume is not concentration\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "C = n * V"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef clamp_005308(x, lo, hi):\n    if lo > hi:\n        raise ValueError('lo must be <= hi')\n    return min(max(x, lo), hi)\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"clamp_005308\"}", "dedupe_signature": "52c54090e927ae2a70d3a928d111dcf4263653e6e4b4db45f18c10f18f0c1956", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "clamp_005308"}, "id": "code_005308_clamp_005308", "license": "Apache-2.0", "prompt": "Write a Python function clamp_005308(x, lo, hi) that clips x into the inclusive interval [lo, hi]. It must raise ValueError if lo > hi. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "clamp_005308"}, "verifier": {"function": "clamp_005308", "tests": ["assert clamp_005308(5, 0, 10) == 5", "assert clamp_005308(-2, 0, 10) == 0", "assert clamp_005308(12, 0, 10) == 10", "try:\n    clamp_005308(1, 3, 2)\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=19 degrees through the sine of 2 theta.\n3. Substitute v=49.9 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 156.2694, \"unit\": \"m\"}", "dedupe_signature": "e6562eee37e28c6bc60be2f1cfbca2612d681b2cb84bdb8a07a3422de5b258fe", "difficulty": "medium", "final_answer": {"answer": 156.2694, "unit": "m"}, "id": "projectile_range_005312_49.9_19", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 49.9 m/s and angle 19 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=19 degrees through the sine of 2 theta.\nSubstitute v=49.9 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 19, "gravity": 9.81, "speed": 49.9}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 3.63 * 8.314 * 511 / 116.5.\nFinal: {\"answer\": 132.3767, \"unit\": \"kPa\"}", "dedupe_signature": "7e1a4484e64e71c3e220143b2ec3b395deea3117d134c91ce5d2422fcd96df85", "difficulty": "medium", "final_answer": {"answer": 132.3767, "unit": "kPa"}, "id": "ideal_gas_005313_3.63_511_116.5", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=3.63 mol, T=511 K, and V=116.5 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 3.63 * 8.314 * 511 / 116.5.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 3.63, "temp_k": 511, "volume_l": 116.5}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=11.2 V and R=160 ohm.\nFinal: {\"answer\": 0.784, \"unit\": \"W\"}", "dedupe_signature": "00fbb5529fd549beac4689e3b0269bcc82b05f5d22412500bda9d4391c47bc40", "difficulty": "easy", "final_answer": {"answer": 0.784, "unit": "W"}, "id": "ohm_power_005315_11.2_160", "license": "Apache-2.0", "prompt": "A resistor has resistance 160 ohm and voltage 11.2 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=11.2 V and R=160 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 160.0, "voltage": 11.2}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=717 mg, t=353.5 h, and T_half=33.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 0.4775, \"unit\": \"mg\"}", "dedupe_signature": "f31f67ed00e669ebc84fddb631c8801b82a699af8e738dd57412d1a331a37746", "difficulty": "medium", "final_answer": {"answer": 0.4775, "unit": "mg"}, "id": "half_life_005316_717_33.5_353.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 717 mg. Its half-life is 33.5 hours. How many mg remain after 353.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=717 mg, t=353.5 h, and T_half=33.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 353.5, "half_life": 33.5, "initial_amount": 717.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 5.19 mol * 58.44 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 303.3036, \"unit\": \"g\"}", "dedupe_signature": "4b10770f6178912eab57e94e93406b58f83554b59092ff4c4faaa0c8752b325e", "difficulty": "medium", "final_answer": {"answer": 303.3036, "unit": "g"}, "id": "stoich_mass_005317_sodium_chloride_5.19", "license": "Apache-2.0", "prompt": "A sample contains 5.19 mol of sodium chloride. Using molar mass 58.44 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 5.19 mol * 58.44 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "sodium chloride", "molar_mass": 58.44, "moles": 5.19}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.61 y, so each step multiplies y by 1 - h*0.61.\n3. Apply that update for 10 steps and round the final state.\nFinal: {\"answer\": 0.1698, \"unit\": \"state_units\"}", "dedupe_signature": "40b2bcf7150d5820e86e791567a09566e82fc8ba831c526c33b0d2a15f9976e3", "difficulty": "medium", "final_answer": {"answer": 0.1698, "unit": "state_units"}, "id": "euler_decay_005319_44.5_0.61_0.7_10", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.61 y with y(0)=44.5, step size h=0.7, for 10 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.61 y, so each step multiplies y by 1 - h*0.61.\nApply that update for 10 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 44.5, "rate": 0.61, "step": 0.7, "steps": 10}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-0.6)=15.94 and f(0.7)=20.62.\n3. The interval width is 1.3.\nFinal: {\"answer\": 23.764, \"unit\": \"area_units\"}", "dedupe_signature": "b58437da8f8684d66800f612636d03fdcaa46ff95ac0f2c1a1e750ce246cf16b", "difficulty": "medium", "final_answer": {"answer": 23.764, "unit": "area_units"}, "id": "trapz_linear_005320_3.6_18.1_-0.6_0.7", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=3.6x+18.1 from x=-0.6 to x=0.7. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-0.6)=15.94 and f(0.7)=20.62.\nThe interval width is 1.3.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 18.1, "slope": 3.6, "x0": -0.6, "x1": 0.7000000000000001}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=220 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-52.091, -43.7096], \"unit\": \"N\"}", "dedupe_signature": "fe0aa7d0ca84485a04f88596ceb374862e31ba6aaed3fdeecbff3678ea339db6", "difficulty": "medium", "final_answer": {"answer": [-52.091, -43.7096], "unit": "N"}, "id": "vector_components_005323_68_220", "license": "Apache-2.0", "prompt": "A vector has magnitude 68 N at 220 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=220 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 220, "magnitude": 68.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-0.6, 4.25], \"unit\": \"dimensionless\"}", "dedupe_signature": "960a3b1246ce82f0d59ee14789cc403c406a40cc20991ae51b0024542eacdef7", "difficulty": "medium", "final_answer": {"answer": [-0.6, 4.25], "unit": "dimensionless"}, "id": "line_two_point_005324_-12_0_-0.6_4.25", "license": "Apache-2.0", "prompt": "A line passes through points (-12, 11.45) and (0, 4.25). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -12.0, "x2": 0.0, "y1": 11.45, "y2": 4.25}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. amount times volume is not concentration\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "7a5e5b4f1491d72a77d66af051460e02b3025ea9fc8bff27aa297a08a79ca7b1", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_005325_inconsistent_74ac0b02_345739", "license": "Apache-2.0", "prompt": "In instrument manual case 345739, check dimensional consistency for C = n * V. The left side has dimensions mol/L and the right side has dimensions mol*L. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\namount times volume is not concentration\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "C = n * V"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: recurrence, objective, tie_breaking_rule.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"recurrence\", \"objective\", \"tie_breaking_rule\"]}", "dedupe_signature": "f020a7f22caff773a7eafedae6e7ca32ecf7cea4c5c376163fbe47aa606a0eef", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["recurrence", "objective", "tie_breaking_rule"]}, "id": "abstain_005327_recurrence_objective_tie_breaking_rule", "license": "Apache-2.0", "prompt": "Write a dynamic-programming solver for a scheduler scoring problem with 4349 items and budget 40045, but the recurrence, objective, and tie-breaking rule are all absent. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: recurrence, objective, tie_breaking_rule.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["recurrence", "objective", "tie_breaking_rule"]}, "verifier": {"missing": ["recurrence", "objective", "tie_breaking_rule"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 3 kg and a = 7.9 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 23.7, \"unit\": \"N\"}", "dedupe_signature": "0b2ed1912d9411b296f8c8885f32af2218055ba69e9b38c878a188e1dc015ca6", "difficulty": "easy", "final_answer": {"answer": 23.7, "unit": "N"}, "id": "force_005328_3_7.9", "license": "Apache-2.0", "prompt": "A cart has mass 3 kg and measured acceleration 7.9 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 3 kg and a = 7.9 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 7.9, "mass": 3.0}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=36 degrees through the sine of 2 theta.\n3. Substitute v=60.5 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 354.8527, \"unit\": \"m\"}", "dedupe_signature": "5b8705d35c74ab4219c6189f7f305453f0d91ed1cdf0e3a7de742fafb370547a", "difficulty": "medium", "final_answer": {"answer": 354.8527, "unit": "m"}, "id": "projectile_range_005330_60.5_36", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 60.5 m/s and angle 36 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=36 degrees through the sine of 2 theta.\nSubstitute v=60.5 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 36, "gravity": 9.81, "speed": 60.5}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 2.22 * 8.314 * 561 / 85.7.\nFinal: {\"answer\": 120.8217, \"unit\": \"kPa\"}", "dedupe_signature": "b0820d99b8ac133e865bc2b3241c7c30011b69e85b29df4d4538f22463838186", "difficulty": "medium", "final_answer": {"answer": 120.8217, "unit": "kPa"}, "id": "ideal_gas_005331_2.22_561_85.7", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=2.22 mol, T=561 K, and V=85.7 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 2.22 * 8.314 * 561 / 85.7.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 2.22, "temp_k": 561, "volume_l": 85.7}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1490 * 3.76 * 95.\nFinal: {\"answer\": 532228.0, \"unit\": \"J\"}", "dedupe_signature": "2c0d67665899bf87bd064166e176151656985855b43729191172c21740824ebb", "difficulty": "easy", "final_answer": {"answer": 532228.0, "unit": "J"}, "id": "heat_q_005332_1490_3.76_95", "license": "Apache-2.0", "prompt": "A 1490 g sample has specific heat 3.76 J/(g*K). How much heat is needed to raise its temperature by 95 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1490 * 3.76 * 95.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 95, "heat_capacity": 3.76, "mass_g": 1490}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=765.5 mg, t=212.5 h, and T_half=59.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 64.3929, \"unit\": \"mg\"}", "dedupe_signature": "049bca249184ecea8e64d9fdb911c66001baab704afe9cddad40aa0eeac3ea44", "difficulty": "medium", "final_answer": {"answer": 64.3929, "unit": "mg"}, "id": "half_life_005334_765.5_59.5_212.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 765.5 mg. Its half-life is 59.5 hours. How many mg remain after 212.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=765.5 mg, t=212.5 h, and T_half=59.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 212.5, "half_life": 59.5, "initial_amount": 765.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 4.79 mol * 44.01 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 210.8079, \"unit\": \"g\"}", "dedupe_signature": "98cbdab72a9213cc6c2c4fca4bd82b4e928045b7e9088c96f33fad4987b89090", "difficulty": "medium", "final_answer": {"answer": 210.8079, "unit": "g"}, "id": "stoich_mass_005335_carbon_dioxide_4.79", "license": "Apache-2.0", "prompt": "A sample contains 4.79 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 4.79 mol * 44.01 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "carbon dioxide", "molar_mass": 44.01, "moles": 4.79}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 2135 mL to 2.135 L.\n3. Compute M = 1.655 / 2.135.\nFinal: {\"answer\": 0.7752, \"unit\": \"mol/L\"}", "dedupe_signature": "6ecee9b4402536e9b969720533c1b7c693d574c2264bc100e3eb50a585349493", "difficulty": "medium", "final_answer": {"answer": 0.7752, "unit": "mol/L"}, "id": "molarity_005336_1.655_2135", "license": "Apache-2.0", "prompt": "A solution contains 1.655 mol of solute in 2135 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 2135 mL to 2.135 L.\nCompute M = 1.655 / 2.135.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 1.655, "volume_ml": 2135}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.33 y, so each step multiplies y by 1 - h*0.33.\n3. Apply that update for 9 steps and round the final state.\nFinal: {\"answer\": 1.3728, \"unit\": \"state_units\"}", "dedupe_signature": "3b2346454a58ca20549617b89875fd8ffb8e678fc82e373593ea0fe5a224dcd2", "difficulty": "medium", "final_answer": {"answer": 1.3728, "unit": "state_units"}, "id": "euler_decay_005337_79.5_0.33_1.1_9", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.33 y with y(0)=79.5, step size h=1.1, for 9 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.33 y, so each step multiplies y by 1 - h*0.33.\nApply that update for 9 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 79.5, "rate": 0.33, "step": 1.1, "steps": 9}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-1.2)=-3.5 and f(3.5)=24.7.\n3. The interval width is 4.7.\nFinal: {\"answer\": 49.82, \"unit\": \"area_units\"}", "dedupe_signature": "9021df0520ed8a1cb2783585c4ee9d85f202aac589a47f080e6cd095f46e6e04", "difficulty": "medium", "final_answer": {"answer": 49.82, "unit": "area_units"}, "id": "trapz_linear_005338_6_3.7_-1.2_3.5", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=6x+3.7 from x=-1.2 to x=3.5. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-1.2)=-3.5 and f(3.5)=24.7.\nThe interval width is 4.7.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 3.7, "slope": 6.0, "x0": -1.2, "x1": 3.5}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.4 and add it to the current value.\nFinal: {\"answer\": [0.13, 1.63, 0.87], \"unit\": \"temperature_units\"}", "dedupe_signature": "c3e7e96c4d6101aa5f677e1e21512fa13c254d4d646ab059cf2fa9b704bbca37", "difficulty": "hard", "final_answer": {"answer": [0.13, 1.63, 0.87], "unit": "temperature_units"}, "id": "heat_step_005339_0.4_-1.6_1.15_1.35_2.25_-0.3", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-1.6, right=-0.3; current interior values are [1.15, 1.35, 2.25]. Use r=0.4. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.4 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [1.15, 1.35, 2.25], "left": -1.6, "r": 0.4, "right": -0.3}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 100 centimeters in one meter.\n2. Apply the conversion factor directly to the given value.\n3. Compute 1468.5 / 100.\nFinal: {\"answer\": 14.685, \"unit\": \"m\"}", "dedupe_signature": "58f9939a11d08fef0826ca81b0e67e22c8407f97612e70231da86b1f14331f65", "difficulty": "easy", "final_answer": {"answer": 14.685, "unit": "m"}, "id": "unit_convert_005340_cm_to_m_1468.5", "license": "Apache-2.0", "prompt": "Convert 1468.5 cm to m. Return the converted value with unit.", "reasoning_trace": "There are 100 centimeters in one meter.\nApply the conversion factor directly to the given value.\nCompute 1468.5 / 100.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 1468.5}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=10 degrees and keep the unit as newtons.\nFinal: {\"answer\": [219.6121, 38.7235], \"unit\": \"N\"}", "dedupe_signature": "3fd5a67de43e3d335505568d584c22e15f8f91a9557ee32c82029724d14dd4bb", "difficulty": "medium", "final_answer": {"answer": [219.6121, 38.7235], "unit": "N"}, "id": "vector_components_005341_223_10", "license": "Apache-2.0", "prompt": "A vector has magnitude 223 N at 10 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=10 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 10, "magnitude": 223.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [2.3, -22.75], \"unit\": \"dimensionless\"}", "dedupe_signature": "a607deae4ca1d1f1845d3c1bd0bc45a1c78dfd99baf71105340f38e613897138", "difficulty": "medium", "final_answer": {"answer": [2.3, -22.75], "unit": "dimensionless"}, "id": "line_two_point_005342_20_27.25_2.3_-22.75", "license": "Apache-2.0", "prompt": "A line passes through points (20, 23.25) and (27.25, 39.925). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 20.0, "x2": 27.25, "y1": 23.25, "y2": 39.925}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: left_boundary, right_boundary.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"left_boundary\", \"right_boundary\"]}", "dedupe_signature": "10e7d0aa0a2e64c6bb37653ccd0dc9c61eaf9f4ed753496b85ed8692033a016d", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["left_boundary", "right_boundary"]}, "id": "abstain_005345_left_boundary_right_boundary", "license": "Apache-2.0", "prompt": "Solve the 1D heat equation after one finite-difference step. The prompt gives r=0.48 and interior values [-0.1, -0.05, 0.05], but gives no boundary values. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: left_boundary, right_boundary.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["left_boundary", "right_boundary"]}, "verifier": {"missing": ["left_boundary", "right_boundary"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 19.85 kg and a = 7.8 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 154.83, \"unit\": \"N\"}", "dedupe_signature": "2bbf0a80db3e4fd1129d2dd0b30069f68d02ac1815f82cbe097460625c406d1a", "difficulty": "easy", "final_answer": {"answer": 154.83, "unit": "N"}, "id": "force_005346_19.85_7.8", "license": "Apache-2.0", "prompt": "A cart has mass 19.85 kg and measured acceleration 7.8 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 19.85 kg and a = 7.8 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 7.8, "mass": 19.85}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 32.35^2 and multiply by 0.5 * 15.1.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 7901.2449, \"unit\": \"J\"}", "dedupe_signature": "ed9090c9c69afe336a062ec9ab368b1247ded5ab9952f7a004f27eb0b3be480f", "difficulty": "easy", "final_answer": {"answer": 7901.2449, "unit": "J"}, "id": "ke_005347_15.1_32.35", "license": "Apache-2.0", "prompt": "A body of mass 15.1 kg moves at 32.35 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 32.35^2 and multiply by 0.5 * 15.1.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 15.1, "velocity": 32.35}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=72 degrees through the sine of 2 theta.\n3. Substitute v=13.7 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 11.2458, \"unit\": \"m\"}", "dedupe_signature": "45961bf9e3e43b08849c252bd53147c70c830c985e1a9769a4a913a5de767624", "difficulty": "medium", "final_answer": {"answer": 11.2458, "unit": "m"}, "id": "projectile_range_005348_13.7_72", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 13.7 m/s and angle 72 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=72 degrees through the sine of 2 theta.\nSubstitute v=13.7 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 72, "gravity": 9.81, "speed": 13.7}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 4.01 * 8.314 * 506 / 17.1.\nFinal: {\"answer\": 986.5266, \"unit\": \"kPa\"}", "dedupe_signature": "64e582d4ac738ca411d08657726cbc9f4df3612485f492219fc56101e75eea79", "difficulty": "medium", "final_answer": {"answer": 986.5266, "unit": "kPa"}, "id": "ideal_gas_005349_4.01_506_17.1", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=4.01 mol, T=506 K, and V=17.1 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 4.01 * 8.314 * 506 / 17.1.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 4.01, "temp_k": 506, "volume_l": 17.1}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1725 * 3.8 * 4.\nFinal: {\"answer\": 26220.0, \"unit\": \"J\"}", "dedupe_signature": "6a2f3b028df0605e6b184dc303af39fcbc4705aa8f5fbb26a34acad0d06aa7df", "difficulty": "easy", "final_answer": {"answer": 26220.0, "unit": "J"}, "id": "heat_q_005350_1725_3.8_4", "license": "Apache-2.0", "prompt": "A 1725 g sample has specific heat 3.8 J/(g*K). How much heat is needed to raise its temperature by 4 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1725 * 3.8 * 4.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 4, "heat_capacity": 3.8, "mass_g": 1725}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=269 mg, t=57.5 h, and T_half=102 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 181.9927, \"unit\": \"mg\"}", "dedupe_signature": "d6a37dd9d5d50b6406c6eab58b4d288f3151be3fad3d5a997f9622d38fa8cf61", "difficulty": "medium", "final_answer": {"answer": 181.9927, "unit": "mg"}, "id": "half_life_005352_269_102_57.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 269 mg. Its half-life is 102 hours. How many mg remain after 57.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=269 mg, t=57.5 h, and T_half=102 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 57.5, "half_life": 102.0, "initial_amount": 269.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 1.43 mol * 100.087 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 143.1244, \"unit\": \"g\"}", "dedupe_signature": "f3c0e8afc5a440520b9759fc6e1b618e553e94f41ffe6334f89b40059f3a61c4", "difficulty": "medium", "final_answer": {"answer": 143.1244, "unit": "g"}, "id": "stoich_mass_005353_calcium_carbonate_1.43", "license": "Apache-2.0", "prompt": "A sample contains 1.43 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 1.43 mol * 100.087 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "calcium carbonate", "molar_mass": 100.087, "moles": 1.43}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 1450 mL to 1.45 L.\n3. Compute M = 1.425 / 1.45.\nFinal: {\"answer\": 0.9828, \"unit\": \"mol/L\"}", "dedupe_signature": "e90f5d2487e21dc15c8e8deef01b2c5ee2f7dbddeaa27ae329ed7cb3eb0fdd42", "difficulty": "medium", "final_answer": {"answer": 0.9828, "unit": "mol/L"}, "id": "molarity_005354_1.425_1450", "license": "Apache-2.0", "prompt": "A solution contains 1.425 mol of solute in 1450 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 1450 mL to 1.45 L.\nCompute M = 1.425 / 1.45.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 1.425, "volume_ml": 1450}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.57 y, so each step multiplies y by 1 - h*0.57.\n3. Apply that update for 11 steps and round the final state.\nFinal: {\"answer\": 0.0, \"unit\": \"state_units\"}", "dedupe_signature": "701128b57338e265ff8ced5ad88b00de0342c56b437d2d8d660964832f3b6913", "difficulty": "medium", "final_answer": {"answer": 0.0, "unit": "state_units"}, "id": "euler_decay_005355_13_0.57_1.9_11", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.57 y with y(0)=13, step size h=1.9, for 11 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.57 y, so each step multiplies y by 1 - h*0.57.\nApply that update for 11 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 13.0, "rate": 0.57, "step": 1.9, "steps": 11}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(1.7)=-18.8 and f(2.1)=-20.\n3. The interval width is 0.4.\nFinal: {\"answer\": -7.76, \"unit\": \"area_units\"}", "dedupe_signature": "d3ac2ae0e738de030180671717217a73dfa95e298db8438ef5284757d0385064", "difficulty": "medium", "final_answer": {"answer": -7.76, "unit": "area_units"}, "id": "trapz_linear_005356_-3_-13.7_1.7_2.1", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-3x+-13.7 from x=1.7 to x=2.1. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(1.7)=-18.8 and f(2.1)=-20.\nThe interval width is 0.4.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -13.7, "slope": -3.0, "x0": 1.7, "x1": 2.1}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.22 and add it to the current value.\nFinal: {\"answer\": [-0.758, -0.9, -0.396], \"unit\": \"temperature_units\"}", "dedupe_signature": "cd878c04d00178bd6bf70d67f32353406e43e9475f850dca210a9591b9542be7", "difficulty": "hard", "final_answer": {"answer": [-0.758, -0.9, -0.396], "unit": "temperature_units"}, "id": "heat_step_005357_0.22_0.85_-1.55_-0.35_-1.65_2.75", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=0.85, right=2.75; current interior values are [-1.55, -0.35, -1.65]. Use r=0.22. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.22 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-1.55, -0.35, -1.65], "left": 0.85, "r": 0.22, "right": 2.75}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [5.15, -22.25], \"unit\": \"dimensionless\"}", "dedupe_signature": "20771acdab0c4f1e68ab84d1b3017c4353a9c67f010152d1cbd75c9907bbf5ae", "difficulty": "medium", "final_answer": {"answer": [5.15, -22.25], "unit": "dimensionless"}, "id": "line_two_point_005360_-3.5_9.25_5.15_-22.25", "license": "Apache-2.0", "prompt": "A line passes through points (-3.5, -40.275) and (9.25, 25.3875). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -3.5, "x2": 9.25, "y1": -40.275000000000006, "y2": 25.387500000000003}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. density times acceleration times height gives kg/(m*s^2), or pascal\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "37e0181977687e2007e67e05f78161ea978be89348c94b7b0fb8875e7e7a0224", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_005361_consistent_b7d3eed1_390731", "license": "Apache-2.0", "prompt": "In student derivation case 390731, check dimensional consistency for p = rho * g * h. The left side has dimensions Pa and the right side has dimensions Pa. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\ndensity times acceleration times height gives kg/(m*s^2), or pascal\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "p = rho * g * h"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: rate_constant, number_of_steps.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"rate_constant\", \"number_of_steps\"]}", "dedupe_signature": "54a086d95ab2d3f88d1625134828ddfc38517e7350da3c97cee5d44916b95815", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["rate_constant", "number_of_steps"]}, "id": "abstain_005363_rate_constant_number_of_steps", "license": "Apache-2.0", "prompt": "Use explicit Euler for dy/dt = -k y. The prompt gives y(0)=27 and h=1.3, but omits both k and the number of steps. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: rate_constant, number_of_steps.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["rate_constant", "number_of_steps"]}, "verifier": {"missing": ["rate_constant", "number_of_steps"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 4.2 kg and a = 4.5 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 18.9, \"unit\": \"N\"}", "dedupe_signature": "d3502e26c2ec012fb4612ff3b547c958a13b69393a8383a8644dc575b56c3a93", "difficulty": "easy", "final_answer": {"answer": 18.9, "unit": "N"}, "id": "force_005364_4.2_4.5", "license": "Apache-2.0", "prompt": "A cart has mass 4.2 kg and measured acceleration 4.5 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 4.2 kg and a = 4.5 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 4.5, "mass": 4.2}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=55 degrees through the sine of 2 theta.\n3. Substitute v=49 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 229.99, \"unit\": \"m\"}", "dedupe_signature": "b1a5b6b9d363df462e71780637edc154e5962419a901f0f275f9a44a8a9b7d9f", "difficulty": "medium", "final_answer": {"answer": 229.99, "unit": "m"}, "id": "projectile_range_005366_49_55", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 49 m/s and angle 55 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=55 degrees through the sine of 2 theta.\nSubstitute v=49 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 55, "gravity": 9.81, "speed": 49.0}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 0.31 * 8.314 * 391 / 38.7.\nFinal: {\"answer\": 26.0398, \"unit\": \"kPa\"}", "dedupe_signature": "f0c51939944cb2d33cc0056b0bbf4122cc7409c499dd32c1186f188c0ae6265d", "difficulty": "medium", "final_answer": {"answer": 26.0398, "unit": "kPa"}, "id": "ideal_gas_005367_0.31_391_38.7", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=0.31 mol, T=391 K, and V=38.7 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 0.31 * 8.314 * 391 / 38.7.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 0.31, "temp_k": 391, "volume_l": 38.7}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=191 mg, t=206 h, and T_half=45.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 8.2819, \"unit\": \"mg\"}", "dedupe_signature": "1a74419b97e5c179b5dcdb3993d928cefb8ee2eaa8633ed46baa0bcd7294bc96", "difficulty": "medium", "final_answer": {"answer": 8.2819, "unit": "mg"}, "id": "half_life_005370_191_45.5_206", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 191 mg. Its half-life is 45.5 hours. How many mg remain after 206 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=191 mg, t=206 h, and T_half=45.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 206.0, "half_life": 45.5, "initial_amount": 191.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 985 mL to 0.985 L.\n3. Compute M = 3.88 / 0.985.\nFinal: {\"answer\": 3.9391, \"unit\": \"mol/L\"}", "dedupe_signature": "641031934735d06f128527a598274d48b1448cdfdc21264fc50bfa69bcdfebf3", "difficulty": "medium", "final_answer": {"answer": 3.9391, "unit": "mol/L"}, "id": "molarity_005372_3.88_985", "license": "Apache-2.0", "prompt": "A solution contains 3.88 mol of solute in 985 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 985 mL to 0.985 L.\nCompute M = 3.88 / 0.985.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 3.88, "volume_ml": 985}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.19 y, so each step multiplies y by 1 - h*0.19.\n3. Apply that update for 6 steps and round the final state.\nFinal: {\"answer\": 6.8787, \"unit\": \"state_units\"}", "dedupe_signature": "ff4657057c3abf79a2cbe06195c2b99d0f8165d1d54ff3c1b9eed639ede779e3", "difficulty": "medium", "final_answer": {"answer": 6.8787, "unit": "state_units"}, "id": "euler_decay_005373_35_0.19_1.25_6", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.19 y with y(0)=35, step size h=1.25, for 6 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.19 y, so each step multiplies y by 1 - h*0.19.\nApply that update for 6 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 35.0, "rate": 0.19, "step": 1.25, "steps": 6}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(5.9)=-10.86 and f(14.7)=-31.98.\n3. The interval width is 8.8.\nFinal: {\"answer\": -188.496, \"unit\": \"area_units\"}", "dedupe_signature": "619f38404e3b700ee00a61f28bbcae72e06215f624cb4d0406ee9a427da7ff92", "difficulty": "medium", "final_answer": {"answer": -188.496, "unit": "area_units"}, "id": "trapz_linear_005374_-2.4_3.3_5.9_14.7", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-2.4x+3.3 from x=5.9 to x=14.7. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(5.9)=-10.86 and f(14.7)=-31.98.\nThe interval width is 8.8.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 3.3, "slope": -2.4, "x0": 5.9, "x1": 14.700000000000001}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=178 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-272.8337, 9.5276], \"unit\": \"N\"}", "dedupe_signature": "e68baf381afb5dbb4195e7f9dac350a2d786684507326edeeb6831ddda5c616b", "difficulty": "medium", "final_answer": {"answer": [-272.8337, 9.5276], "unit": "N"}, "id": "vector_components_005377_273_178", "license": "Apache-2.0", "prompt": "A vector has magnitude 273 N at 178 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=178 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 178, "magnitude": 273.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. speed squared over acceleration has units of meters\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "e9e913d7358d708e4be2821d715ed44de60a5fb92aecea4bc7d5cf6e945ec081", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_005379_consistent_741d4e34_213457", "license": "Apache-2.0", "prompt": "In model card equation case 213457, check dimensional consistency for R = v^2 * sin(theta) / g. The left side has dimensions m and the right side has dimensions m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nspeed squared over acceleration has units of meters\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "R = v^2 * sin(theta) / g"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef center_values_005380(values):\n    if not values:\n        raise ValueError('center_values requires at least one value')\n    mean = sum(values) / len(values)\n    return [value - mean for value in values]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"center_values_005380\"}", "dedupe_signature": "83ed6b9f35905c3f6bfba1b2d9c334bf7c8629835343530b71b19f8e5eefdf14", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "center_values_005380"}, "id": "code_005380_center_values_005380", "license": "Apache-2.0", "prompt": "Write a Python function center_values_005380(values) that subtracts the arithmetic mean from each value and returns a new list. Raise ValueError for an empty input. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "center_values_005380"}, "verifier": {"function": "center_values_005380", "tests": ["out = center_values_005380([1, 2, 3]); assert out == [-1, 0, 1]", "assert center_values_005380([5]) == [0]", "try:\n    center_values_005380([])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 9.8 kg and a = 3.9 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 38.22, \"unit\": \"N\"}", "dedupe_signature": "b028a7a1985e75b87ef8c0042bcdc91e0a0257bc55f93c9157401e41b7fd9d98", "difficulty": "easy", "final_answer": {"answer": 38.22, "unit": "N"}, "id": "force_005382_9.8_3.9", "license": "Apache-2.0", "prompt": "A cart has mass 9.8 kg and measured acceleration 3.9 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 9.8 kg and a = 3.9 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 3.9, "mass": 9.8}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=77 degrees through the sine of 2 theta.\n3. Substitute v=41.4 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 76.5903, \"unit\": \"m\"}", "dedupe_signature": "55c9ea3f46f9a62177dc7906dc65af97d817d1cb750982c3dff0dd0049d516fa", "difficulty": "medium", "final_answer": {"answer": 76.5903, "unit": "m"}, "id": "projectile_range_005384_41.4_77", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 41.4 m/s and angle 77 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=77 degrees through the sine of 2 theta.\nSubstitute v=41.4 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 77, "gravity": 9.81, "speed": 41.4}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 1.03 * 8.314 * 334 / 89.9.\nFinal: {\"answer\": 31.8152, \"unit\": \"kPa\"}", "dedupe_signature": "a0892950958fed05a2f99736ab9a152bcf5b9e44794271ff56632a6fe30fdaa1", "difficulty": "medium", "final_answer": {"answer": 31.8152, "unit": "kPa"}, "id": "ideal_gas_005385_1.03_334_89.9", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=1.03 mol, T=334 K, and V=89.9 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 1.03 * 8.314 * 334 / 89.9.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 1.03, "temp_k": 334, "volume_l": 89.9}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1280 * 3.92 * 34.\nFinal: {\"answer\": 170598.4, \"unit\": \"J\"}", "dedupe_signature": "686a530f4d863a2fa7f008d3ec715569280b7d6f0b8cf2149e982dde3b3c3b92", "difficulty": "easy", "final_answer": {"answer": 170598.4, "unit": "J"}, "id": "heat_q_005386_1280_3.92_34", "license": "Apache-2.0", "prompt": "A 1280 g sample has specific heat 3.92 J/(g*K). How much heat is needed to raise its temperature by 34 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1280 * 3.92 * 34.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 34, "heat_capacity": 3.92, "mass_g": 1280}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=74.8 V and R=178.2 ohm.\nFinal: {\"answer\": 31.3975, \"unit\": \"W\"}", "dedupe_signature": "953d3cf6468450ba8c80d44a0dce00ef7f1664a2c6a6ce4d70f52dcc2707f662", "difficulty": "easy", "final_answer": {"answer": 31.3975, "unit": "W"}, "id": "ohm_power_005387_74.8_178.2", "license": "Apache-2.0", "prompt": "A resistor has resistance 178.2 ohm and voltage 74.8 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=74.8 V and R=178.2 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 178.2, "voltage": 74.8}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=634.5 mg, t=307 h, and T_half=40.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 3.3155, \"unit\": \"mg\"}", "dedupe_signature": "8f55b6c8c70332b27e081c7a31fa3299e3b4d5b205a22a1895e6746a7028154d", "difficulty": "medium", "final_answer": {"answer": 3.3155, "unit": "mg"}, "id": "half_life_005388_634.5_40.5_307", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 634.5 mg. Its half-life is 40.5 hours. How many mg remain after 307 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=634.5 mg, t=307 h, and T_half=40.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 307.0, "half_life": 40.5, "initial_amount": 634.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 2.69 mol * 100.087 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 269.234, \"unit\": \"g\"}", "dedupe_signature": "0ce92baa2d181aeabcf1f0c58bbfcb5c7bb4ec3ae4c454aab48ca85a1abb21d7", "difficulty": "medium", "final_answer": {"answer": 269.234, "unit": "g"}, "id": "stoich_mass_005389_calcium_carbonate_2.69", "license": "Apache-2.0", "prompt": "A sample contains 2.69 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 2.69 mol * 100.087 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "calcium carbonate", "molar_mass": 100.087, "moles": 2.69}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 4480 mL to 4.48 L.\n3. Compute M = 0.885 / 4.48.\nFinal: {\"answer\": 0.1975, \"unit\": \"mol/L\"}", "dedupe_signature": "b210d249f939dbc280c5022fb281fecf82bc7f197d655a55367570962a994b3b", "difficulty": "medium", "final_answer": {"answer": 0.1975, "unit": "mol/L"}, "id": "molarity_005390_0.885_4480", "license": "Apache-2.0", "prompt": "A solution contains 0.885 mol of solute in 4480 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 4480 mL to 4.48 L.\nCompute M = 0.885 / 4.48.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 0.885, "volume_ml": 4480}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(3.6)=-9.7 and f(4.9)=-11.65.\n3. The interval width is 1.3.\nFinal: {\"answer\": -13.8775, \"unit\": \"area_units\"}", "dedupe_signature": "1caa436f7cefca86d6249e0657f410b4eefa3ff9b52537de48bb2e0c2ef2e29b", "difficulty": "medium", "final_answer": {"answer": -13.8775, "unit": "area_units"}, "id": "trapz_linear_005392_-1.5_-4.3_3.6_4.9", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-1.5x+-4.3 from x=3.6 to x=4.9. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(3.6)=-9.7 and f(4.9)=-11.65.\nThe interval width is 1.3.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -4.3, "slope": -1.5, "x0": 3.6, "x1": 4.9}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.22 and add it to the current value.\nFinal: {\"answer\": [0.843, 1.018, 0.216], \"unit\": \"temperature_units\"}", "dedupe_signature": "3811b90acddc31f797aee2b323ec967c012c8b27acbf119a39e82e9c17340f6a", "difficulty": "hard", "final_answer": {"answer": [0.843, 1.018, 0.216], "unit": "temperature_units"}, "id": "heat_step_005393_0.22_1.75_0.15_1.7_0.15_-1.1", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.75, right=-1.1; current interior values are [0.15, 1.7, 0.15]. Use r=0.22. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.22 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [0.15, 1.7, 0.15], "left": 1.75, "r": 0.22, "right": -1.1}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 38020.0 / 1000.\nFinal: {\"answer\": 38.02, \"unit\": \"kg\"}", "dedupe_signature": "a7dc971be4320450c131c8b1e2f61bc937692b25382a080e8c5d12e24b78dec3", "difficulty": "easy", "final_answer": {"answer": 38.02, "unit": "kg"}, "id": "unit_convert_005394_g_to_kg_38020", "license": "Apache-2.0", "prompt": "Convert 38020 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 38020.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 38020.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=39 degrees and keep the unit as newtons.\nFinal: {\"answer\": [190.0122, 153.8688], \"unit\": \"N\"}", "dedupe_signature": "41f321ee81b72a01fd619edd70705e91b5b38ee7fead578489d7236fa29160f1", "difficulty": "medium", "final_answer": {"answer": [190.0122, 153.8688], "unit": "N"}, "id": "vector_components_005395_244.5_39", "license": "Apache-2.0", "prompt": "A vector has magnitude 244.5 N at 39 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=39 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 39, "magnitude": 244.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [1.4, -2.25], \"unit\": \"dimensionless\"}", "dedupe_signature": "d1f96659b2e3f1668c72c8a456c960aa3d3245ea23eb6a822a32e67bcdfd44f3", "difficulty": "medium", "final_answer": {"answer": [1.4, -2.25], "unit": "dimensionless"}, "id": "line_two_point_005396_9.5_23.5_1.4_-2.25", "license": "Apache-2.0", "prompt": "A line passes through points (9.5, 11.05) and (23.5, 30.65). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 9.5, "x2": 23.5, "y1": 11.049999999999999, "y2": 30.65}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. energy divided by length is force, not spring constant\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "1acb0c3c6430688314cb899197c3c0474d7eabfa2db813da3dfcea94596b395c", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_005397_inconsistent_56040f5d_171647", "license": "Apache-2.0", "prompt": "In field worksheet case 171647, check dimensional consistency for k = E / x. The left side has dimensions N/m and the right side has dimensions J/m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nenergy divided by length is force, not spring constant\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "k = E / x"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef weighted_sum_005398(values, weights):\n    if len(values) != len(weights):\n        raise ValueError('length mismatch')\n    return sum(value * weight for value, weight in zip(values, weights))\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"weighted_sum_005398\"}", "dedupe_signature": "b72b7ddfec06991ab0393162c0f96e720cd06bdf32f188cefd25008446635e1f", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "weighted_sum_005398"}, "id": "code_005398_weighted_sum_005398", "license": "Apache-2.0", "prompt": "Write a Python function weighted_sum_005398(values, weights) that returns sum(value*weight). Raise ValueError when the two inputs have different lengths. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "weighted_sum_005398"}, "verifier": {"function": "weighted_sum_005398", "tests": ["assert weighted_sum_005398([2, 3], [4, 5]) == 23", "assert weighted_sum_005398([], []) == 0", "try:\n    weighted_sum_005398([1], [1, 2])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: left_boundary, right_boundary.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"left_boundary\", \"right_boundary\"]}", "dedupe_signature": "809abeaaa596fcbf73a36cefca8e38f1929834216494d4bb94be84b3bb206c76", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["left_boundary", "right_boundary"]}, "id": "abstain_005399_left_boundary_right_boundary", "license": "Apache-2.0", "prompt": "Solve the 1D heat equation after one finite-difference step. The prompt gives r=0.18 and interior values [-1.1, 1.75, -0.4], but gives no boundary values. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: left_boundary, right_boundary.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["left_boundary", "right_boundary"]}, "verifier": {"missing": ["left_boundary", "right_boundary"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 4.5 kg and a = 5.65 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 25.425, \"unit\": \"N\"}", "dedupe_signature": "9aa626e77add9282c7abdbd9e078bfcc0086565131517d7899eaf234265afc9d", "difficulty": "easy", "final_answer": {"answer": 25.425, "unit": "N"}, "id": "force_005400_4.5_5.65", "license": "Apache-2.0", "prompt": "A cart has mass 4.5 kg and measured acceleration 5.65 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 4.5 kg and a = 5.65 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 5.65, "mass": 4.5}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 43.9^2 and multiply by 0.5 * 27.85.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 26836.3992, \"unit\": \"J\"}", "dedupe_signature": "57a44dae100a6f12dfe38ee5695b916b639d26704597405d044e687c7a1afde5", "difficulty": "easy", "final_answer": {"answer": 26836.3992, "unit": "J"}, "id": "ke_005401_27.85_43.9", "license": "Apache-2.0", "prompt": "A body of mass 27.85 kg moves at 43.9 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 43.9^2 and multiply by 0.5 * 27.85.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 27.85, "velocity": 43.9}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=69 degrees through the sine of 2 theta.\n3. Substitute v=37.7 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 96.9448, \"unit\": \"m\"}", "dedupe_signature": "97b773d02154c1e7a4dd782419425d28fe758a2cdcce9b1b1e4ec984dfe6d0eb", "difficulty": "medium", "final_answer": {"answer": 96.9448, "unit": "m"}, "id": "projectile_range_005402_37.7_69", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 37.7 m/s and angle 69 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=69 degrees through the sine of 2 theta.\nSubstitute v=37.7 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 69, "gravity": 9.81, "speed": 37.7}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 1.99 * 8.314 * 456 / 108.3.\nFinal: {\"answer\": 69.6626, \"unit\": \"kPa\"}", "dedupe_signature": "db75262e9b2bf9bb4c0dfe1f54010cb699de7f4eb9946ae38c94368201e4990b", "difficulty": "medium", "final_answer": {"answer": 69.6626, "unit": "kPa"}, "id": "ideal_gas_005403_1.99_456_108.3", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=1.99 mol, T=456 K, and V=108.3 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 1.99 * 8.314 * 456 / 108.3.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 1.99, "temp_k": 456, "volume_l": 108.3}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=218.8 V and R=151.7 ohm.\nFinal: {\"answer\": 315.5797, \"unit\": \"W\"}", "dedupe_signature": "d303a54f4b6acf9a9ad2bfd782c5d80f5bb6c9231de809d0a3b4d4e233461efa", "difficulty": "easy", "final_answer": {"answer": 315.5797, "unit": "W"}, "id": "ohm_power_005405_218.8_151.7", "license": "Apache-2.0", "prompt": "A resistor has resistance 151.7 ohm and voltage 218.8 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=218.8 V and R=151.7 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 151.7, "voltage": 218.8}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 5.56 mol * 44.01 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 244.6956, \"unit\": \"g\"}", "dedupe_signature": "c7d2f2c1e040450398213eb4cee213c4005d1d4f80c43a00afc079049c7710ee", "difficulty": "medium", "final_answer": {"answer": 244.6956, "unit": "g"}, "id": "stoich_mass_005407_carbon_dioxide_5.56", "license": "Apache-2.0", "prompt": "A sample contains 5.56 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 5.56 mol * 44.01 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "carbon dioxide", "molar_mass": 44.01, "moles": 5.56}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 325 mL to 0.325 L.\n3. Compute M = 4.81 / 0.325.\nFinal: {\"answer\": 14.8, \"unit\": \"mol/L\"}", "dedupe_signature": "6d5f9b68adf3679986c7ef5420d2f4940b27f21e2c2a012385324a8293bf2b2c", "difficulty": "medium", "final_answer": {"answer": 14.8, "unit": "mol/L"}, "id": "molarity_005408_4.81_325", "license": "Apache-2.0", "prompt": "A solution contains 4.81 mol of solute in 325 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 325 mL to 0.325 L.\nCompute M = 4.81 / 0.325.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 4.81, "volume_ml": 325}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.59 y, so each step multiplies y by 1 - h*0.59.\n3. Apply that update for 12 steps and round the final state.\nFinal: {\"answer\": 0.0, \"unit\": \"state_units\"}", "dedupe_signature": "afab87294c11d843b4cc8ca8d9e373b01525c4e35d3f8a9f637e9f3f503f52c3", "difficulty": "medium", "final_answer": {"answer": 0.0, "unit": "state_units"}, "id": "euler_decay_005409_20_0.59_1.15_12", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.59 y with y(0)=20, step size h=1.15, for 12 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.59 y, so each step multiplies y by 1 - h*0.59.\nApply that update for 12 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 20.0, "rate": 0.59, "step": 1.15, "steps": 12}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-7.7)=-4.85 and f(-2.3)=8.65.\n3. The interval width is 5.4.\nFinal: {\"answer\": 10.26, \"unit\": \"area_units\"}", "dedupe_signature": "55783a9270ba562caeaf7b989853d794f5d23ab00ab81949d58f914327ffb800", "difficulty": "medium", "final_answer": {"answer": 10.26, "unit": "area_units"}, "id": "trapz_linear_005410_2.5_14.4_-7.7_-2.3", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=2.5x+14.4 from x=-7.7 to x=-2.3. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-7.7)=-4.85 and f(-2.3)=8.65.\nThe interval width is 5.4.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 14.4, "slope": 2.5, "x0": -7.7, "x1": -2.3}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.22 and add it to the current value.\nFinal: {\"answer\": [-0.369, -0.369, 0.874], \"unit\": \"temperature_units\"}", "dedupe_signature": "d4a55c7cc1ce1a2455f9f7e36213f9b1f56e99e61b8eebe6ee661d0010ed8d1f", "difficulty": "hard", "final_answer": {"answer": [-0.369, -0.369, 0.874], "unit": "temperature_units"}, "id": "heat_step_005411_0.22_-1.25_0.5_-1.7_2.15_0.2", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-1.25, right=0.2; current interior values are [0.5, -1.7, 2.15]. Use r=0.22. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.22 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [0.5, -1.7, 2.15], "left": -1.25, "r": 0.22, "right": 0.2}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 100 centimeters in one meter.\n2. Apply the conversion factor directly to the given value.\n3. Compute 4539.5 / 100.\nFinal: {\"answer\": 45.395, \"unit\": \"m\"}", "dedupe_signature": "7e595a62cfbf554bc450627626834578982f111065ba01547e90714895d8c067", "difficulty": "easy", "final_answer": {"answer": 45.395, "unit": "m"}, "id": "unit_convert_005412_cm_to_m_4539.5", "license": "Apache-2.0", "prompt": "Convert 4539.5 cm to m. Return the converted value with unit.", "reasoning_trace": "There are 100 centimeters in one meter.\nApply the conversion factor directly to the given value.\nCompute 4539.5 / 100.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 4539.5}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=282 degrees and keep the unit as newtons.\nFinal: {\"answer\": [68.4029, -321.8106], \"unit\": \"N\"}", "dedupe_signature": "dd7a806b071d9ae86c56f40a9bfd55f0da929fa774e2e72569b6d69da4fa94a9", "difficulty": "medium", "final_answer": {"answer": [68.4029, -321.8106], "unit": "N"}, "id": "vector_components_005413_329_282", "license": "Apache-2.0", "prompt": "A vector has magnitude 329 N at 282 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=282 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 282, "magnitude": 329.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [4.75, -10.75], \"unit\": \"dimensionless\"}", "dedupe_signature": "698894b9e73090463b2791313bccd58e765c6e0affa2a72afd2a1b7d1b9a7a63", "difficulty": "medium", "final_answer": {"answer": [4.75, -10.75], "unit": "dimensionless"}, "id": "line_two_point_005414_6.25_9_4.75_-10.75", "license": "Apache-2.0", "prompt": "A line passes through points (6.25, 18.9375) and (9, 32). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 6.25, "x2": 9.0, "y1": 18.9375, "y2": 32.0}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. velocity divided by time is acceleration\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "e6482a967e0adc473e3c8a97db995ecd37f7965fa97d5a0ef8790d62188e2788", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_005415_inconsistent_c1271127_333421", "license": "Apache-2.0", "prompt": "In field worksheet case 333421, check dimensional consistency for x = v / t. The left side has dimensions m and the right side has dimensions m/s^2. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nvelocity divided by time is acceleration\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "x = v / t"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 10.7 kg and a = 7.25 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 77.575, \"unit\": \"N\"}", "dedupe_signature": "bfd342658cfa7946977d67b9ff39e984ea56c2154f3cf7965d4adda096ea39a4", "difficulty": "easy", "final_answer": {"answer": 77.575, "unit": "N"}, "id": "force_005418_10.7_7.25", "license": "Apache-2.0", "prompt": "A cart has mass 10.7 kg and measured acceleration 7.25 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 10.7 kg and a = 7.25 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 7.25, "mass": 10.7}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=33 degrees through the sine of 2 theta.\n3. Substitute v=82.2 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 629.2233, \"unit\": \"m\"}", "dedupe_signature": "41cbf1b755aba8606f6b5144358b5172283dc702571afa58b00fb54249cd8cd3", "difficulty": "medium", "final_answer": {"answer": 629.2233, "unit": "m"}, "id": "projectile_range_005420_82.2_33", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 82.2 m/s and angle 33 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=33 degrees through the sine of 2 theta.\nSubstitute v=82.2 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 33, "gravity": 9.81, "speed": 82.2}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 0.55 * 8.314 * 489 / 36.4.\nFinal: {\"answer\": 61.43, \"unit\": \"kPa\"}", "dedupe_signature": "5311604135747a07cbfae45f692c891d523dd605b8885834e5301894694ba588", "difficulty": "medium", "final_answer": {"answer": 61.43, "unit": "kPa"}, "id": "ideal_gas_005421_0.55_489_36.4", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=0.55 mol, T=489 K, and V=36.4 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 0.55 * 8.314 * 489 / 36.4.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 0.55, "temp_k": 489, "volume_l": 36.4}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 260 * 1.72 * 4.\nFinal: {\"answer\": 1788.8, \"unit\": \"J\"}", "dedupe_signature": "9c861be6d562fe505bb60f660f7e360de785482dac01ec40d0c1e055b0759326", "difficulty": "easy", "final_answer": {"answer": 1788.8, "unit": "J"}, "id": "heat_q_005422_260_1.72_4", "license": "Apache-2.0", "prompt": "A 260 g sample has specific heat 1.72 J/(g*K). How much heat is needed to raise its temperature by 4 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 260 * 1.72 * 4.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 4, "heat_capacity": 1.72, "mass_g": 260}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=197.3 V and R=12.9 ohm.\nFinal: {\"answer\": 3017.6194, \"unit\": \"W\"}", "dedupe_signature": "73af34ad025a6be6d91d0392fa47a9a0f9d4fccf1acb6e315cf23c3d914d7c95", "difficulty": "easy", "final_answer": {"answer": 3017.6194, "unit": "W"}, "id": "ohm_power_005423_197.3_12.9", "license": "Apache-2.0", "prompt": "A resistor has resistance 12.9 ohm and voltage 197.3 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=197.3 V and R=12.9 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 12.9, "voltage": 197.3}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=108 mg, t=230 h, and T_half=65 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 9.2948, \"unit\": \"mg\"}", "dedupe_signature": "155123a120a6c3b4a05845d885257865eb9113b333862cc24c862ad2cd2692b0", "difficulty": "medium", "final_answer": {"answer": 9.2948, "unit": "mg"}, "id": "half_life_005424_108_65_230", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 108 mg. Its half-life is 65 hours. How many mg remain after 230 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=108 mg, t=230 h, and T_half=65 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 230.0, "half_life": 65.0, "initial_amount": 108.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 1.1 mol * 180.156 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 198.1716, \"unit\": \"g\"}", "dedupe_signature": "23ba6cd04a5edb84983f281573f5a4299778ce5dcee93cb52659fe2c4bcca1d6", "difficulty": "medium", "final_answer": {"answer": 198.1716, "unit": "g"}, "id": "stoich_mass_005425_glucose_1.1", "license": "Apache-2.0", "prompt": "A sample contains 1.1 mol of glucose. Using molar mass 180.156 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 1.1 mol * 180.156 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "glucose", "molar_mass": 180.156, "moles": 1.1}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 1430 mL to 1.43 L.\n3. Compute M = 2.52 / 1.43.\nFinal: {\"answer\": 1.7622, \"unit\": \"mol/L\"}", "dedupe_signature": "0b2139bd70b72a60e275b9fc78aeaf87351cf240c8c8ad9f74e542be1fb91e97", "difficulty": "medium", "final_answer": {"answer": 1.7622, "unit": "mol/L"}, "id": "molarity_005426_2.52_1430", "license": "Apache-2.0", "prompt": "A solution contains 2.52 mol of solute in 1430 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 1430 mL to 1.43 L.\nCompute M = 2.52 / 1.43.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 2.52, "volume_ml": 1430}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.96 y, so each step multiplies y by 1 - h*0.96.\n3. Apply that update for 7 steps and round the final state.\nFinal: {\"answer\": -0.2307, \"unit\": \"state_units\"}", "dedupe_signature": "ba588c7e5588dc1fdbbf2b9f1b74394ec15bb66d8a98db2ab7b7e7fd6ca438e5", "difficulty": "medium", "final_answer": {"answer": -0.2307, "unit": "state_units"}, "id": "euler_decay_005427_35_0.96_1.55_7", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.96 y with y(0)=35, step size h=1.55, for 7 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.96 y, so each step multiplies y by 1 - h*0.96.\nApply that update for 7 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 35.0, "rate": 0.96, "step": 1.55, "steps": 7}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-8.2)=-10.3 and f(0.5)=-10.3.\n3. The interval width is 8.7.\nFinal: {\"answer\": -89.61, \"unit\": \"area_units\"}", "dedupe_signature": "2091120df9e2d1ea40f18d12bf342bae243cbc17f823e9e816d31cb5015b17f4", "difficulty": "medium", "final_answer": {"answer": -89.61, "unit": "area_units"}, "id": "trapz_linear_005428_0_-10.3_-8.2_0.5", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=0x+-10.3 from x=-8.2 to x=0.5. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-8.2)=-10.3 and f(0.5)=-10.3.\nThe interval width is 8.7.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -10.3, "slope": 0.0, "x0": -8.2, "x1": 0.5}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.06 and add it to the current value.\nFinal: {\"answer\": [-0.383, 1.985, 2.215], \"unit\": \"temperature_units\"}", "dedupe_signature": "29c870a34207844cd297d41c2f43b7a363476d2bcb0483ccea325954ba832ea2", "difficulty": "hard", "final_answer": {"answer": [-0.383, 1.985, 2.215], "unit": "temperature_units"}, "id": "heat_step_005429_0.06_1.0_-0.65_2.15_2.2_2.5", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1, right=2.5; current interior values are [-0.65, 2.15, 2.2]. Use r=0.06. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.06 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-0.65, 2.15, 2.2], "left": 1.0, "r": 0.06, "right": 2.5}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=326 degrees and keep the unit as newtons.\nFinal: {\"answer\": [118.9669, -80.2442], \"unit\": \"N\"}", "dedupe_signature": "681dcf2385f99b488e58e19e7619e51fba5f3bad2ce5d8fd36da5d9c0a201321", "difficulty": "medium", "final_answer": {"answer": [118.9669, -80.2442], "unit": "N"}, "id": "vector_components_005431_143.5_326", "license": "Apache-2.0", "prompt": "A vector has magnitude 143.5 N at 326 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=326 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 326, "magnitude": 143.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-5.1, -21.5], \"unit\": \"dimensionless\"}", "dedupe_signature": "d4638362b186adcc1dd7ffcfeae0c8d837f962bc61c14a169eba7f688949b93c", "difficulty": "medium", "final_answer": {"answer": [-5.1, -21.5], "unit": "dimensionless"}, "id": "line_two_point_005432_1_14.25_-5.1_-21.5", "license": "Apache-2.0", "prompt": "A line passes through points (1, -26.6) and (14.25, -94.175). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 1.0, "x2": 14.25, "y1": -26.6, "y2": -94.175}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. grams cancel with J/(g*K), and kelvin cancels, leaving joules\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "52e8e0afaedc767c092614e5e8df0bc46bb51d38d7b6726d75d5a888ab04a069", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_005433_consistent_4153435f_237901", "license": "Apache-2.0", "prompt": "In simulation spec case 237901, check dimensional consistency for Q = m * c * DeltaT. The left side has dimensions J and the right side has dimensions J. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\ngrams cancel with J/(g*K), and kelvin cancels, leaving joules\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "Q = m * c * DeltaT"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef safe_mean_005434(values):\n    if not values:\n        raise ValueError('safe_mean requires at least one value')\n    return sum(values) / len(values)\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"safe_mean_005434\"}", "dedupe_signature": "44927c6b3fc89e379b165768947b07f39aba3f77ca48a2f778bd242c9742645a", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "safe_mean_005434"}, "id": "code_005434_safe_mean_005434", "license": "Apache-2.0", "prompt": "Write a Python function safe_mean_005434(values) that returns the arithmetic mean. It must raise ValueError for an empty input and must not mutate the input list. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "safe_mean_005434"}, "verifier": {"function": "safe_mean_005434", "tests": ["assert safe_mean_005434([2, 4, 6]) == 4", "xs = [1, 2, 3]; assert safe_mean_005434(xs) == 2 and xs == [1, 2, 3]", "try:\n    safe_mean_005434([])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: required_fields, allowed_transformations.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"required_fields\", \"allowed_transformations\"]}", "dedupe_signature": "b31d182422348bb6f0e77533d800f815a19e120888b1744b5fae95566233f0dd", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["required_fields", "allowed_transformations"]}, "id": "abstain_005435_required_fields_allowed_transformations", "license": "Apache-2.0", "prompt": "Write a sanitizer for valid warehouse survey records in release 283515, but the prompt does not state which fields are required or which transformations are allowed. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: required_fields, allowed_transformations.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["required_fields", "allowed_transformations"]}, "verifier": {"missing": ["required_fields", "allowed_transformations"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=10 degrees through the sine of 2 theta.\n3. Substitute v=6 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 1.2551, \"unit\": \"m\"}", "dedupe_signature": "23505a595c6b248efa881ecce240c8a55f90b0d90d56a16c519cf9ff26f79e26", "difficulty": "medium", "final_answer": {"answer": 1.2551, "unit": "m"}, "id": "projectile_range_005438_6_10", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 6 m/s and angle 10 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=10 degrees through the sine of 2 theta.\nSubstitute v=6 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 10, "gravity": 9.81, "speed": 6.0}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 4.67 * 8.314 * 365 / 75.2.\nFinal: {\"answer\": 188.4525, \"unit\": \"kPa\"}", "dedupe_signature": "9adaae1ccc6199761043317486a94f7ec11b58ffb073333a41509be58b58b8d4", "difficulty": "medium", "final_answer": {"answer": 188.4525, "unit": "kPa"}, "id": "ideal_gas_005439_4.67_365_75.2", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=4.67 mol, T=365 K, and V=75.2 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 4.67 * 8.314 * 365 / 75.2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 4.67, "temp_k": 365, "volume_l": 75.2}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=95.4 V and R=17.1 ohm.\nFinal: {\"answer\": 532.2316, \"unit\": \"W\"}", "dedupe_signature": "dbbe1d008eb18f27da5dec1adf5ac61dd1ffda69de33dce59ea5e6645525591b", "difficulty": "easy", "final_answer": {"answer": 532.2316, "unit": "W"}, "id": "ohm_power_005441_95.4_17.1", "license": "Apache-2.0", "prompt": "A resistor has resistance 17.1 ohm and voltage 95.4 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=95.4 V and R=17.1 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 17.1, "voltage": 95.4}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=82.5 mg, t=144 h, and T_half=64.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 17.5544, \"unit\": \"mg\"}", "dedupe_signature": "d7d9d437d69f804d8f1947b59435cc3ea346668e2c0ac820ca3cdde58d897223", "difficulty": "medium", "final_answer": {"answer": 17.5544, "unit": "mg"}, "id": "half_life_005442_82.5_64.5_144", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 82.5 mg. Its half-life is 64.5 hours. How many mg remain after 144 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=82.5 mg, t=144 h, and T_half=64.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 144.0, "half_life": 64.5, "initial_amount": 82.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 1.48 mol * 58.44 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 86.4912, \"unit\": \"g\"}", "dedupe_signature": "91a0f5255a9053c409dc01c1b91eb88c3bbfb5ec4f1bc10cdec4f8295274ab6d", "difficulty": "medium", "final_answer": {"answer": 86.4912, "unit": "g"}, "id": "stoich_mass_005443_sodium_chloride_1.48", "license": "Apache-2.0", "prompt": "A sample contains 1.48 mol of sodium chloride. Using molar mass 58.44 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 1.48 mol * 58.44 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "sodium chloride", "molar_mass": 58.44, "moles": 1.48}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 2690 mL to 2.69 L.\n3. Compute M = 1.475 / 2.69.\nFinal: {\"answer\": 0.5483, \"unit\": \"mol/L\"}", "dedupe_signature": "3754a6a5b9f74a2421849e05a792a456ee93a0052c657ce1759119a88edc1624", "difficulty": "medium", "final_answer": {"answer": 0.5483, "unit": "mol/L"}, "id": "molarity_005444_1.475_2690", "license": "Apache-2.0", "prompt": "A solution contains 1.475 mol of solute in 2690 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 2690 mL to 2.69 L.\nCompute M = 1.475 / 2.69.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 1.475, "volume_ml": 2690}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.45 y, so each step multiplies y by 1 - h*0.45.\n3. Apply that update for 10 steps and round the final state.\nFinal: {\"answer\": 0.0, \"unit\": \"state_units\"}", "dedupe_signature": "c74d5d03792e35ac0213fb309e94d11e8f2b785d74372e3535007184f8e2c7ec", "difficulty": "medium", "final_answer": {"answer": 0.0, "unit": "state_units"}, "id": "euler_decay_005445_20.5_0.45_1.65_10", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.45 y with y(0)=20.5, step size h=1.65, for 10 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.45 y, so each step multiplies y by 1 - h*0.45.\nApply that update for 10 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 20.5, "rate": 0.45, "step": 1.65, "steps": 10}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-9.8)=66.32 and f(-0.7)=-1.02.\n3. The interval width is 9.1.\nFinal: {\"answer\": 297.115, \"unit\": \"area_units\"}", "dedupe_signature": "3e4f6ee11134ce953b18015630903007df86b158c91e9b69386737208be04a67", "difficulty": "medium", "final_answer": {"answer": 297.115, "unit": "area_units"}, "id": "trapz_linear_005446_-7.4_-6.2_-9.8_-0.7", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-7.4x+-6.2 from x=-9.8 to x=-0.7. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-9.8)=66.32 and f(-0.7)=-1.02.\nThe interval width is 9.1.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -6.2, "slope": -7.4, "x0": -9.8, "x1": -0.7000000000000011}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.08 and add it to the current value.\nFinal: {\"answer\": [0.824, 1.54, 2.512], \"unit\": \"temperature_units\"}", "dedupe_signature": "5c872a191eaeb1b3e925d90ec02d37f363b2179fbb8597fcbf91571e7a5b19da", "difficulty": "hard", "final_answer": {"answer": [0.824, 1.54, 2.512], "unit": "temperature_units"}, "id": "heat_step_005447_0.08_1.45_0.7_1.5_2.8_0.5", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.45, right=0.5; current interior values are [0.7, 1.5, 2.8]. Use r=0.08. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.08 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [0.7, 1.5, 2.8], "left": 1.45, "r": 0.08, "right": 0.5}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=171 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-393.1, 62.2609], \"unit\": \"N\"}", "dedupe_signature": "6a35c61d749298062915d74f4fe1b8685456ade7388846e0c5eb2094da943ced", "difficulty": "medium", "final_answer": {"answer": [-393.1, 62.2609], "unit": "N"}, "id": "vector_components_005449_398_171", "license": "Apache-2.0", "prompt": "A vector has magnitude 398 N at 171 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=171 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 171, "magnitude": 398.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-5.65, 30.0], \"unit\": \"dimensionless\"}", "dedupe_signature": "d27b686d6fcbce3d67245911cf36841d9b7fee4a9dc0140fff0402e702f54b64", "difficulty": "medium", "final_answer": {"answer": [-5.65, 30.0], "unit": "dimensionless"}, "id": "line_two_point_005450_-3_2.75_-5.65_30", "license": "Apache-2.0", "prompt": "A line passes through points (-3, 46.95) and (2.75, 14.4625). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -3.0, "x2": 2.75, "y1": 46.95, "y2": 14.462499999999999}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. velocity times time gives distance, not acceleration\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "96320beeb3a74a72d007dd0bbf5052b3f379e7c4f16c3eef3f3eb25e12f1a3d3", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_005451_inconsistent_7481c798_93857", "license": "Apache-2.0", "prompt": "In instrument manual case 93857, check dimensional consistency for a = v * t. The left side has dimensions m/s^2 and the right side has dimensions m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nvelocity times time gives distance, not acceleration\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "a = v * t"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef center_values_005452(values):\n    if not values:\n        raise ValueError('center_values requires at least one value')\n    mean = sum(values) / len(values)\n    return [value - mean for value in values]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"center_values_005452\"}", "dedupe_signature": "590a6287b37f9ea2379d848455363af3dedcb2a94e2325c28eaab30fc8cf861c", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "center_values_005452"}, "id": "code_005452_center_values_005452", "license": "Apache-2.0", "prompt": "Write a Python function center_values_005452(values) that subtracts the arithmetic mean from each value and returns a new list. Raise ValueError for an empty input. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "center_values_005452"}, "verifier": {"function": "center_values_005452", "tests": ["out = center_values_005452([1, 2, 3]); assert out == [-1, 0, 1]", "assert center_values_005452([5]) == [0]", "try:\n    center_values_005452([])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: left_boundary, right_boundary.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"left_boundary\", \"right_boundary\"]}", "dedupe_signature": "61d64fb831260c47681e4c598227c2a0690378428f93eba97b0a57225bc30366", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["left_boundary", "right_boundary"]}, "id": "abstain_005453_left_boundary_right_boundary", "license": "Apache-2.0", "prompt": "Solve the 1D heat equation after one finite-difference step. The prompt gives r=0.46 and interior values [-1.5, 2.3, 1.25], but gives no boundary values. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: left_boundary, right_boundary.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["left_boundary", "right_boundary"]}, "verifier": {"missing": ["left_boundary", "right_boundary"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 19.95 kg and a = 4.05 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 80.7975, \"unit\": \"N\"}", "dedupe_signature": "2546a3be3811354bb6fcc424dc1fa87d5614cb61a4e65ebd186ff6c69eeb588b", "difficulty": "easy", "final_answer": {"answer": 80.7975, "unit": "N"}, "id": "force_005454_19.95_4.05", "license": "Apache-2.0", "prompt": "A cart has mass 19.95 kg and measured acceleration 4.05 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 19.95 kg and a = 4.05 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 4.05, "mass": 19.95}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 34.5^2 and multiply by 0.5 * 20.55.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 12229.8188, \"unit\": \"J\"}", "dedupe_signature": "b07e9bae8de1ce00c3f035be092f18969b784e2330f240718d7f2a2578778fc6", "difficulty": "easy", "final_answer": {"answer": 12229.8188, "unit": "J"}, "id": "ke_005455_20.55_34.5", "license": "Apache-2.0", "prompt": "A body of mass 20.55 kg moves at 34.5 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 34.5^2 and multiply by 0.5 * 20.55.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 20.55, "velocity": 34.5}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=34 degrees through the sine of 2 theta.\n3. Substitute v=50.7 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 242.9477, \"unit\": \"m\"}", "dedupe_signature": "781d94e6098ca7e10bc71bbbb907e96296e898c8a1d8285bb7df22c2b723a8fd", "difficulty": "medium", "final_answer": {"answer": 242.9477, "unit": "m"}, "id": "projectile_range_005456_50.7_34", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 50.7 m/s and angle 34 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=34 degrees through the sine of 2 theta.\nSubstitute v=50.7 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 34, "gravity": 9.81, "speed": 50.7}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 1.76 * 8.314 * 454 / 114.4.\nFinal: {\"answer\": 58.0701, \"unit\": \"kPa\"}", "dedupe_signature": "59074360f3d942b4c0ad5b942e47b600e7dba91371f78cc4fa67aef3220e8652", "difficulty": "medium", "final_answer": {"answer": 58.0701, "unit": "kPa"}, "id": "ideal_gas_005457_1.76_454_114.4", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=1.76 mol, T=454 K, and V=114.4 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 1.76 * 8.314 * 454 / 114.4.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 1.76, "temp_k": 454, "volume_l": 114.4}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=166.8 V and R=110.5 ohm.\nFinal: {\"answer\": 251.785, \"unit\": \"W\"}", "dedupe_signature": "9a1cce0715eeef6c0d4e738e21edf408e43c250a391b1ab2506e9162e14eb34f", "difficulty": "easy", "final_answer": {"answer": 251.785, "unit": "W"}, "id": "ohm_power_005459_166.8_110.5", "license": "Apache-2.0", "prompt": "A resistor has resistance 110.5 ohm and voltage 166.8 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=166.8 V and R=110.5 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 110.5, "voltage": 166.8}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=523.5 mg, t=246 h, and T_half=101.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 97.5723, \"unit\": \"mg\"}", "dedupe_signature": "1170455beb9399511be0d7a3980e110b7b934c3792ae5835e89e3150ad79767b", "difficulty": "medium", "final_answer": {"answer": 97.5723, "unit": "mg"}, "id": "half_life_005460_523.5_101.5_246", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 523.5 mg. Its half-life is 101.5 hours. How many mg remain after 246 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=523.5 mg, t=246 h, and T_half=101.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 246.0, "half_life": 101.5, "initial_amount": 523.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 2.98 mol * 100.087 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 298.2593, \"unit\": \"g\"}", "dedupe_signature": "92f3c8ba620644a63b6c0a133272d361a47d15413a62d711ab95ea6326e23941", "difficulty": "medium", "final_answer": {"answer": 298.2593, "unit": "g"}, "id": "stoich_mass_005461_calcium_carbonate_2.98", "license": "Apache-2.0", "prompt": "A sample contains 2.98 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 2.98 mol * 100.087 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "calcium carbonate", "molar_mass": 100.087, "moles": 2.98}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 3265 mL to 3.265 L.\n3. Compute M = 3.135 / 3.265.\nFinal: {\"answer\": 0.9602, \"unit\": \"mol/L\"}", "dedupe_signature": "dc1a363ec3a099336a420396123d53b3939469081aa0da10fe73ae9fb1afca4d", "difficulty": "medium", "final_answer": {"answer": 0.9602, "unit": "mol/L"}, "id": "molarity_005462_3.135_3265", "license": "Apache-2.0", "prompt": "A solution contains 3.135 mol of solute in 3265 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 3265 mL to 3.265 L.\nCompute M = 3.135 / 3.265.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 3.135, "volume_ml": 3265}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.32 y, so each step multiplies y by 1 - h*0.32.\n3. Apply that update for 11 steps and round the final state.\nFinal: {\"answer\": 0.0545, \"unit\": \"state_units\"}", "dedupe_signature": "728520005fc73f785ede44c4fda284aa329deea9f28294fe5c8359d5782a047c", "difficulty": "medium", "final_answer": {"answer": 0.0545, "unit": "state_units"}, "id": "euler_decay_005463_72.5_0.32_1.5_11", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.32 y with y(0)=72.5, step size h=1.5, for 11 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.32 y, so each step multiplies y by 1 - h*0.32.\nApply that update for 11 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 72.5, "rate": 0.32, "step": 1.5, "steps": 11}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 22640.0 / 1000.\nFinal: {\"answer\": 22.64, \"unit\": \"kg\"}", "dedupe_signature": "959a19536aa40ff04bd80bdadf876e9e2a4c7e986a13efb3b00faebd85991811", "difficulty": "easy", "final_answer": {"answer": 22.64, "unit": "kg"}, "id": "unit_convert_005466_g_to_kg_22640", "license": "Apache-2.0", "prompt": "Convert 22640 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 22640.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 22640.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. velocity times time gives distance, not acceleration\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "daa9c746823cab8a33703c66034853f91a34ea50db3ade5655310784bbfb220c", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_005469_inconsistent_7481c798_125187", "license": "Apache-2.0", "prompt": "In quality-control check case 125187, check dimensional consistency for a = v * t. The left side has dimensions m/s^2 and the right side has dimensions m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nvelocity times time gives distance, not acceleration\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "a = v * t"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef pairwise_ratios_005470(numerators, denominators):\n    if len(numerators) != len(denominators):\n        raise ValueError('length mismatch')\n    out = []\n    for numerator, denominator in zip(numerators, denominators):\n        if denominator == 0:\n            raise ValueError('zero denominator')\n        out.append(numerator / denominator)\n    return out\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"pairwise_ratios_005470\"}", "dedupe_signature": "97c96a0557ad01caad03fd5d6055ada7e86b88f1bcf53ec889ffebbd91c0ad3c", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "pairwise_ratios_005470"}, "id": "code_005470_pairwise_ratios_005470", "license": "Apache-2.0", "prompt": "Write a Python function pairwise_ratios_005470(numerators, denominators) that returns a list of n/d values. Raise ValueError if lengths differ or any denominator is zero. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "pairwise_ratios_005470"}, "verifier": {"function": "pairwise_ratios_005470", "tests": ["assert pairwise_ratios_005470([2, 9], [4, 3]) == [0.5, 3.0]", "try:\n    pairwise_ratios_005470([1], [0])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass", "try:\n    pairwise_ratios_005470([1, 2], [1])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: target_schema, valid_examples.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"target_schema\", \"valid_examples\"]}", "dedupe_signature": "2ac3f89f8b1ba8926f3848df13ad8519ba8b5db1bcd0ed01188d0d38ad4ec860", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["target_schema", "valid_examples"]}, "id": "abstain_005471_target_schema_valid_examples", "license": "Apache-2.0", "prompt": "Write a parser that converts each mobile survey record from batch 521439 into the correct schema, but the prompt does not include the target schema or examples. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: target_schema, valid_examples.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["target_schema", "valid_examples"]}, "verifier": {"missing": ["target_schema", "valid_examples"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 7.35 kg and a = 2.3 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 16.905, \"unit\": \"N\"}", "dedupe_signature": "649ea428eacfa10122561053e6b2f847c918e0f4433a283999ae2c91bfc42e1c", "difficulty": "easy", "final_answer": {"answer": 16.905, "unit": "N"}, "id": "force_005472_7.35_2.3", "license": "Apache-2.0", "prompt": "A cart has mass 7.35 kg and measured acceleration 2.3 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 7.35 kg and a = 2.3 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 2.3, "mass": 7.35}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=54 degrees through the sine of 2 theta.\n3. Substitute v=63 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 384.7853, \"unit\": \"m\"}", "dedupe_signature": "f35d8a644d7777aa9c1234556f2454d66c5828dc5d86603ca0c7904eea0bc831", "difficulty": "medium", "final_answer": {"answer": 384.7853, "unit": "m"}, "id": "projectile_range_005474_63_54", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 63 m/s and angle 54 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=54 degrees through the sine of 2 theta.\nSubstitute v=63 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 54, "gravity": 9.81, "speed": 63.0}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 4.81 * 8.314 * 477 / 111.7.\nFinal: {\"answer\": 170.7734, \"unit\": \"kPa\"}", "dedupe_signature": "3780f4f3b22d1740f826b4824b18c4dbcc5228d4205bfba0d22145b2bcd27c51", "difficulty": "medium", "final_answer": {"answer": 170.7734, "unit": "kPa"}, "id": "ideal_gas_005475_4.81_477_111.7", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=4.81 mol, T=477 K, and V=111.7 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 4.81 * 8.314 * 477 / 111.7.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 4.81, "temp_k": 477, "volume_l": 111.7}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1010 * 1.745 * 21.\nFinal: {\"answer\": 37011.45, \"unit\": \"J\"}", "dedupe_signature": "116199237eb138b0c3575bcc611da2c7d5ee521d65f9b99531110e93bca95411", "difficulty": "easy", "final_answer": {"answer": 37011.45, "unit": "J"}, "id": "heat_q_005476_1010_1.745_21", "license": "Apache-2.0", "prompt": "A 1010 g sample has specific heat 1.745 J/(g*K). How much heat is needed to raise its temperature by 21 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1010 * 1.745 * 21.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 21, "heat_capacity": 1.745, "mass_g": 1010}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=724 mg, t=347 h, and T_half=120 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 97.5574, \"unit\": \"mg\"}", "dedupe_signature": "c6903a2ab26966cd0fd6c7d50486510a12d75e5024f6b52820bf2d59220aa266", "difficulty": "medium", "final_answer": {"answer": 97.5574, "unit": "mg"}, "id": "half_life_005478_724_120_347", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 724 mg. Its half-life is 120 hours. How many mg remain after 347 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=724 mg, t=347 h, and T_half=120 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 347.0, "half_life": 120.0, "initial_amount": 724.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 0.46 mol * 44.01 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 20.2446, \"unit\": \"g\"}", "dedupe_signature": "1612e21373652eddc9b85f74a908963dfcfa0aca5b9b606db18a43995af5b89c", "difficulty": "medium", "final_answer": {"answer": 20.2446, "unit": "g"}, "id": "stoich_mass_005479_carbon_dioxide_0.46", "license": "Apache-2.0", "prompt": "A sample contains 0.46 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 0.46 mol * 44.01 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "carbon dioxide", "molar_mass": 44.01, "moles": 0.46}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 4095 mL to 4.095 L.\n3. Compute M = 4.955 / 4.095.\nFinal: {\"answer\": 1.21, \"unit\": \"mol/L\"}", "dedupe_signature": "02ed30bc54f4c10f4eb3e29fc1e8c791d9759b25ff3ac114568805b7d8ec2d94", "difficulty": "medium", "final_answer": {"answer": 1.21, "unit": "mol/L"}, "id": "molarity_005480_4.955_4095", "license": "Apache-2.0", "prompt": "A solution contains 4.955 mol of solute in 4095 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 4095 mL to 4.095 L.\nCompute M = 4.955 / 4.095.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 4.955, "volume_ml": 4095}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.11 y, so each step multiplies y by 1 - h*0.11.\n3. Apply that update for 3 steps and round the final state.\nFinal: {\"answer\": 20.8372, \"unit\": \"state_units\"}", "dedupe_signature": "d75a26281aeaeeb716b09400961feac8417f59f42ca42c720f0256ab46a4c5c5", "difficulty": "medium", "final_answer": {"answer": 20.8372, "unit": "state_units"}, "id": "euler_decay_005481_38_0.11_1.65_3", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.11 y with y(0)=38, step size h=1.65, for 3 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.11 y, so each step multiplies y by 1 - h*0.11.\nApply that update for 3 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 38.0, "rate": 0.11, "step": 1.65, "steps": 3}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(2.4)=15.82 and f(10.9)=82.12.\n3. The interval width is 8.5.\nFinal: {\"answer\": 416.245, \"unit\": \"area_units\"}", "dedupe_signature": "35a178410e9ea753c02e9a66fad1b5bd61c187f56c4b2bec178075f1ecdba64e", "difficulty": "medium", "final_answer": {"answer": 416.245, "unit": "area_units"}, "id": "trapz_linear_005482_7.8_-2.9_2.4_10.9", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=7.8x+-2.9 from x=2.4 to x=10.9. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(2.4)=15.82 and f(10.9)=82.12.\nThe interval width is 8.5.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -2.9, "slope": 7.8, "x0": 2.4, "x1": 10.9}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.1 and add it to the current value.\nFinal: {\"answer\": [0.875, -0.71, 2.205], \"unit\": \"temperature_units\"}", "dedupe_signature": "5f88f7ce72f534754e2608041c8227fdef4b6842b9134d3a07270ffb20f8c19d", "difficulty": "hard", "final_answer": {"answer": [0.875, -0.71, 2.205], "unit": "temperature_units"}, "id": "heat_step_005483_0.1_1.7_1.05_-1.35_2.65_2.2", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.7, right=2.2; current interior values are [1.05, -1.35, 2.65]. Use r=0.1. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.1 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [1.05, -1.35, 2.65], "left": 1.7, "r": 0.1, "right": 2.2}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 100 centimeters in one meter.\n2. Apply the conversion factor directly to the given value.\n3. Compute 110.5 / 100.\nFinal: {\"answer\": 1.105, \"unit\": \"m\"}", "dedupe_signature": "e604275da716ec19b4b2f081fd225e2e1bbba086d6e92770cec2b517ebec8199", "difficulty": "easy", "final_answer": {"answer": 1.105, "unit": "m"}, "id": "unit_convert_005484_cm_to_m_110.5", "license": "Apache-2.0", "prompt": "Convert 110.5 cm to m. Return the converted value with unit.", "reasoning_trace": "There are 100 centimeters in one meter.\nApply the conversion factor directly to the given value.\nCompute 110.5 / 100.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 110.5}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=106 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-63.5344, 221.5708], \"unit\": \"N\"}", "dedupe_signature": "badc8a08cb9630b8b2e0c72a5f03f548f75f7237baae2cd754063b468c1cfb5f", "difficulty": "medium", "final_answer": {"answer": [-63.5344, 221.5708], "unit": "N"}, "id": "vector_components_005485_230.5_106", "license": "Apache-2.0", "prompt": "A vector has magnitude 230.5 N at 106 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=106 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 106, "magnitude": 230.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [3.2, 20.75], \"unit\": \"dimensionless\"}", "dedupe_signature": "e39ecfb296cab11b246989e6ee5a7772f3882b040b41855e0a9e54eb528cf9af", "difficulty": "medium", "final_answer": {"answer": [3.2, 20.75], "unit": "dimensionless"}, "id": "line_two_point_005486_-15.75_-5.75_3.2_20.75", "license": "Apache-2.0", "prompt": "A line passes through points (-15.75, -29.65) and (-5.75, 2.35). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -15.75, "x2": -5.75, "y1": -29.650000000000006, "y2": 2.349999999999998}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef safe_mean_005488(values):\n    if not values:\n        raise ValueError('safe_mean requires at least one value')\n    return sum(values) / len(values)\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"safe_mean_005488\"}", "dedupe_signature": "aeabe1593bb08de5ee010fe54c716fcfc969b4b6fc9f709b0c17c2fcbca956ca", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "safe_mean_005488"}, "id": "code_005488_safe_mean_005488", "license": "Apache-2.0", "prompt": "Write a Python function safe_mean_005488(values) that returns the arithmetic mean. It must raise ValueError for an empty input and must not mutate the input list. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "safe_mean_005488"}, "verifier": {"function": "safe_mean_005488", "tests": ["assert safe_mean_005488([2, 4, 6]) == 4", "xs = [1, 2, 3]; assert safe_mean_005488(xs) == 2 and xs == [1, 2, 3]", "try:\n    safe_mean_005488([])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: target_schema, valid_examples.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"target_schema\", \"valid_examples\"]}", "dedupe_signature": "a3dba7fbe8a64a568cb34627cc0cd3ceddff5bb72d36a8f0298d52c45a7ebf96", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["target_schema", "valid_examples"]}, "id": "abstain_005489_target_schema_valid_examples", "license": "Apache-2.0", "prompt": "Write a parser that converts each laboratory sensor record from batch 449099 into the correct schema, but the prompt does not include the target schema or examples. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: target_schema, valid_examples.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["target_schema", "valid_examples"]}, "verifier": {"missing": ["target_schema", "valid_examples"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 5.05 kg and a = 11 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 55.55, \"unit\": \"N\"}", "dedupe_signature": "4da566cc14f7a8d6453bb33362013ba832ba580986594476d1f716c06c1de2ca", "difficulty": "easy", "final_answer": {"answer": 55.55, "unit": "N"}, "id": "force_005490_5.05_11", "license": "Apache-2.0", "prompt": "A cart has mass 5.05 kg and measured acceleration 11 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 5.05 kg and a = 11 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 11.0, "mass": 5.05}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 37.1^2 and multiply by 0.5 * 13.05.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 8981.0753, \"unit\": \"J\"}", "dedupe_signature": "3bc49fd28647537a858e0445a525ee8501456a3cf67f3912a2751b5de3199be0", "difficulty": "easy", "final_answer": {"answer": 8981.0753, "unit": "J"}, "id": "ke_005491_13.05_37.1", "license": "Apache-2.0", "prompt": "A body of mass 13.05 kg moves at 37.1 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 37.1^2 and multiply by 0.5 * 13.05.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 13.05, "velocity": 37.1}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=76 degrees through the sine of 2 theta.\n3. Substitute v=54.8 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 143.7148, \"unit\": \"m\"}", "dedupe_signature": "c50c05628adc556aa66849f40d43724145fe053ef6178383addeebe9df77d811", "difficulty": "medium", "final_answer": {"answer": 143.7148, "unit": "m"}, "id": "projectile_range_005492_54.8_76", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 54.8 m/s and angle 76 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=76 degrees through the sine of 2 theta.\nSubstitute v=54.8 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 76, "gravity": 9.81, "speed": 54.8}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 2.51 * 8.314 * 377 / 39.2.\nFinal: {\"answer\": 200.6961, \"unit\": \"kPa\"}", "dedupe_signature": "0a61a190fc41cc21aab4bba435c96a020fee55b17c9a051af18e69bdebdeb0ee", "difficulty": "medium", "final_answer": {"answer": 200.6961, "unit": "kPa"}, "id": "ideal_gas_005493_2.51_377_39.2", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=2.51 mol, T=377 K, and V=39.2 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 2.51 * 8.314 * 377 / 39.2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 2.51, "temp_k": 377, "volume_l": 39.2}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1445 * 1.055 * 1.\nFinal: {\"answer\": 1524.475, \"unit\": \"J\"}", "dedupe_signature": "4f798dcc6cc51a8d843ed4f707d24796dc28a024db77ccedc9c6193f4e9178d4", "difficulty": "easy", "final_answer": {"answer": 1524.475, "unit": "J"}, "id": "heat_q_005494_1445_1.055_1", "license": "Apache-2.0", "prompt": "A 1445 g sample has specific heat 1.055 J/(g*K). How much heat is needed to raise its temperature by 1 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1445 * 1.055 * 1.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 1, "heat_capacity": 1.055, "mass_g": 1445}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=148.5 V and R=2.5 ohm.\nFinal: {\"answer\": 8820.9, \"unit\": \"W\"}", "dedupe_signature": "305c8d14a7a2e980aaee28bb0b7b8ccfe69dc506f31bb5809c6be12da71d1343", "difficulty": "easy", "final_answer": {"answer": 8820.9, "unit": "W"}, "id": "ohm_power_005495_148.5_2.5", "license": "Apache-2.0", "prompt": "A resistor has resistance 2.5 ohm and voltage 148.5 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=148.5 V and R=2.5 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 2.5, "voltage": 148.5}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 4465 mL to 4.465 L.\n3. Compute M = 3.28 / 4.465.\nFinal: {\"answer\": 0.7346, \"unit\": \"mol/L\"}", "dedupe_signature": "488e10ca366d23e4ad5fe7df59a53742e1ee948745f4354f6a4aa5f4d92a0f86", "difficulty": "medium", "final_answer": {"answer": 0.7346, "unit": "mol/L"}, "id": "molarity_005498_3.28_4465", "license": "Apache-2.0", "prompt": "A solution contains 3.28 mol of solute in 4465 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 4465 mL to 4.465 L.\nCompute M = 3.28 / 4.465.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 3.28, "volume_ml": 4465}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-2.8)=1.22 and f(-0.4)=-2.14.\n3. The interval width is 2.4.\nFinal: {\"answer\": -1.104, \"unit\": \"area_units\"}", "dedupe_signature": "aeed787dfbf280e1ec1afece588ce0c16c770e95ce05498178f12225b3058ab3", "difficulty": "medium", "final_answer": {"answer": -1.104, "unit": "area_units"}, "id": "trapz_linear_005500_-1.4_-2.7_-2.8_-0.4", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-1.4x+-2.7 from x=-2.8 to x=-0.4. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-2.8)=1.22 and f(-0.4)=-2.14.\nThe interval width is 2.4.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -2.7, "slope": -1.4, "x0": -2.8, "x1": -0.3999999999999999}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kelvin equals Celsius plus 273.15.\n2. Apply the conversion factor directly to the given value.\n3. Compute 29.5 + 273.15.\nFinal: {\"answer\": 302.65, \"unit\": \"K\"}", "dedupe_signature": "d90916300c54c06114b6add2c09127e0c50c3c5c251af31c27ae582b7d8c2e9f", "difficulty": "easy", "final_answer": {"answer": 302.65, "unit": "K"}, "id": "unit_convert_005502_c_to_k_29.5", "license": "Apache-2.0", "prompt": "Convert 29.5 degC to K. Return the converted value with unit.", "reasoning_trace": "Kelvin equals Celsius plus 273.15.\nApply the conversion factor directly to the given value.\nCompute 29.5 + 273.15.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 29.5}, "verifier": {"formula": "value + 273.15", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [9.4, -13.5], \"unit\": \"dimensionless\"}", "dedupe_signature": "a201f090d752eea62cf39f178791cea25ef6b50fb720e72c8ab64ffbb15f8507", "difficulty": "medium", "final_answer": {"answer": [9.4, -13.5], "unit": "dimensionless"}, "id": "line_two_point_005504_4_15.25_9.4_-13.5", "license": "Apache-2.0", "prompt": "A line passes through points (4, 24.1) and (15.25, 129.85). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 4.0, "x2": 15.25, "y1": 24.1, "y2": 129.85}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. lever arm times force has torque dimensions\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "210c40ea52f55e9389da0ddb2a99cdfaa29b3939aff98c29dd72c31742874fb1", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_005505_consistent_5ca82cb9_936103", "license": "Apache-2.0", "prompt": "In quality-control check case 936103, check dimensional consistency for tau = r * F. The left side has dimensions N*m and the right side has dimensions N*m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nlever arm times force has torque dimensions\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "tau = r * F"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef running_total_005506(values):\n    total = 0\n    out = []\n    for value in values:\n        total += value\n        out.append(total)\n    return out\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"running_total_005506\"}", "dedupe_signature": "0ebac6820e7e52d2fa128e95a8cb992d77bd7d9368f4b4c6d68764d221b61ae8", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "running_total_005506"}, "id": "code_005506_running_total_005506", "license": "Apache-2.0", "prompt": "Write a Python function running_total_005506(values) that returns cumulative sums as a new list. It must not mutate the input list. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "running_total_005506"}, "verifier": {"function": "running_total_005506", "tests": ["assert running_total_005506([1, 2, 3]) == [1, 3, 6]", "xs = [4, -1, 2]; assert running_total_005506(xs) == [4, 3, 5] and xs == [4, -1, 2]", "assert running_total_005506([]) == []"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: rate_constant, number_of_steps.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"rate_constant\", \"number_of_steps\"]}", "dedupe_signature": "75bcd29b7189e281270f1e2aeb7d13b23d0e729ee85c17be0b48bd29d9d280a6", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["rate_constant", "number_of_steps"]}, "id": "abstain_005507_rate_constant_number_of_steps", "license": "Apache-2.0", "prompt": "Use explicit Euler for dy/dt = -k y. The prompt gives y(0)=24.5 and h=0.3, but omits both k and the number of steps. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: rate_constant, number_of_steps.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["rate_constant", "number_of_steps"]}, "verifier": {"missing": ["rate_constant", "number_of_steps"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 20.85 kg and a = 5.4 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 112.59, \"unit\": \"N\"}", "dedupe_signature": "46f181ee59e5af4c5393b2d5da436868bce048f34b0298cb75c28eba68de8a46", "difficulty": "easy", "final_answer": {"answer": 112.59, "unit": "N"}, "id": "force_005508_20.85_5.4", "license": "Apache-2.0", "prompt": "A cart has mass 20.85 kg and measured acceleration 5.4 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 20.85 kg and a = 5.4 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 5.4, "mass": 20.85}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 17.15^2 and multiply by 0.5 * 17.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 2500.0412, \"unit\": \"J\"}", "dedupe_signature": "149e6c15933454b63b97c3cd2ce500872179c2fb8e69813cd269935ef74bf7ac", "difficulty": "easy", "final_answer": {"answer": 2500.0412, "unit": "J"}, "id": "ke_005509_17_17.15", "license": "Apache-2.0", "prompt": "A body of mass 17 kg moves at 17.15 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 17.15^2 and multiply by 0.5 * 17.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 17.0, "velocity": 17.15}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=25 degrees through the sine of 2 theta.\n3. Substitute v=6.7 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 3.5054, \"unit\": \"m\"}", "dedupe_signature": "ecfaa6242a57aa2fbf11f38ea99fd0d5389bf72806ef2daf4f88be61342e7230", "difficulty": "medium", "final_answer": {"answer": 3.5054, "unit": "m"}, "id": "projectile_range_005510_6.7_25", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 6.7 m/s and angle 25 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=25 degrees through the sine of 2 theta.\nSubstitute v=6.7 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 25, "gravity": 9.81, "speed": 6.7}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 2.32 * 8.314 * 581 / 92.3.\nFinal: {\"answer\": 121.415, \"unit\": \"kPa\"}", "dedupe_signature": "9b5b3d20f833889d643835ba5283a6801f9178f80f8736dba7c3a74f260788f3", "difficulty": "medium", "final_answer": {"answer": 121.415, "unit": "kPa"}, "id": "ideal_gas_005511_2.32_581_92.3", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=2.32 mol, T=581 K, and V=92.3 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 2.32 * 8.314 * 581 / 92.3.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 2.32, "temp_k": 581, "volume_l": 92.3}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=226.5 V and R=30.3 ohm.\nFinal: {\"answer\": 1693.1436, \"unit\": \"W\"}", "dedupe_signature": "ca5f6697d625b8f906ed16cc6cbd19bd5ec81587a94662efcef49a7e58e69392", "difficulty": "easy", "final_answer": {"answer": 1693.1436, "unit": "W"}, "id": "ohm_power_005513_226.5_30.3", "license": "Apache-2.0", "prompt": "A resistor has resistance 30.3 ohm and voltage 226.5 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=226.5 V and R=30.3 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 30.3, "voltage": 226.5}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=192 mg, t=192.5 h, and T_half=102 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 51.9016, \"unit\": \"mg\"}", "dedupe_signature": "38002a367cf577a7d37dc048a79a2a3615ff5ea0dc6443d2d67275b4bb1755a1", "difficulty": "medium", "final_answer": {"answer": 51.9016, "unit": "mg"}, "id": "half_life_005514_192_102_192.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 192 mg. Its half-life is 102 hours. How many mg remain after 192.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=192 mg, t=192.5 h, and T_half=102 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 192.5, "half_life": 102.0, "initial_amount": 192.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 6.98 mol * 44.01 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 307.1898, \"unit\": \"g\"}", "dedupe_signature": "27f324b3ed4f6536bdf34448426e45a46fc1fbea85aef5f400b72eaeb9fee235", "difficulty": "medium", "final_answer": {"answer": 307.1898, "unit": "g"}, "id": "stoich_mass_005515_carbon_dioxide_6.98", "license": "Apache-2.0", "prompt": "A sample contains 6.98 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 6.98 mol * 44.01 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "carbon dioxide", "molar_mass": 44.01, "moles": 6.98}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 3930 mL to 3.93 L.\n3. Compute M = 0.245 / 3.93.\nFinal: {\"answer\": 0.0623, \"unit\": \"mol/L\"}", "dedupe_signature": "e8d5f58a82a021b1162ad81247b6ca80cbdc074ab8ee31f9b3b5baf2d4edc214", "difficulty": "medium", "final_answer": {"answer": 0.0623, "unit": "mol/L"}, "id": "molarity_005516_0.245_3930", "license": "Apache-2.0", "prompt": "A solution contains 0.245 mol of solute in 3930 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 3930 mL to 3.93 L.\nCompute M = 0.245 / 3.93.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 0.245, "volume_ml": 3930}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.48 y, so each step multiplies y by 1 - h*0.48.\n3. Apply that update for 6 steps and round the final state.\nFinal: {\"answer\": 0.4665, \"unit\": \"state_units\"}", "dedupe_signature": "d75a42ea8fdaf4167d94668d848bfe7c8fd722b8e1ac614a3ce5f6bd509d2846", "difficulty": "medium", "final_answer": {"answer": 0.4665, "unit": "state_units"}, "id": "euler_decay_005517_18_0.48_0.95_6", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.48 y with y(0)=18, step size h=0.95, for 6 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.48 y, so each step multiplies y by 1 - h*0.48.\nApply that update for 6 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 18.0, "rate": 0.48, "step": 0.95, "steps": 6}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-9.4)=-5.76 and f(0.1)=2.79.\n3. The interval width is 9.5.\nFinal: {\"answer\": -14.1075, \"unit\": \"area_units\"}", "dedupe_signature": "be5bf3c4506199067f7835ce3be1b0c48b90c50b00f1429ce52bf8f4d169dd24", "difficulty": "medium", "final_answer": {"answer": -14.1075, "unit": "area_units"}, "id": "trapz_linear_005518_0.9_2.7_-9.4_0.1", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=0.9x+2.7 from x=-9.4 to x=0.1. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-9.4)=-5.76 and f(0.1)=2.79.\nThe interval width is 9.5.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 2.7, "slope": 0.9, "x0": -9.4, "x1": 0.09999999999999964}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 43201.0 / 1000.\nFinal: {\"answer\": 43.201, \"unit\": \"kg\"}", "dedupe_signature": "6e6953cdab106911efafcf0cf16e17bdba632c9c0c4b889078e455dca682cbc6", "difficulty": "easy", "final_answer": {"answer": 43.201, "unit": "kg"}, "id": "unit_convert_005520_g_to_kg_43201", "license": "Apache-2.0", "prompt": "Convert 43201 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 43201.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 43201.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=26 degrees and keep the unit as newtons.\nFinal: {\"answer\": [3.5952, 1.7535], \"unit\": \"N\"}", "dedupe_signature": "86b9ee34ffdd090d812d7fa8a6c4c587c78738bebb4ac939a03f750bfbbaaa21", "difficulty": "medium", "final_answer": {"answer": [3.5952, 1.7535], "unit": "N"}, "id": "vector_components_005521_4_26", "license": "Apache-2.0", "prompt": "A vector has magnitude 4 N at 26 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=26 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 26, "magnitude": 4.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [1.05, -27.75], \"unit\": \"dimensionless\"}", "dedupe_signature": "ee46f6c6b272a5d56bc5cd9e05099977fc11d4c2fc4e9dc0b4602e86ef4d9f90", "difficulty": "medium", "final_answer": {"answer": [1.05, -27.75], "unit": "dimensionless"}, "id": "line_two_point_005522_-10.25_-6.75_1.05_-27.75", "license": "Apache-2.0", "prompt": "A line passes through points (-10.25, -38.5125) and (-6.75, -34.8375). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -10.25, "x2": -6.75, "y1": -38.5125, "y2": -34.8375}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. lever arm times force has torque dimensions\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "860b39f499ff444d18ac183403d784ac8641316ea99b528f654819b2c379d59c", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_005523_consistent_5ca82cb9_24095", "license": "Apache-2.0", "prompt": "In quality-control check case 24095, check dimensional consistency for tau = r * F. The left side has dimensions N*m and the right side has dimensions N*m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nlever arm times force has torque dimensions\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "tau = r * F"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef normalize_005524(values):\n    total = sum(values)\n    if total == 0:\n        raise ValueError('cannot normalize zero-sum values')\n    return [v / total for v in values]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"normalize_005524\"}", "dedupe_signature": "d5bee565d822c56749dbb4bd1523f32ab1b2b1ed93965e090e19c6f4403336ad", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "normalize_005524"}, "id": "code_005524_normalize_005524", "license": "Apache-2.0", "prompt": "Write a Python function normalize_005524(values) that returns a new list whose values sum to 1. Raise ValueError if the sum is zero. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "normalize_005524"}, "verifier": {"function": "normalize_005524", "tests": ["out = normalize_005524([2, 3, 5]); assert len(out) == 3", "assert abs(sum(normalize_005524([2, 3, 5])) - 1.0) < 1e-12", "assert normalize_005524([1, 1]) == [0.5, 0.5]", "try:\n    normalize_005524([1, -1])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 24.15 kg and a = 9.15 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 220.9725, \"unit\": \"N\"}", "dedupe_signature": "84112c46ac8370027cef184f4d18690fa7522154791f87743969783d71629584", "difficulty": "easy", "final_answer": {"answer": 220.9725, "unit": "N"}, "id": "force_005526_24.15_9.15", "license": "Apache-2.0", "prompt": "A cart has mass 24.15 kg and measured acceleration 9.15 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 24.15 kg and a = 9.15 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 9.15, "mass": 24.15}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 1.35^2 and multiply by 0.5 * 18.5.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 16.8581, \"unit\": \"J\"}", "dedupe_signature": "a74070c86289f13836da7a3d9c093cee7b6e82c18b30865ae962fa445c43de7d", "difficulty": "easy", "final_answer": {"answer": 16.8581, "unit": "J"}, "id": "ke_005527_18.5_1.35", "license": "Apache-2.0", "prompt": "A body of mass 18.5 kg moves at 1.35 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 1.35^2 and multiply by 0.5 * 18.5.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 18.5, "velocity": 1.35}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 2.4 * 8.314 * 397 / 106.4.\nFinal: {\"answer\": 74.4509, \"unit\": \"kPa\"}", "dedupe_signature": "79326db09412e7ea1844f9882ea664dce2ae2f8c4db3da423434a34b97a50f94", "difficulty": "medium", "final_answer": {"answer": 74.4509, "unit": "kPa"}, "id": "ideal_gas_005529_2.4_397_106.4", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=2.4 mol, T=397 K, and V=106.4 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 2.4 * 8.314 * 397 / 106.4.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 2.4, "temp_k": 397, "volume_l": 106.4}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=152.7 V and R=5.3 ohm.\nFinal: {\"answer\": 4399.4887, \"unit\": \"W\"}", "dedupe_signature": "a0f6f1b13430c6bb424780e538784f5dbee6b0f5138031cfa86926d61c9ce939", "difficulty": "easy", "final_answer": {"answer": 4399.4887, "unit": "W"}, "id": "ohm_power_005531_152.7_5.3", "license": "Apache-2.0", "prompt": "A resistor has resistance 5.3 ohm and voltage 152.7 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=152.7 V and R=5.3 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 5.3, "voltage": 152.7}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 760 mL to 0.76 L.\n3. Compute M = 0.73 / 0.76.\nFinal: {\"answer\": 0.9605, \"unit\": \"mol/L\"}", "dedupe_signature": "08e8bad19825b7dd46734cd8bdb9140554e63d48c28a7cf73bc5e32b49ea7e8f", "difficulty": "medium", "final_answer": {"answer": 0.9605, "unit": "mol/L"}, "id": "molarity_005534_0.73_760", "license": "Apache-2.0", "prompt": "A solution contains 0.73 mol of solute in 760 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 760 mL to 0.76 L.\nCompute M = 0.73 / 0.76.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 0.73, "volume_ml": 760}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.07 y, so each step multiplies y by 1 - h*0.07.\n3. Apply that update for 6 steps and round the final state.\nFinal: {\"answer\": 3.0459, \"unit\": \"state_units\"}", "dedupe_signature": "701a714ffb3a1f93047a151bc63d3b93d663e988389345db369631ad13820647", "difficulty": "medium", "final_answer": {"answer": 3.0459, "unit": "state_units"}, "id": "euler_decay_005535_7_0.07_1.85_6", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.07 y with y(0)=7, step size h=1.85, for 6 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.07 y, so each step multiplies y by 1 - h*0.07.\nApply that update for 6 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 7.0, "rate": 0.07, "step": 1.85, "steps": 6}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-3.1)=3.72 and f(-2.6)=6.12.\n3. The interval width is 0.5.\nFinal: {\"answer\": 2.46, \"unit\": \"area_units\"}", "dedupe_signature": "ba9fead43c851ee79128407e2421b298045f96507d3c34d1f23a118a726ded85", "difficulty": "medium", "final_answer": {"answer": 2.46, "unit": "area_units"}, "id": "trapz_linear_005536_4.8_18.6_-3.1_-2.6", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=4.8x+18.6 from x=-3.1 to x=-2.6. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-3.1)=3.72 and f(-2.6)=6.12.\nThe interval width is 0.5.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 18.6, "slope": 4.8, "x0": -3.1, "x1": -2.6}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 100 centimeters in one meter.\n2. Apply the conversion factor directly to the given value.\n3. Compute 2627.0 / 100.\nFinal: {\"answer\": 26.27, \"unit\": \"m\"}", "dedupe_signature": "fa3af9ac75f59d9dd6c34f09d4871eedbd8a2df1f626cf161bdc65b2f3ee8d8c", "difficulty": "easy", "final_answer": {"answer": 26.27, "unit": "m"}, "id": "unit_convert_005538_cm_to_m_2627", "license": "Apache-2.0", "prompt": "Convert 2627 cm to m. Return the converted value with unit.", "reasoning_trace": "There are 100 centimeters in one meter.\nApply the conversion factor directly to the given value.\nCompute 2627.0 / 100.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 2627.0}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=330 degrees and keep the unit as newtons.\nFinal: {\"answer\": [92.2317, -53.25], \"unit\": \"N\"}", "dedupe_signature": "ef3562e452315cfa680ab56261b7b98b558b4532d0f0950490dfc7be45398506", "difficulty": "medium", "final_answer": {"answer": [92.2317, -53.25], "unit": "N"}, "id": "vector_components_005539_106.5_330", "license": "Apache-2.0", "prompt": "A vector has magnitude 106.5 N at 330 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=330 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 330, "magnitude": 106.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. volt squared divided by ohm is watt\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "db491959d98412913523189aab5ec0161b21fbfad85b7d41b705fd25aa169b3f", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_005541_consistent_82e93f3d_197464", "license": "Apache-2.0", "prompt": "In field worksheet case 197464, check dimensional consistency for P = V^2 / R. The left side has dimensions W and the right side has dimensions W. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nvolt squared divided by ohm is watt\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "P = V^2 / R"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: target_schema, valid_examples.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"target_schema\", \"valid_examples\"]}", "dedupe_signature": "bb8059ad9560fe1877d7d93ba2ce29f24a1ef3f54e4f980eef161044aba74141", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["target_schema", "valid_examples"]}, "id": "abstain_005543_target_schema_valid_examples", "license": "Apache-2.0", "prompt": "Write a parser that converts each field invoice record from batch 827211 into the correct schema, but the prompt does not include the target schema or examples. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: target_schema, valid_examples.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["target_schema", "valid_examples"]}, "verifier": {"missing": ["target_schema", "valid_examples"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 2.95 kg and a = 10.75 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 31.7125, \"unit\": \"N\"}", "dedupe_signature": "0479592e4087d94ed27efe1d18e94c2473d46907c580d672df5cb36582d0bab6", "difficulty": "easy", "final_answer": {"answer": 31.7125, "unit": "N"}, "id": "force_005544_2.95_10.75", "license": "Apache-2.0", "prompt": "A cart has mass 2.95 kg and measured acceleration 10.75 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 2.95 kg and a = 10.75 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 10.75, "mass": 2.95}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 35.75^2 and multiply by 0.5 * 4.3.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 2747.8344, \"unit\": \"J\"}", "dedupe_signature": "b1636e30c2abec76735cf50e0f8b32595530542bed90b79a59bba14decb11450", "difficulty": "easy", "final_answer": {"answer": 2747.8344, "unit": "J"}, "id": "ke_005545_4.3_35.75", "license": "Apache-2.0", "prompt": "A body of mass 4.3 kg moves at 35.75 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 35.75^2 and multiply by 0.5 * 4.3.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 4.3, "velocity": 35.75}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=31 degrees through the sine of 2 theta.\n3. Substitute v=31.1 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 87.0536, \"unit\": \"m\"}", "dedupe_signature": "5883a6ea63c5fd90b3ff95d1f229499c890139e1d5719cbc753a469ede30c72a", "difficulty": "medium", "final_answer": {"answer": 87.0536, "unit": "m"}, "id": "projectile_range_005546_31.1_31", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 31.1 m/s and angle 31 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=31 degrees through the sine of 2 theta.\nSubstitute v=31.1 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 31, "gravity": 9.81, "speed": 31.1}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 3.12 * 8.314 * 398 / 102.0.\nFinal: {\"answer\": 101.2156, \"unit\": \"kPa\"}", "dedupe_signature": "8bf261e33e6a624d41e5d3c1c52cd601f15f2f0fd1492c6205dbc46a37a5b51e", "difficulty": "medium", "final_answer": {"answer": 101.2156, "unit": "kPa"}, "id": "ideal_gas_005547_3.12_398_102.0", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=3.12 mol, T=398 K, and V=102.0 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 3.12 * 8.314 * 398 / 102.0.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 3.12, "temp_k": 398, "volume_l": 102.0}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=179.7 V and R=166.9 ohm.\nFinal: {\"answer\": 193.4817, \"unit\": \"W\"}", "dedupe_signature": "d2b03d209dd5458b720c4c4239b91e5ea2afcaf182c4c33c589b32dbc83dd99d", "difficulty": "easy", "final_answer": {"answer": 193.4817, "unit": "W"}, "id": "ohm_power_005549_179.7_166.9", "license": "Apache-2.0", "prompt": "A resistor has resistance 166.9 ohm and voltage 179.7 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=179.7 V and R=166.9 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 166.9, "voltage": 179.7}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=636.5 mg, t=153 h, and T_half=5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 0.0, \"unit\": \"mg\"}", "dedupe_signature": "6b8b0e7ecd2dbd69566ffc886dd704d02521c3cc07185fb0356cc01794f7ae54", "difficulty": "medium", "final_answer": {"answer": 0.0, "unit": "mg"}, "id": "half_life_005550_636.5_5_153", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 636.5 mg. Its half-life is 5 hours. How many mg remain after 153 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=636.5 mg, t=153 h, and T_half=5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 153.0, "half_life": 5.0, "initial_amount": 636.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 4.33 mol * 100.087 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 433.3767, \"unit\": \"g\"}", "dedupe_signature": "17dd74c7f055f574105fc2ec636981108402f0b156202f1b5691d2ef067e70ed", "difficulty": "medium", "final_answer": {"answer": 433.3767, "unit": "g"}, "id": "stoich_mass_005551_calcium_carbonate_4.33", "license": "Apache-2.0", "prompt": "A sample contains 4.33 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 4.33 mol * 100.087 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "calcium carbonate", "molar_mass": 100.087, "moles": 4.33}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(6.4)=-46.86 and f(7)=-50.4.\n3. The interval width is 0.6.\nFinal: {\"answer\": -29.178, \"unit\": \"area_units\"}", "dedupe_signature": "35abb4d1aab03cba5e7f1de53d40989cfaa2d3366969b18fdb173333fead10fa", "difficulty": "medium", "final_answer": {"answer": -29.178, "unit": "area_units"}, "id": "trapz_linear_005554_-5.9_-9.1_6.4_7", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-5.9x+-9.1 from x=6.4 to x=7. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(6.4)=-46.86 and f(7)=-50.4.\nThe interval width is 0.6.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -9.1, "slope": -5.9, "x0": 6.4, "x1": 7.0}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.22 and add it to the current value.\nFinal: {\"answer\": [0.746, 1.042, -0.15], \"unit\": \"temperature_units\"}", "dedupe_signature": "2bc77a43d8d270bf41c12bcb9f980b58ebf9e465c239736a379b9eec7c09ed1d", "difficulty": "hard", "final_answer": {"answer": [0.746, 1.042, -0.15], "unit": "temperature_units"}, "id": "heat_step_005555_0.22_-1.65_1.45_1.35_-0.15_-1.65", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-1.65, right=-1.65; current interior values are [1.45, 1.35, -0.15]. Use r=0.22. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.22 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [1.45, 1.35, -0.15], "left": -1.65, "r": 0.22, "right": -1.65}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 31844.0 / 1000.\nFinal: {\"answer\": 31.844, \"unit\": \"kg\"}", "dedupe_signature": "bad37696fdb38151d397ff509e778d9af5ef5eec77076a4209f6a1643d2561ce", "difficulty": "easy", "final_answer": {"answer": 31.844, "unit": "kg"}, "id": "unit_convert_005556_g_to_kg_31844", "license": "Apache-2.0", "prompt": "Convert 31844 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 31844.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 31844.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=17 degrees and keep the unit as newtons.\nFinal: {\"answer\": [144.402, 44.1481], \"unit\": \"N\"}", "dedupe_signature": "64c18a2014a828dba789b2b25ef940726fc20e4c38166c81e75d74429212e463", "difficulty": "medium", "final_answer": {"answer": [144.402, 44.1481], "unit": "N"}, "id": "vector_components_005557_151_17", "license": "Apache-2.0", "prompt": "A vector has magnitude 151 N at 17 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=17 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 17, "magnitude": 151.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-8.0, -24.0], \"unit\": \"dimensionless\"}", "dedupe_signature": "5a57e6a90795f305ea0c26d658d08976d3b3ec24d27525efd8fe333d853738a2", "difficulty": "medium", "final_answer": {"answer": [-8.0, -24.0], "unit": "dimensionless"}, "id": "line_two_point_005558_14.5_16.75_-8_-24", "license": "Apache-2.0", "prompt": "A line passes through points (14.5, -140) and (16.75, -158). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 14.5, "x2": 16.75, "y1": -140.0, "y2": -158.0}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. velocity divided by time is acceleration\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "e113d6890899955a727e54a1f1a039dfc99b93043417ecc46847c462592ae4eb", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_005559_inconsistent_c1271127_466428", "license": "Apache-2.0", "prompt": "In lab notebook case 466428, check dimensional consistency for x = v / t. The left side has dimensions m and the right side has dimensions m/s^2. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nvelocity divided by time is acceleration\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "x = v / t"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef center_values_005560(values):\n    if not values:\n        raise ValueError('center_values requires at least one value')\n    mean = sum(values) / len(values)\n    return [value - mean for value in values]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"center_values_005560\"}", "dedupe_signature": "56a47efcbc3945e928b0273e3c427868a2bbb95c8f4122351a79b83333e352f0", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "center_values_005560"}, "id": "code_005560_center_values_005560", "license": "Apache-2.0", "prompt": "Write a Python function center_values_005560(values) that subtracts the arithmetic mean from each value and returns a new list. Raise ValueError for an empty input. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "center_values_005560"}, "verifier": {"function": "center_values_005560", "tests": ["out = center_values_005560([1, 2, 3]); assert out == [-1, 0, 1]", "assert center_values_005560([5]) == [0]", "try:\n    center_values_005560([])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: volume.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"volume\"]}", "dedupe_signature": "16abe32c0637858b654dbe02adf040bbb509ee7f8661eb139923d05b10e0019c", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["volume"]}, "id": "abstain_005561_volume", "license": "Apache-2.0", "prompt": "Compute pressure from the ideal gas law. The prompt gives n=2.15 mol and T=373 K, but does not give volume. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: volume.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["volume"]}, "verifier": {"missing": ["volume"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 25.45^2 and multiply by 0.5 * 28.65.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 9278.3383, \"unit\": \"J\"}", "dedupe_signature": "58cd727af71f68d083e23558ecf590d39f4a0f42370aa6215fb4bc2bc07384ed", "difficulty": "easy", "final_answer": {"answer": 9278.3383, "unit": "J"}, "id": "ke_005563_28.65_25.45", "license": "Apache-2.0", "prompt": "A body of mass 28.65 kg moves at 25.45 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 25.45^2 and multiply by 0.5 * 28.65.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 28.65, "velocity": 25.45}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=25 degrees through the sine of 2 theta.\n3. Substitute v=12.8 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 12.794, \"unit\": \"m\"}", "dedupe_signature": "d39c8297a793356fe428d5a171a57f0cf29a4dc258fa3486a0c1631ff63fa461", "difficulty": "medium", "final_answer": {"answer": 12.794, "unit": "m"}, "id": "projectile_range_005564_12.8_25", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 12.8 m/s and angle 25 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=25 degrees through the sine of 2 theta.\nSubstitute v=12.8 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 25, "gravity": 9.81, "speed": 12.8}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 2.59 * 8.314 * 541 / 66.3.\nFinal: {\"answer\": 175.7088, \"unit\": \"kPa\"}", "dedupe_signature": "d71fa96ba245e41762990f0419468324dee515feab339fdbdc8038672213c98f", "difficulty": "medium", "final_answer": {"answer": 175.7088, "unit": "kPa"}, "id": "ideal_gas_005565_2.59_541_66.3", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=2.59 mol, T=541 K, and V=66.3 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 2.59 * 8.314 * 541 / 66.3.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 2.59, "temp_k": 541, "volume_l": 66.3}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=5.7 V and R=29.3 ohm.\nFinal: {\"answer\": 1.1089, \"unit\": \"W\"}", "dedupe_signature": "ee65d1ce74ad1d6029ee6b026a49f10aff7a3e92f63c644a748d220554da65d5", "difficulty": "easy", "final_answer": {"answer": 1.1089, "unit": "W"}, "id": "ohm_power_005567_5.7_29.3", "license": "Apache-2.0", "prompt": "A resistor has resistance 29.3 ohm and voltage 5.7 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=5.7 V and R=29.3 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 29.3, "voltage": 5.7}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 4.49 mol * 100.087 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 449.3906, \"unit\": \"g\"}", "dedupe_signature": "f69f3aab5dfd6e3a2a909c7ab28753357018852190457b8f58b03d0fa940ea1d", "difficulty": "medium", "final_answer": {"answer": 449.3906, "unit": "g"}, "id": "stoich_mass_005569_calcium_carbonate_4.49", "license": "Apache-2.0", "prompt": "A sample contains 4.49 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 4.49 mol * 100.087 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "calcium carbonate", "molar_mass": 100.087, "moles": 4.49}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.09 y, so each step multiplies y by 1 - h*0.09.\n3. Apply that update for 5 steps and round the final state.\nFinal: {\"answer\": 26.517, \"unit\": \"state_units\"}", "dedupe_signature": "10e1c055de21cdd4f258ef7fd52a0a15758442f4d830c80e3a490a87275e5e94", "difficulty": "medium", "final_answer": {"answer": 26.517, "unit": "state_units"}, "id": "euler_decay_005571_35_0.09_0.6_5", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.09 y with y(0)=35, step size h=0.6, for 5 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.09 y, so each step multiplies y by 1 - h*0.09.\nApply that update for 5 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 35.0, "rate": 0.09, "step": 0.6, "steps": 5}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(1.8)=-22.02 and f(8.4)=-31.26.\n3. The interval width is 6.6.\nFinal: {\"answer\": -175.824, \"unit\": \"area_units\"}", "dedupe_signature": "1fed0847a66951ceaf791fdf60705633e433a01694df8a821457c96780a81b08", "difficulty": "medium", "final_answer": {"answer": -175.824, "unit": "area_units"}, "id": "trapz_linear_005572_-1.4_-19.5_1.8_8.4", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-1.4x+-19.5 from x=1.8 to x=8.4. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(1.8)=-22.02 and f(8.4)=-31.26.\nThe interval width is 6.6.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -19.5, "slope": -1.4, "x0": 1.8, "x1": 8.4}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.22 and add it to the current value.\nFinal: {\"answer\": [-0.177, 0.902, 0.987], \"unit\": \"temperature_units\"}", "dedupe_signature": "b7afaf1878f7a0fda1ebaa8274421fece6b849b3ff9fda04a981487f2edad16c", "difficulty": "hard", "final_answer": {"answer": [-0.177, 0.902, 0.987], "unit": "temperature_units"}, "id": "heat_step_005573_0.22_1.45_-1.75_2.2_0.25_1.65", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.45, right=1.65; current interior values are [-1.75, 2.2, 0.25]. Use r=0.22. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.22 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-1.75, 2.2, 0.25], "left": 1.45, "r": 0.22, "right": 1.65}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kelvin equals Celsius plus 273.15.\n2. Apply the conversion factor directly to the given value.\n3. Compute -67.5 + 273.15.\nFinal: {\"answer\": 205.65, \"unit\": \"K\"}", "dedupe_signature": "6b90e5795da86fab3a207586750d9fa696b08464ebb70669ad663d0f28e1d31a", "difficulty": "easy", "final_answer": {"answer": 205.65, "unit": "K"}, "id": "unit_convert_005574_c_to_k_-67.5", "license": "Apache-2.0", "prompt": "Convert -67.5 degC to K. Return the converted value with unit.", "reasoning_trace": "Kelvin equals Celsius plus 273.15.\nApply the conversion factor directly to the given value.\nCompute -67.5 + 273.15.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": -67.5}, "verifier": {"formula": "value + 273.15", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [1.0, -30.0], \"unit\": \"dimensionless\"}", "dedupe_signature": "dc65b6534ab9a7e93891c526a7a0e2dfea043908611c9cf5f72ccc24ef06ad88", "difficulty": "medium", "final_answer": {"answer": [1.0, -30.0], "unit": "dimensionless"}, "id": "line_two_point_005576_-7.5_-4_1_-30", "license": "Apache-2.0", "prompt": "A line passes through points (-7.5, -37.5) and (-4, -34). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -7.5, "x2": -4.0, "y1": -37.5, "y2": -34.0}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. velocity times time gives distance, not acceleration\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "86ae2136937a293365fdc71f82750b21c3f7062bbf0902aa670a3103178c73c6", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_005577_inconsistent_7481c798_18968", "license": "Apache-2.0", "prompt": "In lab notebook case 18968, check dimensional consistency for a = v * t. The left side has dimensions m/s^2 and the right side has dimensions m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nvelocity times time gives distance, not acceleration\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "a = v * t"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef weighted_sum_005578(values, weights):\n    if len(values) != len(weights):\n        raise ValueError('length mismatch')\n    return sum(value * weight for value, weight in zip(values, weights))\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"weighted_sum_005578\"}", "dedupe_signature": "4bfffc4dc2a1c74748ad96d92c18262cfcd9ddf02309426df146e8dadf500c3f", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "weighted_sum_005578"}, "id": "code_005578_weighted_sum_005578", "license": "Apache-2.0", "prompt": "Write a Python function weighted_sum_005578(values, weights) that returns sum(value*weight). Raise ValueError when the two inputs have different lengths. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "weighted_sum_005578"}, "verifier": {"function": "weighted_sum_005578", "tests": ["assert weighted_sum_005578([2, 3], [4, 5]) == 23", "assert weighted_sum_005578([], []) == 0", "try:\n    weighted_sum_005578([1], [1, 2])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: recurrence, objective, tie_breaking_rule.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"recurrence\", \"objective\", \"tie_breaking_rule\"]}", "dedupe_signature": "fe0c8b7e0a92120617ab17f464050c111bada6013b413e8abd31d259ff5d7108", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["recurrence", "objective", "tie_breaking_rule"]}, "id": "abstain_005579_recurrence_objective_tie_breaking_rule", "license": "Apache-2.0", "prompt": "Write a dynamic-programming solver for a knapsack scoring problem with 2308 items and budget 10860, but the recurrence, objective, and tie-breaking rule are all absent. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: recurrence, objective, tie_breaking_rule.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["recurrence", "objective", "tie_breaking_rule"]}, "verifier": {"missing": ["recurrence", "objective", "tie_breaking_rule"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 16.15 kg and a = 12.65 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 204.2975, \"unit\": \"N\"}", "dedupe_signature": "412c3db0baa0aa88735bd720c0e13c217c8a7ea6aba86941cdfd7239d738eb1a", "difficulty": "easy", "final_answer": {"answer": 204.2975, "unit": "N"}, "id": "force_005580_16.15_12.65", "license": "Apache-2.0", "prompt": "A cart has mass 16.15 kg and measured acceleration 12.65 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 16.15 kg and a = 12.65 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 12.65, "mass": 16.15}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 44.5^2 and multiply by 0.5 * 9.4.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 9307.175, \"unit\": \"J\"}", "dedupe_signature": "9e317e214f613ff48ba4918c19b190a339e60defa83c5cb0ca20a74cf47f0e31", "difficulty": "easy", "final_answer": {"answer": 9307.175, "unit": "J"}, "id": "ke_005581_9.4_44.5", "license": "Apache-2.0", "prompt": "A body of mass 9.4 kg moves at 44.5 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 44.5^2 and multiply by 0.5 * 9.4.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 9.4, "velocity": 44.5}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 2.45 * 8.314 * 516 / 118.3.\nFinal: {\"answer\": 88.8467, \"unit\": \"kPa\"}", "dedupe_signature": "c1baab3ed136b9912cce9cac3ec470ef225e6b4a8cf7d326a75ff107cc0cb8e9", "difficulty": "medium", "final_answer": {"answer": 88.8467, "unit": "kPa"}, "id": "ideal_gas_005583_2.45_516_118.3", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=2.45 mol, T=516 K, and V=118.3 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 2.45 * 8.314 * 516 / 118.3.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 2.45, "temp_k": 516, "volume_l": 118.3}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 870 * 1.765 * 54.\nFinal: {\"answer\": 82919.7, \"unit\": \"J\"}", "dedupe_signature": "2dcbe86f7d2031983270eefef76bf79e4d2b335cc1325d8f54220e6858a0d0a9", "difficulty": "easy", "final_answer": {"answer": 82919.7, "unit": "J"}, "id": "heat_q_005584_870_1.765_54", "license": "Apache-2.0", "prompt": "A 870 g sample has specific heat 1.765 J/(g*K). How much heat is needed to raise its temperature by 54 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 870 * 1.765 * 54.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 54, "heat_capacity": 1.765, "mass_g": 870}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=60.4 V and R=43.5 ohm.\nFinal: {\"answer\": 83.8657, \"unit\": \"W\"}", "dedupe_signature": "2368961b0b34e3f052e04c20f43966322dddfa83e9c55e309170494530693fe1", "difficulty": "easy", "final_answer": {"answer": 83.8657, "unit": "W"}, "id": "ohm_power_005585_60.4_43.5", "license": "Apache-2.0", "prompt": "A resistor has resistance 43.5 ohm and voltage 60.4 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=60.4 V and R=43.5 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 43.5, "voltage": 60.4}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=814 mg, t=2.5 h, and T_half=51 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 786.8067, \"unit\": \"mg\"}", "dedupe_signature": "7cfe164c45e0c14e5ce787ad3ac24c9d6a6beaed551c46953f800a4b64d2509e", "difficulty": "medium", "final_answer": {"answer": 786.8067, "unit": "mg"}, "id": "half_life_005586_814_51_2.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 814 mg. Its half-life is 51 hours. How many mg remain after 2.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=814 mg, t=2.5 h, and T_half=51 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 2.5, "half_life": 51.0, "initial_amount": 814.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 5.42 mol * 58.44 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 316.7448, \"unit\": \"g\"}", "dedupe_signature": "169b90a5302f9afcf8a867f69ed9f7d48b288d23d79b0c3bdd032dd3a513ea42", "difficulty": "medium", "final_answer": {"answer": 316.7448, "unit": "g"}, "id": "stoich_mass_005587_sodium_chloride_5.42", "license": "Apache-2.0", "prompt": "A sample contains 5.42 mol of sodium chloride. Using molar mass 58.44 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 5.42 mol * 58.44 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "sodium chloride", "molar_mass": 58.44, "moles": 5.42}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 2725 mL to 2.725 L.\n3. Compute M = 0.095 / 2.725.\nFinal: {\"answer\": 0.0349, \"unit\": \"mol/L\"}", "dedupe_signature": "cee4121bc20051387f171d2632ce01b5f45533b8a18395408c3e1bad54d5f1c8", "difficulty": "medium", "final_answer": {"answer": 0.0349, "unit": "mol/L"}, "id": "molarity_005588_0.095_2725", "license": "Apache-2.0", "prompt": "A solution contains 0.095 mol of solute in 2725 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 2725 mL to 2.725 L.\nCompute M = 0.095 / 2.725.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 0.095, "volume_ml": 2725}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.36 y, so each step multiplies y by 1 - h*0.36.\n3. Apply that update for 3 steps and round the final state.\nFinal: {\"answer\": 21.5738, \"unit\": \"state_units\"}", "dedupe_signature": "dc840c345cdc588fec34431e259e1a3bbc1d8b67d1afa5245fdf74722ab3033d", "difficulty": "medium", "final_answer": {"answer": 21.5738, "unit": "state_units"}, "id": "euler_decay_005589_48_0.36_0.65_3", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.36 y with y(0)=48, step size h=0.65, for 3 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.36 y, so each step multiplies y by 1 - h*0.36.\nApply that update for 3 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 48.0, "rate": 0.36, "step": 0.65, "steps": 3}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-7.3)=-20 and f(-0.3)=15.\n3. The interval width is 7.\nFinal: {\"answer\": -17.5, \"unit\": \"area_units\"}", "dedupe_signature": "d711f625b312576a31f5db6c997be8038c21285db4ea718b4365dc73c7047ebc", "difficulty": "medium", "final_answer": {"answer": -17.5, "unit": "area_units"}, "id": "trapz_linear_005590_5_16.5_-7.3_-0.3", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=5x+16.5 from x=-7.3 to x=-0.3. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-7.3)=-20 and f(-0.3)=15.\nThe interval width is 7.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 16.5, "slope": 5.0, "x0": -7.3, "x1": -0.2999999999999998}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.34 and add it to the current value.\nFinal: {\"answer\": [1.567, 0.838, 0.978], \"unit\": \"temperature_units\"}", "dedupe_signature": "9f7cbc24c3670e5d5ffb190df7bdce8539877c00f25aca008ba10ea35b3f792e", "difficulty": "hard", "final_answer": {"answer": [1.567, 0.838, 0.978], "unit": "temperature_units"}, "id": "heat_step_005591_0.34_1.7_1.55_1.45_-0.45_1.85", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.7, right=1.85; current interior values are [1.55, 1.45, -0.45]. Use r=0.34. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.34 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [1.55, 1.45, -0.45], "left": 1.7, "r": 0.34, "right": 1.85}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=121 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-173.0528, 288.0082], \"unit\": \"N\"}", "dedupe_signature": "f8cfce3be91f511125e8bf5c530d69adb7a785fbf3f743bde66419c5006603fe", "difficulty": "medium", "final_answer": {"answer": [-173.0528, 288.0082], "unit": "N"}, "id": "vector_components_005593_336_121", "license": "Apache-2.0", "prompt": "A vector has magnitude 336 N at 121 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=121 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 121, "magnitude": 336.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [1.1, 29.0], \"unit\": \"dimensionless\"}", "dedupe_signature": "7dfc298ff19cfc2f6b977afc7830a54619e7d29d6674323580784bc5445e1072", "difficulty": "medium", "final_answer": {"answer": [1.1, 29.0], "unit": "dimensionless"}, "id": "line_two_point_005594_-3_10.5_1.1_29", "license": "Apache-2.0", "prompt": "A line passes through points (-3, 25.7) and (10.5, 40.55). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -3.0, "x2": 10.5, "y1": 25.7, "y2": 40.55}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. energy divided by length is force, not spring constant\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "965d7c8143e00e46b4a773f1819b1b748bd83781cad76cb89616b2334d91fda7", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_005595_inconsistent_56040f5d_87092", "license": "Apache-2.0", "prompt": "In field worksheet case 87092, check dimensional consistency for k = E / x. The left side has dimensions N/m and the right side has dimensions J/m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nenergy divided by length is force, not spring constant\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "k = E / x"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef finite_differences_005596(values):\n    return [values[i + 1] - values[i] for i in range(len(values) - 1)]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"finite_differences_005596\"}", "dedupe_signature": "28c54fa8286cd78ed1634cbd906259ffeded1dc3c32f3ab81af265ea4d6780dd", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "finite_differences_005596"}, "id": "code_005596_finite_differences_005596", "license": "Apache-2.0", "prompt": "Write a Python function finite_differences_005596(values) that returns the list of successive differences values[i+1] - values[i]. It must return [] for fewer than two values. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "finite_differences_005596"}, "verifier": {"function": "finite_differences_005596", "tests": ["assert finite_differences_005596([1, 4, 9, 16]) == [3, 5, 7]", "assert finite_differences_005596([5]) == []", "assert finite_differences_005596([]) == []"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: launch_angle_or_vertical_velocity.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"launch_angle_or_vertical_velocity\"]}", "dedupe_signature": "777b652e83024c95ecf036e9cd8d2a995c655e9aaf7ad41560b7eb2eeedc0847", "difficulty": "easy", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["launch_angle_or_vertical_velocity"]}, "id": "abstain_005597_launch_angle_or_vertical_velocity", "license": "Apache-2.0", "prompt": "Compute projectile range on level ground. The prompt gives initial speed 83 m/s but does not give launch angle or vertical velocity. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: launch_angle_or_vertical_velocity.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["launch_angle_or_vertical_velocity"]}, "verifier": {"missing": ["launch_angle_or_vertical_velocity"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 4.45 kg and a = 14.6 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 64.97, \"unit\": \"N\"}", "dedupe_signature": "5317e0fcef983c4394a98a6a7830124dc280110804279c09325fe5528d0dcea0", "difficulty": "easy", "final_answer": {"answer": 64.97, "unit": "N"}, "id": "force_005598_4.45_14.6", "license": "Apache-2.0", "prompt": "A cart has mass 4.45 kg and measured acceleration 14.6 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 4.45 kg and a = 14.6 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 14.6, "mass": 4.45}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 41.15^2 and multiply by 0.5 * 19.5.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 16509.8944, \"unit\": \"J\"}", "dedupe_signature": "dda1bdfaea29738d36ca1561f2096aca4e3e3f956c663779271f283276627fc5", "difficulty": "easy", "final_answer": {"answer": 16509.8944, "unit": "J"}, "id": "ke_005599_19.5_41.15", "license": "Apache-2.0", "prompt": "A body of mass 19.5 kg moves at 41.15 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 41.15^2 and multiply by 0.5 * 19.5.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 19.5, "velocity": 41.15}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=27 degrees through the sine of 2 theta.\n3. Substitute v=65.9 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 358.1455, \"unit\": \"m\"}", "dedupe_signature": "0546b1e51fa9a8c791719bcb3275862a861d5bb0e8ef27e31a97e79a76fa281f", "difficulty": "medium", "final_answer": {"answer": 358.1455, "unit": "m"}, "id": "projectile_range_005600_65.9_27", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 65.9 m/s and angle 27 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=27 degrees through the sine of 2 theta.\nSubstitute v=65.9 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 27, "gravity": 9.81, "speed": 65.9}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 1.56 * 8.314 * 435 / 61.7.\nFinal: {\"answer\": 91.4405, \"unit\": \"kPa\"}", "dedupe_signature": "28bacc7af8de2c83417aefa79494ee2a1cbb9f7970ba5917456e91f566fc3330", "difficulty": "medium", "final_answer": {"answer": 91.4405, "unit": "kPa"}, "id": "ideal_gas_005601_1.56_435_61.7", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=1.56 mol, T=435 K, and V=61.7 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 1.56 * 8.314 * 435 / 61.7.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 1.56, "temp_k": 435, "volume_l": 61.7}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=102.4 V and R=99.7 ohm.\nFinal: {\"answer\": 105.1731, \"unit\": \"W\"}", "dedupe_signature": "bc9d6e22af2c8b820e19221ad33c5458334034939b48b42cc9a075a7fbbc634b", "difficulty": "easy", "final_answer": {"answer": 105.1731, "unit": "W"}, "id": "ohm_power_005603_102.4_99.7", "license": "Apache-2.0", "prompt": "A resistor has resistance 99.7 ohm and voltage 102.4 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=102.4 V and R=99.7 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 99.7, "voltage": 102.4}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=644.5 mg, t=217 h, and T_half=74.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 85.5849, \"unit\": \"mg\"}", "dedupe_signature": "6d58b1297431cf4b09d6cddbdbfeb87f98e5b46312a8af4ae6b336a7dc96dcf7", "difficulty": "medium", "final_answer": {"answer": 85.5849, "unit": "mg"}, "id": "half_life_005604_644.5_74.5_217", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 644.5 mg. Its half-life is 74.5 hours. How many mg remain after 217 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=644.5 mg, t=217 h, and T_half=74.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 217.0, "half_life": 74.5, "initial_amount": 644.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 0.72 mol * 58.44 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 42.0768, \"unit\": \"g\"}", "dedupe_signature": "f3c44081d77606839daa3cf83914091eb73fc909c480e69bea525f99070b4003", "difficulty": "medium", "final_answer": {"answer": 42.0768, "unit": "g"}, "id": "stoich_mass_005605_sodium_chloride_0.72", "license": "Apache-2.0", "prompt": "A sample contains 0.72 mol of sodium chloride. Using molar mass 58.44 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 0.72 mol * 58.44 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "sodium chloride", "molar_mass": 58.44, "moles": 0.72}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 1305 mL to 1.305 L.\n3. Compute M = 1.665 / 1.305.\nFinal: {\"answer\": 1.2759, \"unit\": \"mol/L\"}", "dedupe_signature": "0ba2c87239a4889f8b142de0b8eadeadcbb2b2ca7d349f036fb3e382adaaac2a", "difficulty": "medium", "final_answer": {"answer": 1.2759, "unit": "mol/L"}, "id": "molarity_005606_1.665_1305", "license": "Apache-2.0", "prompt": "A solution contains 1.665 mol of solute in 1305 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 1305 mL to 1.305 L.\nCompute M = 1.665 / 1.305.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 1.665, "volume_ml": 1305}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.44 y, so each step multiplies y by 1 - h*0.44.\n3. Apply that update for 6 steps and round the final state.\nFinal: {\"answer\": 6.629, \"unit\": \"state_units\"}", "dedupe_signature": "77d9c66fbb93dc8c1aadf9bcbd563e24eb3b72622e494ebeefbf85bad7513c71", "difficulty": "medium", "final_answer": {"answer": 6.629, "unit": "state_units"}, "id": "euler_decay_005607_15.5_0.44_0.3_6", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.44 y with y(0)=15.5, step size h=0.3, for 6 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.44 y, so each step multiplies y by 1 - h*0.44.\nApply that update for 6 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 15.5, "rate": 0.44, "step": 0.3, "steps": 6}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-9.4)=6.22 and f(-9.2)=6.36.\n3. The interval width is 0.2.\nFinal: {\"answer\": 1.258, \"unit\": \"area_units\"}", "dedupe_signature": "8344c55e676be08a87c063df9cd9f88d40809b1ec4c1941892201ea99c9cfcb8", "difficulty": "medium", "final_answer": {"answer": 1.258, "unit": "area_units"}, "id": "trapz_linear_005608_0.7_12.8_-9.4_-9.2", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=0.7x+12.8 from x=-9.4 to x=-9.2. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-9.4)=6.22 and f(-9.2)=6.36.\nThe interval width is 0.2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 12.8, "slope": 0.7, "x0": -9.4, "x1": -9.200000000000001}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.46 and add it to the current value.\nFinal: {\"answer\": [0.755, 0.421, 0.209], \"unit\": \"temperature_units\"}", "dedupe_signature": "b1d7c35876cf2df01418033634737c9025914b5bf25c30d022d8fd59502f142c", "difficulty": "hard", "final_answer": {"answer": [0.755, 0.421, 0.209], "unit": "temperature_units"}, "id": "heat_step_005609_0.46_-0.45_-0.05_2.1_0.6_-1.75", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-0.45, right=-1.75; current interior values are [-0.05, 2.1, 0.6]. Use r=0.46. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.46 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-0.05, 2.1, 0.6], "left": -0.45, "r": 0.46, "right": -1.75}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=69 degrees and keep the unit as newtons.\nFinal: {\"answer\": [162.3407, 422.9119], \"unit\": \"N\"}", "dedupe_signature": "6cded5afa04bc0b0c5307764d39801a3a9a73b8f8daecf5abe2717c45f9d2427", "difficulty": "medium", "final_answer": {"answer": [162.3407, 422.9119], "unit": "N"}, "id": "vector_components_005611_453_69", "license": "Apache-2.0", "prompt": "A vector has magnitude 453 N at 69 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=69 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 69, "magnitude": 453.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-9.95, 21.25], \"unit\": \"dimensionless\"}", "dedupe_signature": "9edcaaeb483db3517f83ad37e066ad53a37becf9c85051c67dabb17b392aa9fb", "difficulty": "medium", "final_answer": {"answer": [-9.95, 21.25], "unit": "dimensionless"}, "id": "line_two_point_005612_4.25_16_-9.95_21.25", "license": "Apache-2.0", "prompt": "A line passes through points (4.25, -21.0375) and (16, -137.95). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 4.25, "x2": 16.0, "y1": -21.037499999999994, "y2": -137.95}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. energy divided by length is force, not spring constant\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "8161d05df4b78e9dbcf70e1aabf3d21cc779dc88d9a0b8498e19062d86868e55", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_005613_inconsistent_56040f5d_392387", "license": "Apache-2.0", "prompt": "In simulation spec case 392387, check dimensional consistency for k = E / x. The left side has dimensions N/m and the right side has dimensions J/m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nenergy divided by length is force, not spring constant\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "k = E / x"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: target_schema, valid_examples.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"target_schema\", \"valid_examples\"]}", "dedupe_signature": "d0305045d5fcc38afe3d84ad7a9daad422ff7f27d8350117508a6061c20e3c1d", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["target_schema", "valid_examples"]}, "id": "abstain_005615_target_schema_valid_examples", "license": "Apache-2.0", "prompt": "Write a parser that converts each registry survey record from batch 615205 into the correct schema, but the prompt does not include the target schema or examples. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: target_schema, valid_examples.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["target_schema", "valid_examples"]}, "verifier": {"missing": ["target_schema", "valid_examples"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 4.35 kg and a = 9.35 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 40.6725, \"unit\": \"N\"}", "dedupe_signature": "e7c05ed58053833725d1ea88c22300f6891a2193dc567f370611832ca9520ae9", "difficulty": "easy", "final_answer": {"answer": 40.6725, "unit": "N"}, "id": "force_005616_4.35_9.35", "license": "Apache-2.0", "prompt": "A cart has mass 4.35 kg and measured acceleration 9.35 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 4.35 kg and a = 9.35 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 9.35, "mass": 4.35}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=31 degrees through the sine of 2 theta.\n3. Substitute v=11.2 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 11.2902, \"unit\": \"m\"}", "dedupe_signature": "a295b744f10f2c8935fa780f6a5bdde3b6295bd22dc11537d82c10985f2f200d", "difficulty": "medium", "final_answer": {"answer": 11.2902, "unit": "m"}, "id": "projectile_range_005618_11.2_31", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 11.2 m/s and angle 31 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=31 degrees through the sine of 2 theta.\nSubstitute v=11.2 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 31, "gravity": 9.81, "speed": 11.2}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=20 mg, t=335.5 h, and T_half=0.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 0.0, \"unit\": \"mg\"}", "dedupe_signature": "8269b81af4b29ba6042b37477e4446d52339a34166e60af81f8e138352f1cf32", "difficulty": "medium", "final_answer": {"answer": 0.0, "unit": "mg"}, "id": "half_life_005622_20_0.5_335.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 20 mg. Its half-life is 0.5 hours. How many mg remain after 335.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=20 mg, t=335.5 h, and T_half=0.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 335.5, "half_life": 0.5, "initial_amount": 20.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 5.83 mol * 58.44 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 340.7052, \"unit\": \"g\"}", "dedupe_signature": "ab7c8f5e0e4ecf2c8955ee7c8462cdec55cfaaf23cdc6e7d91f482a4d62a9cf8", "difficulty": "medium", "final_answer": {"answer": 340.7052, "unit": "g"}, "id": "stoich_mass_005623_sodium_chloride_5.83", "license": "Apache-2.0", "prompt": "A sample contains 5.83 mol of sodium chloride. Using molar mass 58.44 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 5.83 mol * 58.44 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "sodium chloride", "molar_mass": 58.44, "moles": 5.83}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 1795 mL to 1.795 L.\n3. Compute M = 3.745 / 1.795.\nFinal: {\"answer\": 2.0864, \"unit\": \"mol/L\"}", "dedupe_signature": "b58ace9dfd7b2cc2492c4fe0498866a7304449e2aaa859bd135cceed18c8fecb", "difficulty": "medium", "final_answer": {"answer": 2.0864, "unit": "mol/L"}, "id": "molarity_005624_3.745_1795", "license": "Apache-2.0", "prompt": "A solution contains 3.745 mol of solute in 1795 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 1795 mL to 1.795 L.\nCompute M = 3.745 / 1.795.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 3.745, "volume_ml": 1795}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-9.7)=-61.37 and f(-7.6)=-46.46.\n3. The interval width is 2.1.\nFinal: {\"answer\": -113.2215, \"unit\": \"area_units\"}", "dedupe_signature": "df538ed69015b6553bdf5b6cec030bb78e07f58bc5190509690a0f24338183c3", "difficulty": "medium", "final_answer": {"answer": -113.2215, "unit": "area_units"}, "id": "trapz_linear_005626_7.1_7.5_-9.7_-7.6", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=7.1x+7.5 from x=-9.7 to x=-7.6. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-9.7)=-61.37 and f(-7.6)=-46.46.\nThe interval width is 2.1.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 7.5, "slope": 7.1, "x0": -9.7, "x1": -7.6}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.38 and add it to the current value.\nFinal: {\"answer\": [-0.827, -0.365, -0.301], \"unit\": \"temperature_units\"}", "dedupe_signature": "c276ac7c7de164448b4e3f9b7f46078de49ae040c802a3aaebe0640b9e2fd840", "difficulty": "hard", "final_answer": {"answer": [-0.827, -0.365, -0.301], "unit": "temperature_units"}, "id": "heat_step_005627_0.38_-0.45_-0.2_-1.6_0.25_0.65", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-0.45, right=0.65; current interior values are [-0.2, -1.6, 0.25]. Use r=0.38. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.38 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-0.2, -1.6, 0.25], "left": -0.45, "r": 0.38, "right": 0.65}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=120 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-212.25, 367.6278], \"unit\": \"N\"}", "dedupe_signature": "920d30795cc0b6d1a692d50f08074b2e0b5c21efba08dd587b17bebb27e911a2", "difficulty": "medium", "final_answer": {"answer": [-212.25, 367.6278], "unit": "N"}, "id": "vector_components_005629_424.5_120", "license": "Apache-2.0", "prompt": "A vector has magnitude 424.5 N at 120 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=120 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 120, "magnitude": 424.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [8.6, -3.25], \"unit\": \"dimensionless\"}", "dedupe_signature": "0560ea97e5266e47bd686eec234284ffe23eb17cd00eb2fd55ecb26b29f0bc30", "difficulty": "medium", "final_answer": {"answer": [8.6, -3.25], "unit": "dimensionless"}, "id": "line_two_point_005630_-15.5_-3.5_8.6_-3.25", "license": "Apache-2.0", "prompt": "A line passes through points (-15.5, -136.55) and (-3.5, -33.35). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -15.5, "x2": -3.5, "y1": -136.54999999999998, "y2": -33.349999999999994}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. amount times volume is not concentration\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "f5b5cca33cb76f24a16c3d3770e3caeff41bb0705689bfd190603918679cd82e", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_005631_inconsistent_74ac0b02_768634", "license": "Apache-2.0", "prompt": "In quality-control check case 768634, check dimensional consistency for C = n * V. The left side has dimensions mol/L and the right side has dimensions mol*L. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\namount times volume is not concentration\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "C = n * V"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef threshold_flags_005632(values, threshold):\n    return [value >= threshold for value in values]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"threshold_flags_005632\"}", "dedupe_signature": "b377f8483ef2b6faba5d6c3026c1ddddecc5258dac82abe0fac921812f89397c", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "threshold_flags_005632"}, "id": "code_005632_threshold_flags_005632", "license": "Apache-2.0", "prompt": "Write a Python function threshold_flags_005632(values, threshold) that returns a list of booleans showing whether each value is greater than or equal to threshold. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "threshold_flags_005632"}, "verifier": {"function": "threshold_flags_005632", "tests": ["assert threshold_flags_005632([1, 2, 3], 2) == [False, True, True]", "assert threshold_flags_005632([], 5) == []", "assert threshold_flags_005632([-1, 0], 0) == [False, True]"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: volume.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"volume\"]}", "dedupe_signature": "e20ac4dfaf249a475a37180af9bbfc03b474e6df46014d77f24169d3ae2d1b63", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["volume"]}, "id": "abstain_005633_volume", "license": "Apache-2.0", "prompt": "Compute pressure from the ideal gas law. The prompt gives n=4.48 mol and T=280 K, but does not give volume. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: volume.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["volume"]}, "verifier": {"missing": ["volume"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 1.25 kg and a = 11.25 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 14.0625, \"unit\": \"N\"}", "dedupe_signature": "cebadd6b866eaded016f0c7f61695288e6ee3936f96bff009e68d5281e4130f3", "difficulty": "easy", "final_answer": {"answer": 14.0625, "unit": "N"}, "id": "force_005634_1.25_11.25", "license": "Apache-2.0", "prompt": "A cart has mass 1.25 kg and measured acceleration 11.25 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 1.25 kg and a = 11.25 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 11.25, "mass": 1.25}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 23.7^2 and multiply by 0.5 * 18.3.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 5139.4635, \"unit\": \"J\"}", "dedupe_signature": "d3d3e7c3aea50528d39c0a264da3bfe0452185400fd471c74bae108539b19ab9", "difficulty": "easy", "final_answer": {"answer": 5139.4635, "unit": "J"}, "id": "ke_005635_18.3_23.7", "license": "Apache-2.0", "prompt": "A body of mass 18.3 kg moves at 23.7 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 23.7^2 and multiply by 0.5 * 18.3.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 18.3, "velocity": 23.7}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 2.62 * 8.314 * 346 / 104.2.\nFinal: {\"answer\": 72.3302, \"unit\": \"kPa\"}", "dedupe_signature": "97fe904428a6157fe4e53d7f0545ea36446bd8d78c58849060ebfdf44b7f0142", "difficulty": "medium", "final_answer": {"answer": 72.3302, "unit": "kPa"}, "id": "ideal_gas_005637_2.62_346_104.2", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=2.62 mol, T=346 K, and V=104.2 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 2.62 * 8.314 * 346 / 104.2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 2.62, "temp_k": 346, "volume_l": 104.2}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1960 * 3.83 * 64.\nFinal: {\"answer\": 480435.2, \"unit\": \"J\"}", "dedupe_signature": "06abf0f9c6b58e3d2133cc767e5e005a6ada57d024fc3cfa2e8f836a085f8f5c", "difficulty": "easy", "final_answer": {"answer": 480435.2, "unit": "J"}, "id": "heat_q_005638_1960_3.83_64", "license": "Apache-2.0", "prompt": "A 1960 g sample has specific heat 3.83 J/(g*K). How much heat is needed to raise its temperature by 64 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1960 * 3.83 * 64.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 64, "heat_capacity": 3.83, "mass_g": 1960}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=54.3 V and R=114.9 ohm.\nFinal: {\"answer\": 25.6614, \"unit\": \"W\"}", "dedupe_signature": "9f443aa3e9c9568ccc400a511a0449bb977e4c523e179104a43a559aec85fb16", "difficulty": "easy", "final_answer": {"answer": 25.6614, "unit": "W"}, "id": "ohm_power_005639_54.3_114.9", "license": "Apache-2.0", "prompt": "A resistor has resistance 114.9 ohm and voltage 54.3 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=54.3 V and R=114.9 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 114.9, "voltage": 54.3}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=878 mg, t=204 h, and T_half=34.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 14.5711, \"unit\": \"mg\"}", "dedupe_signature": "b7b1c37211aefd390a27b35dd4dcebcffd54d24469152cd71a661ab8ca902d2f", "difficulty": "medium", "final_answer": {"answer": 14.5711, "unit": "mg"}, "id": "half_life_005640_878_34.5_204", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 878 mg. Its half-life is 34.5 hours. How many mg remain after 204 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=878 mg, t=204 h, and T_half=34.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 204.0, "half_life": 34.5, "initial_amount": 878.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 6.96 mol * 44.01 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 306.3096, \"unit\": \"g\"}", "dedupe_signature": "ad4c06b76d67950e4ce54733a2bd1a77f903eb73e90a92836df3e974d54e8a29", "difficulty": "medium", "final_answer": {"answer": 306.3096, "unit": "g"}, "id": "stoich_mass_005641_carbon_dioxide_6.96", "license": "Apache-2.0", "prompt": "A sample contains 6.96 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 6.96 mol * 44.01 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "carbon dioxide", "molar_mass": 44.01, "moles": 6.96}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 1325 mL to 1.325 L.\n3. Compute M = 1.685 / 1.325.\nFinal: {\"answer\": 1.2717, \"unit\": \"mol/L\"}", "dedupe_signature": "5e9cddb126fc3ca8856560f9c59b6fe0a9a3d6cce653c1e6c3bc16a2cc17a495", "difficulty": "medium", "final_answer": {"answer": 1.2717, "unit": "mol/L"}, "id": "molarity_005642_1.685_1325", "license": "Apache-2.0", "prompt": "A solution contains 1.685 mol of solute in 1325 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 1325 mL to 1.325 L.\nCompute M = 1.685 / 1.325.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 1.685, "volume_ml": 1325}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.7 y, so each step multiplies y by 1 - h*0.7.\n3. Apply that update for 10 steps and round the final state.\nFinal: {\"answer\": 0.0, \"unit\": \"state_units\"}", "dedupe_signature": "8fb02c56b356a218d4f1152109765cac0180ba3bb5f2a8e5f116801b9e3e8582", "difficulty": "medium", "final_answer": {"answer": 0.0, "unit": "state_units"}, "id": "euler_decay_005643_15_0.7_1.55_10", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.7 y with y(0)=15, step size h=1.55, for 10 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.7 y, so each step multiplies y by 1 - h*0.7.\nApply that update for 10 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 15.0, "rate": 0.7, "step": 1.55, "steps": 10}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-7.6)=1.6 and f(-4.1)=-7.15.\n3. The interval width is 3.5.\nFinal: {\"answer\": -9.7125, \"unit\": \"area_units\"}", "dedupe_signature": "2bcebaa73d644b155087739c7c4ad7f1a524e18810c3b0447048f302291c5002", "difficulty": "medium", "final_answer": {"answer": -9.7125, "unit": "area_units"}, "id": "trapz_linear_005644_-2.5_-17.4_-7.6_-4.1", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-2.5x+-17.4 from x=-7.6 to x=-4.1. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-7.6)=1.6 and f(-4.1)=-7.15.\nThe interval width is 3.5.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -17.4, "slope": -2.5, "x0": -7.6, "x1": -4.1}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.34 and add it to the current value.\nFinal: {\"answer\": [-1.061, -0.055, -0.766], \"unit\": \"temperature_units\"}", "dedupe_signature": "70efa9da42a56fb68acca0963f4778f12e5dace0f1626c8423a69ae07f4af480", "difficulty": "hard", "final_answer": {"answer": [-1.061, -0.055, -0.766], "unit": "temperature_units"}, "id": "heat_step_005645_0.34_-1.95_0.35_-1.5_0.9_-1.6", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-1.95, right=-1.6; current interior values are [0.35, -1.5, 0.9]. Use r=0.34. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.34 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [0.35, -1.5, 0.9], "left": -1.95, "r": 0.34, "right": -1.6}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=124 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-20.1309, 29.8454], \"unit\": \"N\"}", "dedupe_signature": "47a4b29d60bc00df9636eda1d7a428053c3b6e837b9112d79e8442ef2194c160", "difficulty": "medium", "final_answer": {"answer": [-20.1309, 29.8454], "unit": "N"}, "id": "vector_components_005647_36_124", "license": "Apache-2.0", "prompt": "A vector has magnitude 36 N at 124 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=124 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 124, "magnitude": 36.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [2.05, -28.5], \"unit\": \"dimensionless\"}", "dedupe_signature": "6a63b5bb56a9507e830addfcc754003e6c5dc0c2793308a1093490f3d242b8b7", "difficulty": "medium", "final_answer": {"answer": [2.05, -28.5], "unit": "dimensionless"}, "id": "line_two_point_005648_3_5_2.05_-28.5", "license": "Apache-2.0", "prompt": "A line passes through points (3, -22.35) and (5, -18.25). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 3.0, "x2": 5.0, "y1": -22.35, "y2": -18.25}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. velocity times time gives distance, not acceleration\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "e00133373cf98dffa15914707aa11318530fe60619fba37526705f8a16542528", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_005649_inconsistent_7481c798_755367", "license": "Apache-2.0", "prompt": "In model card equation case 755367, check dimensional consistency for a = v * t. The left side has dimensions m/s^2 and the right side has dimensions m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nvelocity times time gives distance, not acceleration\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "a = v * t"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: left_boundary, right_boundary.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"left_boundary\", \"right_boundary\"]}", "dedupe_signature": "25d85a423ba8527190a14f741e06910febee5ae7cdcb46fa3e648d4463ba1277", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["left_boundary", "right_boundary"]}, "id": "abstain_005651_left_boundary_right_boundary", "license": "Apache-2.0", "prompt": "Solve the 1D heat equation after one finite-difference step. The prompt gives r=0.02 and interior values [-0.9, 2.3, 0.45], but gives no boundary values. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: left_boundary, right_boundary.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["left_boundary", "right_boundary"]}, "verifier": {"missing": ["left_boundary", "right_boundary"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 23.1 kg and a = 3.85 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 88.935, \"unit\": \"N\"}", "dedupe_signature": "c7883cafeb9566b672f80f0f13df6ea63adac5583574c22284dd5f60d550dfd6", "difficulty": "easy", "final_answer": {"answer": 88.935, "unit": "N"}, "id": "force_005652_23.1_3.85", "license": "Apache-2.0", "prompt": "A cart has mass 23.1 kg and measured acceleration 3.85 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 23.1 kg and a = 3.85 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 3.85, "mass": 23.1}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=22 degrees through the sine of 2 theta.\n3. Substitute v=35.5 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 89.2399, \"unit\": \"m\"}", "dedupe_signature": "b9e5c8b49dffe3641c63a9f68c8b4e73784cad494821222cfe96bc340ad82f84", "difficulty": "medium", "final_answer": {"answer": 89.2399, "unit": "m"}, "id": "projectile_range_005654_35.5_22", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 35.5 m/s and angle 22 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=22 degrees through the sine of 2 theta.\nSubstitute v=35.5 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 22, "gravity": 9.81, "speed": 35.5}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 3.94 * 8.314 * 344 / 2.3.\nFinal: {\"answer\": 4899.3318, \"unit\": \"kPa\"}", "dedupe_signature": "a512d3efad5cfde2c65f803663b72e7b72efbc0a0c2f43fc0e1f3ddb1ba068d7", "difficulty": "medium", "final_answer": {"answer": 4899.3318, "unit": "kPa"}, "id": "ideal_gas_005655_3.94_344_2.3", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=3.94 mol, T=344 K, and V=2.3 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 3.94 * 8.314 * 344 / 2.3.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 3.94, "temp_k": 344, "volume_l": 2.3}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 630 * 0.985 * 118.\nFinal: {\"answer\": 73224.9, \"unit\": \"J\"}", "dedupe_signature": "254f652de3c15b041f496a8c297ddf2fc0741272f591d99b57dd32e9684c8536", "difficulty": "easy", "final_answer": {"answer": 73224.9, "unit": "J"}, "id": "heat_q_005656_630_0.985_118", "license": "Apache-2.0", "prompt": "A 630 g sample has specific heat 0.985 J/(g*K). How much heat is needed to raise its temperature by 118 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 630 * 0.985 * 118.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 118, "heat_capacity": 0.985, "mass_g": 630}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=148.7 V and R=97 ohm.\nFinal: {\"answer\": 227.9556, \"unit\": \"W\"}", "dedupe_signature": "9113d1255129270d820c1359d0e2c12b319163a9c5f14fe270cbdbe3688018bf", "difficulty": "easy", "final_answer": {"answer": 227.9556, "unit": "W"}, "id": "ohm_power_005657_148.7_97", "license": "Apache-2.0", "prompt": "A resistor has resistance 97 ohm and voltage 148.7 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=148.7 V and R=97 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 97.0, "voltage": 148.7}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 6.39 mol * 44.01 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 281.2239, \"unit\": \"g\"}", "dedupe_signature": "177d6ea51e06c8ee8708056fbfeecf277f013dd0a10a5a4338ac9561d34b6548", "difficulty": "medium", "final_answer": {"answer": 281.2239, "unit": "g"}, "id": "stoich_mass_005659_carbon_dioxide_6.39", "license": "Apache-2.0", "prompt": "A sample contains 6.39 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 6.39 mol * 44.01 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "carbon dioxide", "molar_mass": 44.01, "moles": 6.39}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 4415 mL to 4.415 L.\n3. Compute M = 1.8 / 4.415.\nFinal: {\"answer\": 0.4077, \"unit\": \"mol/L\"}", "dedupe_signature": "5ebc9aa47f2f149762b9f7a30bf9f48a7856a183aece3ac09935ae182d413d98", "difficulty": "medium", "final_answer": {"answer": 0.4077, "unit": "mol/L"}, "id": "molarity_005660_1.8_4415", "license": "Apache-2.0", "prompt": "A solution contains 1.8 mol of solute in 4415 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 4415 mL to 4.415 L.\nCompute M = 1.8 / 4.415.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 1.8, "volume_ml": 4415}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.08 and add it to the current value.\nFinal: {\"answer\": [-0.32, -1.63, 0.092], \"unit\": \"temperature_units\"}", "dedupe_signature": "58df0c606ebe43da9fb420f5b63bb632c408d7a44771d46db649ae5fea8521ba", "difficulty": "hard", "final_answer": {"answer": [-0.32, -1.63, 0.092], "unit": "temperature_units"}, "id": "heat_step_005663_0.08_0.05_-0.2_-1.95_0.3_-0.05", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=0.05, right=-0.05; current interior values are [-0.2, -1.95, 0.3]. Use r=0.08. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.08 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-0.2, -1.95, 0.3], "left": 0.05, "r": 0.08, "right": -0.05}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kelvin equals Celsius plus 273.15.\n2. Apply the conversion factor directly to the given value.\n3. Compute 218.5 + 273.15.\nFinal: {\"answer\": 491.65, \"unit\": \"K\"}", "dedupe_signature": "7ac5b77656a47e06e2ecd24d4060145f58209089630161747d15f863543cbc6e", "difficulty": "easy", "final_answer": {"answer": 491.65, "unit": "K"}, "id": "unit_convert_005664_c_to_k_218.5", "license": "Apache-2.0", "prompt": "Convert 218.5 degC to K. Return the converted value with unit.", "reasoning_trace": "Kelvin equals Celsius plus 273.15.\nApply the conversion factor directly to the given value.\nCompute 218.5 + 273.15.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 218.5}, "verifier": {"formula": "value + 273.15", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef finite_differences_005668(values):\n    return [values[i + 1] - values[i] for i in range(len(values) - 1)]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"finite_differences_005668\"}", "dedupe_signature": "2ac8bb4a65d431035e449ae5fad4e70f083042660a0bde601c00480f49ff4e2f", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "finite_differences_005668"}, "id": "code_005668_finite_differences_005668", "license": "Apache-2.0", "prompt": "Write a Python function finite_differences_005668(values) that returns the list of successive differences values[i+1] - values[i]. It must return [] for fewer than two values. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "finite_differences_005668"}, "verifier": {"function": "finite_differences_005668", "tests": ["assert finite_differences_005668([1, 4, 9, 16]) == [3, 5, 7]", "assert finite_differences_005668([5]) == []", "assert finite_differences_005668([]) == []"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: volume.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"volume\"]}", "dedupe_signature": "123842d2b1103428f500529f044fd31a41898ef3d4cd57e0058b855c39e165ab", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["volume"]}, "id": "abstain_005669_volume", "license": "Apache-2.0", "prompt": "Compute pressure from the ideal gas law. The prompt gives n=4.54 mol and T=285 K, but does not give volume. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: volume.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["volume"]}, "verifier": {"missing": ["volume"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 23.85 kg and a = 8.9 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 212.265, \"unit\": \"N\"}", "dedupe_signature": "4067985fe0fb8903aa7a13254ff7aa18d583441f6dcc05bdbbcd801c8a5443bb", "difficulty": "easy", "final_answer": {"answer": 212.265, "unit": "N"}, "id": "force_005670_23.85_8.9", "license": "Apache-2.0", "prompt": "A cart has mass 23.85 kg and measured acceleration 8.9 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 23.85 kg and a = 8.9 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 8.9, "mass": 23.85}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 27.65^2 and multiply by 0.5 * 3.1.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 1185.0099, \"unit\": \"J\"}", "dedupe_signature": "64481d5d2ebd8bd22cf9a34a412d04ec5a6013c6c273ab8608d7ef547831775b", "difficulty": "easy", "final_answer": {"answer": 1185.0099, "unit": "J"}, "id": "ke_005671_3.1_27.65", "license": "Apache-2.0", "prompt": "A body of mass 3.1 kg moves at 27.65 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 27.65^2 and multiply by 0.5 * 3.1.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 3.1, "velocity": 27.65}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=24 degrees through the sine of 2 theta.\n3. Substitute v=8.5 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 5.4732, \"unit\": \"m\"}", "dedupe_signature": "e530e5d4ab55ea188cbf52b93bce7fe2d62aa29ce985bc62e3fd9c55ff804ff9", "difficulty": "medium", "final_answer": {"answer": 5.4732, "unit": "m"}, "id": "projectile_range_005672_8.5_24", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 8.5 m/s and angle 24 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=24 degrees through the sine of 2 theta.\nSubstitute v=8.5 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 24, "gravity": 9.81, "speed": 8.5}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 3.39 * 8.314 * 366 / 40.8.\nFinal: {\"answer\": 252.8312, \"unit\": \"kPa\"}", "dedupe_signature": "d6a56d3f6ffbb4a2c83a31e51a20a76d75eff32cb9ac40da0edb012b32f75949", "difficulty": "medium", "final_answer": {"answer": 252.8312, "unit": "kPa"}, "id": "ideal_gas_005673_3.39_366_40.8", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=3.39 mol, T=366 K, and V=40.8 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 3.39 * 8.314 * 366 / 40.8.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 3.39, "temp_k": 366, "volume_l": 40.8}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=105.6 V and R=179.5 ohm.\nFinal: {\"answer\": 62.1246, \"unit\": \"W\"}", "dedupe_signature": "1311165a3749110f708580021e5cb8401caa3717b6419903c735b1f1dfbbc6cb", "difficulty": "easy", "final_answer": {"answer": 62.1246, "unit": "W"}, "id": "ohm_power_005675_105.6_179.5", "license": "Apache-2.0", "prompt": "A resistor has resistance 179.5 ohm and voltage 105.6 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=105.6 V and R=179.5 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 179.5, "voltage": 105.6}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=889 mg, t=100 h, and T_half=41.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 167.3125, \"unit\": \"mg\"}", "dedupe_signature": "b06ac4969794fb529c0b7316cc5fb16fa138c7bae805a5d94a71c31db65e2bf1", "difficulty": "medium", "final_answer": {"answer": 167.3125, "unit": "mg"}, "id": "half_life_005676_889_41.5_100", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 889 mg. Its half-life is 41.5 hours. How many mg remain after 100 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=889 mg, t=100 h, and T_half=41.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 100.0, "half_life": 41.5, "initial_amount": 889.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.74 y, so each step multiplies y by 1 - h*0.74.\n3. Apply that update for 3 steps and round the final state.\nFinal: {\"answer\": -2.3603, \"unit\": \"state_units\"}", "dedupe_signature": "00ca2a308822fa2eab5b72cc6ec3489cebdd64bb85cef39e5ce4350a6ad332b9", "difficulty": "medium", "final_answer": {"answer": -2.3603, "unit": "state_units"}, "id": "euler_decay_005679_64.5_0.74_1.8_3", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.74 y with y(0)=64.5, step size h=1.8, for 3 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.74 y, so each step multiplies y by 1 - h*0.74.\nApply that update for 3 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 64.5, "rate": 0.74, "step": 1.8, "steps": 3}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(6.8)=-33.36 and f(16.5)=-108.05.\n3. The interval width is 9.7.\nFinal: {\"answer\": -685.8385, \"unit\": \"area_units\"}", "dedupe_signature": "42fe8ff52679c610e5369fb956c4034f11560c4b7d06a3e6294d814dce6ca451", "difficulty": "medium", "final_answer": {"answer": -685.8385, "unit": "area_units"}, "id": "trapz_linear_005680_-7.7_19_6.8_16.5", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-7.7x+19 from x=6.8 to x=16.5. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(6.8)=-33.36 and f(16.5)=-108.05.\nThe interval width is 9.7.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 19.0, "slope": -7.7, "x0": 6.8, "x1": 16.5}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.3 and add it to the current value.\nFinal: {\"answer\": [0.66, 1.35, 0.475], \"unit\": \"temperature_units\"}", "dedupe_signature": "be51c9aef3e6b24d2d78802a8cfcd6c70584cc2e313c3110120ddd3d24395ba2", "difficulty": "hard", "final_answer": {"answer": [0.66, 1.35, 0.475], "unit": "temperature_units"}, "id": "heat_step_005681_0.3_-1.45_1.95_1.05_1.15_-1.0", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-1.45, right=-1; current interior values are [1.95, 1.05, 1.15]. Use r=0.3. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.3 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [1.95, 1.05, 1.15], "left": -1.45, "r": 0.3, "right": -1.0}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 100 centimeters in one meter.\n2. Apply the conversion factor directly to the given value.\n3. Compute 2332.0 / 100.\nFinal: {\"answer\": 23.32, \"unit\": \"m\"}", "dedupe_signature": "5929aea285582c042e01a6ac806bea57b1d7c01d0e9a500b17fc2d0896a17f96", "difficulty": "easy", "final_answer": {"answer": 23.32, "unit": "m"}, "id": "unit_convert_005682_cm_to_m_2332", "license": "Apache-2.0", "prompt": "Convert 2332 cm to m. Return the converted value with unit.", "reasoning_trace": "There are 100 centimeters in one meter.\nApply the conversion factor directly to the given value.\nCompute 2332.0 / 100.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 2332.0}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. volt squared divided by ohm is watt\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "eac38cb370005ca0b7c1823ccb147a73bbd5f1b184e8e9066bdc8f5c925e17a3", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_005685_consistent_82e93f3d_610144", "license": "Apache-2.0", "prompt": "In quality-control check case 610144, check dimensional consistency for P = V^2 / R. The left side has dimensions W and the right side has dimensions W. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nvolt squared divided by ohm is watt\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "P = V^2 / R"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef running_total_005686(values):\n    total = 0\n    out = []\n    for value in values:\n        total += value\n        out.append(total)\n    return out\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"running_total_005686\"}", "dedupe_signature": "864ce992d3f5ae650c5320ed6e46369917f0d8a839090590ff623a054209733b", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "running_total_005686"}, "id": "code_005686_running_total_005686", "license": "Apache-2.0", "prompt": "Write a Python function running_total_005686(values) that returns cumulative sums as a new list. It must not mutate the input list. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "running_total_005686"}, "verifier": {"function": "running_total_005686", "tests": ["assert running_total_005686([1, 2, 3]) == [1, 3, 6]", "xs = [4, -1, 2]; assert running_total_005686(xs) == [4, 3, 5] and xs == [4, -1, 2]", "assert running_total_005686([]) == []"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 3.3 kg and a = 15.85 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 52.305, \"unit\": \"N\"}", "dedupe_signature": "cd8d72b391f249297fa24eb83a613c230afd4166f4d137abbbbc7bf3a2ec87b6", "difficulty": "easy", "final_answer": {"answer": 52.305, "unit": "N"}, "id": "force_005688_3.3_15.85", "license": "Apache-2.0", "prompt": "A cart has mass 3.3 kg and measured acceleration 15.85 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 3.3 kg and a = 15.85 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 15.85, "mass": 3.3}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 13.35^2 and multiply by 0.5 * 26.2.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 2334.7148, \"unit\": \"J\"}", "dedupe_signature": "3255cbac021921c61c5dd7cb17f3cce874b8ae4b273736e299f3857374ef8d64", "difficulty": "easy", "final_answer": {"answer": 2334.7148, "unit": "J"}, "id": "ke_005689_26.2_13.35", "license": "Apache-2.0", "prompt": "A body of mass 26.2 kg moves at 13.35 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 13.35^2 and multiply by 0.5 * 26.2.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 26.2, "velocity": 13.35}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 3.04 * 8.314 * 606 / 63.1.\nFinal: {\"answer\": 242.7319, \"unit\": \"kPa\"}", "dedupe_signature": "21f168bec90521b84cba166ff7050f55281fa49df7fb3b681580f61edf0486cc", "difficulty": "medium", "final_answer": {"answer": 242.7319, "unit": "kPa"}, "id": "ideal_gas_005691_3.04_606_63.1", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=3.04 mol, T=606 K, and V=63.1 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 3.04 * 8.314 * 606 / 63.1.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 3.04, "temp_k": 606, "volume_l": 63.1}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 395 * 1.32 * 68.\nFinal: {\"answer\": 35455.2, \"unit\": \"J\"}", "dedupe_signature": "7f704dadabf66a7f087b968f91f2e7095c9b8e8a9ae4893a47144a4efb98ea2e", "difficulty": "easy", "final_answer": {"answer": 35455.2, "unit": "J"}, "id": "heat_q_005692_395_1.32_68", "license": "Apache-2.0", "prompt": "A 395 g sample has specific heat 1.32 J/(g*K). How much heat is needed to raise its temperature by 68 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 395 * 1.32 * 68.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 68, "heat_capacity": 1.32, "mass_g": 395}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=32 V and R=79.2 ohm.\nFinal: {\"answer\": 12.9293, \"unit\": \"W\"}", "dedupe_signature": "d4c4db68740065f471197b2848be70983fbe3bfb254620cd70d53323c892eff9", "difficulty": "easy", "final_answer": {"answer": 12.9293, "unit": "W"}, "id": "ohm_power_005693_32_79.2", "license": "Apache-2.0", "prompt": "A resistor has resistance 79.2 ohm and voltage 32 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=32 V and R=79.2 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 79.2, "voltage": 32.0}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=259.5 mg, t=205.5 h, and T_half=44.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 10.5679, \"unit\": \"mg\"}", "dedupe_signature": "3b6413d68bc1e696bb106f958efef06544068b4786332d15949dc51338ef6e21", "difficulty": "medium", "final_answer": {"answer": 10.5679, "unit": "mg"}, "id": "half_life_005694_259.5_44.5_205.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 259.5 mg. Its half-life is 44.5 hours. How many mg remain after 205.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=259.5 mg, t=205.5 h, and T_half=44.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 205.5, "half_life": 44.5, "initial_amount": 259.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 7.96 mol * 180.156 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 1434.0418, \"unit\": \"g\"}", "dedupe_signature": "8e7ec47ba08edcbec65bd35f6d85922b82bba56b02cd9b47733f6c000fa11844", "difficulty": "medium", "final_answer": {"answer": 1434.0418, "unit": "g"}, "id": "stoich_mass_005695_glucose_7.96", "license": "Apache-2.0", "prompt": "A sample contains 7.96 mol of glucose. Using molar mass 180.156 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 7.96 mol * 180.156 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "glucose", "molar_mass": 180.156, "moles": 7.96}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 1040 mL to 1.04 L.\n3. Compute M = 2.58 / 1.04.\nFinal: {\"answer\": 2.4808, \"unit\": \"mol/L\"}", "dedupe_signature": "1617b5c87b0414330061d07b824061bde7e9f4ba53fe477c3ba1951c6fcd6b2b", "difficulty": "medium", "final_answer": {"answer": 2.4808, "unit": "mol/L"}, "id": "molarity_005696_2.58_1040", "license": "Apache-2.0", "prompt": "A solution contains 2.58 mol of solute in 1040 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 1040 mL to 1.04 L.\nCompute M = 2.58 / 1.04.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 2.58, "volume_ml": 1040}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.16 y, so each step multiplies y by 1 - h*0.16.\n3. Apply that update for 5 steps and round the final state.\nFinal: {\"answer\": 35.0403, \"unit\": \"state_units\"}", "dedupe_signature": "a77af7fd4b58541450405e3f093fb3ae21efa55fb4096e025198937cfca4029a", "difficulty": "medium", "final_answer": {"answer": 35.0403, "unit": "state_units"}, "id": "euler_decay_005697_69.5_0.16_0.8_5", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.16 y with y(0)=69.5, step size h=0.8, for 5 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.16 y, so each step multiplies y by 1 - h*0.16.\nApply that update for 5 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 69.5, "rate": 0.16, "step": 0.8, "steps": 5}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(3.4)=-8.62 and f(9.6)=5.02.\n3. The interval width is 6.2.\nFinal: {\"answer\": -11.16, \"unit\": \"area_units\"}", "dedupe_signature": "0c595c017b4936b42cd0e18059e27038c5050fcf70ae58ad073bc165e8aaff1f", "difficulty": "medium", "final_answer": {"answer": -11.16, "unit": "area_units"}, "id": "trapz_linear_005698_2.2_-16.1_3.4_9.6", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=2.2x+-16.1 from x=3.4 to x=9.6. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(3.4)=-8.62 and f(9.6)=5.02.\nThe interval width is 6.2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -16.1, "slope": 2.2, "x0": 3.4, "x1": 9.6}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.04 and add it to the current value.\nFinal: {\"answer\": [-0.624, 2.088, 0.122], \"unit\": \"temperature_units\"}", "dedupe_signature": "e2ecdc9adf9e67c06d99f8d8780461b7c51add42eb2b614426e9cb2e784a37be", "difficulty": "hard", "final_answer": {"answer": [-0.624, 2.088, 0.122], "unit": "temperature_units"}, "id": "heat_step_005699_0.04_-0.65_-0.75_2.3_0.05_-0.4", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-0.65, right=-0.4; current interior values are [-0.75, 2.3, 0.05]. Use r=0.04. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.04 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-0.75, 2.3, 0.05], "left": -0.65, "r": 0.04, "right": -0.4}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=108 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-116.1904, 357.5973], \"unit\": \"N\"}", "dedupe_signature": "800e1ca593eba573ea1cf47c1efc10f440e3d9bfb486fdd5d904a58f1e54fbdc", "difficulty": "medium", "final_answer": {"answer": [-116.1904, 357.5973], "unit": "N"}, "id": "vector_components_005701_376_108", "license": "Apache-2.0", "prompt": "A vector has magnitude 376 N at 108 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=108 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 108, "magnitude": 376.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-5.9, 8.0], \"unit\": \"dimensionless\"}", "dedupe_signature": "e15988c761fb8896236f7a6aad545c2e06f99d786d66bbeae73216b6427d5357", "difficulty": "medium", "final_answer": {"answer": [-5.9, 8.0], "unit": "dimensionless"}, "id": "line_two_point_005702_0_9_-5.9_8", "license": "Apache-2.0", "prompt": "A line passes through points (0, 8) and (9, -45.1). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 0.0, "x2": 9.0, "y1": 8.0, "y2": -45.1}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. volt squared divided by ohm is watt\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "74547487f7c10a0a968e21905d7c0423c3fa9628389c80af5244143d8b251ff8", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_005703_consistent_82e93f3d_242114", "license": "Apache-2.0", "prompt": "In model card equation case 242114, check dimensional consistency for P = V^2 / R. The left side has dimensions W and the right side has dimensions W. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nvolt squared divided by ohm is watt\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "P = V^2 / R"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\nimport math\n\ndef unit_vector_005704(x, y):\n    norm = math.hypot(x, y)\n    if norm == 0:\n        raise ValueError('zero vector has no direction')\n    return (x / norm, y / norm)\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"unit_vector_005704\"}", "dedupe_signature": "69ba3904e6f5c15e93c257fbd77a0a00efb0df4c8ea825b71a6ca667cecaed61", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "unit_vector_005704"}, "id": "code_005704_unit_vector_005704", "license": "Apache-2.0", "prompt": "Write a Python function unit_vector_005704(x, y) that returns the 2D unit vector as a tuple. Raise ValueError for the zero vector. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "unit_vector_005704"}, "verifier": {"function": "unit_vector_005704", "tests": ["ux, uy = unit_vector_005704(3, 4); assert abs(ux - 0.6) < 1e-12 and abs(uy - 0.8) < 1e-12", "assert unit_vector_005704(0, 5) == (0, 1)", "try:\n    unit_vector_005704(0, 0)\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 21.65 kg and a = 1.8 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 38.97, \"unit\": \"N\"}", "dedupe_signature": "cb9a5bd0787049aedbb0aa110874ccc98ecec2a24c20bc15ba98b2a34a1efd57", "difficulty": "easy", "final_answer": {"answer": 38.97, "unit": "N"}, "id": "force_005706_21.65_1.8", "license": "Apache-2.0", "prompt": "A cart has mass 21.65 kg and measured acceleration 1.8 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 21.65 kg and a = 1.8 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 1.8, "mass": 21.65}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 10.65^2 and multiply by 0.5 * 24.1.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 1366.7411, \"unit\": \"J\"}", "dedupe_signature": "e52827c5550ddc793775433040c9fdbdfc569dcfc119c00cff37e0ab95efd6e8", "difficulty": "easy", "final_answer": {"answer": 1366.7411, "unit": "J"}, "id": "ke_005707_24.1_10.65", "license": "Apache-2.0", "prompt": "A body of mass 24.1 kg moves at 10.65 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 10.65^2 and multiply by 0.5 * 24.1.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 24.1, "velocity": 10.65}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=22 degrees through the sine of 2 theta.\n3. Substitute v=63.6 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 286.4287, \"unit\": \"m\"}", "dedupe_signature": "43d2bcf2551c00cb52bf7c13bccd0bc46f3b62af3a1e1c4b857eeb3576717039", "difficulty": "medium", "final_answer": {"answer": 286.4287, "unit": "m"}, "id": "projectile_range_005708_63.6_22", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 63.6 m/s and angle 22 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=22 degrees through the sine of 2 theta.\nSubstitute v=63.6 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 22, "gravity": 9.81, "speed": 63.6}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 2.82 * 8.314 * 267 / 17.4.\nFinal: {\"answer\": 359.7668, \"unit\": \"kPa\"}", "dedupe_signature": "003e3235c45ef238dd572d893ee0d514788ffd1f3511eae3a406ab9249457f26", "difficulty": "medium", "final_answer": {"answer": 359.7668, "unit": "kPa"}, "id": "ideal_gas_005709_2.82_267_17.4", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=2.82 mol, T=267 K, and V=17.4 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 2.82 * 8.314 * 267 / 17.4.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 2.82, "temp_k": 267, "volume_l": 17.4}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 30 * 2.44 * 88.\nFinal: {\"answer\": 6441.6, \"unit\": \"J\"}", "dedupe_signature": "11f6d7a33e2f01263179577e21fe014abb94f74016b9393fab183d4fda700c29", "difficulty": "easy", "final_answer": {"answer": 6441.6, "unit": "J"}, "id": "heat_q_005710_30_2.44_88", "license": "Apache-2.0", "prompt": "A 30 g sample has specific heat 2.44 J/(g*K). How much heat is needed to raise its temperature by 88 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 30 * 2.44 * 88.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 88, "heat_capacity": 2.44, "mass_g": 30}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=48.6 V and R=38.7 ohm.\nFinal: {\"answer\": 61.0326, \"unit\": \"W\"}", "dedupe_signature": "35a1489de8b80ee3488951fa4ee14905045b7a7ad2e7a44bfaabd925071ee7aa", "difficulty": "easy", "final_answer": {"answer": 61.0326, "unit": "W"}, "id": "ohm_power_005711_48.6_38.7", "license": "Apache-2.0", "prompt": "A resistor has resistance 38.7 ohm and voltage 48.6 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=48.6 V and R=38.7 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 38.7, "voltage": 48.6}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=926 mg, t=163.5 h, and T_half=101.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 303.18, \"unit\": \"mg\"}", "dedupe_signature": "bd1db03052b9b1661b0eeb331a3ae24d6f43bb7b3d7f4817f9de651fc9323b3d", "difficulty": "medium", "final_answer": {"answer": 303.18, "unit": "mg"}, "id": "half_life_005712_926_101.5_163.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 926 mg. Its half-life is 101.5 hours. How many mg remain after 163.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=926 mg, t=163.5 h, and T_half=101.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 163.5, "half_life": 101.5, "initial_amount": 926.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.78 y, so each step multiplies y by 1 - h*0.78.\n3. Apply that update for 9 steps and round the final state.\nFinal: {\"answer\": 1.1235, \"unit\": \"state_units\"}", "dedupe_signature": "9b9ada36d41af1d5faf755bd69f62c6e19dcddf8e2ef7cb7e7eb54f6c930d591", "difficulty": "medium", "final_answer": {"answer": 1.1235, "unit": "state_units"}, "id": "euler_decay_005715_55_0.78_0.45_9", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.78 y with y(0)=55, step size h=0.45, for 9 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.78 y, so each step multiplies y by 1 - h*0.78.\nApply that update for 9 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 55.0, "rate": 0.78, "step": 0.45, "steps": 9}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(6.9)=7.76 and f(13.5)=23.6.\n3. The interval width is 6.6.\nFinal: {\"answer\": 103.488, \"unit\": \"area_units\"}", "dedupe_signature": "678794cbe05202cc20ee700c7ac83aa8b1332db4641621b7dc0ec400270d1891", "difficulty": "medium", "final_answer": {"answer": 103.488, "unit": "area_units"}, "id": "trapz_linear_005716_2.4_-8.8_6.9_13.5", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=2.4x+-8.8 from x=6.9 to x=13.5. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(6.9)=7.76 and f(13.5)=23.6.\nThe interval width is 6.6.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -8.8, "slope": 2.4, "x0": 6.9, "x1": 13.5}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.14 and add it to the current value.\nFinal: {\"answer\": [0.431, 2.008, 0.679], \"unit\": \"temperature_units\"}", "dedupe_signature": "b4e2beb3b749467c15a398faa824520f983b60b5487bb60d01c58cc837c68817", "difficulty": "hard", "final_answer": {"answer": [0.431, 2.008, 0.679], "unit": "temperature_units"}, "id": "heat_step_005717_0.14_1.1_-0.15_2.75_0.35_0.3", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.1, right=0.3; current interior values are [-0.15, 2.75, 0.35]. Use r=0.14. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.14 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-0.15, 2.75, 0.35], "left": 1.1, "r": 0.14, "right": 0.3}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 35905.0 / 1000.\nFinal: {\"answer\": 35.905, \"unit\": \"kg\"}", "dedupe_signature": "dacbd92f9c6af233be6f7a0f235bf588e4e6d29a98fcbceab1d45ad28186bd1a", "difficulty": "easy", "final_answer": {"answer": 35.905, "unit": "kg"}, "id": "unit_convert_005718_g_to_kg_35905", "license": "Apache-2.0", "prompt": "Convert 35905 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 35905.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 35905.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=262 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-33.5407, -238.6546], \"unit\": \"N\"}", "dedupe_signature": "f58f8aeea87fcdd2acaec4e0b52d280207b1271d74922c4a48a174aeb05026c3", "difficulty": "medium", "final_answer": {"answer": [-33.5407, -238.6546], "unit": "N"}, "id": "vector_components_005719_241_262", "license": "Apache-2.0", "prompt": "A vector has magnitude 241 N at 262 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=262 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 262, "magnitude": 241.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [7.45, 29.25], \"unit\": \"dimensionless\"}", "dedupe_signature": "eaca9f83806935e18148515127dfa16df2d3a7aa04d8a8ed15cf87a3ca083327", "difficulty": "medium", "final_answer": {"answer": [7.45, 29.25], "unit": "dimensionless"}, "id": "line_two_point_005720_11_25.75_7.45_29.25", "license": "Apache-2.0", "prompt": "A line passes through points (11, 111.2) and (25.75, 221.088). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 11.0, "x2": 25.75, "y1": 111.2, "y2": 221.0875}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. coulomb per second is ampere\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "9f6f84d378906e8a965c76e0e40808fe67e40836dc96d342365ea0cc28c01f40", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_005721_consistent_8b38953d_318056", "license": "Apache-2.0", "prompt": "In sensor calibration case 318056, check dimensional consistency for I = Q / t. The left side has dimensions A and the right side has dimensions A. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\ncoulomb per second is ampere\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "I = Q / t"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef pairwise_ratios_005722(numerators, denominators):\n    if len(numerators) != len(denominators):\n        raise ValueError('length mismatch')\n    out = []\n    for numerator, denominator in zip(numerators, denominators):\n        if denominator == 0:\n            raise ValueError('zero denominator')\n        out.append(numerator / denominator)\n    return out\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"pairwise_ratios_005722\"}", "dedupe_signature": "523a6f61012f679837bb869bd24449bb9c4e08f4106f2b16751015add42a98a3", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "pairwise_ratios_005722"}, "id": "code_005722_pairwise_ratios_005722", "license": "Apache-2.0", "prompt": "Write a Python function pairwise_ratios_005722(numerators, denominators) that returns a list of n/d values. Raise ValueError if lengths differ or any denominator is zero. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "pairwise_ratios_005722"}, "verifier": {"function": "pairwise_ratios_005722", "tests": ["assert pairwise_ratios_005722([2, 9], [4, 3]) == [0.5, 3.0]", "try:\n    pairwise_ratios_005722([1], [0])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass", "try:\n    pairwise_ratios_005722([1, 2], [1])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: target_schema, valid_examples.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"target_schema\", \"valid_examples\"]}", "dedupe_signature": "3a21a4502ef66196e961f9c25e65f77918a2d6f42d25bf2fddd116789e5812b5", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["target_schema", "valid_examples"]}, "id": "abstain_005723_target_schema_valid_examples", "license": "Apache-2.0", "prompt": "Write a parser that converts each registry clinical record from batch 796402 into the correct schema, but the prompt does not include the target schema or examples. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: target_schema, valid_examples.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["target_schema", "valid_examples"]}, "verifier": {"missing": ["target_schema", "valid_examples"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 9.85 kg and a = 1.25 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 12.3125, \"unit\": \"N\"}", "dedupe_signature": "212b60dc36e3adc22cba17ffea7db306e28c282534759adcc65d71c57e92fd17", "difficulty": "easy", "final_answer": {"answer": 12.3125, "unit": "N"}, "id": "force_005724_9.85_1.25", "license": "Apache-2.0", "prompt": "A cart has mass 9.85 kg and measured acceleration 1.25 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 9.85 kg and a = 1.25 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 1.25, "mass": 9.85}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 31.6^2 and multiply by 0.5 * 20.7.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 10335.096, \"unit\": \"J\"}", "dedupe_signature": "e218a7ab6250125c45f06240ae4ae5811db911704266ab29b6f1a0c1c550e114", "difficulty": "easy", "final_answer": {"answer": 10335.096, "unit": "J"}, "id": "ke_005725_20.7_31.6", "license": "Apache-2.0", "prompt": "A body of mass 20.7 kg moves at 31.6 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 31.6^2 and multiply by 0.5 * 20.7.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 20.7, "velocity": 31.6}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=33 degrees through the sine of 2 theta.\n3. Substitute v=11.6 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 12.5308, \"unit\": \"m\"}", "dedupe_signature": "452dbfedf26e81b823d8ae1ddc62af69ece90febf8d0bd2a38c24390403f21cd", "difficulty": "medium", "final_answer": {"answer": 12.5308, "unit": "m"}, "id": "projectile_range_005726_11.6_33", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 11.6 m/s and angle 33 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=33 degrees through the sine of 2 theta.\nSubstitute v=11.6 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 33, "gravity": 9.81, "speed": 11.6}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 2.04 * 8.314 * 553 / 9.1.\nFinal: {\"answer\": 1030.6802, \"unit\": \"kPa\"}", "dedupe_signature": "5a2875ae1d47ac6ea527ac6cbf7ece140b79c5305bc32f7da939b0f0f49350e4", "difficulty": "medium", "final_answer": {"answer": 1030.6802, "unit": "kPa"}, "id": "ideal_gas_005727_2.04_553_9.1", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=2.04 mol, T=553 K, and V=9.1 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 2.04 * 8.314 * 553 / 9.1.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 2.04, "temp_k": 553, "volume_l": 9.1}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1390 * 1.555 * 116.\nFinal: {\"answer\": 250728.2, \"unit\": \"J\"}", "dedupe_signature": "88111075c5adbb72c3cc3bfcecfee3b897809d431250b641c6caf0f383dbf265", "difficulty": "easy", "final_answer": {"answer": 250728.2, "unit": "J"}, "id": "heat_q_005728_1390_1.555_116", "license": "Apache-2.0", "prompt": "A 1390 g sample has specific heat 1.555 J/(g*K). How much heat is needed to raise its temperature by 116 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1390 * 1.555 * 116.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 116, "heat_capacity": 1.555, "mass_g": 1390}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=81 V and R=95 ohm.\nFinal: {\"answer\": 69.0632, \"unit\": \"W\"}", "dedupe_signature": "67b324a4a8435420ea4ce8887b0ce55102d6d2ddaa419d9af9f6cb57b5da31dc", "difficulty": "easy", "final_answer": {"answer": 69.0632, "unit": "W"}, "id": "ohm_power_005729_81_95", "license": "Apache-2.0", "prompt": "A resistor has resistance 95 ohm and voltage 81 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=81 V and R=95 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 95.0, "voltage": 81.0}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 2.49 mol * 100.087 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 249.2166, \"unit\": \"g\"}", "dedupe_signature": "23464735580be122e13f1bcd644728147415b6a5911cdbc020ed4a2f36c91169", "difficulty": "medium", "final_answer": {"answer": 249.2166, "unit": "g"}, "id": "stoich_mass_005731_calcium_carbonate_2.49", "license": "Apache-2.0", "prompt": "A sample contains 2.49 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 2.49 mol * 100.087 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "calcium carbonate", "molar_mass": 100.087, "moles": 2.49}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 3130 mL to 3.13 L.\n3. Compute M = 4.59 / 3.13.\nFinal: {\"answer\": 1.4665, \"unit\": \"mol/L\"}", "dedupe_signature": "561cb3f1cc1e0b0c17ef5cdfd175f7067166046236426e43db901086e44a7562", "difficulty": "medium", "final_answer": {"answer": 1.4665, "unit": "mol/L"}, "id": "molarity_005732_4.59_3130", "license": "Apache-2.0", "prompt": "A solution contains 4.59 mol of solute in 3130 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 3130 mL to 3.13 L.\nCompute M = 4.59 / 3.13.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 4.59, "volume_ml": 3130}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.12 y, so each step multiplies y by 1 - h*0.12.\n3. Apply that update for 11 steps and round the final state.\nFinal: {\"answer\": 17.9141, \"unit\": \"state_units\"}", "dedupe_signature": "40b34330a0b27b69fc75a0b78043c5a43a9ff8eb461ad807d52aa4508f6f3124", "difficulty": "medium", "final_answer": {"answer": 17.9141, "unit": "state_units"}, "id": "euler_decay_005733_58.5_0.12_0.85_11", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.12 y with y(0)=58.5, step size h=0.85, for 11 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.12 y, so each step multiplies y by 1 - h*0.12.\nApply that update for 11 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 58.5, "rate": 0.12, "step": 0.85, "steps": 11}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(9.4)=-20.98 and f(14.9)=-33.08.\n3. The interval width is 5.5.\nFinal: {\"answer\": -148.665, \"unit\": \"area_units\"}", "dedupe_signature": "1fa704a974193507f781eed4b48fc03ac9af96124ceaa9e5be6bb3525381afae", "difficulty": "medium", "final_answer": {"answer": -148.665, "unit": "area_units"}, "id": "trapz_linear_005734_-2.2_-0.3_9.4_14.9", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-2.2x+-0.3 from x=9.4 to x=14.9. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(9.4)=-20.98 and f(14.9)=-33.08.\nThe interval width is 5.5.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -0.3, "slope": -2.2, "x0": 9.4, "x1": 14.9}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 100 centimeters in one meter.\n2. Apply the conversion factor directly to the given value.\n3. Compute 679.5 / 100.\nFinal: {\"answer\": 6.795, \"unit\": \"m\"}", "dedupe_signature": "855e18e6c20a338111fefa2053e269c2d4da0efafea95ae4fac0412dc1190a83", "difficulty": "easy", "final_answer": {"answer": 6.795, "unit": "m"}, "id": "unit_convert_005736_cm_to_m_679.5", "license": "Apache-2.0", "prompt": "Convert 679.5 cm to m. Return the converted value with unit.", "reasoning_trace": "There are 100 centimeters in one meter.\nApply the conversion factor directly to the given value.\nCompute 679.5 / 100.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 679.5}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=126 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-6.4656, 8.8992], \"unit\": \"N\"}", "dedupe_signature": "650e8cad4efca1f96df115f8197d9f596c4846e07b46279d59b72e3118459343", "difficulty": "medium", "final_answer": {"answer": [-6.4656, 8.8992], "unit": "N"}, "id": "vector_components_005737_11_126", "license": "Apache-2.0", "prompt": "A vector has magnitude 11 N at 126 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=126 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 126, "magnitude": 11.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [6.35, -9.75], \"unit\": \"dimensionless\"}", "dedupe_signature": "3eaa6a0c80b0c7b7829840b1edb6e472155e51af421b0b1bcb97ed3bc1d0e953", "difficulty": "medium", "final_answer": {"answer": [6.35, -9.75], "unit": "dimensionless"}, "id": "line_two_point_005738_13.75_21_6.35_-9.75", "license": "Apache-2.0", "prompt": "A line passes through points (13.75, 77.5625) and (21, 123.6). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 13.75, "x2": 21.0, "y1": 77.5625, "y2": 123.6}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. density times acceleration times height gives kg/(m*s^2), or pascal\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "e468791af34620d4147c07f6bfdf41261250b8713ecd33784ffac90bd2345557", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_005739_consistent_b7d3eed1_787427", "license": "Apache-2.0", "prompt": "In sensor calibration case 787427, check dimensional consistency for p = rho * g * h. The left side has dimensions Pa and the right side has dimensions Pa. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\ndensity times acceleration times height gives kg/(m*s^2), or pascal\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "p = rho * g * h"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef weighted_sum_005740(values, weights):\n    if len(values) != len(weights):\n        raise ValueError('length mismatch')\n    return sum(value * weight for value, weight in zip(values, weights))\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"weighted_sum_005740\"}", "dedupe_signature": "a8f577938e0401c2ea100dfacc91c5bf66e6ca3da7153c786ad1eae661eb672e", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "weighted_sum_005740"}, "id": "code_005740_weighted_sum_005740", "license": "Apache-2.0", "prompt": "Write a Python function weighted_sum_005740(values, weights) that returns sum(value*weight). Raise ValueError when the two inputs have different lengths. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "weighted_sum_005740"}, "verifier": {"function": "weighted_sum_005740", "tests": ["assert weighted_sum_005740([2, 3], [4, 5]) == 23", "assert weighted_sum_005740([], []) == 0", "try:\n    weighted_sum_005740([1], [1, 2])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 20.05 kg and a = 13.1 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 262.655, \"unit\": \"N\"}", "dedupe_signature": "a3a8f8b20847b7e14d33463a049fcd2b04d42a204c31fd1db9a0ba17eb35a822", "difficulty": "easy", "final_answer": {"answer": 262.655, "unit": "N"}, "id": "force_005742_20.05_13.1", "license": "Apache-2.0", "prompt": "A cart has mass 20.05 kg and measured acceleration 13.1 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 20.05 kg and a = 13.1 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 13.1, "mass": 20.05}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=29 degrees through the sine of 2 theta.\n3. Substitute v=81.5 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 574.2046, \"unit\": \"m\"}", "dedupe_signature": "857ccc244f12d1595fa7b1ba600365c56f9e78f815d67a1947805bc8862daab9", "difficulty": "medium", "final_answer": {"answer": 574.2046, "unit": "m"}, "id": "projectile_range_005744_81.5_29", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 81.5 m/s and angle 29 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=29 degrees through the sine of 2 theta.\nSubstitute v=81.5 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 29, "gravity": 9.81, "speed": 81.5}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 1.6 * 8.314 * 425 / 96.4.\nFinal: {\"answer\": 58.6465, \"unit\": \"kPa\"}", "dedupe_signature": "63f6f215fad85480c0c06b5f1c4fa3ace2a1aa70fa7b8b224489221aa7145671", "difficulty": "medium", "final_answer": {"answer": 58.6465, "unit": "kPa"}, "id": "ideal_gas_005745_1.6_425_96.4", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=1.6 mol, T=425 K, and V=96.4 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 1.6 * 8.314 * 425 / 96.4.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 1.6, "temp_k": 425, "volume_l": 96.4}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 555 * 1.33 * 66.\nFinal: {\"answer\": 48717.9, \"unit\": \"J\"}", "dedupe_signature": "bac3b2da86a511e59fcc6a0096380b2e490214b9f7cb2bbfb97a118c07f3b17c", "difficulty": "easy", "final_answer": {"answer": 48717.9, "unit": "J"}, "id": "heat_q_005746_555_1.33_66", "license": "Apache-2.0", "prompt": "A 555 g sample has specific heat 1.33 J/(g*K). How much heat is needed to raise its temperature by 66 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 555 * 1.33 * 66.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 66, "heat_capacity": 1.33, "mass_g": 555}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=46 V and R=114.9 ohm.\nFinal: {\"answer\": 18.416, \"unit\": \"W\"}", "dedupe_signature": "01b8a47e8c1ed0b0f24485155b0aa567c6bae2cb2fe58a03cea06048dc872320", "difficulty": "easy", "final_answer": {"answer": 18.416, "unit": "W"}, "id": "ohm_power_005747_46_114.9", "license": "Apache-2.0", "prompt": "A resistor has resistance 114.9 ohm and voltage 46 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=46 V and R=114.9 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 114.9, "voltage": 46.0}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=934 mg, t=115.5 h, and T_half=19 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 13.8166, \"unit\": \"mg\"}", "dedupe_signature": "ed785219aa5016e77507a380ac05c8cba3f760f09c6bf29552b15801bc97a05a", "difficulty": "medium", "final_answer": {"answer": 13.8166, "unit": "mg"}, "id": "half_life_005748_934_19_115.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 934 mg. Its half-life is 19 hours. How many mg remain after 115.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=934 mg, t=115.5 h, and T_half=19 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 115.5, "half_life": 19.0, "initial_amount": 934.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 7.37 mol * 44.01 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 324.3537, \"unit\": \"g\"}", "dedupe_signature": "cfb2a11c0209f2128977e9d2e7a989573626ab4b2df6b30da0c60687120c550d", "difficulty": "medium", "final_answer": {"answer": 324.3537, "unit": "g"}, "id": "stoich_mass_005749_carbon_dioxide_7.37", "license": "Apache-2.0", "prompt": "A sample contains 7.37 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 7.37 mol * 44.01 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "carbon dioxide", "molar_mass": 44.01, "moles": 7.37}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.23 y, so each step multiplies y by 1 - h*0.23.\n3. Apply that update for 12 steps and round the final state.\nFinal: {\"answer\": 22.1638, \"unit\": \"state_units\"}", "dedupe_signature": "23d8a570566f477f19ea8806a067277015b7dcea8e76b49472c088285ce6ef0e", "difficulty": "medium", "final_answer": {"answer": 22.1638, "unit": "state_units"}, "id": "euler_decay_005751_39_0.23_0.2_12", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.23 y with y(0)=39, step size h=0.2, for 12 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.23 y, so each step multiplies y by 1 - h*0.23.\nApply that update for 12 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 39.0, "rate": 0.23, "step": 0.2, "steps": 12}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-8)=75 and f(0.1)=17.49.\n3. The interval width is 8.1.\nFinal: {\"answer\": 374.5845, \"unit\": \"area_units\"}", "dedupe_signature": "c4c0bdf88b5a8dbd0595e55a4ed9be40d945bcc02208a6c903e89ea03cfcf0cf", "difficulty": "medium", "final_answer": {"answer": 374.5845, "unit": "area_units"}, "id": "trapz_linear_005752_-7.1_18.2_-8_0.1", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-7.1x+18.2 from x=-8 to x=0.1. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-8)=75 and f(0.1)=17.49.\nThe interval width is 8.1.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 18.2, "slope": -7.1, "x0": -8.0, "x1": 0.09999999999999964}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=245 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-149.1842, -319.9266], \"unit\": \"N\"}", "dedupe_signature": "41e0b9e62bab94b81a620f41930caec26f65c5e82cb72187bf4e20148fec81ec", "difficulty": "medium", "final_answer": {"answer": [-149.1842, -319.9266], "unit": "N"}, "id": "vector_components_005755_353_245", "license": "Apache-2.0", "prompt": "A vector has magnitude 353 N at 245 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=245 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 245, "magnitude": 353.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-7.8, -7.5], \"unit\": \"dimensionless\"}", "dedupe_signature": "ab93e8ef23d5a86116490d369ad5569ac914402f0342592a73c97d022c5fba58", "difficulty": "medium", "final_answer": {"answer": [-7.8, -7.5], "unit": "dimensionless"}, "id": "line_two_point_005756_-16.5_-6.25_-7.8_-7.5", "license": "Apache-2.0", "prompt": "A line passes through points (-16.5, 121.2) and (-6.25, 41.25). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -16.5, "x2": -6.25, "y1": 121.19999999999999, "y2": 41.25}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. amount times volume is not concentration\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "7c772c7be0610ff33c8454edc8d80b7297138d0bb859582318550c13d03be267", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_005757_inconsistent_74ac0b02_326907", "license": "Apache-2.0", "prompt": "In simulation spec case 326907, check dimensional consistency for C = n * V. The left side has dimensions mol/L and the right side has dimensions mol*L. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\namount times volume is not concentration\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "C = n * V"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef clamp_005758(x, lo, hi):\n    if lo > hi:\n        raise ValueError('lo must be <= hi')\n    return min(max(x, lo), hi)\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"clamp_005758\"}", "dedupe_signature": "56a6523845279a29a5e87584bdfbfb893ba577c234edbf148879b48e1c223caa", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "clamp_005758"}, "id": "code_005758_clamp_005758", "license": "Apache-2.0", "prompt": "Write a Python function clamp_005758(x, lo, hi) that clips x into the inclusive interval [lo, hi]. It must raise ValueError if lo > hi. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "clamp_005758"}, "verifier": {"function": "clamp_005758", "tests": ["assert clamp_005758(5, 0, 10) == 5", "assert clamp_005758(-2, 0, 10) == 0", "assert clamp_005758(12, 0, 10) == 10", "try:\n    clamp_005758(1, 3, 2)\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: left_boundary, right_boundary.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"left_boundary\", \"right_boundary\"]}", "dedupe_signature": "ff9a0fc282757732d25f663c6bc2bf270395fd5e117897bf56e49ecd4697ca31", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["left_boundary", "right_boundary"]}, "id": "abstain_005759_left_boundary_right_boundary", "license": "Apache-2.0", "prompt": "Solve the 1D heat equation after one finite-difference step. The prompt gives r=0.12 and interior values [-0.25, -1.9, 2.85], but gives no boundary values. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: left_boundary, right_boundary.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["left_boundary", "right_boundary"]}, "verifier": {"missing": ["left_boundary", "right_boundary"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 22.2 kg and a = 11.35 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 251.97, \"unit\": \"N\"}", "dedupe_signature": "1cf5e3db244d2dc791ae7abf9c07a04c999f7e937f7d4611af97abc99a0f3158", "difficulty": "easy", "final_answer": {"answer": 251.97, "unit": "N"}, "id": "force_005760_22.2_11.35", "license": "Apache-2.0", "prompt": "A cart has mass 22.2 kg and measured acceleration 11.35 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 22.2 kg and a = 11.35 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 11.35, "mass": 22.2}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=46 degrees through the sine of 2 theta.\n3. Substitute v=10.7 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 11.6636, \"unit\": \"m\"}", "dedupe_signature": "f15ca42ff82d311dfcf255e3209c7d7ac4b2dc7c2f39d4b27297280a78a724c6", "difficulty": "medium", "final_answer": {"answer": 11.6636, "unit": "m"}, "id": "projectile_range_005762_10.7_46", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 10.7 m/s and angle 46 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=46 degrees through the sine of 2 theta.\nSubstitute v=10.7 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 46, "gravity": 9.81, "speed": 10.7}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 3.25 * 8.314 * 568 / 116.3.\nFinal: {\"answer\": 131.966, \"unit\": \"kPa\"}", "dedupe_signature": "5159b1261988c47860e25f1ff41d867391e4d0714e939daaeb4a79d2b1d8a2a0", "difficulty": "medium", "final_answer": {"answer": 131.966, "unit": "kPa"}, "id": "ideal_gas_005763_3.25_568_116.3", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=3.25 mol, T=568 K, and V=116.3 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 3.25 * 8.314 * 568 / 116.3.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 3.25, "temp_k": 568, "volume_l": 116.3}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1500 * 2.8 * 61.\nFinal: {\"answer\": 256200.0, \"unit\": \"J\"}", "dedupe_signature": "0859ae17206e7bc9b687e5f2bd6351652908592cf76f05ceb0a790c405db46a9", "difficulty": "easy", "final_answer": {"answer": 256200.0, "unit": "J"}, "id": "heat_q_005764_1500_2.8_61", "license": "Apache-2.0", "prompt": "A 1500 g sample has specific heat 2.8 J/(g*K). How much heat is needed to raise its temperature by 61 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1500 * 2.8 * 61.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 61, "heat_capacity": 2.8, "mass_g": 1500}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=362 mg, t=120 h, and T_half=5.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 0.0001, \"unit\": \"mg\"}", "dedupe_signature": "48d38c5f3c7d4f7eb604a17ed4cd1920c1b9424ce7b2c9bd5b81b5f12e6f378e", "difficulty": "medium", "final_answer": {"answer": 0.0001, "unit": "mg"}, "id": "half_life_005766_362_5.5_120", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 362 mg. Its half-life is 5.5 hours. How many mg remain after 120 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=362 mg, t=120 h, and T_half=5.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 120.0, "half_life": 5.5, "initial_amount": 362.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 5.77 mol * 100.087 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 577.502, \"unit\": \"g\"}", "dedupe_signature": "46efd61252e2bcc5b225182c810738bcff29e3808db35de0e17ef97d235f6767", "difficulty": "medium", "final_answer": {"answer": 577.502, "unit": "g"}, "id": "stoich_mass_005767_calcium_carbonate_5.77", "license": "Apache-2.0", "prompt": "A sample contains 5.77 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 5.77 mol * 100.087 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "calcium carbonate", "molar_mass": 100.087, "moles": 5.77}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(1.5)=2.85 and f(1.7)=1.43.\n3. The interval width is 0.2.\nFinal: {\"answer\": 0.428, \"unit\": \"area_units\"}", "dedupe_signature": "55fbdcb6c70cbcecc658a4b6e5812b618dfd07ef5e5b9da0fa5be0d38409a179", "difficulty": "medium", "final_answer": {"answer": 0.428, "unit": "area_units"}, "id": "trapz_linear_005770_-7.1_13.5_1.5_1.7", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-7.1x+13.5 from x=1.5 to x=1.7. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(1.5)=2.85 and f(1.7)=1.43.\nThe interval width is 0.2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 13.5, "slope": -7.1, "x0": 1.5, "x1": 1.7}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.26 and add it to the current value.\nFinal: {\"answer\": [1.165, 1.19, 0.783], \"unit\": \"temperature_units\"}", "dedupe_signature": "efd1ee87ab1fd8c87a16e692d52970cfa5815aca4d77d31f019969982494ba3a", "difficulty": "hard", "final_answer": {"answer": [1.165, 1.19, 0.783], "unit": "temperature_units"}, "id": "heat_step_005771_0.26_2.75_-0.2_2.1_0.9_-0.75", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=2.75, right=-0.75; current interior values are [-0.2, 2.1, 0.9]. Use r=0.26. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.26 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-0.2, 2.1, 0.9], "left": 2.75, "r": 0.26, "right": -0.75}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 9837.0 / 1000.\nFinal: {\"answer\": 9.837, \"unit\": \"kg\"}", "dedupe_signature": "24630326d997b92f43aaeec6345783271d44ceafc3608265d03cdfcc786b83ad", "difficulty": "easy", "final_answer": {"answer": 9.837, "unit": "kg"}, "id": "unit_convert_005772_g_to_kg_9837", "license": "Apache-2.0", "prompt": "Convert 9837 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 9837.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 9837.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=309 degrees and keep the unit as newtons.\nFinal: {\"answer\": [142.5411, -176.0236], \"unit\": \"N\"}", "dedupe_signature": "eec1ce1dd8df331f8317fa5612076a7fa22677a1fffcea7918e0ba8add8ec9d8", "difficulty": "medium", "final_answer": {"answer": [142.5411, -176.0236], "unit": "N"}, "id": "vector_components_005773_226.5_309", "license": "Apache-2.0", "prompt": "A vector has magnitude 226.5 N at 309 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=309 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 309, "magnitude": 226.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [2.7, -15.25], \"unit\": \"dimensionless\"}", "dedupe_signature": "714774ae596d26bed8f2c2074ba78c0e64804597dd91838da50ba779e9ca6e78", "difficulty": "medium", "final_answer": {"answer": [2.7, -15.25], "unit": "dimensionless"}, "id": "line_two_point_005774_-6.75_-3.25_2.7_-15.25", "license": "Apache-2.0", "prompt": "A line passes through points (-6.75, -33.475) and (-3.25, -24.025). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -6.75, "x2": -3.25, "y1": -33.475, "y2": -24.025}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. volt squared divided by ohm is watt\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "46a8a4c38870425ccd88871f34ed2dfca3e8cae7144d59c7bf6b2054e8be586b", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_005775_consistent_82e93f3d_514464", "license": "Apache-2.0", "prompt": "In model card equation case 514464, check dimensional consistency for P = V^2 / R. The left side has dimensions W and the right side has dimensions W. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nvolt squared divided by ohm is watt\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "P = V^2 / R"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: left_boundary, right_boundary.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"left_boundary\", \"right_boundary\"]}", "dedupe_signature": "1b1a9c49fcb06ca070fa7cae5df0f444dd36716af8be31bf85c929ee439985a8", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["left_boundary", "right_boundary"]}, "id": "abstain_005777_left_boundary_right_boundary", "license": "Apache-2.0", "prompt": "Solve the 1D heat equation after one finite-difference step. The prompt gives r=0.48 and interior values [-0.1, 1.1, 2.9], but gives no boundary values. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: left_boundary, right_boundary.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["left_boundary", "right_boundary"]}, "verifier": {"missing": ["left_boundary", "right_boundary"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 24.9 kg and a = 11.95 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 297.555, \"unit\": \"N\"}", "dedupe_signature": "59b291ace8447fbdf86c794a6dc3913eb65b6f49b755dd9929d890074c5f4e70", "difficulty": "easy", "final_answer": {"answer": 297.555, "unit": "N"}, "id": "force_005778_24.9_11.95", "license": "Apache-2.0", "prompt": "A cart has mass 24.9 kg and measured acceleration 11.95 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 24.9 kg and a = 11.95 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 11.95, "mass": 24.9}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 1.2^2 and multiply by 0.5 * 22.75.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 16.38, \"unit\": \"J\"}", "dedupe_signature": "0cb82c8599dbee55063f99e03773fc18ca792600ef5c2b443841dba9d7e9b14d", "difficulty": "easy", "final_answer": {"answer": 16.38, "unit": "J"}, "id": "ke_005779_22.75_1.2", "license": "Apache-2.0", "prompt": "A body of mass 22.75 kg moves at 1.2 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 1.2^2 and multiply by 0.5 * 22.75.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 22.75, "velocity": 1.2}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=6 degrees through the sine of 2 theta.\n3. Substitute v=62.8 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 83.5852, \"unit\": \"m\"}", "dedupe_signature": "c8cf924d6415592710ce0b59673276a64a1e302529be9901cd6943b1e608943b", "difficulty": "medium", "final_answer": {"answer": 83.5852, "unit": "m"}, "id": "projectile_range_005780_62.8_6", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 62.8 m/s and angle 6 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=6 degrees through the sine of 2 theta.\nSubstitute v=62.8 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 6, "gravity": 9.81, "speed": 62.8}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1475 * 1.675 * 117.\nFinal: {\"answer\": 289063.125, \"unit\": \"J\"}", "dedupe_signature": "ae330a23b38ba08883edd21f97353e1fae5be39e8291d9d2a6dedf45d1ae69ce", "difficulty": "easy", "final_answer": {"answer": 289063.125, "unit": "J"}, "id": "heat_q_005782_1475_1.675_117", "license": "Apache-2.0", "prompt": "A 1475 g sample has specific heat 1.675 J/(g*K). How much heat is needed to raise its temperature by 117 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1475 * 1.675 * 117.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 117, "heat_capacity": 1.675, "mass_g": 1475}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=1 mg, t=244 h, and T_half=56 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 0.0488, \"unit\": \"mg\"}", "dedupe_signature": "e978b126bf65026f9fad79db16f2a9e35058c0059f15b98c555bb3610c209b4f", "difficulty": "medium", "final_answer": {"answer": 0.0488, "unit": "mg"}, "id": "half_life_005784_1_56_244", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 1 mg. Its half-life is 56 hours. How many mg remain after 244 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=1 mg, t=244 h, and T_half=56 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 244.0, "half_life": 56.0, "initial_amount": 1.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 4.93 mol * 58.44 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 288.1092, \"unit\": \"g\"}", "dedupe_signature": "3ed2359d6b1b2bec2689fa16dbbf5409bc29689c49ef27b5cbdae2e9471176f1", "difficulty": "medium", "final_answer": {"answer": 288.1092, "unit": "g"}, "id": "stoich_mass_005785_sodium_chloride_4.93", "license": "Apache-2.0", "prompt": "A sample contains 4.93 mol of sodium chloride. Using molar mass 58.44 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 4.93 mol * 58.44 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "sodium chloride", "molar_mass": 58.44, "moles": 4.93}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 2620 mL to 2.62 L.\n3. Compute M = 0.6 / 2.62.\nFinal: {\"answer\": 0.229, \"unit\": \"mol/L\"}", "dedupe_signature": "354740a668df4a0270bfd08f67b10586ce51e089e172442e4433380e989117f5", "difficulty": "medium", "final_answer": {"answer": 0.229, "unit": "mol/L"}, "id": "molarity_005786_0.6_2620", "license": "Apache-2.0", "prompt": "A solution contains 0.6 mol of solute in 2620 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 2620 mL to 2.62 L.\nCompute M = 0.6 / 2.62.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 0.6, "volume_ml": 2620}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.93 y, so each step multiplies y by 1 - h*0.93.\n3. Apply that update for 9 steps and round the final state.\nFinal: {\"answer\": -20.5862, \"unit\": \"state_units\"}", "dedupe_signature": "62744a1840df181abfc0db84e935058270e746b4fc1a4fc357c35870216d63c3", "difficulty": "medium", "final_answer": {"answer": -20.5862, "unit": "state_units"}, "id": "euler_decay_005787_80_0.93_2_9", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.93 y with y(0)=80, step size h=2, for 9 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.93 y, so each step multiplies y by 1 - h*0.93.\nApply that update for 9 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 80.0, "rate": 0.93, "step": 2.0, "steps": 9}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.34 and add it to the current value.\nFinal: {\"answer\": [-0.825, -0.114, -0.804], \"unit\": \"temperature_units\"}", "dedupe_signature": "f3ed932643d0e7b2a81cad6d1590424b95a777f14d35bfdc0d10e072ccdd18d1", "difficulty": "hard", "final_answer": {"answer": [-0.825, -0.114, -0.804], "unit": "temperature_units"}, "id": "heat_step_005789_0.34_-1.75_0.45_-1.1_0.25_-1.5", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-1.75, right=-1.5; current interior values are [0.45, -1.1, 0.25]. Use r=0.34. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.34 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [0.45, -1.1, 0.25], "left": -1.75, "r": 0.34, "right": -1.5}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=306 degrees and keep the unit as newtons.\nFinal: {\"answer\": [147.2402, -202.6588], \"unit\": \"N\"}", "dedupe_signature": "64bb1863428ecae95ae5570e84c888a877dcbfaa7b74704ec41cc1d4869b599d", "difficulty": "medium", "final_answer": {"answer": [147.2402, -202.6588], "unit": "N"}, "id": "vector_components_005791_250.5_306", "license": "Apache-2.0", "prompt": "A vector has magnitude 250.5 N at 306 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=306 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 306, "magnitude": 250.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [8.35, 1.0], \"unit\": \"dimensionless\"}", "dedupe_signature": "d53899f8963113003cb0faa235bc1d852b8246054033acf6889f1b3e53c32b19", "difficulty": "medium", "final_answer": {"answer": [8.35, 1.0], "unit": "dimensionless"}, "id": "line_two_point_005792_-8.5_3.75_8.35_1", "license": "Apache-2.0", "prompt": "A line passes through points (-8.5, -69.975) and (3.75, 32.3125). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -8.5, "x2": 3.75, "y1": -69.975, "y2": 32.3125}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. mass times acceleration has newton dimensions\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "682ad641fecde1ffd0f0dbb9b9f29786731c923800901d07c080a0bbf4edc9e1", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_005793_consistent_03f5e041_223814", "license": "Apache-2.0", "prompt": "In instrument manual case 223814, check dimensional consistency for F = m * a. The left side has dimensions kg*m/s^2 and the right side has dimensions kg*m/s^2. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nmass times acceleration has newton dimensions\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "F = m * a"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: recurrence, objective, tie_breaking_rule.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"recurrence\", \"objective\", \"tie_breaking_rule\"]}", "dedupe_signature": "08527e55b8dee841cdfec619e0c98eba71b94efab595c84b91f16f2c4e3ed499", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["recurrence", "objective", "tie_breaking_rule"]}, "id": "abstain_005795_recurrence_objective_tie_breaking_rule", "license": "Apache-2.0", "prompt": "Write a dynamic-programming solver for a alignment scoring problem with 946 items and budget 29985, but the recurrence, objective, and tie-breaking rule are all absent. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: recurrence, objective, tie_breaking_rule.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["recurrence", "objective", "tie_breaking_rule"]}, "verifier": {"missing": ["recurrence", "objective", "tie_breaking_rule"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 16.55 kg and a = 10.35 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 171.2925, \"unit\": \"N\"}", "dedupe_signature": "be41631dd8c18fdd4cd7053a9a463b3f73bf054d5b0c39527ca1109ee67ceeb4", "difficulty": "easy", "final_answer": {"answer": 171.2925, "unit": "N"}, "id": "force_005796_16.55_10.35", "license": "Apache-2.0", "prompt": "A cart has mass 16.55 kg and measured acceleration 10.35 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 16.55 kg and a = 10.35 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 10.35, "mass": 16.55}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 43.7^2 and multiply by 0.5 * 18.45.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 17616.8903, \"unit\": \"J\"}", "dedupe_signature": "778dff20301fe8397a3c38f4121f681d403d1981ecaa686b5dd4af9805ea7b83", "difficulty": "easy", "final_answer": {"answer": 17616.8903, "unit": "J"}, "id": "ke_005797_18.45_43.7", "license": "Apache-2.0", "prompt": "A body of mass 18.45 kg moves at 43.7 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 43.7^2 and multiply by 0.5 * 18.45.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 18.45, "velocity": 43.7}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=65 degrees through the sine of 2 theta.\n3. Substitute v=48.3 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 182.171, \"unit\": \"m\"}", "dedupe_signature": "c487fed40fb463178fcbdd7cbb124a4e6d02a0218ac954ea0dc80bbe7e577bd0", "difficulty": "medium", "final_answer": {"answer": 182.171, "unit": "m"}, "id": "projectile_range_005798_48.3_65", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 48.3 m/s and angle 65 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=65 degrees through the sine of 2 theta.\nSubstitute v=48.3 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 65, "gravity": 9.81, "speed": 48.3}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 0.68 * 8.314 * 322 / 61.3.\nFinal: {\"answer\": 29.6971, \"unit\": \"kPa\"}", "dedupe_signature": "3358b002bdaac847356e37dbd66ca7b8df3a1ad600c87e0b19f16970f30c579c", "difficulty": "medium", "final_answer": {"answer": 29.6971, "unit": "kPa"}, "id": "ideal_gas_005799_0.68_322_61.3", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=0.68 mol, T=322 K, and V=61.3 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 0.68 * 8.314 * 322 / 61.3.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 0.68, "temp_k": 322, "volume_l": 61.3}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=184.1 V and R=144 ohm.\nFinal: {\"answer\": 235.3667, \"unit\": \"W\"}", "dedupe_signature": "52b2b4435e29b7b1d2d39d02a22e483ba858c34e1e9e09fdf1c1edf5e8e726c8", "difficulty": "easy", "final_answer": {"answer": 235.3667, "unit": "W"}, "id": "ohm_power_005801_184.1_144", "license": "Apache-2.0", "prompt": "A resistor has resistance 144 ohm and voltage 184.1 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=184.1 V and R=144 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 144.0, "voltage": 184.1}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=239.5 mg, t=256 h, and T_half=53 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 8.4193, \"unit\": \"mg\"}", "dedupe_signature": "9ac3a63eb28e931f0cf03668cfce7b53d4c24c1927708ac79b93cc8bab79a6c6", "difficulty": "medium", "final_answer": {"answer": 8.4193, "unit": "mg"}, "id": "half_life_005802_239.5_53_256", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 239.5 mg. Its half-life is 53 hours. How many mg remain after 256 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=239.5 mg, t=256 h, and T_half=53 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 256.0, "half_life": 53.0, "initial_amount": 239.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 3.6 mol * 100.087 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 360.3132, \"unit\": \"g\"}", "dedupe_signature": "a85bce3f3c18c6f78bd178a949e74def2ba323abbab7f1938b62454149c9827d", "difficulty": "medium", "final_answer": {"answer": 360.3132, "unit": "g"}, "id": "stoich_mass_005803_calcium_carbonate_3.6", "license": "Apache-2.0", "prompt": "A sample contains 3.6 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 3.6 mol * 100.087 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "calcium carbonate", "molar_mass": 100.087, "moles": 3.6}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 2235 mL to 2.235 L.\n3. Compute M = 4.145 / 2.235.\nFinal: {\"answer\": 1.8546, \"unit\": \"mol/L\"}", "dedupe_signature": "99d4080f7785876e1815f8f5225e732c041e14901fd1769359c3deb6c4e8291e", "difficulty": "medium", "final_answer": {"answer": 1.8546, "unit": "mol/L"}, "id": "molarity_005804_4.145_2235", "license": "Apache-2.0", "prompt": "A solution contains 4.145 mol of solute in 2235 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 2235 mL to 2.235 L.\nCompute M = 4.145 / 2.235.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 4.145, "volume_ml": 2235}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.57 y, so each step multiplies y by 1 - h*0.57.\n3. Apply that update for 9 steps and round the final state.\nFinal: {\"answer\": 1.8965, \"unit\": \"state_units\"}", "dedupe_signature": "44d8b725cc1e5265e4ed465c9f3b6d67ed9d622b7fa37977c5bc0051e831bf5c", "difficulty": "medium", "final_answer": {"answer": 1.8965, "unit": "state_units"}, "id": "euler_decay_005805_56_0.57_0.55_9", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.57 y with y(0)=56, step size h=0.55, for 9 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.57 y, so each step multiplies y by 1 - h*0.57.\nApply that update for 9 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 56.0, "rate": 0.57, "step": 0.55, "steps": 9}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-7.5)=28.3 and f(1.7)=-21.38.\n3. The interval width is 9.2.\nFinal: {\"answer\": 31.832, \"unit\": \"area_units\"}", "dedupe_signature": "311eac49552bde0177d7d6a2bc7131b18eb2898d80ffe083231c14ea3bf643f9", "difficulty": "medium", "final_answer": {"answer": 31.832, "unit": "area_units"}, "id": "trapz_linear_005806_-5.4_-12.2_-7.5_1.7", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-5.4x+-12.2 from x=-7.5 to x=1.7. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-7.5)=28.3 and f(1.7)=-21.38.\nThe interval width is 9.2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -12.2, "slope": -5.4, "x0": -7.5, "x1": 1.6999999999999993}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.36 and add it to the current value.\nFinal: {\"answer\": [0.49, 0.574, -1.008], \"unit\": \"temperature_units\"}", "dedupe_signature": "146460fc0cfbd67485eee492ef791e6f0b0158d364fbabae2aaa25db88387e4d", "difficulty": "hard", "final_answer": {"answer": [0.49, 0.574, -1.008], "unit": "temperature_units"}, "id": "heat_step_005807_0.36_-0.5_2.65_-0.2_-0.9_-1.9", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-0.5, right=-1.9; current interior values are [2.65, -0.2, -0.9]. Use r=0.36. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.36 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [2.65, -0.2, -0.9], "left": -0.5, "r": 0.36, "right": -1.9}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kelvin equals Celsius plus 273.15.\n2. Apply the conversion factor directly to the given value.\n3. Compute 121.5 + 273.15.\nFinal: {\"answer\": 394.65, \"unit\": \"K\"}", "dedupe_signature": "0291152e5b48ba14203529b98772b15ebc3e3f64d9bd565e642c3e2cee9c507f", "difficulty": "easy", "final_answer": {"answer": 394.65, "unit": "K"}, "id": "unit_convert_005808_c_to_k_121.5", "license": "Apache-2.0", "prompt": "Convert 121.5 degC to K. Return the converted value with unit.", "reasoning_trace": "Kelvin equals Celsius plus 273.15.\nApply the conversion factor directly to the given value.\nCompute 121.5 + 273.15.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 121.5}, "verifier": {"formula": "value + 273.15", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=330 degrees and keep the unit as newtons.\nFinal: {\"answer\": [307.872, -177.75], \"unit\": \"N\"}", "dedupe_signature": "4226f4eb54331d095988bb26d72b97f5b2d714c5bc4f97e3c572a882ec822384", "difficulty": "medium", "final_answer": {"answer": [307.872, -177.75], "unit": "N"}, "id": "vector_components_005809_355.5_330", "license": "Apache-2.0", "prompt": "A vector has magnitude 355.5 N at 330 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=330 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 330, "magnitude": 355.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-7.55, 5.25], \"unit\": \"dimensionless\"}", "dedupe_signature": "f31f2e11291fd392ce39283ff3054a168fab0b59ebd7028e1f27b5514710beb7", "difficulty": "medium", "final_answer": {"answer": [-7.55, 5.25], "unit": "dimensionless"}, "id": "line_two_point_005810_12_20_-7.55_5.25", "license": "Apache-2.0", "prompt": "A line passes through points (12, -85.35) and (20, -145.75). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 12.0, "x2": 20.0, "y1": -85.35, "y2": -145.75}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. speed squared over acceleration has units of meters\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "7004a870ed4b376cc5bf0de83968a7d5423b04944c225bbd189de01aaf209867", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_005811_consistent_741d4e34_741237", "license": "Apache-2.0", "prompt": "In field worksheet case 741237, check dimensional consistency for R = v^2 * sin(theta) / g. The left side has dimensions m and the right side has dimensions m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nspeed squared over acceleration has units of meters\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "R = v^2 * sin(theta) / g"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef clamp_005812(x, lo, hi):\n    if lo > hi:\n        raise ValueError('lo must be <= hi')\n    return min(max(x, lo), hi)\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"clamp_005812\"}", "dedupe_signature": "0a942d82f67a75eb1e9f526b27800cc0669661ee33d2c92be1f7d732bcc1f6d5", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "clamp_005812"}, "id": "code_005812_clamp_005812", "license": "Apache-2.0", "prompt": "Write a Python function clamp_005812(x, lo, hi) that clips x into the inclusive interval [lo, hi]. It must raise ValueError if lo > hi. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "clamp_005812"}, "verifier": {"function": "clamp_005812", "tests": ["assert clamp_005812(5, 0, 10) == 5", "assert clamp_005812(-2, 0, 10) == 0", "assert clamp_005812(12, 0, 10) == 10", "try:\n    clamp_005812(1, 3, 2)\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: volume.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"volume\"]}", "dedupe_signature": "a85c7ccedb85f76bb17e17145b1117a8b5fb5128a215cda696de60fe69501c84", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["volume"]}, "id": "abstain_005813_volume", "license": "Apache-2.0", "prompt": "Compute pressure from the ideal gas law. The prompt gives n=1.15 mol and T=603 K, but does not give volume. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: volume.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["volume"]}, "verifier": {"missing": ["volume"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 21.55 kg and a = 3.85 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 82.9675, \"unit\": \"N\"}", "dedupe_signature": "0774497172e10a88348d2e27eb7536822bf8c49ed9989e4a59cc915d7c27569c", "difficulty": "easy", "final_answer": {"answer": 82.9675, "unit": "N"}, "id": "force_005814_21.55_3.85", "license": "Apache-2.0", "prompt": "A cart has mass 21.55 kg and measured acceleration 3.85 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 21.55 kg and a = 3.85 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 3.85, "mass": 21.55}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 16.05^2 and multiply by 0.5 * 20.15.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 2595.3452, \"unit\": \"J\"}", "dedupe_signature": "42185ec52dd18df7623599e0ce3536f4c672182d0e1fb5ee4aea626040ca5f9b", "difficulty": "easy", "final_answer": {"answer": 2595.3452, "unit": "J"}, "id": "ke_005815_20.15_16.05", "license": "Apache-2.0", "prompt": "A body of mass 20.15 kg moves at 16.05 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 16.05^2 and multiply by 0.5 * 20.15.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 20.15, "velocity": 16.05}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1950 * 4.175 * 48.\nFinal: {\"answer\": 390780.0, \"unit\": \"J\"}", "dedupe_signature": "b9dfa4ee345197fb10ec7408b16f753e25b7014a5e4f9ac0974421daf1b86d1d", "difficulty": "easy", "final_answer": {"answer": 390780.0, "unit": "J"}, "id": "heat_q_005818_1950_4.175_48", "license": "Apache-2.0", "prompt": "A 1950 g sample has specific heat 4.175 J/(g*K). How much heat is needed to raise its temperature by 48 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1950 * 4.175 * 48.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 48, "heat_capacity": 4.175, "mass_g": 1950}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=52.4 V and R=149.5 ohm.\nFinal: {\"answer\": 18.3663, \"unit\": \"W\"}", "dedupe_signature": "94f778bc770161593760e3b419501e6cc0caa33ffa7901b887e6cb278f7370e6", "difficulty": "easy", "final_answer": {"answer": 18.3663, "unit": "W"}, "id": "ohm_power_005819_52.4_149.5", "license": "Apache-2.0", "prompt": "A resistor has resistance 149.5 ohm and voltage 52.4 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=52.4 V and R=149.5 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 149.5, "voltage": 52.4}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=711 mg, t=263.5 h, and T_half=41 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 8.2642, \"unit\": \"mg\"}", "dedupe_signature": "8794251ae94b8d378ec6863b49f98fb5202e69cf43c26fb4653f24ca04c0dc8f", "difficulty": "medium", "final_answer": {"answer": 8.2642, "unit": "mg"}, "id": "half_life_005820_711_41_263.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 711 mg. Its half-life is 41 hours. How many mg remain after 263.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=711 mg, t=263.5 h, and T_half=41 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 263.5, "half_life": 41.0, "initial_amount": 711.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 1.39 mol * 180.156 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 250.4168, \"unit\": \"g\"}", "dedupe_signature": "f14b7e8dbcaf7e3de35dda5a41af2e392d9c8aeeb1f29b5e64cbb2273389a730", "difficulty": "medium", "final_answer": {"answer": 250.4168, "unit": "g"}, "id": "stoich_mass_005821_glucose_1.39", "license": "Apache-2.0", "prompt": "A sample contains 1.39 mol of glucose. Using molar mass 180.156 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 1.39 mol * 180.156 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "glucose", "molar_mass": 180.156, "moles": 1.39}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.12 y, so each step multiplies y by 1 - h*0.12.\n3. Apply that update for 12 steps and round the final state.\nFinal: {\"answer\": 4.9921, \"unit\": \"state_units\"}", "dedupe_signature": "2fcfdd82869d74730cc94fc63d96b76fbac762c4d4f786c5779c11ede1e2c097", "difficulty": "medium", "final_answer": {"answer": 4.9921, "unit": "state_units"}, "id": "euler_decay_005823_70.5_0.12_1.65_12", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.12 y with y(0)=70.5, step size h=1.65, for 12 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.12 y, so each step multiplies y by 1 - h*0.12.\nApply that update for 12 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 70.5, "rate": 0.12, "step": 1.65, "steps": 12}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(2.1)=-2.57 and f(4.6)=-19.32.\n3. The interval width is 2.5.\nFinal: {\"answer\": -27.3625, \"unit\": \"area_units\"}", "dedupe_signature": "d8697db7be1a3b0b8ff02e28aa2e1b0f8a9d2af50a5a66a58871488a666da1cb", "difficulty": "medium", "final_answer": {"answer": -27.3625, "unit": "area_units"}, "id": "trapz_linear_005824_-6.7_11.5_2.1_4.6", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-6.7x+11.5 from x=2.1 to x=4.6. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(2.1)=-2.57 and f(4.6)=-19.32.\nThe interval width is 2.5.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 11.5, "slope": -6.7, "x0": 2.1, "x1": 4.6}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.06 and add it to the current value.\nFinal: {\"answer\": [2.13, -0.758, 0.722], \"unit\": \"temperature_units\"}", "dedupe_signature": "40051c0fc822f47d9fbae844dc5b826839f18cb18230a6ed3ba1806315631f4d", "difficulty": "hard", "final_answer": {"answer": [2.13, -0.758, 0.722], "unit": "temperature_units"}, "id": "heat_step_005825_0.06_-0.8_2.55_-1.1_0.95_-0.8", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-0.8, right=-0.8; current interior values are [2.55, -1.1, 0.95]. Use r=0.06. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.06 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [2.55, -1.1, 0.95], "left": -0.8, "r": 0.06, "right": -0.8}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 24445.0 / 1000.\nFinal: {\"answer\": 24.445, \"unit\": \"kg\"}", "dedupe_signature": "1189513de5199f64e9188f065f223a8033efca5723f3156573c80829dbca9945", "difficulty": "easy", "final_answer": {"answer": 24.445, "unit": "kg"}, "id": "unit_convert_005826_g_to_kg_24445", "license": "Apache-2.0", "prompt": "Convert 24445 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 24445.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 24445.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [5.5, 22.5], \"unit\": \"dimensionless\"}", "dedupe_signature": "a6711b4de43cbde4514252b2cd5645117da88d7c1e48e6d6569b864b9a73de8d", "difficulty": "medium", "final_answer": {"answer": [5.5, 22.5], "unit": "dimensionless"}, "id": "line_two_point_005828_18.5_30_5.5_22.5", "license": "Apache-2.0", "prompt": "A line passes through points (18.5, 124.25) and (30, 187.5). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 18.5, "x2": 30.0, "y1": 124.25, "y2": 187.5}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef center_values_005830(values):\n    if not values:\n        raise ValueError('center_values requires at least one value')\n    mean = sum(values) / len(values)\n    return [value - mean for value in values]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"center_values_005830\"}", "dedupe_signature": "881cc605677e4fe86a732ed45c2616e9bf65aba694eec76d4927f7b496db815d", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "center_values_005830"}, "id": "code_005830_center_values_005830", "license": "Apache-2.0", "prompt": "Write a Python function center_values_005830(values) that subtracts the arithmetic mean from each value and returns a new list. Raise ValueError for an empty input. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "center_values_005830"}, "verifier": {"function": "center_values_005830", "tests": ["out = center_values_005830([1, 2, 3]); assert out == [-1, 0, 1]", "assert center_values_005830([5]) == [0]", "try:\n    center_values_005830([])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: recurrence, objective, tie_breaking_rule.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"recurrence\", \"objective\", \"tie_breaking_rule\"]}", "dedupe_signature": "786786f8298a1d0535f29ee0df8dcc777df4cf76a79f515170d4acfa7d30f0b4", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["recurrence", "objective", "tie_breaking_rule"]}, "id": "abstain_005831_recurrence_objective_tie_breaking_rule", "license": "Apache-2.0", "prompt": "Write a dynamic-programming solver for a segmentation scoring problem with 843 items and budget 71610, but the recurrence, objective, and tie-breaking rule are all absent. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: recurrence, objective, tie_breaking_rule.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["recurrence", "objective", "tie_breaking_rule"]}, "verifier": {"missing": ["recurrence", "objective", "tie_breaking_rule"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 20.85 kg and a = 7.4 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 154.29, \"unit\": \"N\"}", "dedupe_signature": "09224ac632b7c5f7b0f6dbe80f63026a2948da00ab751b9284bc54e69e3c6efa", "difficulty": "easy", "final_answer": {"answer": 154.29, "unit": "N"}, "id": "force_005832_20.85_7.4", "license": "Apache-2.0", "prompt": "A cart has mass 20.85 kg and measured acceleration 7.4 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 20.85 kg and a = 7.4 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 7.4, "mass": 20.85}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 20.55^2 and multiply by 0.5 * 26.8.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 5658.8535, \"unit\": \"J\"}", "dedupe_signature": "43d88767afe2fc08e04a1102522201c8198566f7cb846960cebf77fd355545a0", "difficulty": "easy", "final_answer": {"answer": 5658.8535, "unit": "J"}, "id": "ke_005833_26.8_20.55", "license": "Apache-2.0", "prompt": "A body of mass 26.8 kg moves at 20.55 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 20.55^2 and multiply by 0.5 * 26.8.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 26.8, "velocity": 20.55}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=22 degrees through the sine of 2 theta.\n3. Substitute v=15.8 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 17.6773, \"unit\": \"m\"}", "dedupe_signature": "6b5d70edc39e2aa638eea2eb5c3762c0b2190c9ebe217633b60e1c442b5df8c9", "difficulty": "medium", "final_answer": {"answer": 17.6773, "unit": "m"}, "id": "projectile_range_005834_15.8_22", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 15.8 m/s and angle 22 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=22 degrees through the sine of 2 theta.\nSubstitute v=15.8 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 22, "gravity": 9.81, "speed": 15.8}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 0.58 * 8.314 * 464 / 100.9.\nFinal: {\"answer\": 22.1751, \"unit\": \"kPa\"}", "dedupe_signature": "20082bf773aa6ad98d6fa1c370af25c73a71859c5b459fbed19fe8349d179035", "difficulty": "medium", "final_answer": {"answer": 22.1751, "unit": "kPa"}, "id": "ideal_gas_005835_0.58_464_100.9", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=0.58 mol, T=464 K, and V=100.9 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 0.58 * 8.314 * 464 / 100.9.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 0.58, "temp_k": 464, "volume_l": 100.9}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=208.9 V and R=147.4 ohm.\nFinal: {\"answer\": 296.0598, \"unit\": \"W\"}", "dedupe_signature": "c1efbd62ff169eb43d9968822112a287bbe1d9668453e05b5e6bdfae222c6ce5", "difficulty": "easy", "final_answer": {"answer": 296.0598, "unit": "W"}, "id": "ohm_power_005837_208.9_147.4", "license": "Apache-2.0", "prompt": "A resistor has resistance 147.4 ohm and voltage 208.9 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=208.9 V and R=147.4 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 147.4, "voltage": 208.9}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=662 mg, t=72.5 h, and T_half=106 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 412.0641, \"unit\": \"mg\"}", "dedupe_signature": "e623730496073a7d619bfceb74009fbbca956b85d936b0d511e40d10c9fe05bc", "difficulty": "medium", "final_answer": {"answer": 412.0641, "unit": "mg"}, "id": "half_life_005838_662_106_72.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 662 mg. Its half-life is 106 hours. How many mg remain after 72.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=662 mg, t=72.5 h, and T_half=106 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 72.5, "half_life": 106.0, "initial_amount": 662.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 6.55 mol * 180.156 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 1180.0218, \"unit\": \"g\"}", "dedupe_signature": "fd7b38c29fa423ddad2aae8bfe2e4a3d6ef1a9e2e73cc7e3b515bb94799a12df", "difficulty": "medium", "final_answer": {"answer": 1180.0218, "unit": "g"}, "id": "stoich_mass_005839_glucose_6.55", "license": "Apache-2.0", "prompt": "A sample contains 6.55 mol of glucose. Using molar mass 180.156 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 6.55 mol * 180.156 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "glucose", "molar_mass": 180.156, "moles": 6.55}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.83 y, so each step multiplies y by 1 - h*0.83.\n3. Apply that update for 2 steps and round the final state.\nFinal: {\"answer\": 13.191, \"unit\": \"state_units\"}", "dedupe_signature": "fb0836b67da5e5264d7a20cd9c1c9ce6f741fcf5e33439feb43c7be7bfb9b439", "difficulty": "medium", "final_answer": {"answer": 13.191, "unit": "state_units"}, "id": "euler_decay_005841_46_0.83_1.85_2", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.83 y with y(0)=46, step size h=1.85, for 2 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.83 y, so each step multiplies y by 1 - h*0.83.\nApply that update for 2 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 46.0, "rate": 0.83, "step": 1.85, "steps": 2}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-3.4)=8.18 and f(-3.1)=8.72.\n3. The interval width is 0.3.\nFinal: {\"answer\": 2.535, \"unit\": \"area_units\"}", "dedupe_signature": "ba82060141d09561e95d4e3ae9c889f3f4b8659351db89e352c9762ccc1d3b0a", "difficulty": "medium", "final_answer": {"answer": 2.535, "unit": "area_units"}, "id": "trapz_linear_005842_1.8_14.3_-3.4_-3.1", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=1.8x+14.3 from x=-3.4 to x=-3.1. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-3.4)=8.18 and f(-3.1)=8.72.\nThe interval width is 0.3.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 14.3, "slope": 1.8, "x0": -3.4, "x1": -3.1}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 24657.0 / 1000.\nFinal: {\"answer\": 24.657, \"unit\": \"kg\"}", "dedupe_signature": "45106c9cc0b450ca68601b274d88eff8b519808966dc4896254f36067a5b8d13", "difficulty": "easy", "final_answer": {"answer": 24.657, "unit": "kg"}, "id": "unit_convert_005844_g_to_kg_24657", "license": "Apache-2.0", "prompt": "Convert 24657 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 24657.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 24657.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=169 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-260.1312, 50.5644], \"unit\": \"N\"}", "dedupe_signature": "86e94d0c389f526e51b406de94e818a7788a3f747ad4c9418c20f92e37ccf226", "difficulty": "medium", "final_answer": {"answer": [-260.1312, 50.5644], "unit": "N"}, "id": "vector_components_005845_265_169", "license": "Apache-2.0", "prompt": "A vector has magnitude 265 N at 169 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=169 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 169, "magnitude": 265.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-7.45, 28.25], \"unit\": \"dimensionless\"}", "dedupe_signature": "8a1a9c6135e4f576854dc183f04217a896389a1ff5fa6b0797134a57d3ab20a9", "difficulty": "medium", "final_answer": {"answer": [-7.45, 28.25], "unit": "dimensionless"}, "id": "line_two_point_005846_2_14.75_-7.45_28.25", "license": "Apache-2.0", "prompt": "A line passes through points (2, 13.35) and (14.75, -81.6375). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 2.0, "x2": 14.75, "y1": 13.35, "y2": -81.6375}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. velocity divided by time is acceleration\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "6738c1b8c261b10418ca024066fed9733e3cf0762be1dd8e323367d1709b5225", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_005847_inconsistent_c1271127_747565", "license": "Apache-2.0", "prompt": "In model card equation case 747565, check dimensional consistency for x = v / t. The left side has dimensions m and the right side has dimensions m/s^2. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nvelocity divided by time is acceleration\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "x = v / t"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\nimport math\n\ndef unit_vector_005848(x, y):\n    norm = math.hypot(x, y)\n    if norm == 0:\n        raise ValueError('zero vector has no direction')\n    return (x / norm, y / norm)\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"unit_vector_005848\"}", "dedupe_signature": "e3dc9c60ce5ecf098bb72389dbc42d80038f6ce8df4d68a0216a70c2a16ebeda", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "unit_vector_005848"}, "id": "code_005848_unit_vector_005848", "license": "Apache-2.0", "prompt": "Write a Python function unit_vector_005848(x, y) that returns the 2D unit vector as a tuple. Raise ValueError for the zero vector. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "unit_vector_005848"}, "verifier": {"function": "unit_vector_005848", "tests": ["ux, uy = unit_vector_005848(3, 4); assert abs(ux - 0.6) < 1e-12 and abs(uy - 0.8) < 1e-12", "assert unit_vector_005848(0, 5) == (0, 1)", "try:\n    unit_vector_005848(0, 0)\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 4.75 kg and a = 11.75 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 55.8125, \"unit\": \"N\"}", "dedupe_signature": "31459033686974d0e2540b73d822f371643231ce6844cf59a9b77edbd253d5dd", "difficulty": "easy", "final_answer": {"answer": 55.8125, "unit": "N"}, "id": "force_005850_4.75_11.75", "license": "Apache-2.0", "prompt": "A cart has mass 4.75 kg and measured acceleration 11.75 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 4.75 kg and a = 11.75 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 11.75, "mass": 4.75}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 6.6^2 and multiply by 0.5 * 25.7.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 559.746, \"unit\": \"J\"}", "dedupe_signature": "fdac2caacfc40cc9f4c675e11e6306b6e52e453165fedb698973e56ec9a74572", "difficulty": "easy", "final_answer": {"answer": 559.746, "unit": "J"}, "id": "ke_005851_25.7_6.6", "license": "Apache-2.0", "prompt": "A body of mass 25.7 kg moves at 6.6 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 6.6^2 and multiply by 0.5 * 25.7.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 25.7, "velocity": 6.6}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=27 degrees through the sine of 2 theta.\n3. Substitute v=60.1 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 297.8774, \"unit\": \"m\"}", "dedupe_signature": "d252590ef645d85a81c83b7ae44fef12275c09f5b441be39177a9b482ce881ee", "difficulty": "medium", "final_answer": {"answer": 297.8774, "unit": "m"}, "id": "projectile_range_005852_60.1_27", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 60.1 m/s and angle 27 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=27 degrees through the sine of 2 theta.\nSubstitute v=60.1 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 27, "gravity": 9.81, "speed": 60.1}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 4.37 * 8.314 * 253 / 48.4.\nFinal: {\"answer\": 189.9182, \"unit\": \"kPa\"}", "dedupe_signature": "10d4a04c2a975c0aa9457a809d1c03fa7df2e8c8ecb9574ef228d6db6f8c4d9d", "difficulty": "medium", "final_answer": {"answer": 189.9182, "unit": "kPa"}, "id": "ideal_gas_005853_4.37_253_48.4", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=4.37 mol, T=253 K, and V=48.4 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 4.37 * 8.314 * 253 / 48.4.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 4.37, "temp_k": 253, "volume_l": 48.4}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1940 * 4.16 * 84.\nFinal: {\"answer\": 677913.6, \"unit\": \"J\"}", "dedupe_signature": "4d4fb043dc0bf1a861d02861d6d54644dc218ddb3c5b3695cd53c4a4ba649bf1", "difficulty": "easy", "final_answer": {"answer": 677913.6, "unit": "J"}, "id": "heat_q_005854_1940_4.16_84", "license": "Apache-2.0", "prompt": "A 1940 g sample has specific heat 4.16 J/(g*K). How much heat is needed to raise its temperature by 84 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1940 * 4.16 * 84.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 84, "heat_capacity": 4.16, "mass_g": 1940}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=40.4 V and R=195.3 ohm.\nFinal: {\"answer\": 8.3572, \"unit\": \"W\"}", "dedupe_signature": "28e482b166fc69676ad80a8ccf245261972762d124be86fa101eda422a096391", "difficulty": "easy", "final_answer": {"answer": 8.3572, "unit": "W"}, "id": "ohm_power_005855_40.4_195.3", "license": "Apache-2.0", "prompt": "A resistor has resistance 195.3 ohm and voltage 40.4 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=40.4 V and R=195.3 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 195.3, "voltage": 40.4}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=608.5 mg, t=233.5 h, and T_half=105.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 131.22, \"unit\": \"mg\"}", "dedupe_signature": "98b57f0b0d159617d2a3dcc59ebe71ba7852b1de3a920bdd16d4b3435596d37c", "difficulty": "medium", "final_answer": {"answer": 131.22, "unit": "mg"}, "id": "half_life_005856_608.5_105.5_233.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 608.5 mg. Its half-life is 105.5 hours. How many mg remain after 233.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=608.5 mg, t=233.5 h, and T_half=105.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 233.5, "half_life": 105.5, "initial_amount": 608.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 3.97 mol * 100.087 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 397.3454, \"unit\": \"g\"}", "dedupe_signature": "bdbdeb37290a5f98e85e3ac50f989e63a35cd40e3e2d13a0333115eaea440e42", "difficulty": "medium", "final_answer": {"answer": 397.3454, "unit": "g"}, "id": "stoich_mass_005857_calcium_carbonate_3.97", "license": "Apache-2.0", "prompt": "A sample contains 3.97 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 3.97 mol * 100.087 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "calcium carbonate", "molar_mass": 100.087, "moles": 3.97}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 830 mL to 0.83 L.\n3. Compute M = 4.405 / 0.83.\nFinal: {\"answer\": 5.3072, \"unit\": \"mol/L\"}", "dedupe_signature": "08dd931201810a29e3663cfb0d27b5bef7bc9862cc1dd6ae9295ce45eb228ca9", "difficulty": "medium", "final_answer": {"answer": 5.3072, "unit": "mol/L"}, "id": "molarity_005858_4.405_830", "license": "Apache-2.0", "prompt": "A solution contains 4.405 mol of solute in 830 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 830 mL to 0.83 L.\nCompute M = 4.405 / 0.83.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 4.405, "volume_ml": 830}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.58 y, so each step multiplies y by 1 - h*0.58.\n3. Apply that update for 4 steps and round the final state.\nFinal: {\"answer\": 0.0006, \"unit\": \"state_units\"}", "dedupe_signature": "7a4e288ff53d2ec6381218a34afc7e32d5f237906dbab99c70c95e27ac0e6520", "difficulty": "medium", "final_answer": {"answer": 0.0006, "unit": "state_units"}, "id": "euler_decay_005859_23.5_0.58_1.6_4", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.58 y with y(0)=23.5, step size h=1.6, for 4 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.58 y, so each step multiplies y by 1 - h*0.58.\nApply that update for 4 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 23.5, "rate": 0.58, "step": 1.6, "steps": 4}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-5.3)=0.09 and f(-2.7)=9.71.\n3. The interval width is 2.6.\nFinal: {\"answer\": 12.74, \"unit\": \"area_units\"}", "dedupe_signature": "5537ac9aeb56aa909644d38ddf8d3ccdd7d4baa965490460ae2b0f9a9ba34ae4", "difficulty": "medium", "final_answer": {"answer": 12.74, "unit": "area_units"}, "id": "trapz_linear_005860_3.7_19.7_-5.3_-2.7", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=3.7x+19.7 from x=-5.3 to x=-2.7. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-5.3)=0.09 and f(-2.7)=9.71.\nThe interval width is 2.6.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 19.7, "slope": 3.7, "x0": -5.3, "x1": -2.6999999999999997}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.46 and add it to the current value.\nFinal: {\"answer\": [2.266, -0.158, 0.024], \"unit\": \"temperature_units\"}", "dedupe_signature": "f8d3d2c786143fe40b60d999ee7b6864697cf68da69c37bbecdf22288e10e531", "difficulty": "hard", "final_answer": {"answer": [2.266, -0.158, 0.024], "unit": "temperature_units"}, "id": "heat_step_005861_0.46_2.85_0.15_2.05_-0.85_-1.85", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=2.85, right=-1.85; current interior values are [0.15, 2.05, -0.85]. Use r=0.46. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.46 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [0.15, 2.05, -0.85], "left": 2.85, "r": 0.46, "right": -1.85}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=178 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-115.9293, 4.0483], \"unit\": \"N\"}", "dedupe_signature": "b3c954e835645aa21a8317de04e49a191acb56866ff7494a55fb6ad0fff665e2", "difficulty": "medium", "final_answer": {"answer": [-115.9293, 4.0483], "unit": "N"}, "id": "vector_components_005863_116_178", "license": "Apache-2.0", "prompt": "A vector has magnitude 116 N at 178 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=178 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 178, "magnitude": 116.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [2.65, -27.0], \"unit\": \"dimensionless\"}", "dedupe_signature": "ade11e0b0078d47c48cb7da895cbc7557d95afca153fe30e7e63c80f5fe42ec9", "difficulty": "medium", "final_answer": {"answer": [2.65, -27.0], "unit": "dimensionless"}, "id": "line_two_point_005864_-18.5_-14.25_2.65_-27", "license": "Apache-2.0", "prompt": "A line passes through points (-18.5, -76.025) and (-14.25, -64.7625). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -18.5, "x2": -14.25, "y1": -76.025, "y2": -64.76249999999999}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef threshold_flags_005866(values, threshold):\n    return [value >= threshold for value in values]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"threshold_flags_005866\"}", "dedupe_signature": "15e4980122566e1990bfe7aa0e0ac046a24df7c277993746fc9794cc55b05df1", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "threshold_flags_005866"}, "id": "code_005866_threshold_flags_005866", "license": "Apache-2.0", "prompt": "Write a Python function threshold_flags_005866(values, threshold) that returns a list of booleans showing whether each value is greater than or equal to threshold. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "threshold_flags_005866"}, "verifier": {"function": "threshold_flags_005866", "tests": ["assert threshold_flags_005866([1, 2, 3], 2) == [False, True, True]", "assert threshold_flags_005866([], 5) == []", "assert threshold_flags_005866([-1, 0], 0) == [False, True]"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 21.65 kg and a = 1.95 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 42.2175, \"unit\": \"N\"}", "dedupe_signature": "f89a025c6b40a44336cd39122f34b7a4f47e438d902d3f76e8ce12a7e7a3c4b3", "difficulty": "easy", "final_answer": {"answer": 42.2175, "unit": "N"}, "id": "force_005868_21.65_1.95", "license": "Apache-2.0", "prompt": "A cart has mass 21.65 kg and measured acceleration 1.95 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 21.65 kg and a = 1.95 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 1.95, "mass": 21.65}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 31.25^2 and multiply by 0.5 * 14.5.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 7080.0781, \"unit\": \"J\"}", "dedupe_signature": "36d41430b34c4dd3b98dcb6db5d4c6b6f6fbe936e1d8ab32a20831439cf600dd", "difficulty": "easy", "final_answer": {"answer": 7080.0781, "unit": "J"}, "id": "ke_005869_14.5_31.25", "license": "Apache-2.0", "prompt": "A body of mass 14.5 kg moves at 31.25 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 31.25^2 and multiply by 0.5 * 14.5.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 14.5, "velocity": 31.25}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=47 degrees through the sine of 2 theta.\n3. Substitute v=22.1 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 49.6657, \"unit\": \"m\"}", "dedupe_signature": "1041e450bdbc86fdb138d91b2a560234d47b744a667a6443394a105ce273d74c", "difficulty": "medium", "final_answer": {"answer": 49.6657, "unit": "m"}, "id": "projectile_range_005870_22.1_47", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 22.1 m/s and angle 47 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=47 degrees through the sine of 2 theta.\nSubstitute v=22.1 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 47, "gravity": 9.81, "speed": 22.1}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 3.1 * 8.314 * 240 / 7.0.\nFinal: {\"answer\": 883.6594, \"unit\": \"kPa\"}", "dedupe_signature": "4ca7ad0200fca03b12143ac2c2306a244c47144b4ed5507206651ec06fb81bb0", "difficulty": "medium", "final_answer": {"answer": 883.6594, "unit": "kPa"}, "id": "ideal_gas_005871_3.1_240_7.0", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=3.1 mol, T=240 K, and V=7.0 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 3.1 * 8.314 * 240 / 7.0.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 3.1, "temp_k": 240, "volume_l": 7.0}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1315 * 4.64 * 108.\nFinal: {\"answer\": 658972.8, \"unit\": \"J\"}", "dedupe_signature": "78e591ba1294a390bbcd48f4e2bad9b5ffeeeb87c2becc89bdf8970d5885b3a2", "difficulty": "easy", "final_answer": {"answer": 658972.8, "unit": "J"}, "id": "heat_q_005872_1315_4.64_108", "license": "Apache-2.0", "prompt": "A 1315 g sample has specific heat 4.64 J/(g*K). How much heat is needed to raise its temperature by 108 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1315 * 4.64 * 108.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 108, "heat_capacity": 4.64, "mass_g": 1315}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=172.1 V and R=126 ohm.\nFinal: {\"answer\": 235.0667, \"unit\": \"W\"}", "dedupe_signature": "c5d5e828c4e6652b67aa15fb0549da421812e77906ba29430653fce47dfe31a5", "difficulty": "easy", "final_answer": {"answer": 235.0667, "unit": "W"}, "id": "ohm_power_005873_172.1_126", "license": "Apache-2.0", "prompt": "A resistor has resistance 126 ohm and voltage 172.1 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=172.1 V and R=126 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 126.0, "voltage": 172.1}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=19 mg, t=52 h, and T_half=52.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 9.5629, \"unit\": \"mg\"}", "dedupe_signature": "de27e77072893df5ba35f9e17b5264b013430e9511530fa328725ec54fdc8d54", "difficulty": "medium", "final_answer": {"answer": 9.5629, "unit": "mg"}, "id": "half_life_005874_19_52.5_52", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 19 mg. Its half-life is 52.5 hours. How many mg remain after 52 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=19 mg, t=52 h, and T_half=52.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 52.0, "half_life": 52.5, "initial_amount": 19.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 4.8 mol * 100.087 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 480.4176, \"unit\": \"g\"}", "dedupe_signature": "a56ed36d060f5230db168fc7804da17f252da0a682f37bda181d2981edb3d355", "difficulty": "medium", "final_answer": {"answer": 480.4176, "unit": "g"}, "id": "stoich_mass_005875_calcium_carbonate_4.8", "license": "Apache-2.0", "prompt": "A sample contains 4.8 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 4.8 mol * 100.087 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "calcium carbonate", "molar_mass": 100.087, "moles": 4.8}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 4680 mL to 4.68 L.\n3. Compute M = 1.575 / 4.68.\nFinal: {\"answer\": 0.3365, \"unit\": \"mol/L\"}", "dedupe_signature": "a8244d3104febec1ef3b4f730814a82fb14bfbf3b37035a72e615367cb639a13", "difficulty": "medium", "final_answer": {"answer": 0.3365, "unit": "mol/L"}, "id": "molarity_005876_1.575_4680", "license": "Apache-2.0", "prompt": "A solution contains 1.575 mol of solute in 4680 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 4680 mL to 4.68 L.\nCompute M = 1.575 / 4.68.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 1.575, "volume_ml": 4680}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.95 y, so each step multiplies y by 1 - h*0.95.\n3. Apply that update for 5 steps and round the final state.\nFinal: {\"answer\": 0.1519, \"unit\": \"state_units\"}", "dedupe_signature": "419dabd7e0bfe8471e90002de9c7d8cc9ac9ecbb91dc403413ddbe3b05912017", "difficulty": "medium", "final_answer": {"answer": 0.1519, "unit": "state_units"}, "id": "euler_decay_005877_36_0.95_0.7_5", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.95 y with y(0)=36, step size h=0.7, for 5 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.95 y, so each step multiplies y by 1 - h*0.95.\nApply that update for 5 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 36.0, "rate": 0.95, "step": 0.7, "steps": 5}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-9.2)=60.02 and f(-0.1)=4.51.\n3. The interval width is 9.1.\nFinal: {\"answer\": 293.6115, \"unit\": \"area_units\"}", "dedupe_signature": "3244564d06d78735b7af9d449ff8f4585181d3485a2dcbf73fd3af1c746e9584", "difficulty": "medium", "final_answer": {"answer": 293.6115, "unit": "area_units"}, "id": "trapz_linear_005878_-6.1_3.9_-9.2_-0.1", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-6.1x+3.9 from x=-9.2 to x=-0.1. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-9.2)=60.02 and f(-0.1)=4.51.\nThe interval width is 9.1.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 3.9, "slope": -6.1, "x0": -9.2, "x1": -0.09999999999999964}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.02 and add it to the current value.\nFinal: {\"answer\": [1.273, 0.015, 1.754], \"unit\": \"temperature_units\"}", "dedupe_signature": "bd07ae18b723172a0f5b84fbc03297af3c6b56f32cd6917aaf43e0058c16f27d", "difficulty": "hard", "final_answer": {"answer": [1.273, 0.015, 1.754], "unit": "temperature_units"}, "id": "heat_step_005879_0.02_-1.1_1.35_-0.05_1.8_1.35", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-1.1, right=1.35; current interior values are [1.35, -0.05, 1.8]. Use r=0.02. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.02 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [1.35, -0.05, 1.8], "left": -1.1, "r": 0.02, "right": 1.35}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 21985.0 / 1000.\nFinal: {\"answer\": 21.985, \"unit\": \"kg\"}", "dedupe_signature": "8e9e611cc9f88ed38c256f15b0f19217b1c1e43abe58105bac888acec8d0839f", "difficulty": "easy", "final_answer": {"answer": 21.985, "unit": "kg"}, "id": "unit_convert_005880_g_to_kg_21985", "license": "Apache-2.0", "prompt": "Convert 21985 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 21985.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 21985.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=43 degrees and keep the unit as newtons.\nFinal: {\"answer\": [42.0528, 39.2149], \"unit\": \"N\"}", "dedupe_signature": "9c89d97be22c38d96539b2136027d692b2b500572d8b49a334ea75f9b2763337", "difficulty": "medium", "final_answer": {"answer": [42.0528, 39.2149], "unit": "N"}, "id": "vector_components_005881_57.5_43", "license": "Apache-2.0", "prompt": "A vector has magnitude 57.5 N at 43 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=43 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 43, "magnitude": 57.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-1.9, -1.0], \"unit\": \"dimensionless\"}", "dedupe_signature": "03f54b399c622890bf646c00d8d36041baad33af2a3e8d8e18cd608f4a5c49ec", "difficulty": "medium", "final_answer": {"answer": [-1.9, -1.0], "unit": "dimensionless"}, "id": "line_two_point_005882_10.75_11.5_-1.9_-1", "license": "Apache-2.0", "prompt": "A line passes through points (10.75, -21.425) and (11.5, -22.85). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 10.75, "x2": 11.5, "y1": -21.425, "y2": -22.849999999999998}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. volt squared divided by ohm is watt\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "66627de6958a2111ebbd6a514a64819ef87f106bf2af65cbcadf3fdbdc8a1d09", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_005883_consistent_82e93f3d_813207", "license": "Apache-2.0", "prompt": "In simulation spec case 813207, check dimensional consistency for P = V^2 / R. The left side has dimensions W and the right side has dimensions W. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nvolt squared divided by ohm is watt\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "P = V^2 / R"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef running_total_005884(values):\n    total = 0\n    out = []\n    for value in values:\n        total += value\n        out.append(total)\n    return out\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"running_total_005884\"}", "dedupe_signature": "74ac1151e7344dbd5cd688d7a42246f2bb5e005d4df3a36ebbacc95cbc0341af", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "running_total_005884"}, "id": "code_005884_running_total_005884", "license": "Apache-2.0", "prompt": "Write a Python function running_total_005884(values) that returns cumulative sums as a new list. It must not mutate the input list. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "running_total_005884"}, "verifier": {"function": "running_total_005884", "tests": ["assert running_total_005884([1, 2, 3]) == [1, 3, 6]", "xs = [4, -1, 2]; assert running_total_005884(xs) == [4, 3, 5] and xs == [4, -1, 2]", "assert running_total_005884([]) == []"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: target_schema, valid_examples.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"target_schema\", \"valid_examples\"]}", "dedupe_signature": "bc3d7ced177806fc2042be526d312e5b53e2e3aa310ae87711e42e0b02e3a9ba", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["target_schema", "valid_examples"]}, "id": "abstain_005885_target_schema_valid_examples", "license": "Apache-2.0", "prompt": "Write a parser that converts each warehouse survey record from batch 200223 into the correct schema, but the prompt does not include the target schema or examples. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: target_schema, valid_examples.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["target_schema", "valid_examples"]}, "verifier": {"missing": ["target_schema", "valid_examples"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 3.75 kg and a = 6.5 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 24.375, \"unit\": \"N\"}", "dedupe_signature": "b5ae18bc24272badc30ab3fdf4c6e038701030389dd20a17e906a9f19c21bf7b", "difficulty": "easy", "final_answer": {"answer": 24.375, "unit": "N"}, "id": "force_005886_3.75_6.5", "license": "Apache-2.0", "prompt": "A cart has mass 3.75 kg and measured acceleration 6.5 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 3.75 kg and a = 6.5 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 6.5, "mass": 3.75}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=12.3 V and R=189.5 ohm.\nFinal: {\"answer\": 0.7984, \"unit\": \"W\"}", "dedupe_signature": "32df912016261949152be54896bdf8abc26739988d7c0d00398a203c130b7d9a", "difficulty": "easy", "final_answer": {"answer": 0.7984, "unit": "W"}, "id": "ohm_power_005891_12.3_189.5", "license": "Apache-2.0", "prompt": "A resistor has resistance 189.5 ohm and voltage 12.3 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=12.3 V and R=189.5 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 189.5, "voltage": 12.3}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=790.5 mg, t=342.5 h, and T_half=65.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 21.0772, \"unit\": \"mg\"}", "dedupe_signature": "29f4cc2a687276706954468546b381a547aa96a538c8bb655d39a893af13c8a4", "difficulty": "medium", "final_answer": {"answer": 21.0772, "unit": "mg"}, "id": "half_life_005892_790.5_65.5_342.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 790.5 mg. Its half-life is 65.5 hours. How many mg remain after 342.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=790.5 mg, t=342.5 h, and T_half=65.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 342.5, "half_life": 65.5, "initial_amount": 790.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 2.08 mol * 180.156 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 374.7245, \"unit\": \"g\"}", "dedupe_signature": "d0e09d05820e3866b9c45506a4c0b5a73a8eb217ec0911da69fcb93963dfafb0", "difficulty": "medium", "final_answer": {"answer": 374.7245, "unit": "g"}, "id": "stoich_mass_005893_glucose_2.08", "license": "Apache-2.0", "prompt": "A sample contains 2.08 mol of glucose. Using molar mass 180.156 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 2.08 mol * 180.156 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "glucose", "molar_mass": 180.156, "moles": 2.08}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 3170 mL to 3.17 L.\n3. Compute M = 0.91 / 3.17.\nFinal: {\"answer\": 0.2871, \"unit\": \"mol/L\"}", "dedupe_signature": "9813b4cc92ffae739378b60301e1ee833478d2b9e3e530f65da087f9e0591319", "difficulty": "medium", "final_answer": {"answer": 0.2871, "unit": "mol/L"}, "id": "molarity_005894_0.91_3170", "license": "Apache-2.0", "prompt": "A solution contains 0.91 mol of solute in 3170 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 3170 mL to 3.17 L.\nCompute M = 0.91 / 3.17.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 0.91, "volume_ml": 3170}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.42 y, so each step multiplies y by 1 - h*0.42.\n3. Apply that update for 5 steps and round the final state.\nFinal: {\"answer\": 3.2148, \"unit\": \"state_units\"}", "dedupe_signature": "629d51da308d7fe119a6df3eb7642bad29bedab0b4a44efe5a6e55c2ff5b6f7e", "difficulty": "medium", "final_answer": {"answer": 3.2148, "unit": "state_units"}, "id": "euler_decay_005895_41_0.42_0.95_5", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.42 y with y(0)=41, step size h=0.95, for 5 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.42 y, so each step multiplies y by 1 - h*0.42.\nApply that update for 5 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 41.0, "rate": 0.42, "step": 0.95, "steps": 5}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(2.4)=-20.2 and f(11.5)=-70.25.\n3. The interval width is 9.1.\nFinal: {\"answer\": -411.5475, \"unit\": \"area_units\"}", "dedupe_signature": "3062554b92c8c7687873090837c8f3ff0432fa83ebd23bc8fd29cfd6d78fc4d9", "difficulty": "medium", "final_answer": {"answer": -411.5475, "unit": "area_units"}, "id": "trapz_linear_005896_-5.5_-7_2.4_11.5", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-5.5x+-7 from x=2.4 to x=11.5. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(2.4)=-20.2 and f(11.5)=-70.25.\nThe interval width is 9.1.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -7.0, "slope": -5.5, "x0": 2.4, "x1": 11.5}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 18964.0 / 1000.\nFinal: {\"answer\": 18.964, \"unit\": \"kg\"}", "dedupe_signature": "a4d3f7cef30c771bf02001f57703adb0e4bd36ad66c505e271444b56f66db477", "difficulty": "easy", "final_answer": {"answer": 18.964, "unit": "kg"}, "id": "unit_convert_005898_g_to_kg_18964", "license": "Apache-2.0", "prompt": "Convert 18964 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 18964.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 18964.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=62 degrees and keep the unit as newtons.\nFinal: {\"answer\": [69.9513, 131.5592], \"unit\": \"N\"}", "dedupe_signature": "72aa7638821c45f553cd7f582c068d45d3e88aa55a9f7dbe4f76fff85322e232", "difficulty": "medium", "final_answer": {"answer": [69.9513, 131.5592], "unit": "N"}, "id": "vector_components_005899_149_62", "license": "Apache-2.0", "prompt": "A vector has magnitude 149 N at 62 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=62 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 62, "magnitude": 149.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [5.05, 24.75], \"unit\": \"dimensionless\"}", "dedupe_signature": "216bed57e442c3c4e1db2e9f9ca24c9daa575d185b0ecc591f9d980457d2b5d0", "difficulty": "medium", "final_answer": {"answer": [5.05, 24.75], "unit": "dimensionless"}, "id": "line_two_point_005900_-9.5_-7_5.05_24.75", "license": "Apache-2.0", "prompt": "A line passes through points (-9.5, -23.225) and (-7, -10.6). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -9.5, "x2": -7.0, "y1": -23.225, "y2": -10.600000000000001}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef pairwise_ratios_005902(numerators, denominators):\n    if len(numerators) != len(denominators):\n        raise ValueError('length mismatch')\n    out = []\n    for numerator, denominator in zip(numerators, denominators):\n        if denominator == 0:\n            raise ValueError('zero denominator')\n        out.append(numerator / denominator)\n    return out\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"pairwise_ratios_005902\"}", "dedupe_signature": "6cb4e9545bc609c539d8458bedfbeb6118b3f09f8f3ca65ec8115ed386b1266e", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "pairwise_ratios_005902"}, "id": "code_005902_pairwise_ratios_005902", "license": "Apache-2.0", "prompt": "Write a Python function pairwise_ratios_005902(numerators, denominators) that returns a list of n/d values. Raise ValueError if lengths differ or any denominator is zero. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "pairwise_ratios_005902"}, "verifier": {"function": "pairwise_ratios_005902", "tests": ["assert pairwise_ratios_005902([2, 9], [4, 3]) == [0.5, 3.0]", "try:\n    pairwise_ratios_005902([1], [0])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass", "try:\n    pairwise_ratios_005902([1, 2], [1])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 23.55 kg and a = 2.85 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 67.1175, \"unit\": \"N\"}", "dedupe_signature": "45057ffe5d9c4405e0b8a3bb86594274cbc7eaf12d8f5dfdc9cc4bc22ece7080", "difficulty": "easy", "final_answer": {"answer": 67.1175, "unit": "N"}, "id": "force_005904_23.55_2.85", "license": "Apache-2.0", "prompt": "A cart has mass 23.55 kg and measured acceleration 2.85 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 23.55 kg and a = 2.85 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 2.85, "mass": 23.55}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 9.75^2 and multiply by 0.5 * 22.95.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 1090.8422, \"unit\": \"J\"}", "dedupe_signature": "5205139508ecfae983fb313bb79b15d8e3adbccc6dc32ea8b0bbdb4c22a3ad43", "difficulty": "easy", "final_answer": {"answer": 1090.8422, "unit": "J"}, "id": "ke_005905_22.95_9.75", "license": "Apache-2.0", "prompt": "A body of mass 22.95 kg moves at 9.75 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 9.75^2 and multiply by 0.5 * 22.95.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 22.95, "velocity": 9.75}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=38 degrees through the sine of 2 theta.\n3. Substitute v=64.8 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 415.3222, \"unit\": \"m\"}", "dedupe_signature": "e007a65f9b0ea7c2f7a5e8bcba878411eded5eb91e359a80b6a1cfdde0419191", "difficulty": "medium", "final_answer": {"answer": 415.3222, "unit": "m"}, "id": "projectile_range_005906_64.8_38", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 64.8 m/s and angle 38 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=38 degrees through the sine of 2 theta.\nSubstitute v=64.8 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 38, "gravity": 9.81, "speed": 64.8}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 1.22 * 8.314 * 411 / 77.0.\nFinal: {\"answer\": 54.1403, \"unit\": \"kPa\"}", "dedupe_signature": "d406c5a4b26773490afbf28a1ebf6c631f0f49024f418f5f44c3c96020ad2b31", "difficulty": "medium", "final_answer": {"answer": 54.1403, "unit": "kPa"}, "id": "ideal_gas_005907_1.22_411_77.0", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=1.22 mol, T=411 K, and V=77.0 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 1.22 * 8.314 * 411 / 77.0.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 1.22, "temp_k": 411, "volume_l": 77.0}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=45.1 V and R=18.6 ohm.\nFinal: {\"answer\": 109.3554, \"unit\": \"W\"}", "dedupe_signature": "e279f827c7a447e1120fd9a2cc0fda7805473feab157b48945225a2c3b6e7380", "difficulty": "easy", "final_answer": {"answer": 109.3554, "unit": "W"}, "id": "ohm_power_005909_45.1_18.6", "license": "Apache-2.0", "prompt": "A resistor has resistance 18.6 ohm and voltage 45.1 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=45.1 V and R=18.6 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 18.6, "voltage": 45.1}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=519.5 mg, t=160 h, and T_half=66.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 98.0173, \"unit\": \"mg\"}", "dedupe_signature": "ea02e2d6ac0a9b7149657a03315af2780f779b324126356791b077309a87c898", "difficulty": "medium", "final_answer": {"answer": 98.0173, "unit": "mg"}, "id": "half_life_005910_519.5_66.5_160", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 519.5 mg. Its half-life is 66.5 hours. How many mg remain after 160 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=519.5 mg, t=160 h, and T_half=66.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 160.0, "half_life": 66.5, "initial_amount": 519.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 0.01 mol * 58.44 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 0.5844, \"unit\": \"g\"}", "dedupe_signature": "a6005049476b66ac416013688f6602539a44a17e48620d0ff9690c7e970639e7", "difficulty": "medium", "final_answer": {"answer": 0.5844, "unit": "g"}, "id": "stoich_mass_005911_sodium_chloride_0.01", "license": "Apache-2.0", "prompt": "A sample contains 0.01 mol of sodium chloride. Using molar mass 58.44 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 0.01 mol * 58.44 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "sodium chloride", "molar_mass": 58.44, "moles": 0.01}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 190 mL to 0.19 L.\n3. Compute M = 4.97 / 0.19.\nFinal: {\"answer\": 26.1579, \"unit\": \"mol/L\"}", "dedupe_signature": "8235808dec12cd648ec55b85de885440d29bcec04b39d558ab4b73d963c523cc", "difficulty": "medium", "final_answer": {"answer": 26.1579, "unit": "mol/L"}, "id": "molarity_005912_4.97_190", "license": "Apache-2.0", "prompt": "A solution contains 4.97 mol of solute in 190 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 190 mL to 0.19 L.\nCompute M = 4.97 / 0.19.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 4.97, "volume_ml": 190}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.72 y, so each step multiplies y by 1 - h*0.72.\n3. Apply that update for 9 steps and round the final state.\nFinal: {\"answer\": 0.0, \"unit\": \"state_units\"}", "dedupe_signature": "64a0682730a0d3ab05c99b04480f7a18140259b45583a288f478386277fbf6fe", "difficulty": "medium", "final_answer": {"answer": 0.0, "unit": "state_units"}, "id": "euler_decay_005913_25_0.72_1.1_9", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.72 y with y(0)=25, step size h=1.1, for 9 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.72 y, so each step multiplies y by 1 - h*0.72.\nApply that update for 9 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 25.0, "rate": 0.72, "step": 1.1, "steps": 9}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(3.4)=32.82 and f(11.3)=94.44.\n3. The interval width is 7.9.\nFinal: {\"answer\": 502.677, \"unit\": \"area_units\"}", "dedupe_signature": "b3ca0f5d4fa418864272c24f7d37eaeb018b35b0f8a597d8987245cfbecb7b94", "difficulty": "medium", "final_answer": {"answer": 502.677, "unit": "area_units"}, "id": "trapz_linear_005914_7.8_6.3_3.4_11.3", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=7.8x+6.3 from x=3.4 to x=11.3. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(3.4)=32.82 and f(11.3)=94.44.\nThe interval width is 7.9.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 6.3, "slope": 7.8, "x0": 3.4, "x1": 11.3}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.06 and add it to the current value.\nFinal: {\"answer\": [-1.611, -0.107, -1.195], \"unit\": \"temperature_units\"}", "dedupe_signature": "11ed8aa6eda1ca06e9146f7c494b0e3be9c5dbdd1327a86b7e66bf94db0bc858", "difficulty": "hard", "final_answer": {"answer": [-1.611, -0.107, -1.195], "unit": "temperature_units"}, "id": "heat_step_005915_0.06_-0.55_-1.8_0.1_-1.45_1.25", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-0.55, right=1.25; current interior values are [-1.8, 0.1, -1.45]. Use r=0.06. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.06 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-1.8, 0.1, -1.45], "left": -0.55, "r": 0.06, "right": 1.25}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 100 centimeters in one meter.\n2. Apply the conversion factor directly to the given value.\n3. Compute 2174.5 / 100.\nFinal: {\"answer\": 21.745, \"unit\": \"m\"}", "dedupe_signature": "779f29d645efb7cae1045fb63a35eccacee4ac640fc0f1acf60877cfe3c8a406", "difficulty": "easy", "final_answer": {"answer": 21.745, "unit": "m"}, "id": "unit_convert_005916_cm_to_m_2174.5", "license": "Apache-2.0", "prompt": "Convert 2174.5 cm to m. Return the converted value with unit.", "reasoning_trace": "There are 100 centimeters in one meter.\nApply the conversion factor directly to the given value.\nCompute 2174.5 / 100.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 2174.5}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=4 degrees and keep the unit as newtons.\nFinal: {\"answer\": [473.8429, 33.1343], \"unit\": \"N\"}", "dedupe_signature": "4251ad4e16781f3aa04c5a800297e96c82e10d2e04061bbdc622edd34e9a16ad", "difficulty": "medium", "final_answer": {"answer": [473.8429, 33.1343], "unit": "N"}, "id": "vector_components_005917_475_4", "license": "Apache-2.0", "prompt": "A vector has magnitude 475 N at 4 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=4 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 4, "magnitude": 475.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [7.45, -22.0], \"unit\": \"dimensionless\"}", "dedupe_signature": "055a480ad963ecff8ee7c7c0d04c4211f4720757b520702aae61f49d16798c61", "difficulty": "medium", "final_answer": {"answer": [7.45, -22.0], "unit": "dimensionless"}, "id": "line_two_point_005918_4.75_16.25_7.45_-22", "license": "Apache-2.0", "prompt": "A line passes through points (4.75, 13.3875) and (16.25, 99.0625). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 4.75, "x2": 16.25, "y1": 13.387500000000003, "y2": 99.0625}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. lever arm times force has torque dimensions\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "fdf93eb172ba7535d1f68528e3552c5d8b196e6449beeda4a0f95e0148fcf86c", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_005919_consistent_5ca82cb9_59944", "license": "Apache-2.0", "prompt": "In sensor calibration case 59944, check dimensional consistency for tau = r * F. The left side has dimensions N*m and the right side has dimensions N*m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nlever arm times force has torque dimensions\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "tau = r * F"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: recurrence, objective, tie_breaking_rule.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"recurrence\", \"objective\", \"tie_breaking_rule\"]}", "dedupe_signature": "da5457f187a90b9685cb49df3df4e976daa45b62c154ebc6e8d6448c6ae10c5a", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["recurrence", "objective", "tie_breaking_rule"]}, "id": "abstain_005921_recurrence_objective_tie_breaking_rule", "license": "Apache-2.0", "prompt": "Write a dynamic-programming solver for a routing scoring problem with 4891 items and budget 88220, but the recurrence, objective, and tie-breaking rule are all absent. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: recurrence, objective, tie_breaking_rule.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["recurrence", "objective", "tie_breaking_rule"]}, "verifier": {"missing": ["recurrence", "objective", "tie_breaking_rule"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 6.1^2 and multiply by 0.5 * 2.1.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 39.0705, \"unit\": \"J\"}", "dedupe_signature": "25b351ac2f0dab4c1c8d3dbfb977fec9f55e1611dbd6eb8018f44ed7c0a1a152", "difficulty": "easy", "final_answer": {"answer": 39.0705, "unit": "J"}, "id": "ke_005923_2.1_6.1", "license": "Apache-2.0", "prompt": "A body of mass 2.1 kg moves at 6.1 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 6.1^2 and multiply by 0.5 * 2.1.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 2.1, "velocity": 6.1}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=22 degrees through the sine of 2 theta.\n3. Substitute v=36.6 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 94.8559, \"unit\": \"m\"}", "dedupe_signature": "0030e01f12bd6344fca08af76d6b64982da90c8ad843890b8622bca3eb76d3ab", "difficulty": "medium", "final_answer": {"answer": 94.8559, "unit": "m"}, "id": "projectile_range_005924_36.6_22", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 36.6 m/s and angle 22 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=22 degrees through the sine of 2 theta.\nSubstitute v=36.6 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 22, "gravity": 9.81, "speed": 36.6}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 4.18 * 8.314 * 264 / 86.8.\nFinal: {\"answer\": 105.6989, \"unit\": \"kPa\"}", "dedupe_signature": "f2d30b48ea74e5b73731f5817946f4444dce9dd054bfc09e404891320453fc6a", "difficulty": "medium", "final_answer": {"answer": 105.6989, "unit": "kPa"}, "id": "ideal_gas_005925_4.18_264_86.8", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=4.18 mol, T=264 K, and V=86.8 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 4.18 * 8.314 * 264 / 86.8.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 4.18, "temp_k": 264, "volume_l": 86.8}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 815 * 4.63 * 50.\nFinal: {\"answer\": 188672.5, \"unit\": \"J\"}", "dedupe_signature": "cd7f0eef699066cc155b7805c5296f31e15cc1ab639caed38adeaa05ccc594e6", "difficulty": "easy", "final_answer": {"answer": 188672.5, "unit": "J"}, "id": "heat_q_005926_815_4.63_50", "license": "Apache-2.0", "prompt": "A 815 g sample has specific heat 4.63 J/(g*K). How much heat is needed to raise its temperature by 50 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 815 * 4.63 * 50.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 50, "heat_capacity": 4.63, "mass_g": 815}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=786.5 mg, t=90 h, and T_half=60.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 280.4694, \"unit\": \"mg\"}", "dedupe_signature": "1092be5933028a3ca819bc606a866fdd647eaaba4cf3bc6350cc29414bea2264", "difficulty": "medium", "final_answer": {"answer": 280.4694, "unit": "mg"}, "id": "half_life_005928_786.5_60.5_90", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 786.5 mg. Its half-life is 60.5 hours. How many mg remain after 90 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=786.5 mg, t=90 h, and T_half=60.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 90.0, "half_life": 60.5, "initial_amount": 786.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.6 y, so each step multiplies y by 1 - h*0.6.\n3. Apply that update for 5 steps and round the final state.\nFinal: {\"answer\": 5.1904, \"unit\": \"state_units\"}", "dedupe_signature": "0c3e912693c04e0db92692c5629b2967c3def839df7b7707b271713b642ec5aa", "difficulty": "medium", "final_answer": {"answer": 5.1904, "unit": "state_units"}, "id": "euler_decay_005931_14_0.6_0.3_5", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.6 y with y(0)=14, step size h=0.3, for 5 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.6 y, so each step multiplies y by 1 - h*0.6.\nApply that update for 5 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 14.0, "rate": 0.6, "step": 0.3, "steps": 5}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-4)=-12.4 and f(-3.4)=-13.12.\n3. The interval width is 0.6.\nFinal: {\"answer\": -7.656, \"unit\": \"area_units\"}", "dedupe_signature": "81a79b4446a4c35dba17bafad79ce5ab0e6a93c9cdfe7e0d963dc16a7115e09a", "difficulty": "medium", "final_answer": {"answer": -7.656, "unit": "area_units"}, "id": "trapz_linear_005932_-1.2_-17.2_-4_-3.4", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-1.2x+-17.2 from x=-4 to x=-3.4. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-4)=-12.4 and f(-3.4)=-13.12.\nThe interval width is 0.6.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -17.2, "slope": -1.2, "x0": -4.0, "x1": -3.4}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.44 and add it to the current value.\nFinal: {\"answer\": [1.112, 0.15, 0.996], \"unit\": \"temperature_units\"}", "dedupe_signature": "d043ad6f1ecb037aa14d72fa9af633ea457da67d7e85299c750905a4abc0e597", "difficulty": "hard", "final_answer": {"answer": [1.112, 0.15, 0.996], "unit": "temperature_units"}, "id": "heat_step_005933_0.44_1.95_-0.45_0.7_0.6_1.4", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.95, right=1.4; current interior values are [-0.45, 0.7, 0.6]. Use r=0.44. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.44 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-0.45, 0.7, 0.6], "left": 1.95, "r": 0.44, "right": 1.4}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kelvin equals Celsius plus 273.15.\n2. Apply the conversion factor directly to the given value.\n3. Compute 6.0 + 273.15.\nFinal: {\"answer\": 279.15, \"unit\": \"K\"}", "dedupe_signature": "d753c26d33a2ad66bb51c47f262464774502895f2c22c3004a0b1d2edfba0c2f", "difficulty": "easy", "final_answer": {"answer": 279.15, "unit": "K"}, "id": "unit_convert_005934_c_to_k_6", "license": "Apache-2.0", "prompt": "Convert 6 degC to K. Return the converted value with unit.", "reasoning_trace": "Kelvin equals Celsius plus 273.15.\nApply the conversion factor directly to the given value.\nCompute 6.0 + 273.15.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 6.0}, "verifier": {"formula": "value + 273.15", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=324 degrees and keep the unit as newtons.\nFinal: {\"answer\": [306.2129, -222.4767], \"unit\": \"N\"}", "dedupe_signature": "1bed578c9d79c0f8502f6eb71aeaaf4d7ff23ced40ea4132f0053ca1b7a17581", "difficulty": "medium", "final_answer": {"answer": [306.2129, -222.4767], "unit": "N"}, "id": "vector_components_005935_378.5_324", "license": "Apache-2.0", "prompt": "A vector has magnitude 378.5 N at 324 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=324 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 324, "magnitude": 378.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\nimport math\n\ndef unit_vector_005938(x, y):\n    norm = math.hypot(x, y)\n    if norm == 0:\n        raise ValueError('zero vector has no direction')\n    return (x / norm, y / norm)\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"unit_vector_005938\"}", "dedupe_signature": "c4db519c9d6df5624898e89a37c01b0ca79eba9fb0b8db241b9d90fedd8799da", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "unit_vector_005938"}, "id": "code_005938_unit_vector_005938", "license": "Apache-2.0", "prompt": "Write a Python function unit_vector_005938(x, y) that returns the 2D unit vector as a tuple. Raise ValueError for the zero vector. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "unit_vector_005938"}, "verifier": {"function": "unit_vector_005938", "tests": ["ux, uy = unit_vector_005938(3, 4); assert abs(ux - 0.6) < 1e-12 and abs(uy - 0.8) < 1e-12", "assert unit_vector_005938(0, 5) == (0, 1)", "try:\n    unit_vector_005938(0, 0)\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: rate_constant, number_of_steps.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"rate_constant\", \"number_of_steps\"]}", "dedupe_signature": "bd7c7890ab7862d7330ab0bd6a002f65963cc2f98b9dba40d8d7a565dd91f769", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["rate_constant", "number_of_steps"]}, "id": "abstain_005939_rate_constant_number_of_steps", "license": "Apache-2.0", "prompt": "Use explicit Euler for dy/dt = -k y. The prompt gives y(0)=33 and h=1.55, but omits both k and the number of steps. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: rate_constant, number_of_steps.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["rate_constant", "number_of_steps"]}, "verifier": {"missing": ["rate_constant", "number_of_steps"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 19.7 kg and a = 6.6 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 130.02, \"unit\": \"N\"}", "dedupe_signature": "b026a404f538dbcd6fdfbabe913b2e055db058799e23662419413ab870846855", "difficulty": "easy", "final_answer": {"answer": 130.02, "unit": "N"}, "id": "force_005940_19.7_6.6", "license": "Apache-2.0", "prompt": "A cart has mass 19.7 kg and measured acceleration 6.6 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 19.7 kg and a = 6.6 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 6.6, "mass": 19.7}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 42.2^2 and multiply by 0.5 * 15.7.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 13979.594, \"unit\": \"J\"}", "dedupe_signature": "4fc8e0c3293ee55cabf90c81773c6aebce3832538e3ea16982a55473fea7d855", "difficulty": "easy", "final_answer": {"answer": 13979.594, "unit": "J"}, "id": "ke_005941_15.7_42.2", "license": "Apache-2.0", "prompt": "A body of mass 15.7 kg moves at 42.2 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 42.2^2 and multiply by 0.5 * 15.7.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 15.7, "velocity": 42.2}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=82 degrees through the sine of 2 theta.\n3. Substitute v=20.7 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 12.0395, \"unit\": \"m\"}", "dedupe_signature": "00d540dd442eabfe82f37059a11450510c1e3b0543f1e88e7092c8b29439e2ea", "difficulty": "medium", "final_answer": {"answer": 12.0395, "unit": "m"}, "id": "projectile_range_005942_20.7_82", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 20.7 m/s and angle 82 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=82 degrees through the sine of 2 theta.\nSubstitute v=20.7 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 82, "gravity": 9.81, "speed": 20.7}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1200 * 2.55 * 107.\nFinal: {\"answer\": 327420.0, \"unit\": \"J\"}", "dedupe_signature": "87e125198d7245373eafd3d01fbcf6ce253e83416a2a5f2288106ddb9e8714e9", "difficulty": "easy", "final_answer": {"answer": 327420.0, "unit": "J"}, "id": "heat_q_005944_1200_2.55_107", "license": "Apache-2.0", "prompt": "A 1200 g sample has specific heat 2.55 J/(g*K). How much heat is needed to raise its temperature by 107 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1200 * 2.55 * 107.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 107, "heat_capacity": 2.55, "mass_g": 1200}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=79.7 V and R=159.4 ohm.\nFinal: {\"answer\": 39.85, \"unit\": \"W\"}", "dedupe_signature": "35d5430f7519c98852735e8eed2e6c02a02afdbb63e82bec02c360d43453d79c", "difficulty": "easy", "final_answer": {"answer": 39.85, "unit": "W"}, "id": "ohm_power_005945_79.7_159.4", "license": "Apache-2.0", "prompt": "A resistor has resistance 159.4 ohm and voltage 79.7 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=79.7 V and R=159.4 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 159.4, "voltage": 79.7}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 6.96 mol * 100.087 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 696.6055, \"unit\": \"g\"}", "dedupe_signature": "04943cdc38c7c7b93e57474db30f33c06d89310062ee3d44c20d16c4d07868b6", "difficulty": "medium", "final_answer": {"answer": 696.6055, "unit": "g"}, "id": "stoich_mass_005947_calcium_carbonate_6.96", "license": "Apache-2.0", "prompt": "A sample contains 6.96 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 6.96 mol * 100.087 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "calcium carbonate", "molar_mass": 100.087, "moles": 6.96}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 1980 mL to 1.98 L.\n3. Compute M = 3.175 / 1.98.\nFinal: {\"answer\": 1.6035, \"unit\": \"mol/L\"}", "dedupe_signature": "4f2538bad6f918fdc750f4db127a0b47fb53d09e26a54ec0dbc3ff2c7cae1c7b", "difficulty": "medium", "final_answer": {"answer": 1.6035, "unit": "mol/L"}, "id": "molarity_005948_3.175_1980", "license": "Apache-2.0", "prompt": "A solution contains 3.175 mol of solute in 1980 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 1980 mL to 1.98 L.\nCompute M = 3.175 / 1.98.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 3.175, "volume_ml": 1980}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.67 y, so each step multiplies y by 1 - h*0.67.\n3. Apply that update for 4 steps and round the final state.\nFinal: {\"answer\": 0.4889, \"unit\": \"state_units\"}", "dedupe_signature": "09fcdc1388977d1b490cd60f47699901e971240c9701ca2041c22fc76db20375", "difficulty": "medium", "final_answer": {"answer": 0.4889, "unit": "state_units"}, "id": "euler_decay_005949_28_0.67_0.95_4", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.67 y with y(0)=28, step size h=0.95, for 4 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.67 y, so each step multiplies y by 1 - h*0.67.\nApply that update for 4 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 28.0, "rate": 0.67, "step": 0.95, "steps": 4}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.02 and add it to the current value.\nFinal: {\"answer\": [-1.89, -1.891, 0.941], \"unit\": \"temperature_units\"}", "dedupe_signature": "8500019a5787a0ecf8cc07e6db8209d039c1f09f97adba7e91462fbac26b36ca", "difficulty": "hard", "final_answer": {"answer": [-1.89, -1.891, 0.941], "unit": "temperature_units"}, "id": "heat_step_005951_0.02_1.05_-1.95_-1.95_1.0_1.0", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.05, right=1; current interior values are [-1.95, -1.95, 1.0]. Use r=0.02. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.02 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-1.95, -1.95, 1.0], "left": 1.05, "r": 0.02, "right": 1.0}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 100 centimeters in one meter.\n2. Apply the conversion factor directly to the given value.\n3. Compute 358.5 / 100.\nFinal: {\"answer\": 3.585, \"unit\": \"m\"}", "dedupe_signature": "d685e3b03890b6e40c59f361e69fadf48f224032acd107dfe7e06bad2a6e1267", "difficulty": "easy", "final_answer": {"answer": 3.585, "unit": "m"}, "id": "unit_convert_005952_cm_to_m_358.5", "license": "Apache-2.0", "prompt": "Convert 358.5 cm to m. Return the converted value with unit.", "reasoning_trace": "There are 100 centimeters in one meter.\nApply the conversion factor directly to the given value.\nCompute 358.5 / 100.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 358.5}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=341 degrees and keep the unit as newtons.\nFinal: {\"answer\": [85.0967, -29.3011], \"unit\": \"N\"}", "dedupe_signature": "b64d97e1c4bc28591243b91c02b5793c878806a71ab7436e1c2f3f24387409bd", "difficulty": "medium", "final_answer": {"answer": [85.0967, -29.3011], "unit": "N"}, "id": "vector_components_005953_90_341", "license": "Apache-2.0", "prompt": "A vector has magnitude 90 N at 341 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=341 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 341, "magnitude": 90.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [5.85, 4.25], \"unit\": \"dimensionless\"}", "dedupe_signature": "913e2d3bc337a97f79cc23962cdb6f91f2399c0b1dca009ba33096f9c82d84c1", "difficulty": "medium", "final_answer": {"answer": [5.85, 4.25], "unit": "dimensionless"}, "id": "line_two_point_005954_-5.25_-1.5_5.85_4.25", "license": "Apache-2.0", "prompt": "A line passes through points (-5.25, -26.4625) and (-1.5, -4.525). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -5.25, "x2": -1.5, "y1": -26.4625, "y2": -4.524999999999999}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. m*v is momentum, not energy\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "dbdf0bc474ec8de4d59d32138064a0248afcf571523c66fe33bbb7ffea58d481", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_005955_inconsistent_1e14b074_285011", "license": "Apache-2.0", "prompt": "In lab notebook case 285011, check dimensional consistency for E = m * v. The left side has dimensions kg*m^2/s^2 and the right side has dimensions kg*m/s. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nm*v is momentum, not energy\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "E = m * v"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef threshold_flags_005956(values, threshold):\n    return [value >= threshold for value in values]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"threshold_flags_005956\"}", "dedupe_signature": "836e7780ed34488e2b19bf190afb874dd5ddd2754a71281ccadbae3d461484bc", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "threshold_flags_005956"}, "id": "code_005956_threshold_flags_005956", "license": "Apache-2.0", "prompt": "Write a Python function threshold_flags_005956(values, threshold) that returns a list of booleans showing whether each value is greater than or equal to threshold. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "threshold_flags_005956"}, "verifier": {"function": "threshold_flags_005956", "tests": ["assert threshold_flags_005956([1, 2, 3], 2) == [False, True, True]", "assert threshold_flags_005956([], 5) == []", "assert threshold_flags_005956([-1, 0], 0) == [False, True]"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: launch_angle_or_vertical_velocity.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"launch_angle_or_vertical_velocity\"]}", "dedupe_signature": "31435d6638d24512cd5a23d6e654db061dcac9da56d2a797f62796a91974bf2c", "difficulty": "easy", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["launch_angle_or_vertical_velocity"]}, "id": "abstain_005957_launch_angle_or_vertical_velocity", "license": "Apache-2.0", "prompt": "Compute projectile range on level ground. The prompt gives initial speed 23.9 m/s but does not give launch angle or vertical velocity. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: launch_angle_or_vertical_velocity.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["launch_angle_or_vertical_velocity"]}, "verifier": {"missing": ["launch_angle_or_vertical_velocity"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 17.45 kg and a = 9.15 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 159.6675, \"unit\": \"N\"}", "dedupe_signature": "5b5222d120b2340c0de8685dfbb8eabd4aa60c2cdf9b357972e7ad3d37a7fb57", "difficulty": "easy", "final_answer": {"answer": 159.6675, "unit": "N"}, "id": "force_005958_17.45_9.15", "license": "Apache-2.0", "prompt": "A cart has mass 17.45 kg and measured acceleration 9.15 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 17.45 kg and a = 9.15 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 9.15, "mass": 17.45}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 1.14 * 8.314 * 443 / 48.8.\nFinal: {\"answer\": 86.0397, \"unit\": \"kPa\"}", "dedupe_signature": "e46a049c9504de8580714872f2fec0d2f8170fd9a630378aaccb54c15f12ccd5", "difficulty": "medium", "final_answer": {"answer": 86.0397, "unit": "kPa"}, "id": "ideal_gas_005961_1.14_443_48.8", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=1.14 mol, T=443 K, and V=48.8 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 1.14 * 8.314 * 443 / 48.8.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 1.14, "temp_k": 443, "volume_l": 48.8}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 470 * 2.965 * 14.\nFinal: {\"answer\": 19509.7, \"unit\": \"J\"}", "dedupe_signature": "23da71fe741375dea52a9e0992be87221f749e61817039f7e5ac0a61213a64a6", "difficulty": "easy", "final_answer": {"answer": 19509.7, "unit": "J"}, "id": "heat_q_005962_470_2.965_14", "license": "Apache-2.0", "prompt": "A 470 g sample has specific heat 2.965 J/(g*K). How much heat is needed to raise its temperature by 14 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 470 * 2.965 * 14.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 14, "heat_capacity": 2.965, "mass_g": 470}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=48 V and R=50.7 ohm.\nFinal: {\"answer\": 45.4438, \"unit\": \"W\"}", "dedupe_signature": "28cc0a50bb33d4bdb534ef42765fab9a46a077d181872a3412456e99e2f270a7", "difficulty": "easy", "final_answer": {"answer": 45.4438, "unit": "W"}, "id": "ohm_power_005963_48_50.7", "license": "Apache-2.0", "prompt": "A resistor has resistance 50.7 ohm and voltage 48 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=48 V and R=50.7 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 50.7, "voltage": 48.0}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=933.5 mg, t=150.5 h, and T_half=112 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 367.7945, \"unit\": \"mg\"}", "dedupe_signature": "02a9909263c0ee6488163bb06d429d52c3ea48df3af784c43dbe05087a32691b", "difficulty": "medium", "final_answer": {"answer": 367.7945, "unit": "mg"}, "id": "half_life_005964_933.5_112_150.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 933.5 mg. Its half-life is 112 hours. How many mg remain after 150.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=933.5 mg, t=150.5 h, and T_half=112 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 150.5, "half_life": 112.0, "initial_amount": 933.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.61 y, so each step multiplies y by 1 - h*0.61.\n3. Apply that update for 12 steps and round the final state.\nFinal: {\"answer\": 0.1327, \"unit\": \"state_units\"}", "dedupe_signature": "f174a9fb8933d75187d03a897b2fed05fb951037df05a55f5d333ea1c7c3d1fb", "difficulty": "medium", "final_answer": {"answer": 0.1327, "unit": "state_units"}, "id": "euler_decay_005967_1.5_0.61_0.3_12", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.61 y with y(0)=1.5, step size h=0.3, for 12 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.61 y, so each step multiplies y by 1 - h*0.61.\nApply that update for 12 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 1.5, "rate": 0.61, "step": 0.3, "steps": 12}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-5.5)=8.4 and f(2.3)=13.08.\n3. The interval width is 7.8.\nFinal: {\"answer\": 83.772, \"unit\": \"area_units\"}", "dedupe_signature": "48f3aa37b916e880ea616f18bdd841eb37195fdfd786ce297d0c8755c6f8f384", "difficulty": "medium", "final_answer": {"answer": 83.772, "unit": "area_units"}, "id": "trapz_linear_005968_0.6_11.7_-5.5_2.3", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=0.6x+11.7 from x=-5.5 to x=2.3. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-5.5)=8.4 and f(2.3)=13.08.\nThe interval width is 7.8.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 11.7, "slope": 0.6, "x0": -5.5, "x1": 2.3}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.24 and add it to the current value.\nFinal: {\"answer\": [-0.842, -0.612, -0.324], \"unit\": \"temperature_units\"}", "dedupe_signature": "ac4f45eba3ff35890559451422d7170149f4b079b466ae5e9ab7878d9342a9b6", "difficulty": "hard", "final_answer": {"answer": [-0.842, -0.612, -0.324], "unit": "temperature_units"}, "id": "heat_step_005969_0.24_-1.5_-0.65_-0.6_-0.6_0.55", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-1.5, right=0.55; current interior values are [-0.65, -0.6, -0.6]. Use r=0.24. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.24 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-0.65, -0.6, -0.6], "left": -1.5, "r": 0.24, "right": 0.55}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kelvin equals Celsius plus 273.15.\n2. Apply the conversion factor directly to the given value.\n3. Compute -37.5 + 273.15.\nFinal: {\"answer\": 235.65, \"unit\": \"K\"}", "dedupe_signature": "d18dbde63179a946cb9d6256e31e7a1ca1f79a67d57772662110c103a98745fb", "difficulty": "easy", "final_answer": {"answer": 235.65, "unit": "K"}, "id": "unit_convert_005970_c_to_k_-37.5", "license": "Apache-2.0", "prompt": "Convert -37.5 degC to K. Return the converted value with unit.", "reasoning_trace": "Kelvin equals Celsius plus 273.15.\nApply the conversion factor directly to the given value.\nCompute -37.5 + 273.15.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": -37.5}, "verifier": {"formula": "value + 273.15", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=16 degrees and keep the unit as newtons.\nFinal: {\"answer\": [254.7343, 73.0439], \"unit\": \"N\"}", "dedupe_signature": "133683a07cd67cd69c6dc06c2caad9822f7eed6891c0676702534dc91aeb09f4", "difficulty": "medium", "final_answer": {"answer": [254.7343, 73.0439], "unit": "N"}, "id": "vector_components_005971_265_16", "license": "Apache-2.0", "prompt": "A vector has magnitude 265 N at 16 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=16 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 16, "magnitude": 265.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [0.6, -20.0], \"unit\": \"dimensionless\"}", "dedupe_signature": "bc8f4e0517497574fd479ce84253a2e1ae10165d833452248c1740d26bd14131", "difficulty": "medium", "final_answer": {"answer": [0.6, -20.0], "unit": "dimensionless"}, "id": "line_two_point_005972_4_11.25_0.6_-20", "license": "Apache-2.0", "prompt": "A line passes through points (4, -17.6) and (11.25, -13.25). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 4.0, "x2": 11.25, "y1": -17.6, "y2": -13.25}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. lever arm times force has torque dimensions\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "5c89492df06235c46421a3034577d182caabb933ed9748c2a98e6c6f209c6984", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_005973_consistent_5ca82cb9_585118", "license": "Apache-2.0", "prompt": "In quality-control check case 585118, check dimensional consistency for tau = r * F. The left side has dimensions N*m and the right side has dimensions N*m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nlever arm times force has torque dimensions\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "tau = r * F"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef weighted_sum_005974(values, weights):\n    if len(values) != len(weights):\n        raise ValueError('length mismatch')\n    return sum(value * weight for value, weight in zip(values, weights))\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"weighted_sum_005974\"}", "dedupe_signature": "713c92cd51108168450d82c3105919c87adf76bcf8b98131649aa9ad632cb315", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "weighted_sum_005974"}, "id": "code_005974_weighted_sum_005974", "license": "Apache-2.0", "prompt": "Write a Python function weighted_sum_005974(values, weights) that returns sum(value*weight). Raise ValueError when the two inputs have different lengths. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "weighted_sum_005974"}, "verifier": {"function": "weighted_sum_005974", "tests": ["assert weighted_sum_005974([2, 3], [4, 5]) == 23", "assert weighted_sum_005974([], []) == 0", "try:\n    weighted_sum_005974([1], [1, 2])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 14.3^2 and multiply by 0.5 * 20.15.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 2060.2368, \"unit\": \"J\"}", "dedupe_signature": "7a86af58cf9e6092a3569a16d3734cf908538fd099008b50d32b0b190db2738a", "difficulty": "easy", "final_answer": {"answer": 2060.2368, "unit": "J"}, "id": "ke_005977_20.15_14.3", "license": "Apache-2.0", "prompt": "A body of mass 20.15 kg moves at 14.3 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 14.3^2 and multiply by 0.5 * 20.15.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 20.15, "velocity": 14.3}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=74 degrees through the sine of 2 theta.\n3. Substitute v=77.9 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 327.805, \"unit\": \"m\"}", "dedupe_signature": "e416fa3ec66074532d8a9dbc2808264f010374e49655657cb42ff8a59b2c6362", "difficulty": "medium", "final_answer": {"answer": 327.805, "unit": "m"}, "id": "projectile_range_005978_77.9_74", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 77.9 m/s and angle 74 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=74 degrees through the sine of 2 theta.\nSubstitute v=77.9 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 74, "gravity": 9.81, "speed": 77.9}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 1.09 * 8.314 * 591 / 113.4.\nFinal: {\"answer\": 47.2292, \"unit\": \"kPa\"}", "dedupe_signature": "0e09af14a888ba8560d70b24e18d21f64b27c9be1636efbdabac26ab6165c79b", "difficulty": "medium", "final_answer": {"answer": 47.2292, "unit": "kPa"}, "id": "ideal_gas_005979_1.09_591_113.4", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=1.09 mol, T=591 K, and V=113.4 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 1.09 * 8.314 * 591 / 113.4.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 1.09, "temp_k": 591, "volume_l": 113.4}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1150 * 1.325 * 48.\nFinal: {\"answer\": 73140.0, \"unit\": \"J\"}", "dedupe_signature": "30b92b264b3cea91356641b54edbea85a904fe8086a0d854f1d0f93d2cf63dd4", "difficulty": "easy", "final_answer": {"answer": 73140.0, "unit": "J"}, "id": "heat_q_005980_1150_1.325_48", "license": "Apache-2.0", "prompt": "A 1150 g sample has specific heat 1.325 J/(g*K). How much heat is needed to raise its temperature by 48 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1150 * 1.325 * 48.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 48, "heat_capacity": 1.325, "mass_g": 1150}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=229 V and R=114.9 ohm.\nFinal: {\"answer\": 456.4056, \"unit\": \"W\"}", "dedupe_signature": "521c22226203f80f0082a650166ce39d55b3655e76511c8d869e68794aca9f65", "difficulty": "easy", "final_answer": {"answer": 456.4056, "unit": "W"}, "id": "ohm_power_005981_229_114.9", "license": "Apache-2.0", "prompt": "A resistor has resistance 114.9 ohm and voltage 229 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=229 V and R=114.9 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 114.9, "voltage": 229.0}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=754.5 mg, t=206 h, and T_half=42 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 25.1871, \"unit\": \"mg\"}", "dedupe_signature": "ad15f8f4d10dd9bd9477ee65b992e33aa50a1e18416a99fa274b16c6bbe11d9c", "difficulty": "medium", "final_answer": {"answer": 25.1871, "unit": "mg"}, "id": "half_life_005982_754.5_42_206", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 754.5 mg. Its half-life is 42 hours. How many mg remain after 206 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=754.5 mg, t=206 h, and T_half=42 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 206.0, "half_life": 42.0, "initial_amount": 754.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 6.07 mol * 44.01 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 267.1407, \"unit\": \"g\"}", "dedupe_signature": "a95dc27dff5ce5ee45090ba06e33b9b76a3914dc0ee9a0036706e4446b3ffbeb", "difficulty": "medium", "final_answer": {"answer": 267.1407, "unit": "g"}, "id": "stoich_mass_005983_carbon_dioxide_6.07", "license": "Apache-2.0", "prompt": "A sample contains 6.07 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 6.07 mol * 44.01 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "carbon dioxide", "molar_mass": 44.01, "moles": 6.07}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 230 mL to 0.23 L.\n3. Compute M = 4.78 / 0.23.\nFinal: {\"answer\": 20.7826, \"unit\": \"mol/L\"}", "dedupe_signature": "a663d7d28293b1355d2dbe2e94c6b16bb20251c43a0b46d49df904d2785c1f6b", "difficulty": "medium", "final_answer": {"answer": 20.7826, "unit": "mol/L"}, "id": "molarity_005984_4.78_230", "license": "Apache-2.0", "prompt": "A solution contains 4.78 mol of solute in 230 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 230 mL to 0.23 L.\nCompute M = 4.78 / 0.23.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 4.78, "volume_ml": 230}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-8.2)=-19.9 and f(-8.1)=-19.7.\n3. The interval width is 0.1.\nFinal: {\"answer\": -1.98, \"unit\": \"area_units\"}", "dedupe_signature": "0be682aea5266deebd0ccec2ac127fcb320a7e34f9566ba1e0d9a0b1ed2e65ae", "difficulty": "medium", "final_answer": {"answer": -1.98, "unit": "area_units"}, "id": "trapz_linear_005986_2_-3.5_-8.2_-8.1", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=2x+-3.5 from x=-8.2 to x=-8.1. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-8.2)=-19.9 and f(-8.1)=-19.7.\nThe interval width is 0.1.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -3.5, "slope": 2.0, "x0": -8.2, "x1": -8.1}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=159 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-352.4266, 135.2839], \"unit\": \"N\"}", "dedupe_signature": "70fa29db5e731971ed9a0e2a42920a72f5dff79bc169d209f00bf967984a629a", "difficulty": "medium", "final_answer": {"answer": [-352.4266, 135.2839], "unit": "N"}, "id": "vector_components_005989_377.5_159", "license": "Apache-2.0", "prompt": "A vector has magnitude 377.5 N at 159 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=159 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 159, "magnitude": 377.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [1.0, 6.25], \"unit\": \"dimensionless\"}", "dedupe_signature": "8641020838c88387c56ae88a20bab87df11488201eacd376d859b33994d9e210", "difficulty": "medium", "final_answer": {"answer": [1.0, 6.25], "unit": "dimensionless"}, "id": "line_two_point_005990_-4.25_9.5_1_6.25", "license": "Apache-2.0", "prompt": "A line passes through points (-4.25, 2) and (9.5, 15.75). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -4.25, "x2": 9.5, "y1": 2.0, "y2": 15.75}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\nimport math\n\ndef unit_vector_005992(x, y):\n    norm = math.hypot(x, y)\n    if norm == 0:\n        raise ValueError('zero vector has no direction')\n    return (x / norm, y / norm)\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"unit_vector_005992\"}", "dedupe_signature": "20002f4d417e094440937b8ef18ef4aede269194965811239e938985320403bc", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "unit_vector_005992"}, "id": "code_005992_unit_vector_005992", "license": "Apache-2.0", "prompt": "Write a Python function unit_vector_005992(x, y) that returns the 2D unit vector as a tuple. Raise ValueError for the zero vector. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "unit_vector_005992"}, "verifier": {"function": "unit_vector_005992", "tests": ["ux, uy = unit_vector_005992(3, 4); assert abs(ux - 0.6) < 1e-12 and abs(uy - 0.8) < 1e-12", "assert unit_vector_005992(0, 5) == (0, 1)", "try:\n    unit_vector_005992(0, 0)\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: recurrence, objective, tie_breaking_rule.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"recurrence\", \"objective\", \"tie_breaking_rule\"]}", "dedupe_signature": "b5111592bd3e1ee071670adb6ba0c518fd29678526c5bb7591263c90e2970a1a", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["recurrence", "objective", "tie_breaking_rule"]}, "id": "abstain_005993_recurrence_objective_tie_breaking_rule", "license": "Apache-2.0", "prompt": "Write a dynamic-programming solver for a scheduler scoring problem with 4853 items and budget 96495, but the recurrence, objective, and tie-breaking rule are all absent. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: recurrence, objective, tie_breaking_rule.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["recurrence", "objective", "tie_breaking_rule"]}, "verifier": {"missing": ["recurrence", "objective", "tie_breaking_rule"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 14.6 kg and a = 10.3 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 150.38, \"unit\": \"N\"}", "dedupe_signature": "f8f63ed5a7bdb9619593186996f5c7bff11204cd16f10f534d82a09b09f34c53", "difficulty": "easy", "final_answer": {"answer": 150.38, "unit": "N"}, "id": "force_005994_14.6_10.3", "license": "Apache-2.0", "prompt": "A cart has mass 14.6 kg and measured acceleration 10.3 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 14.6 kg and a = 10.3 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 10.3, "mass": 14.6}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 11.5^2 and multiply by 0.5 * 26.8.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 1772.15, \"unit\": \"J\"}", "dedupe_signature": "6e93621e86625049d219af1493e063157b4a99655632b9c9752d3fab50bc6cc1", "difficulty": "easy", "final_answer": {"answer": 1772.15, "unit": "J"}, "id": "ke_005995_26.8_11.5", "license": "Apache-2.0", "prompt": "A body of mass 26.8 kg moves at 11.5 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 11.5^2 and multiply by 0.5 * 26.8.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 26.8, "velocity": 11.5}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=114.4 V and R=129.5 ohm.\nFinal: {\"answer\": 101.0607, \"unit\": \"W\"}", "dedupe_signature": "56bb8d4719ecd9c73e6f67b4541726ebd65d7ae8cfd1025dea4169cd4fa5fcc8", "difficulty": "easy", "final_answer": {"answer": 101.0607, "unit": "W"}, "id": "ohm_power_005999_114.4_129.5", "license": "Apache-2.0", "prompt": "A resistor has resistance 129.5 ohm and voltage 114.4 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=114.4 V and R=129.5 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 129.5, "voltage": 114.4}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 3610 mL to 3.61 L.\n3. Compute M = 0.31 / 3.61.\nFinal: {\"answer\": 0.0859, \"unit\": \"mol/L\"}", "dedupe_signature": "fd4f7e78f8ecc16b4f849c57deb2cf92f0bed3712bcf69cc26352cc221f0c734", "difficulty": "medium", "final_answer": {"answer": 0.0859, "unit": "mol/L"}, "id": "molarity_006002_0.31_3610", "license": "Apache-2.0", "prompt": "A solution contains 0.31 mol of solute in 3610 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 3610 mL to 3.61 L.\nCompute M = 0.31 / 3.61.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 0.31, "volume_ml": 3610}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.37 y, so each step multiplies y by 1 - h*0.37.\n3. Apply that update for 10 steps and round the final state.\nFinal: {\"answer\": 0.0227, \"unit\": \"state_units\"}", "dedupe_signature": "b132626a70992bbf845dbefe70a3eb672cf6f15f99d8dca3d7259a3381927bb2", "difficulty": "medium", "final_answer": {"answer": 0.0227, "unit": "state_units"}, "id": "euler_decay_006003_74.5_0.37_1.5_10", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.37 y with y(0)=74.5, step size h=1.5, for 10 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.37 y, so each step multiplies y by 1 - h*0.37.\nApply that update for 10 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 74.5, "rate": 0.37, "step": 1.5, "steps": 10}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(7.5)=47.45 and f(17)=90.2.\n3. The interval width is 9.5.\nFinal: {\"answer\": 653.8375, \"unit\": \"area_units\"}", "dedupe_signature": "1af34e6487883287c1c3d31036e7f8bfa7bf688099626031cc5f8bf225e21412", "difficulty": "medium", "final_answer": {"answer": 653.8375, "unit": "area_units"}, "id": "trapz_linear_006004_4.5_13.7_7.5_17", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=4.5x+13.7 from x=7.5 to x=17. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(7.5)=47.45 and f(17)=90.2.\nThe interval width is 9.5.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 13.7, "slope": 4.5, "x0": 7.5, "x1": 17.0}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 33527.0 / 1000.\nFinal: {\"answer\": 33.527, \"unit\": \"kg\"}", "dedupe_signature": "d89acd1525cef89992541b7f5a2f35c1ded8603bbdf79a3f0bc451ae1dfe7313", "difficulty": "easy", "final_answer": {"answer": 33.527, "unit": "kg"}, "id": "unit_convert_006006_g_to_kg_33527", "license": "Apache-2.0", "prompt": "Convert 33527 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 33527.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 33527.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=354 degrees and keep the unit as newtons.\nFinal: {\"answer\": [411.2348, -43.2225], \"unit\": \"N\"}", "dedupe_signature": "7d6c025a7321e8fced1658cc8c0e690b1c36d940e17e75739cf53de5327b15ca", "difficulty": "medium", "final_answer": {"answer": [411.2348, -43.2225], "unit": "N"}, "id": "vector_components_006007_413.5_354", "license": "Apache-2.0", "prompt": "A vector has magnitude 413.5 N at 354 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=354 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 354, "magnitude": 413.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-6.25, 18.75], \"unit\": \"dimensionless\"}", "dedupe_signature": "426d7dbdb502b16226be65a2c55bf21a4e0eddf80a70d56caafdd76a985827fa", "difficulty": "medium", "final_answer": {"answer": [-6.25, 18.75], "unit": "dimensionless"}, "id": "line_two_point_006008_16.5_20.25_-6.25_18.75", "license": "Apache-2.0", "prompt": "A line passes through points (16.5, -84.375) and (20.25, -107.812). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 16.5, "x2": 20.25, "y1": -84.375, "y2": -107.8125}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. m*v is momentum, not energy\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "bfda7c4c821adcd8f59625c03a0c4a07145ba93dfbb57e0c3e03c580ce61521c", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_006009_inconsistent_1e14b074_838650", "license": "Apache-2.0", "prompt": "In model card equation case 838650, check dimensional consistency for E = m * v. The left side has dimensions kg*m^2/s^2 and the right side has dimensions kg*m/s. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nm*v is momentum, not energy\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "E = m * v"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef weighted_sum_006010(values, weights):\n    if len(values) != len(weights):\n        raise ValueError('length mismatch')\n    return sum(value * weight for value, weight in zip(values, weights))\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"weighted_sum_006010\"}", "dedupe_signature": "abb5243e0f233223a3b235afde5ca624c205bcb38cbea6408da3ef80afa9f5f7", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "weighted_sum_006010"}, "id": "code_006010_weighted_sum_006010", "license": "Apache-2.0", "prompt": "Write a Python function weighted_sum_006010(values, weights) that returns sum(value*weight). Raise ValueError when the two inputs have different lengths. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "weighted_sum_006010"}, "verifier": {"function": "weighted_sum_006010", "tests": ["assert weighted_sum_006010([2, 3], [4, 5]) == 23", "assert weighted_sum_006010([], []) == 0", "try:\n    weighted_sum_006010([1], [1, 2])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: volume.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"volume\"]}", "dedupe_signature": "caed876cadffaa22faa901a248a3d2980cb6058cca3b805e319155835b15f9d2", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["volume"]}, "id": "abstain_006011_volume", "license": "Apache-2.0", "prompt": "Compute pressure from the ideal gas law. The prompt gives n=4.94 mol and T=606 K, but does not give volume. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: volume.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["volume"]}, "verifier": {"missing": ["volume"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 18 kg and a = 0.95 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 17.1, \"unit\": \"N\"}", "dedupe_signature": "daacad901363a68618262ecedef55148812a1dd821827f13cf5e72ba3d0ac2bc", "difficulty": "easy", "final_answer": {"answer": 17.1, "unit": "N"}, "id": "force_006012_18_0.95", "license": "Apache-2.0", "prompt": "A cart has mass 18 kg and measured acceleration 0.95 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 18 kg and a = 0.95 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 0.95, "mass": 18.0}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=19 degrees through the sine of 2 theta.\n3. Substitute v=8.1 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 4.1176, \"unit\": \"m\"}", "dedupe_signature": "7f0daa53976fb62f54063288347d0fe53289b4e191122775d2183dee4d93d616", "difficulty": "medium", "final_answer": {"answer": 4.1176, "unit": "m"}, "id": "projectile_range_006014_8.1_19", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 8.1 m/s and angle 19 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=19 degrees through the sine of 2 theta.\nSubstitute v=8.1 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 19, "gravity": 9.81, "speed": 8.1}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 0.1 * 8.314 * 444 / 44.9.\nFinal: {\"answer\": 8.2214, \"unit\": \"kPa\"}", "dedupe_signature": "6711f68ca3a4908682ab3cccdd40eeac93346c9de7c0b359505597b16e111516", "difficulty": "medium", "final_answer": {"answer": 8.2214, "unit": "kPa"}, "id": "ideal_gas_006015_0.1_444_44.9", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=0.1 mol, T=444 K, and V=44.9 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 0.1 * 8.314 * 444 / 44.9.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 0.1, "temp_k": 444, "volume_l": 44.9}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=23.6 V and R=28.4 ohm.\nFinal: {\"answer\": 19.6113, \"unit\": \"W\"}", "dedupe_signature": "29bae51b57438f9844faee57ac5c0d467c7475129d552d620944364c5d183a72", "difficulty": "easy", "final_answer": {"answer": 19.6113, "unit": "W"}, "id": "ohm_power_006017_23.6_28.4", "license": "Apache-2.0", "prompt": "A resistor has resistance 28.4 ohm and voltage 23.6 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=23.6 V and R=28.4 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 28.4, "voltage": 23.6}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=289.5 mg, t=318 h, and T_half=2.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 0.0, \"unit\": \"mg\"}", "dedupe_signature": "4bf74947124b4d0a0be440903f9194e3fd84ba6d2e6bce275f662f7f919b205b", "difficulty": "medium", "final_answer": {"answer": 0.0, "unit": "mg"}, "id": "half_life_006018_289.5_2.5_318", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 289.5 mg. Its half-life is 2.5 hours. How many mg remain after 318 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=289.5 mg, t=318 h, and T_half=2.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 318.0, "half_life": 2.5, "initial_amount": 289.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 4715 mL to 4.715 L.\n3. Compute M = 1.84 / 4.715.\nFinal: {\"answer\": 0.3902, \"unit\": \"mol/L\"}", "dedupe_signature": "f63a98ad4aee50625d177d75de4a40060526b503c52a0599d31aadee12050c67", "difficulty": "medium", "final_answer": {"answer": 0.3902, "unit": "mol/L"}, "id": "molarity_006020_1.84_4715", "license": "Apache-2.0", "prompt": "A solution contains 1.84 mol of solute in 4715 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 4715 mL to 4.715 L.\nCompute M = 1.84 / 4.715.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 1.84, "volume_ml": 4715}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.79 y, so each step multiplies y by 1 - h*0.79.\n3. Apply that update for 10 steps and round the final state.\nFinal: {\"answer\": 0.0, \"unit\": \"state_units\"}", "dedupe_signature": "3df654b7b6a5f52fe77ad47c5076ff17d1a05ea2829c9cd576780076e221dae9", "difficulty": "medium", "final_answer": {"answer": 0.0, "unit": "state_units"}, "id": "euler_decay_006021_20.5_0.79_1.05_10", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.79 y with y(0)=20.5, step size h=1.05, for 10 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.79 y, so each step multiplies y by 1 - h*0.79.\nApply that update for 10 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 20.5, "rate": 0.79, "step": 1.05, "steps": 10}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.02 and add it to the current value.\nFinal: {\"answer\": [-0.987, 0.742, -0.216], \"unit\": \"temperature_units\"}", "dedupe_signature": "f08481abd0116fe5baf2b21ad94b577c4cfd8e946d9d9fcda179b575971f012a", "difficulty": "hard", "final_answer": {"answer": [-0.987, 0.742, -0.216], "unit": "temperature_units"}, "id": "heat_step_006023_0.02_0.25_-1.05_0.8_-0.25_0.4", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=0.25, right=0.4; current interior values are [-1.05, 0.8, -0.25]. Use r=0.02. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.02 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-1.05, 0.8, -0.25], "left": 0.25, "r": 0.02, "right": 0.4}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 35068.0 / 1000.\nFinal: {\"answer\": 35.068, \"unit\": \"kg\"}", "dedupe_signature": "9a093d40f5844e34e07503215ce7f2dd8a8c7df9e3ad37e2e1554e4081b3202f", "difficulty": "easy", "final_answer": {"answer": 35.068, "unit": "kg"}, "id": "unit_convert_006024_g_to_kg_35068", "license": "Apache-2.0", "prompt": "Convert 35068 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 35068.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 35068.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=113 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-135.3883, 318.9549], \"unit\": \"N\"}", "dedupe_signature": "6d179b065fbee47b4121d7d07e767684576c89f6d1e2cc11fab6733075fdef85", "difficulty": "medium", "final_answer": {"answer": [-135.3883, 318.9549], "unit": "N"}, "id": "vector_components_006025_346.5_113", "license": "Apache-2.0", "prompt": "A vector has magnitude 346.5 N at 113 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=113 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 113, "magnitude": 346.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-6.8, 9.5], \"unit\": \"dimensionless\"}", "dedupe_signature": "00d334cc1dfbf699b6a899ec689b30c076525cfbe63c7cca952e9982f001128a", "difficulty": "medium", "final_answer": {"answer": [-6.8, 9.5], "unit": "dimensionless"}, "id": "line_two_point_006026_-18.5_-17.75_-6.8_9.5", "license": "Apache-2.0", "prompt": "A line passes through points (-18.5, 135.3) and (-17.75, 130.2). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -18.5, "x2": -17.75, "y1": 135.3, "y2": 130.2}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. mass times acceleration has newton dimensions\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "727b4a921bc3f7c87cb2a372eefdf7f58f3c0967bd5035d87d04044dde617698", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_006027_consistent_03f5e041_835540", "license": "Apache-2.0", "prompt": "In sensor calibration case 835540, check dimensional consistency for F = m * a. The left side has dimensions kg*m/s^2 and the right side has dimensions kg*m/s^2. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nmass times acceleration has newton dimensions\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "F = m * a"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\nimport math\n\ndef unit_vector_006028(x, y):\n    norm = math.hypot(x, y)\n    if norm == 0:\n        raise ValueError('zero vector has no direction')\n    return (x / norm, y / norm)\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"unit_vector_006028\"}", "dedupe_signature": "20fcc6dc5f6ac0769eea038f3ee5a0471984b66b46534aa4c6ba70c4dbe4622e", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "unit_vector_006028"}, "id": "code_006028_unit_vector_006028", "license": "Apache-2.0", "prompt": "Write a Python function unit_vector_006028(x, y) that returns the 2D unit vector as a tuple. Raise ValueError for the zero vector. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "unit_vector_006028"}, "verifier": {"function": "unit_vector_006028", "tests": ["ux, uy = unit_vector_006028(3, 4); assert abs(ux - 0.6) < 1e-12 and abs(uy - 0.8) < 1e-12", "assert unit_vector_006028(0, 5) == (0, 1)", "try:\n    unit_vector_006028(0, 0)\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 7.1 kg and a = 0.3 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 2.13, \"unit\": \"N\"}", "dedupe_signature": "78ad01250738ec3984995e7ce1989d79365232af25cd68243b68857df26fd79b", "difficulty": "easy", "final_answer": {"answer": 2.13, "unit": "N"}, "id": "force_006030_7.1_0.3", "license": "Apache-2.0", "prompt": "A cart has mass 7.1 kg and measured acceleration 0.3 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 7.1 kg and a = 0.3 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 0.3, "mass": 7.1}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 2.7^2 and multiply by 0.5 * 7.15.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 26.0618, \"unit\": \"J\"}", "dedupe_signature": "a59e3cbd9313c430f3d987a788cf89a5a7ffab4cf858876d7c62b541ca6536ff", "difficulty": "easy", "final_answer": {"answer": 26.0618, "unit": "J"}, "id": "ke_006031_7.15_2.7", "license": "Apache-2.0", "prompt": "A body of mass 7.15 kg moves at 2.7 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 2.7^2 and multiply by 0.5 * 7.15.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 7.15, "velocity": 2.7}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 4.02 * 8.314 * 464 / 105.9.\nFinal: {\"answer\": 146.4395, \"unit\": \"kPa\"}", "dedupe_signature": "52fed7e29b9b43eb5b2d80bebeeabc04682293540fd92fe66611a0642ed0eabf", "difficulty": "medium", "final_answer": {"answer": 146.4395, "unit": "kPa"}, "id": "ideal_gas_006033_4.02_464_105.9", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=4.02 mol, T=464 K, and V=105.9 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 4.02 * 8.314 * 464 / 105.9.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 4.02, "temp_k": 464, "volume_l": 105.9}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1005 * 1.595 * 101.\nFinal: {\"answer\": 161900.475, \"unit\": \"J\"}", "dedupe_signature": "08972568475493766fdc6358161e7d117eb79d49986476705577b3fdac813079", "difficulty": "easy", "final_answer": {"answer": 161900.475, "unit": "J"}, "id": "heat_q_006034_1005_1.595_101", "license": "Apache-2.0", "prompt": "A 1005 g sample has specific heat 1.595 J/(g*K). How much heat is needed to raise its temperature by 101 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1005 * 1.595 * 101.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 101, "heat_capacity": 1.595, "mass_g": 1005}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=77.4 V and R=98.3 ohm.\nFinal: {\"answer\": 60.9436, \"unit\": \"W\"}", "dedupe_signature": "0e7a904b49ca0e289923cf565ce321ad34d9235d28efac1f457ceb8ee40d0ada", "difficulty": "easy", "final_answer": {"answer": 60.9436, "unit": "W"}, "id": "ohm_power_006035_77.4_98.3", "license": "Apache-2.0", "prompt": "A resistor has resistance 98.3 ohm and voltage 77.4 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=77.4 V and R=98.3 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 98.3, "voltage": 77.4}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=291.5 mg, t=12 h, and T_half=12.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 149.8476, \"unit\": \"mg\"}", "dedupe_signature": "0549ef120a53aee3c2f0cdafea85d54e899342078af8c92eaa3e285404183f83", "difficulty": "medium", "final_answer": {"answer": 149.8476, "unit": "mg"}, "id": "half_life_006036_291.5_12.5_12", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 291.5 mg. Its half-life is 12.5 hours. How many mg remain after 12 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=291.5 mg, t=12 h, and T_half=12.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 12.0, "half_life": 12.5, "initial_amount": 291.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 1.25 mol * 44.01 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 55.0125, \"unit\": \"g\"}", "dedupe_signature": "a49f644e138be7da5044cf733cba26215662c134fd670a1aaef90e506d2307a1", "difficulty": "medium", "final_answer": {"answer": 55.0125, "unit": "g"}, "id": "stoich_mass_006037_carbon_dioxide_1.25", "license": "Apache-2.0", "prompt": "A sample contains 1.25 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 1.25 mol * 44.01 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "carbon dioxide", "molar_mass": 44.01, "moles": 1.25}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 1035 mL to 1.035 L.\n3. Compute M = 2.7 / 1.035.\nFinal: {\"answer\": 2.6087, \"unit\": \"mol/L\"}", "dedupe_signature": "15cd440830e2f7f13bad6b020349b3f00b2bdd7dd1a9c1195a1bedc71cd63734", "difficulty": "medium", "final_answer": {"answer": 2.6087, "unit": "mol/L"}, "id": "molarity_006038_2.7_1035", "license": "Apache-2.0", "prompt": "A solution contains 2.7 mol of solute in 1035 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 1035 mL to 1.035 L.\nCompute M = 2.7 / 1.035.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 2.7, "volume_ml": 1035}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.78 y, so each step multiplies y by 1 - h*0.78.\n3. Apply that update for 10 steps and round the final state.\nFinal: {\"answer\": 0.0, \"unit\": \"state_units\"}", "dedupe_signature": "90fcff4a4ea70a3e544fcca419fd416e066ed5b33a4b7225ce1bcffd3c60e111", "difficulty": "medium", "final_answer": {"answer": 0.0, "unit": "state_units"}, "id": "euler_decay_006039_19.5_0.78_1.25_10", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.78 y with y(0)=19.5, step size h=1.25, for 10 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.78 y, so each step multiplies y by 1 - h*0.78.\nApply that update for 10 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 19.5, "rate": 0.78, "step": 1.25, "steps": 10}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(3)=25.1 and f(10.4)=55.44.\n3. The interval width is 7.4.\nFinal: {\"answer\": 297.998, \"unit\": \"area_units\"}", "dedupe_signature": "0f190e8e6db06814fd4d6bfb19d4db048c21b13e60e0707e0e5483a7f20f1a0d", "difficulty": "medium", "final_answer": {"answer": 297.998, "unit": "area_units"}, "id": "trapz_linear_006040_4.1_12.8_3_10.4", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=4.1x+12.8 from x=3 to x=10.4. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(3)=25.1 and f(10.4)=55.44.\nThe interval width is 7.4.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 12.8, "slope": 4.1, "x0": 3.0, "x1": 10.4}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.3 and add it to the current value.\nFinal: {\"answer\": [1.475, 1.42, 0.395], \"unit\": \"temperature_units\"}", "dedupe_signature": "1f3e9c52e16bd370adc792d3b4514c8f443a6d7405229f1d8a692d8c730eb6a6", "difficulty": "hard", "final_answer": {"answer": [1.475, 1.42, 0.395], "unit": "temperature_units"}, "id": "heat_step_006041_0.3_-0.9_2.6_2.35_-1.0_0.3", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-0.9, right=0.3; current interior values are [2.6, 2.35, -1.0]. Use r=0.3. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.3 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [2.6, 2.35, -1.0], "left": -0.9, "r": 0.3, "right": 0.3}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 100 centimeters in one meter.\n2. Apply the conversion factor directly to the given value.\n3. Compute 357.5 / 100.\nFinal: {\"answer\": 3.575, \"unit\": \"m\"}", "dedupe_signature": "e918c2de3345401f233c2242b2a7fc18e67258ab842d25b0732c91b040222374", "difficulty": "easy", "final_answer": {"answer": 3.575, "unit": "m"}, "id": "unit_convert_006042_cm_to_m_357.5", "license": "Apache-2.0", "prompt": "Convert 357.5 cm to m. Return the converted value with unit.", "reasoning_trace": "There are 100 centimeters in one meter.\nApply the conversion factor directly to the given value.\nCompute 357.5 / 100.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 357.5}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=258 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-45.8445, -215.6815], \"unit\": \"N\"}", "dedupe_signature": "6ee31cbda4893151fb98b1f312241265b59b12859240ed0e7d682411de6a08ab", "difficulty": "medium", "final_answer": {"answer": [-45.8445, -215.6815], "unit": "N"}, "id": "vector_components_006043_220.5_258", "license": "Apache-2.0", "prompt": "A vector has magnitude 220.5 N at 258 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=258 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 258, "magnitude": 220.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef safe_mean_006046(values):\n    if not values:\n        raise ValueError('safe_mean requires at least one value')\n    return sum(values) / len(values)\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"safe_mean_006046\"}", "dedupe_signature": "9d38242105ead6c8bf01aa728d597b975ddde97080a3df5b122205f560a23d5a", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "safe_mean_006046"}, "id": "code_006046_safe_mean_006046", "license": "Apache-2.0", "prompt": "Write a Python function safe_mean_006046(values) that returns the arithmetic mean. It must raise ValueError for an empty input and must not mutate the input list. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "safe_mean_006046"}, "verifier": {"function": "safe_mean_006046", "tests": ["assert safe_mean_006046([2, 4, 6]) == 4", "xs = [1, 2, 3]; assert safe_mean_006046(xs) == 2 and xs == [1, 2, 3]", "try:\n    safe_mean_006046([])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: rate_constant, number_of_steps.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"rate_constant\", \"number_of_steps\"]}", "dedupe_signature": "bc7bdb77665768b37d6ddb55e54474c968b772a4c48c9ab6aa96f224a2e086f6", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["rate_constant", "number_of_steps"]}, "id": "abstain_006047_rate_constant_number_of_steps", "license": "Apache-2.0", "prompt": "Use explicit Euler for dy/dt = -k y. The prompt gives y(0)=80 and h=0.2, but omits both k and the number of steps. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: rate_constant, number_of_steps.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["rate_constant", "number_of_steps"]}, "verifier": {"missing": ["rate_constant", "number_of_steps"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 7.2 kg and a = 2.45 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 17.64, \"unit\": \"N\"}", "dedupe_signature": "ae99b446889ff34586f6d5769b8adb7504a341b98731631ef68bece1d741ebd7", "difficulty": "easy", "final_answer": {"answer": 17.64, "unit": "N"}, "id": "force_006048_7.2_2.45", "license": "Apache-2.0", "prompt": "A cart has mass 7.2 kg and measured acceleration 2.45 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 7.2 kg and a = 2.45 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 2.45, "mass": 7.2}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=6 degrees through the sine of 2 theta.\n3. Substitute v=75.9 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 122.0938, \"unit\": \"m\"}", "dedupe_signature": "5c4ad6b66fcb9842c4f2be2fa2f09bf169b8ab96572833dcdb2fe14f29fed947", "difficulty": "medium", "final_answer": {"answer": 122.0938, "unit": "m"}, "id": "projectile_range_006050_75.9_6", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 75.9 m/s and angle 6 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=6 degrees through the sine of 2 theta.\nSubstitute v=75.9 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 6, "gravity": 9.81, "speed": 75.9}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 2.56 * 8.314 * 240 / 43.1.\nFinal: {\"answer\": 118.5179, \"unit\": \"kPa\"}", "dedupe_signature": "edba84655ce614ec3a6aa03765f1a75947ebd8cf4440c559c21b44a48bab5303", "difficulty": "medium", "final_answer": {"answer": 118.5179, "unit": "kPa"}, "id": "ideal_gas_006051_2.56_240_43.1", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=2.56 mol, T=240 K, and V=43.1 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 2.56 * 8.314 * 240 / 43.1.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 2.56, "temp_k": 240, "volume_l": 43.1}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=110.8 V and R=100 ohm.\nFinal: {\"answer\": 122.7664, \"unit\": \"W\"}", "dedupe_signature": "6b6cece0444208c0c5dcca501066cd4dd9f265349916e60782c72f3400bff018", "difficulty": "easy", "final_answer": {"answer": 122.7664, "unit": "W"}, "id": "ohm_power_006053_110.8_100", "license": "Apache-2.0", "prompt": "A resistor has resistance 100 ohm and voltage 110.8 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=110.8 V and R=100 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 100.0, "voltage": 110.8}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=310 mg, t=325 h, and T_half=0.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 0.0, \"unit\": \"mg\"}", "dedupe_signature": "bf99b0b0771f89f1c0fd3aebb7b09a536d67fad4263e864e6cd9a167fed025fa", "difficulty": "medium", "final_answer": {"answer": 0.0, "unit": "mg"}, "id": "half_life_006054_310_0.5_325", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 310 mg. Its half-life is 0.5 hours. How many mg remain after 325 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=310 mg, t=325 h, and T_half=0.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 325.0, "half_life": 0.5, "initial_amount": 310.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 6.25 mol * 18.015 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 112.5938, \"unit\": \"g\"}", "dedupe_signature": "69ba3eb72bf4af6bef70e243b9477ea6a40c2db63d0494d694b539a368ffc58c", "difficulty": "medium", "final_answer": {"answer": 112.5938, "unit": "g"}, "id": "stoich_mass_006055_water_6.25", "license": "Apache-2.0", "prompt": "A sample contains 6.25 mol of water. Using molar mass 18.015 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 6.25 mol * 18.015 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "water", "molar_mass": 18.015, "moles": 6.25}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 2355 mL to 2.355 L.\n3. Compute M = 4.24 / 2.355.\nFinal: {\"answer\": 1.8004, \"unit\": \"mol/L\"}", "dedupe_signature": "0b9418bc0694777497df38d22ca9b51402d95dee4a225a993dd2b71661f0f265", "difficulty": "medium", "final_answer": {"answer": 1.8004, "unit": "mol/L"}, "id": "molarity_006056_4.24_2355", "license": "Apache-2.0", "prompt": "A solution contains 4.24 mol of solute in 2355 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 2355 mL to 2.355 L.\nCompute M = 4.24 / 2.355.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 4.24, "volume_ml": 2355}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.88 y, so each step multiplies y by 1 - h*0.88.\n3. Apply that update for 11 steps and round the final state.\nFinal: {\"answer\": -0.6465, \"unit\": \"state_units\"}", "dedupe_signature": "af13e6983db99b06b336b4bdb58cd1cc4df515782bba4fb482dd6f0eeb66ff13", "difficulty": "medium", "final_answer": {"answer": -0.6465, "unit": "state_units"}, "id": "euler_decay_006057_25.5_0.88_1.95_11", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.88 y with y(0)=25.5, step size h=1.95, for 11 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.88 y, so each step multiplies y by 1 - h*0.88.\nApply that update for 11 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 25.5, "rate": 0.88, "step": 1.95, "steps": 11}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(7.1)=13.25 and f(11.1)=27.25.\n3. The interval width is 4.\nFinal: {\"answer\": 81.0, \"unit\": \"area_units\"}", "dedupe_signature": "b8bb03af679bff62d12243b714ba4c21491f43b5f97f502a3cd1f16cd03cddea", "difficulty": "medium", "final_answer": {"answer": 81.0, "unit": "area_units"}, "id": "trapz_linear_006058_3.5_-11.6_7.1_11.1", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=3.5x+-11.6 from x=7.1 to x=11.1. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(7.1)=13.25 and f(11.1)=27.25.\nThe interval width is 4.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -11.6, "slope": 3.5, "x0": 7.1, "x1": 11.1}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.26 and add it to the current value.\nFinal: {\"answer\": [-0.023, -0.844, -0.034], \"unit\": \"temperature_units\"}", "dedupe_signature": "097c730a97bbc9a9e9070f2426be5680e801ecb8db1a5767fbb811fd6f98f8f8", "difficulty": "hard", "final_answer": {"answer": [-0.023, -0.844, -0.034], "unit": "temperature_units"}, "id": "heat_step_006059_0.26_1.1_0.25_-1.65_-0.45_2.35", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.1, right=2.35; current interior values are [0.25, -1.65, -0.45]. Use r=0.26. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.26 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [0.25, -1.65, -0.45], "left": 1.1, "r": 0.26, "right": 2.35}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 100 centimeters in one meter.\n2. Apply the conversion factor directly to the given value.\n3. Compute 3286.0 / 100.\nFinal: {\"answer\": 32.86, \"unit\": \"m\"}", "dedupe_signature": "3196c971cd4de454d2f2b6a17634a037fe4fa7c0c9f147f2bea913adaac2800d", "difficulty": "easy", "final_answer": {"answer": 32.86, "unit": "m"}, "id": "unit_convert_006060_cm_to_m_3286", "license": "Apache-2.0", "prompt": "Convert 3286 cm to m. Return the converted value with unit.", "reasoning_trace": "There are 100 centimeters in one meter.\nApply the conversion factor directly to the given value.\nCompute 3286.0 / 100.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 3286.0}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=326 degrees and keep the unit as newtons.\nFinal: {\"answer\": [309.6455, -208.8585], \"unit\": \"N\"}", "dedupe_signature": "8dffa53bbbe6fa8e778b3332e154db66019ff68b23ce28e88790efb22c48b926", "difficulty": "medium", "final_answer": {"answer": [309.6455, -208.8585], "unit": "N"}, "id": "vector_components_006061_373.5_326", "license": "Apache-2.0", "prompt": "A vector has magnitude 373.5 N at 326 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=326 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 326, "magnitude": 373.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-6.05, 12.75], \"unit\": \"dimensionless\"}", "dedupe_signature": "3c183f70b6232769256b5dbdcac312d07860027940552fa8c32ce0419c34cb7e", "difficulty": "medium", "final_answer": {"answer": [-6.05, 12.75], "unit": "dimensionless"}, "id": "line_two_point_006062_-11.75_-5_-6.05_12.75", "license": "Apache-2.0", "prompt": "A line passes through points (-11.75, 83.8375) and (-5, 43). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -11.75, "x2": -5.0, "y1": 83.83749999999999, "y2": 43.0}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. grams cancel with J/(g*K), and kelvin cancels, leaving joules\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "e3d54eba9aeda4134db060c7b8d6a7305b4e2b5bc134dafc4aee04844798db00", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_006063_consistent_4153435f_852203", "license": "Apache-2.0", "prompt": "In quality-control check case 852203, check dimensional consistency for Q = m * c * DeltaT. The left side has dimensions J and the right side has dimensions J. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\ngrams cancel with J/(g*K), and kelvin cancels, leaving joules\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "Q = m * c * DeltaT"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef weighted_sum_006064(values, weights):\n    if len(values) != len(weights):\n        raise ValueError('length mismatch')\n    return sum(value * weight for value, weight in zip(values, weights))\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"weighted_sum_006064\"}", "dedupe_signature": "90efa3ef4a403bc543d94cdc7fc23c2147fea65625197e43d5ea27c76b9f495a", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "weighted_sum_006064"}, "id": "code_006064_weighted_sum_006064", "license": "Apache-2.0", "prompt": "Write a Python function weighted_sum_006064(values, weights) that returns sum(value*weight). Raise ValueError when the two inputs have different lengths. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "weighted_sum_006064"}, "verifier": {"function": "weighted_sum_006064", "tests": ["assert weighted_sum_006064([2, 3], [4, 5]) == 23", "assert weighted_sum_006064([], []) == 0", "try:\n    weighted_sum_006064([1], [1, 2])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: left_boundary, right_boundary.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"left_boundary\", \"right_boundary\"]}", "dedupe_signature": "42ff1cc56bf0567a43b89a471a8818db08686a6f7d697f709c4dc79865220810", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["left_boundary", "right_boundary"]}, "id": "abstain_006065_left_boundary_right_boundary", "license": "Apache-2.0", "prompt": "Solve the 1D heat equation after one finite-difference step. The prompt gives r=0.06 and interior values [2.2, 3.0, -0.95], but gives no boundary values. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: left_boundary, right_boundary.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["left_boundary", "right_boundary"]}, "verifier": {"missing": ["left_boundary", "right_boundary"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 16 kg and a = 7.85 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 125.6, \"unit\": \"N\"}", "dedupe_signature": "3c005d88023d2f0c982c78ee5674de7291d55adebef645953118016c86a6c6b2", "difficulty": "easy", "final_answer": {"answer": 125.6, "unit": "N"}, "id": "force_006066_16_7.85", "license": "Apache-2.0", "prompt": "A cart has mass 16 kg and measured acceleration 7.85 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 16 kg and a = 7.85 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 7.85, "mass": 16.0}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=62 degrees through the sine of 2 theta.\n3. Substitute v=79.1 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 528.7595, \"unit\": \"m\"}", "dedupe_signature": "01cdd7670ec54c8ecc2a0a854152c8345738a1ba681117ed338cca267221d957", "difficulty": "medium", "final_answer": {"answer": 528.7595, "unit": "m"}, "id": "projectile_range_006068_79.1_62", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 79.1 m/s and angle 62 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=62 degrees through the sine of 2 theta.\nSubstitute v=79.1 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 62, "gravity": 9.81, "speed": 79.1}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 2.35 * 8.314 * 530 / 13.3.\nFinal: {\"answer\": 778.578, \"unit\": \"kPa\"}", "dedupe_signature": "d2efc5ebda746149cda68201723e2abe66f7a46a6cae28c6774f740310abd31c", "difficulty": "medium", "final_answer": {"answer": 778.578, "unit": "kPa"}, "id": "ideal_gas_006069_2.35_530_13.3", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=2.35 mol, T=530 K, and V=13.3 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 2.35 * 8.314 * 530 / 13.3.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 2.35, "temp_k": 530, "volume_l": 13.3}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 450 * 3.23 * 4.\nFinal: {\"answer\": 5814.0, \"unit\": \"J\"}", "dedupe_signature": "d9743e1a142441dd3dd0250a6039c0939168e5aa2379beac6e1a8f00122a42ba", "difficulty": "easy", "final_answer": {"answer": 5814.0, "unit": "J"}, "id": "heat_q_006070_450_3.23_4", "license": "Apache-2.0", "prompt": "A 450 g sample has specific heat 3.23 J/(g*K). How much heat is needed to raise its temperature by 4 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 450 * 3.23 * 4.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 4, "heat_capacity": 3.23, "mass_g": 450}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=3.6 V and R=199.6 ohm.\nFinal: {\"answer\": 0.0649, \"unit\": \"W\"}", "dedupe_signature": "4fc5f369dfc1d2b4c9eec1e426ed7f938f6421d161e84ddb5e6acf1c2f568479", "difficulty": "easy", "final_answer": {"answer": 0.0649, "unit": "W"}, "id": "ohm_power_006071_3.6_199.6", "license": "Apache-2.0", "prompt": "A resistor has resistance 199.6 ohm and voltage 3.6 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=3.6 V and R=199.6 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 199.6, "voltage": 3.6}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=773 mg, t=271 h, and T_half=5.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 0.0, \"unit\": \"mg\"}", "dedupe_signature": "d22d06cf273e85c91dd107f7da5170c5c4ebfda6001c30e7f10f13c5c9d8779a", "difficulty": "medium", "final_answer": {"answer": 0.0, "unit": "mg"}, "id": "half_life_006072_773_5.5_271", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 773 mg. Its half-life is 5.5 hours. How many mg remain after 271 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=773 mg, t=271 h, and T_half=5.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 271.0, "half_life": 5.5, "initial_amount": 773.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 3.92 mol * 58.44 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 229.0848, \"unit\": \"g\"}", "dedupe_signature": "8418bb251814dfb0ac156b80d0361bccdddbd1acee35e1cf12377d3d127d121e", "difficulty": "medium", "final_answer": {"answer": 229.0848, "unit": "g"}, "id": "stoich_mass_006073_sodium_chloride_3.92", "license": "Apache-2.0", "prompt": "A sample contains 3.92 mol of sodium chloride. Using molar mass 58.44 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 3.92 mol * 58.44 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "sodium chloride", "molar_mass": 58.44, "moles": 3.92}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-6.3)=-32.6 and f(-3.6)=-27.2.\n3. The interval width is 2.7.\nFinal: {\"answer\": -80.73, \"unit\": \"area_units\"}", "dedupe_signature": "e63172a47e010a24e35eb55652871bc6a1887923db68a9cb3b750cffe4eea46e", "difficulty": "medium", "final_answer": {"answer": -80.73, "unit": "area_units"}, "id": "trapz_linear_006076_2_-20_-6.3_-3.6", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=2x+-20 from x=-6.3 to x=-3.6. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-6.3)=-32.6 and f(-3.6)=-27.2.\nThe interval width is 2.7.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -20.0, "slope": 2.0, "x0": -6.3, "x1": -3.5999999999999996}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.18 and add it to the current value.\nFinal: {\"answer\": [0.492, 0.864, 1.459], \"unit\": \"temperature_units\"}", "dedupe_signature": "aeaa5633bc0c48d51d418d3fb73c27460298a1f190fd0582790da37b421f31bf", "difficulty": "hard", "final_answer": {"answer": [0.492, 0.864, 1.459], "unit": "temperature_units"}, "id": "heat_step_006077_0.18_2.9_-0.3_0.9_1.9_0.45", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=2.9, right=0.45; current interior values are [-0.3, 0.9, 1.9]. Use r=0.18. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.18 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-0.3, 0.9, 1.9], "left": 2.9, "r": 0.18, "right": 0.45}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 20980.0 / 1000.\nFinal: {\"answer\": 20.98, \"unit\": \"kg\"}", "dedupe_signature": "03726b52c9e2cd2a86f6a21c328a0af592280dea870d3ca3934613c584651d3e", "difficulty": "easy", "final_answer": {"answer": 20.98, "unit": "kg"}, "id": "unit_convert_006078_g_to_kg_20980", "license": "Apache-2.0", "prompt": "Convert 20980 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 20980.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 20980.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=277 degrees and keep the unit as newtons.\nFinal: {\"answer\": [42.4105, -345.4061], \"unit\": \"N\"}", "dedupe_signature": "c1ba2b2fbc47a5ad892cc45b4ac7f966d68174cc0ca24cb6be6a0febaf098698", "difficulty": "medium", "final_answer": {"answer": [42.4105, -345.4061], "unit": "N"}, "id": "vector_components_006079_348_277", "license": "Apache-2.0", "prompt": "A vector has magnitude 348 N at 277 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=277 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 277, "magnitude": 348.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [5.95, 29.5], \"unit\": \"dimensionless\"}", "dedupe_signature": "1d936fa6ec7caf48a14992a9b25e0c23bd454cd4d5fefac90eb0efb80189037e", "difficulty": "medium", "final_answer": {"answer": [5.95, 29.5], "unit": "dimensionless"}, "id": "line_two_point_006080_14.75_16.5_5.95_29.5", "license": "Apache-2.0", "prompt": "A line passes through points (14.75, 117.263) and (16.5, 127.675). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 14.75, "x2": 16.5, "y1": 117.2625, "y2": 127.675}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. volt squared divided by ohm is watt\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "736b4c3f499072de7b1ff69424be610569efc96795a694e547fc4df651499e0d", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_006081_consistent_82e93f3d_187271", "license": "Apache-2.0", "prompt": "In field worksheet case 187271, check dimensional consistency for P = V^2 / R. The left side has dimensions W and the right side has dimensions W. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nvolt squared divided by ohm is watt\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "P = V^2 / R"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef running_total_006082(values):\n    total = 0\n    out = []\n    for value in values:\n        total += value\n        out.append(total)\n    return out\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"running_total_006082\"}", "dedupe_signature": "3e16f35f9a5c41b510d506280407c3fb7d01f09a5a00cdeb54d66603f3e7de72", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "running_total_006082"}, "id": "code_006082_running_total_006082", "license": "Apache-2.0", "prompt": "Write a Python function running_total_006082(values) that returns cumulative sums as a new list. It must not mutate the input list. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "running_total_006082"}, "verifier": {"function": "running_total_006082", "tests": ["assert running_total_006082([1, 2, 3]) == [1, 3, 6]", "xs = [4, -1, 2]; assert running_total_006082(xs) == [4, 3, 5] and xs == [4, -1, 2]", "assert running_total_006082([]) == []"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: required_fields, allowed_transformations.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"required_fields\", \"allowed_transformations\"]}", "dedupe_signature": "a5e9b2ff51d272ead4f75c9df8a54c0b4525869b9dca16fb67b9bddb0821bff3", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["required_fields", "allowed_transformations"]}, "id": "abstain_006083_required_fields_allowed_transformations", "license": "Apache-2.0", "prompt": "Write a sanitizer for valid mobile invoice records in release 304058, but the prompt does not state which fields are required or which transformations are allowed. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: required_fields, allowed_transformations.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["required_fields", "allowed_transformations"]}, "verifier": {"missing": ["required_fields", "allowed_transformations"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 1.45 kg and a = 9.4 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 13.63, \"unit\": \"N\"}", "dedupe_signature": "55293604c8e2ca320d98febbe58ba11bd4ee9d00dbee0bcdba608a75afe521fc", "difficulty": "easy", "final_answer": {"answer": 13.63, "unit": "N"}, "id": "force_006084_1.45_9.4", "license": "Apache-2.0", "prompt": "A cart has mass 1.45 kg and measured acceleration 9.4 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 1.45 kg and a = 9.4 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 9.4, "mass": 1.45}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 820 * 1.29 * 4.\nFinal: {\"answer\": 4231.2, \"unit\": \"J\"}", "dedupe_signature": "050722e2f0c278649cbfc7afb2e9e15f287bde1d0d2dbedf4060dd5e3efebee3", "difficulty": "easy", "final_answer": {"answer": 4231.2, "unit": "J"}, "id": "heat_q_006088_820_1.29_4", "license": "Apache-2.0", "prompt": "A 820 g sample has specific heat 1.29 J/(g*K). How much heat is needed to raise its temperature by 4 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 820 * 1.29 * 4.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 4, "heat_capacity": 1.29, "mass_g": 820}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=130.8 V and R=178.8 ohm.\nFinal: {\"answer\": 95.6859, \"unit\": \"W\"}", "dedupe_signature": "8707f3e4143afb96fa65afa4e42ceba34c9f9c3798f7dd9dcf060b75df20f333", "difficulty": "easy", "final_answer": {"answer": 95.6859, "unit": "W"}, "id": "ohm_power_006089_130.8_178.8", "license": "Apache-2.0", "prompt": "A resistor has resistance 178.8 ohm and voltage 130.8 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=130.8 V and R=178.8 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 178.8, "voltage": 130.8}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 5.59 mol * 58.44 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 326.6796, \"unit\": \"g\"}", "dedupe_signature": "6df62186d4720739fc7b50f2b47441b74ce72a8fae9a470914b390fd51a92197", "difficulty": "medium", "final_answer": {"answer": 326.6796, "unit": "g"}, "id": "stoich_mass_006091_sodium_chloride_5.59", "license": "Apache-2.0", "prompt": "A sample contains 5.59 mol of sodium chloride. Using molar mass 58.44 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 5.59 mol * 58.44 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "sodium chloride", "molar_mass": 58.44, "moles": 5.59}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 700 mL to 0.7 L.\n3. Compute M = 2.935 / 0.7.\nFinal: {\"answer\": 4.1929, \"unit\": \"mol/L\"}", "dedupe_signature": "5dc9382755c133f26a8b0d0393dd998334268b58b194b2b31350063c3cea95f6", "difficulty": "medium", "final_answer": {"answer": 4.1929, "unit": "mol/L"}, "id": "molarity_006092_2.935_700", "license": "Apache-2.0", "prompt": "A solution contains 2.935 mol of solute in 700 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 700 mL to 0.7 L.\nCompute M = 2.935 / 0.7.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 2.935, "volume_ml": 700}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.51 y, so each step multiplies y by 1 - h*0.51.\n3. Apply that update for 4 steps and round the final state.\nFinal: {\"answer\": 0.0, \"unit\": \"state_units\"}", "dedupe_signature": "132ce8bd5d6a38d6b03c7bb60d464df82e8c3738f347977f5db4b7946a220c20", "difficulty": "medium", "final_answer": {"answer": 0.0, "unit": "state_units"}, "id": "euler_decay_006093_76.5_0.51_2_4", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.51 y with y(0)=76.5, step size h=2, for 4 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.51 y, so each step multiplies y by 1 - h*0.51.\nApply that update for 4 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 76.5, "rate": 0.51, "step": 2.0, "steps": 4}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(9.4)=41.28 and f(16.1)=82.82.\n3. The interval width is 6.7.\nFinal: {\"answer\": 415.735, \"unit\": \"area_units\"}", "dedupe_signature": "3ccbe56d2b93bc3af7e2ca9bfcf50564dfb4015b8d02fb097a6f7626ba6c3e4b", "difficulty": "medium", "final_answer": {"answer": 415.735, "unit": "area_units"}, "id": "trapz_linear_006094_6.2_-17_9.4_16.1", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=6.2x+-17 from x=9.4 to x=16.1. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(9.4)=41.28 and f(16.1)=82.82.\nThe interval width is 6.7.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -17.0, "slope": 6.2, "x0": 9.4, "x1": 16.1}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.38 and add it to the current value.\nFinal: {\"answer\": [-0.109, -0.12, 1.018], \"unit\": \"temperature_units\"}", "dedupe_signature": "c5cc167cd0961c718928dc7ddc8789da2c606ec2dc1a9521f4980bb2d5800712", "difficulty": "hard", "final_answer": {"answer": [-0.109, -0.12, 1.018], "unit": "temperature_units"}, "id": "heat_step_006095_0.38_-1.15_-0.85_1.4_-0.35_1.5", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-1.15, right=1.5; current interior values are [-0.85, 1.4, -0.35]. Use r=0.38. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.38 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-0.85, 1.4, -0.35], "left": -1.15, "r": 0.38, "right": 1.5}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 20866.0 / 1000.\nFinal: {\"answer\": 20.866, \"unit\": \"kg\"}", "dedupe_signature": "cd12cf775d7783b780e06c9fc98cb7eea14b64bccdb30c30f613a4a71127a825", "difficulty": "easy", "final_answer": {"answer": 20.866, "unit": "kg"}, "id": "unit_convert_006096_g_to_kg_20866", "license": "Apache-2.0", "prompt": "Convert 20866 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 20866.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 20866.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=258 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-26.8206, -126.181], \"unit\": \"N\"}", "dedupe_signature": "58aa19579a68b5bf676b820679da67e1298cc05947cda61c368ca8eee00c532d", "difficulty": "medium", "final_answer": {"answer": [-26.8206, -126.181], "unit": "N"}, "id": "vector_components_006097_129_258", "license": "Apache-2.0", "prompt": "A vector has magnitude 129 N at 258 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=258 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 258, "magnitude": 129.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [1.35, 1.0], \"unit\": \"dimensionless\"}", "dedupe_signature": "c16d93b580a1c1792ccc35d0d1c16dd45b447210f3852f53c475c9ac6f10d0d7", "difficulty": "medium", "final_answer": {"answer": [1.35, 1.0], "unit": "dimensionless"}, "id": "line_two_point_006098_9.75_14_1.35_1", "license": "Apache-2.0", "prompt": "A line passes through points (9.75, 14.1625) and (14, 19.9). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 9.75, "x2": 14.0, "y1": 14.162500000000001, "y2": 19.900000000000002}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. speed squared over acceleration has units of meters\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "40bb2a51c1232750610683113ccdc25ad6a68f68426a5cab30c843bb82afecd6", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_006099_consistent_741d4e34_3732", "license": "Apache-2.0", "prompt": "In student derivation case 3732, check dimensional consistency for R = v^2 * sin(theta) / g. The left side has dimensions m and the right side has dimensions m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nspeed squared over acceleration has units of meters\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "R = v^2 * sin(theta) / g"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: launch_angle_or_vertical_velocity.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"launch_angle_or_vertical_velocity\"]}", "dedupe_signature": "81ac93c5b8a82ba6f6d8a6eee26742bbaf3e4ca65fa820e40d0d449565e93888", "difficulty": "easy", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["launch_angle_or_vertical_velocity"]}, "id": "abstain_006101_launch_angle_or_vertical_velocity", "license": "Apache-2.0", "prompt": "Compute projectile range on level ground. The prompt gives initial speed 65.9 m/s but does not give launch angle or vertical velocity. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: launch_angle_or_vertical_velocity.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["launch_angle_or_vertical_velocity"]}, "verifier": {"missing": ["launch_angle_or_vertical_velocity"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 2.95 kg and a = 4.1 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 12.095, \"unit\": \"N\"}", "dedupe_signature": "3c8fa04f7653501c8943faffad0428d16752f9313dcff9eecf6b2766dc4f570f", "difficulty": "easy", "final_answer": {"answer": 12.095, "unit": "N"}, "id": "force_006102_2.95_4.1", "license": "Apache-2.0", "prompt": "A cart has mass 2.95 kg and measured acceleration 4.1 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 2.95 kg and a = 4.1 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 4.1, "mass": 2.95}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=76 degrees through the sine of 2 theta.\n3. Substitute v=65.3 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 204.0641, \"unit\": \"m\"}", "dedupe_signature": "f094c622797372949748ea652a0067f5cbb1bede263846e61b1ab054a06a0bcc", "difficulty": "medium", "final_answer": {"answer": 204.0641, "unit": "m"}, "id": "projectile_range_006104_65.3_76", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 65.3 m/s and angle 76 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=76 degrees through the sine of 2 theta.\nSubstitute v=65.3 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 76, "gravity": 9.81, "speed": 65.3}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 3.89 * 8.314 * 360 / 62.1.\nFinal: {\"answer\": 187.4867, \"unit\": \"kPa\"}", "dedupe_signature": "681c8137120d3fca7b16b2ede6350b77e425a6e99526890153400f08145f16c7", "difficulty": "medium", "final_answer": {"answer": 187.4867, "unit": "kPa"}, "id": "ideal_gas_006105_3.89_360_62.1", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=3.89 mol, T=360 K, and V=62.1 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 3.89 * 8.314 * 360 / 62.1.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 3.89, "temp_k": 360, "volume_l": 62.1}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=114.4 V and R=18.4 ohm.\nFinal: {\"answer\": 711.2696, \"unit\": \"W\"}", "dedupe_signature": "b4f68afc4b52a2a802228a939e39fee842086243679acbf62b0f0da7010be1c6", "difficulty": "easy", "final_answer": {"answer": 711.2696, "unit": "W"}, "id": "ohm_power_006107_114.4_18.4", "license": "Apache-2.0", "prompt": "A resistor has resistance 18.4 ohm and voltage 114.4 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=114.4 V and R=18.4 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 18.4, "voltage": 114.4}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=754.5 mg, t=322 h, and T_half=118 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 113.8163, \"unit\": \"mg\"}", "dedupe_signature": "f2189c46c9907699b3c6e5c7cf5bd0c06a17da34a62b172ba31b26335dd11b10", "difficulty": "medium", "final_answer": {"answer": 113.8163, "unit": "mg"}, "id": "half_life_006108_754.5_118_322", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 754.5 mg. Its half-life is 118 hours. How many mg remain after 322 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=754.5 mg, t=322 h, and T_half=118 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 322.0, "half_life": 118.0, "initial_amount": 754.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 1.84 mol * 58.44 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 107.5296, \"unit\": \"g\"}", "dedupe_signature": "b062b854e85f2434a03747e70f1573ba06d6124cafbd760435eace188105b4c7", "difficulty": "medium", "final_answer": {"answer": 107.5296, "unit": "g"}, "id": "stoich_mass_006109_sodium_chloride_1.84", "license": "Apache-2.0", "prompt": "A sample contains 1.84 mol of sodium chloride. Using molar mass 58.44 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 1.84 mol * 58.44 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "sodium chloride", "molar_mass": 58.44, "moles": 1.84}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 2680 mL to 2.68 L.\n3. Compute M = 4.64 / 2.68.\nFinal: {\"answer\": 1.7313, \"unit\": \"mol/L\"}", "dedupe_signature": "d02c2b538bf00939a70fecd1ed8e868129a9e37365e20316c0a2c2f9b54bf332", "difficulty": "medium", "final_answer": {"answer": 1.7313, "unit": "mol/L"}, "id": "molarity_006110_4.64_2680", "license": "Apache-2.0", "prompt": "A solution contains 4.64 mol of solute in 2680 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 2680 mL to 2.68 L.\nCompute M = 4.64 / 2.68.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 4.64, "volume_ml": 2680}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.08 y, so each step multiplies y by 1 - h*0.08.\n3. Apply that update for 6 steps and round the final state.\nFinal: {\"answer\": 45.5398, \"unit\": \"state_units\"}", "dedupe_signature": "c075b41d6924aa84c5e51666921ba9862c27b28bc2a48712d89c13954b2c267c", "difficulty": "medium", "final_answer": {"answer": 45.5398, "unit": "state_units"}, "id": "euler_decay_006111_54_0.08_0.35_6", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.08 y with y(0)=54, step size h=0.35, for 6 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.08 y, so each step multiplies y by 1 - h*0.08.\nApply that update for 6 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 54.0, "rate": 0.08, "step": 0.35, "steps": 6}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(7.7)=6.29 and f(9.6)=3.82.\n3. The interval width is 1.9.\nFinal: {\"answer\": 9.6045, \"unit\": \"area_units\"}", "dedupe_signature": "450152209cf0e501c9deeff7c4a78cb26262e04661e1823f13848f7266515e50", "difficulty": "medium", "final_answer": {"answer": 9.6045, "unit": "area_units"}, "id": "trapz_linear_006112_-1.3_16.3_7.7_9.6", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-1.3x+16.3 from x=7.7 to x=9.6. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(7.7)=6.29 and f(9.6)=3.82.\nThe interval width is 1.9.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 16.3, "slope": -1.3, "x0": 7.7, "x1": 9.6}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.02 and add it to the current value.\nFinal: {\"answer\": [-0.325, 1.317, 1.401], \"unit\": \"temperature_units\"}", "dedupe_signature": "9d406966abd555a8dd41adb22c8272422675f1665b9d176f0a3fd677e5002a03", "difficulty": "hard", "final_answer": {"answer": [-0.325, 1.317, 1.401], "unit": "temperature_units"}, "id": "heat_step_006113_0.02_1.6_-0.4_1.35_1.45_-0.9", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.6, right=-0.9; current interior values are [-0.4, 1.35, 1.45]. Use r=0.02. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.02 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-0.4, 1.35, 1.45], "left": 1.6, "r": 0.02, "right": -0.9}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 46436.0 / 1000.\nFinal: {\"answer\": 46.436, \"unit\": \"kg\"}", "dedupe_signature": "4af6f22633438fb744d77eb178b790910538adafcac7fba22f80224cffe066ba", "difficulty": "easy", "final_answer": {"answer": 46.436, "unit": "kg"}, "id": "unit_convert_006114_g_to_kg_46436", "license": "Apache-2.0", "prompt": "Convert 46436 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 46436.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 46436.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-2.95, 20.25], \"unit\": \"dimensionless\"}", "dedupe_signature": "64c085f5581a09c7a985aafe16dcc469c89e6f26c874b9fbad8e8a78097d5572", "difficulty": "medium", "final_answer": {"answer": [-2.95, 20.25], "unit": "dimensionless"}, "id": "line_two_point_006116_17_25.75_-2.95_20.25", "license": "Apache-2.0", "prompt": "A line passes through points (17, -29.9) and (25.75, -55.7125). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 17.0, "x2": 25.75, "y1": -29.900000000000006, "y2": -55.712500000000006}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. speed squared over acceleration has units of meters\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "5344da024c3516c777e39d62942bbd838f170eba3c7e8b7ae293fcf18393ce68", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_006117_consistent_741d4e34_128848", "license": "Apache-2.0", "prompt": "In lab notebook case 128848, check dimensional consistency for R = v^2 * sin(theta) / g. The left side has dimensions m and the right side has dimensions m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nspeed squared over acceleration has units of meters\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "R = v^2 * sin(theta) / g"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef center_values_006118(values):\n    if not values:\n        raise ValueError('center_values requires at least one value')\n    mean = sum(values) / len(values)\n    return [value - mean for value in values]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"center_values_006118\"}", "dedupe_signature": "f9abff9f289fc8d2e63cfadb5cb6f0b0160cd33d9b2339581077d5552fa2d3e3", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "center_values_006118"}, "id": "code_006118_center_values_006118", "license": "Apache-2.0", "prompt": "Write a Python function center_values_006118(values) that subtracts the arithmetic mean from each value and returns a new list. Raise ValueError for an empty input. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "center_values_006118"}, "verifier": {"function": "center_values_006118", "tests": ["out = center_values_006118([1, 2, 3]); assert out == [-1, 0, 1]", "assert center_values_006118([5]) == [0]", "try:\n    center_values_006118([])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 29.6^2 and multiply by 0.5 * 1.75.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 766.64, \"unit\": \"J\"}", "dedupe_signature": "0c8c751d09968ecf9c72588d397d7bc726df8e281a090b9757141a4cad8de09a", "difficulty": "easy", "final_answer": {"answer": 766.64, "unit": "J"}, "id": "ke_006121_1.75_29.6", "license": "Apache-2.0", "prompt": "A body of mass 1.75 kg moves at 29.6 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 29.6^2 and multiply by 0.5 * 1.75.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 1.75, "velocity": 29.6}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=78 degrees through the sine of 2 theta.\n3. Substitute v=66.7 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 184.4573, \"unit\": \"m\"}", "dedupe_signature": "a00e594926a9c6943f6f89f84e72db64a1e1f53b6f95a13da71d38f65cc69c1d", "difficulty": "medium", "final_answer": {"answer": 184.4573, "unit": "m"}, "id": "projectile_range_006122_66.7_78", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 66.7 m/s and angle 78 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=78 degrees through the sine of 2 theta.\nSubstitute v=66.7 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 78, "gravity": 9.81, "speed": 66.7}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 5.59 * 8.314 * 335 / 108.0.\nFinal: {\"answer\": 144.1594, \"unit\": \"kPa\"}", "dedupe_signature": "c27cea80c28b5369cd96ff378fd358d2bc4d95321db40b894f55ef1aa12e8368", "difficulty": "medium", "final_answer": {"answer": 144.1594, "unit": "kPa"}, "id": "ideal_gas_006123_5.59_335_108.0", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=5.59 mol, T=335 K, and V=108.0 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 5.59 * 8.314 * 335 / 108.0.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 5.59, "temp_k": 335, "volume_l": 108.0}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 425 * 1.205 * 28.\nFinal: {\"answer\": 14339.5, \"unit\": \"J\"}", "dedupe_signature": "7a28ad18d77d19a561ede1c2b9277fbe17bd72dfd327031944546920e929a5c8", "difficulty": "easy", "final_answer": {"answer": 14339.5, "unit": "J"}, "id": "heat_q_006124_425_1.205_28", "license": "Apache-2.0", "prompt": "A 425 g sample has specific heat 1.205 J/(g*K). How much heat is needed to raise its temperature by 28 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 425 * 1.205 * 28.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 28, "heat_capacity": 1.205, "mass_g": 425}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=233 V and R=82.3 ohm.\nFinal: {\"answer\": 659.6476, \"unit\": \"W\"}", "dedupe_signature": "b14004cc82f520d79f96e0c5c602d91b433def81437689fe48fbf7bee2862610", "difficulty": "easy", "final_answer": {"answer": 659.6476, "unit": "W"}, "id": "ohm_power_006125_233_82.3", "license": "Apache-2.0", "prompt": "A resistor has resistance 82.3 ohm and voltage 233 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=233 V and R=82.3 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 82.3, "voltage": 233.0}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=690 mg, t=207.5 h, and T_half=112 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 191.0457, \"unit\": \"mg\"}", "dedupe_signature": "d8325ccd0418eb4258977c03c884795945db25042d800be5bc27bbb919ec9651", "difficulty": "medium", "final_answer": {"answer": 191.0457, "unit": "mg"}, "id": "half_life_006126_690_112_207.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 690 mg. Its half-life is 112 hours. How many mg remain after 207.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=690 mg, t=207.5 h, and T_half=112 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 207.5, "half_life": 112.0, "initial_amount": 690.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 0.62 mol * 100.087 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 62.0539, \"unit\": \"g\"}", "dedupe_signature": "8a2b2f899fe2616e133401f237d27b7948bfd62755490a3666ac3dbd07616c3f", "difficulty": "medium", "final_answer": {"answer": 62.0539, "unit": "g"}, "id": "stoich_mass_006127_calcium_carbonate_0.62", "license": "Apache-2.0", "prompt": "A sample contains 0.62 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 0.62 mol * 100.087 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "calcium carbonate", "molar_mass": 100.087, "moles": 0.62}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 150 mL to 0.15 L.\n3. Compute M = 2.73 / 0.15.\nFinal: {\"answer\": 18.2, \"unit\": \"mol/L\"}", "dedupe_signature": "92f40a059c91c153da9d780b66dc03eb7876839def19067cd7c06f19c269bf34", "difficulty": "medium", "final_answer": {"answer": 18.2, "unit": "mol/L"}, "id": "molarity_006128_2.73_150", "license": "Apache-2.0", "prompt": "A solution contains 2.73 mol of solute in 150 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 150 mL to 0.15 L.\nCompute M = 2.73 / 0.15.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 2.73, "volume_ml": 150}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.78 y, so each step multiplies y by 1 - h*0.78.\n3. Apply that update for 4 steps and round the final state.\nFinal: {\"answer\": 10.7547, \"unit\": \"state_units\"}", "dedupe_signature": "53c96603cd5ac18073bf77b37c55fd811da57f361009df8daa9a586fa1869a80", "difficulty": "medium", "final_answer": {"answer": 10.7547, "unit": "state_units"}, "id": "euler_decay_006129_38.5_0.78_0.35_4", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.78 y with y(0)=38.5, step size h=0.35, for 4 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.78 y, so each step multiplies y by 1 - h*0.78.\nApply that update for 4 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 38.5, "rate": 0.78, "step": 0.35, "steps": 4}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.2 and add it to the current value.\nFinal: {\"answer\": [0.49, 0.67, 0.33], \"unit\": \"temperature_units\"}", "dedupe_signature": "6b3510cba539cd113638dd3a05b43e1cfe259c929c2db84dba7efbb53e441b51", "difficulty": "hard", "final_answer": {"answer": [0.49, 0.67, 0.33], "unit": "temperature_units"}, "id": "heat_step_006131_0.2_2.15_-0.35_1.35_-0.35_1.35", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=2.15, right=1.35; current interior values are [-0.35, 1.35, -0.35]. Use r=0.2. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.2 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-0.35, 1.35, -0.35], "left": 2.15, "r": 0.2, "right": 1.35}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kelvin equals Celsius plus 273.15.\n2. Apply the conversion factor directly to the given value.\n3. Compute 84.5 + 273.15.\nFinal: {\"answer\": 357.65, \"unit\": \"K\"}", "dedupe_signature": "2b8a2595949dc88220e7648f5e30f38eab4210665908deda7303e74b8e0c462e", "difficulty": "easy", "final_answer": {"answer": 357.65, "unit": "K"}, "id": "unit_convert_006132_c_to_k_84.5", "license": "Apache-2.0", "prompt": "Convert 84.5 degC to K. Return the converted value with unit.", "reasoning_trace": "Kelvin equals Celsius plus 273.15.\nApply the conversion factor directly to the given value.\nCompute 84.5 + 273.15.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 84.5}, "verifier": {"formula": "value + 273.15", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [4.4, 5.75], \"unit\": \"dimensionless\"}", "dedupe_signature": "a6e65843cd40e9c5cf3db95432affc477a6d3bc5e0985a6d6d76548218943a63", "difficulty": "medium", "final_answer": {"answer": [4.4, 5.75], "unit": "dimensionless"}, "id": "line_two_point_006134_-7_-6.75_4.4_5.75", "license": "Apache-2.0", "prompt": "A line passes through points (-7, -25.05) and (-6.75, -23.95). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -7.0, "x2": -6.75, "y1": -25.050000000000004, "y2": -23.950000000000003}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. volt squared divided by ohm is watt\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "5c9c52f422b0fdd4f0ad076aec571d93c8908d9cfb4d259b7a989225bfa878e9", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_006135_consistent_82e93f3d_907583", "license": "Apache-2.0", "prompt": "In sensor calibration case 907583, check dimensional consistency for P = V^2 / R. The left side has dimensions W and the right side has dimensions W. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nvolt squared divided by ohm is watt\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "P = V^2 / R"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef weighted_sum_006136(values, weights):\n    if len(values) != len(weights):\n        raise ValueError('length mismatch')\n    return sum(value * weight for value, weight in zip(values, weights))\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"weighted_sum_006136\"}", "dedupe_signature": "9a677bf84a9033a9304ec536a3c174ea1eec0384e4b3379492ad9323a5a06ab3", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "weighted_sum_006136"}, "id": "code_006136_weighted_sum_006136", "license": "Apache-2.0", "prompt": "Write a Python function weighted_sum_006136(values, weights) that returns sum(value*weight). Raise ValueError when the two inputs have different lengths. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "weighted_sum_006136"}, "verifier": {"function": "weighted_sum_006136", "tests": ["assert weighted_sum_006136([2, 3], [4, 5]) == 23", "assert weighted_sum_006136([], []) == 0", "try:\n    weighted_sum_006136([1], [1, 2])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: recurrence, objective, tie_breaking_rule.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"recurrence\", \"objective\", \"tie_breaking_rule\"]}", "dedupe_signature": "cb3b00b630a92a0375c94ee7615a8184284d371a1eb76ec929411b4203df520d", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["recurrence", "objective", "tie_breaking_rule"]}, "id": "abstain_006137_recurrence_objective_tie_breaking_rule", "license": "Apache-2.0", "prompt": "Write a dynamic-programming solver for a knapsack scoring problem with 4911 items and budget 5100, but the recurrence, objective, and tie-breaking rule are all absent. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: recurrence, objective, tie_breaking_rule.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["recurrence", "objective", "tie_breaking_rule"]}, "verifier": {"missing": ["recurrence", "objective", "tie_breaking_rule"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 41^2 and multiply by 0.5 * 2.6.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 2185.3, \"unit\": \"J\"}", "dedupe_signature": "fc8faae81065e0107b127c1dde43b9f846c36d2da9b91dcfb55e198202562c90", "difficulty": "easy", "final_answer": {"answer": 2185.3, "unit": "J"}, "id": "ke_006139_2.6_41", "license": "Apache-2.0", "prompt": "A body of mass 2.6 kg moves at 41 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 41^2 and multiply by 0.5 * 2.6.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 2.6, "velocity": 41.0}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=63 degrees through the sine of 2 theta.\n3. Substitute v=39.5 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 128.6716, \"unit\": \"m\"}", "dedupe_signature": "384cc9948271d063da0a7c63ae40eeef749728bca9636b512816fb795adbc757", "difficulty": "medium", "final_answer": {"answer": 128.6716, "unit": "m"}, "id": "projectile_range_006140_39.5_63", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 39.5 m/s and angle 63 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=63 degrees through the sine of 2 theta.\nSubstitute v=39.5 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 63, "gravity": 9.81, "speed": 39.5}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1855 * 3.82 * 110.\nFinal: {\"answer\": 779471.0, \"unit\": \"J\"}", "dedupe_signature": "c91a6136ae9fc42ee270bdac45944b760fc950158f77d11bb519c27a5b01be04", "difficulty": "easy", "final_answer": {"answer": 779471.0, "unit": "J"}, "id": "heat_q_006142_1855_3.82_110", "license": "Apache-2.0", "prompt": "A 1855 g sample has specific heat 3.82 J/(g*K). How much heat is needed to raise its temperature by 110 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1855 * 3.82 * 110.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 110, "heat_capacity": 3.82, "mass_g": 1855}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=197.8 V and R=104 ohm.\nFinal: {\"answer\": 376.2004, \"unit\": \"W\"}", "dedupe_signature": "bb5a837a4e7ca24f6d5ae594ca02d44104e0435b9d88847d9f39f865bd8780cd", "difficulty": "easy", "final_answer": {"answer": 376.2004, "unit": "W"}, "id": "ohm_power_006143_197.8_104", "license": "Apache-2.0", "prompt": "A resistor has resistance 104 ohm and voltage 197.8 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=197.8 V and R=104 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 104.0, "voltage": 197.8}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=701 mg, t=208.5 h, and T_half=103.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 173.4983, \"unit\": \"mg\"}", "dedupe_signature": "b12d2956b51226715b19a10e09d755928e3620b59158fd66114a3953eae8e43a", "difficulty": "medium", "final_answer": {"answer": 173.4983, "unit": "mg"}, "id": "half_life_006144_701_103.5_208.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 701 mg. Its half-life is 103.5 hours. How many mg remain after 208.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=701 mg, t=208.5 h, and T_half=103.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 208.5, "half_life": 103.5, "initial_amount": 701.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 3 mol * 44.01 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 132.03, \"unit\": \"g\"}", "dedupe_signature": "857eaaa860f2bf3228e1aa8056a72c2abda2869ad620030d74f6b59de98d4394", "difficulty": "medium", "final_answer": {"answer": 132.03, "unit": "g"}, "id": "stoich_mass_006145_carbon_dioxide_3", "license": "Apache-2.0", "prompt": "A sample contains 3 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 3 mol * 44.01 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "carbon dioxide", "molar_mass": 44.01, "moles": 3.0}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 4555 mL to 4.555 L.\n3. Compute M = 4.41 / 4.555.\nFinal: {\"answer\": 0.9682, \"unit\": \"mol/L\"}", "dedupe_signature": "a34a4e18a146272868674b6bdd133810407af2b7d247955ef8afe49014bba9e0", "difficulty": "medium", "final_answer": {"answer": 0.9682, "unit": "mol/L"}, "id": "molarity_006146_4.41_4555", "license": "Apache-2.0", "prompt": "A solution contains 4.41 mol of solute in 4555 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 4555 mL to 4.555 L.\nCompute M = 4.41 / 4.555.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 4.41, "volume_ml": 4555}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.87 y, so each step multiplies y by 1 - h*0.87.\n3. Apply that update for 8 steps and round the final state.\nFinal: {\"answer\": 0.0, \"unit\": \"state_units\"}", "dedupe_signature": "994a18039a0604c0fb61a05f448523ba999e6a0197ca3ea53e945d98bc7c39bb", "difficulty": "medium", "final_answer": {"answer": 0.0, "unit": "state_units"}, "id": "euler_decay_006147_29_0.87_1.25_8", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.87 y with y(0)=29, step size h=1.25, for 8 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.87 y, so each step multiplies y by 1 - h*0.87.\nApply that update for 8 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 29.0, "rate": 0.87, "step": 1.25, "steps": 8}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-0.8)=11.58 and f(0.5)=17.3.\n3. The interval width is 1.3.\nFinal: {\"answer\": 18.772, \"unit\": \"area_units\"}", "dedupe_signature": "3ff3fefb9539a95b880453d7ca816a7d6230990309a4c8cae4eb8545d52d92b4", "difficulty": "medium", "final_answer": {"answer": 18.772, "unit": "area_units"}, "id": "trapz_linear_006148_4.4_15.1_-0.8_0.5", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=4.4x+15.1 from x=-0.8 to x=0.5. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-0.8)=11.58 and f(0.5)=17.3.\nThe interval width is 1.3.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 15.1, "slope": 4.4, "x0": -0.8, "x1": 0.5}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.46 and add it to the current value.\nFinal: {\"answer\": [2.131, 0.697, 0.468], \"unit\": \"temperature_units\"}", "dedupe_signature": "d0b679d02f1c563396554df0837652ed2e5cb14e2c06d43c0988ba40c5997f71", "difficulty": "hard", "final_answer": {"answer": [2.131, 0.697, 0.468], "unit": "temperature_units"}, "id": "heat_step_006149_0.46_2.15_2.2_2.1_-1.05_-0.9", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=2.15, right=-0.9; current interior values are [2.2, 2.1, -1.05]. Use r=0.46. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.46 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [2.2, 2.1, -1.05], "left": 2.15, "r": 0.46, "right": -0.9}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 100 centimeters in one meter.\n2. Apply the conversion factor directly to the given value.\n3. Compute 3075.0 / 100.\nFinal: {\"answer\": 30.75, \"unit\": \"m\"}", "dedupe_signature": "0daefd62fd9c294273c69734b9938d9ebbe7a8110c3e0b16fe402cc273381395", "difficulty": "easy", "final_answer": {"answer": 30.75, "unit": "m"}, "id": "unit_convert_006150_cm_to_m_3075", "license": "Apache-2.0", "prompt": "Convert 3075 cm to m. Return the converted value with unit.", "reasoning_trace": "There are 100 centimeters in one meter.\nApply the conversion factor directly to the given value.\nCompute 3075.0 / 100.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 3075.0}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=165 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-14.9719, 4.0117], \"unit\": \"N\"}", "dedupe_signature": "487479f174f828114bb8a3badabcf84d593a0199223277bed83290cfbbe2bbb6", "difficulty": "medium", "final_answer": {"answer": [-14.9719, 4.0117], "unit": "N"}, "id": "vector_components_006151_15.5_165", "license": "Apache-2.0", "prompt": "A vector has magnitude 15.5 N at 165 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=165 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 165, "magnitude": 15.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [7.65, -8.75], \"unit\": \"dimensionless\"}", "dedupe_signature": "cdc00382e95d10875a3a9e3884cc0890c23536d1aa8702d5371bc3f63f2af30c", "difficulty": "medium", "final_answer": {"answer": [7.65, -8.75], "unit": "dimensionless"}, "id": "line_two_point_006152_-13_-5.25_7.65_-8.75", "license": "Apache-2.0", "prompt": "A line passes through points (-13, -108.2) and (-5.25, -48.9125). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -13.0, "x2": -5.25, "y1": -108.2, "y2": -48.9125}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. velocity divided by time is acceleration\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "9e95a3c7d18fd481524d9037141a87b9fa175f7983ecb737cd8943ff42607884", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_006153_inconsistent_c1271127_930344", "license": "Apache-2.0", "prompt": "In lab notebook case 930344, check dimensional consistency for x = v / t. The left side has dimensions m and the right side has dimensions m/s^2. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nvelocity divided by time is acceleration\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "x = v / t"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef center_values_006154(values):\n    if not values:\n        raise ValueError('center_values requires at least one value')\n    mean = sum(values) / len(values)\n    return [value - mean for value in values]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"center_values_006154\"}", "dedupe_signature": "e5e99943debd2e5154483767c406c885e382997cd06badce40d4d56f6a290b74", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "center_values_006154"}, "id": "code_006154_center_values_006154", "license": "Apache-2.0", "prompt": "Write a Python function center_values_006154(values) that subtracts the arithmetic mean from each value and returns a new list. Raise ValueError for an empty input. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "center_values_006154"}, "verifier": {"function": "center_values_006154", "tests": ["out = center_values_006154([1, 2, 3]); assert out == [-1, 0, 1]", "assert center_values_006154([5]) == [0]", "try:\n    center_values_006154([])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: rate_constant, number_of_steps.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"rate_constant\", \"number_of_steps\"]}", "dedupe_signature": "63ab9d25cbb9851d150954d2ee679fa982e9f075e1f6df0ab34284b1b5949aa3", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["rate_constant", "number_of_steps"]}, "id": "abstain_006155_rate_constant_number_of_steps", "license": "Apache-2.0", "prompt": "Use explicit Euler for dy/dt = -k y. The prompt gives y(0)=48.5 and h=1.5, but omits both k and the number of steps. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: rate_constant, number_of_steps.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["rate_constant", "number_of_steps"]}, "verifier": {"missing": ["rate_constant", "number_of_steps"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 11.25 kg and a = 6.6 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 74.25, \"unit\": \"N\"}", "dedupe_signature": "3ebe480301b3808c68bee1fc21027f5d1ea37fe6de389276a36db753aab07308", "difficulty": "easy", "final_answer": {"answer": 74.25, "unit": "N"}, "id": "force_006156_11.25_6.6", "license": "Apache-2.0", "prompt": "A cart has mass 11.25 kg and measured acceleration 6.6 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 11.25 kg and a = 6.6 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 6.6, "mass": 11.25}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=85 degrees through the sine of 2 theta.\n3. Substitute v=22.4 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 8.8817, \"unit\": \"m\"}", "dedupe_signature": "480027f749acc246339ca9bdef67549ccd320453000a0bd5dc901e1a695e7d1a", "difficulty": "medium", "final_answer": {"answer": 8.8817, "unit": "m"}, "id": "projectile_range_006158_22.4_85", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 22.4 m/s and angle 85 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=85 degrees through the sine of 2 theta.\nSubstitute v=22.4 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 85, "gravity": 9.81, "speed": 22.4}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 3.29 * 8.314 * 418 / 16.1.\nFinal: {\"answer\": 710.1602, \"unit\": \"kPa\"}", "dedupe_signature": "027bf634456c87c9938b4929e8467aaaf9484317af7b403d3c2128fd3a301440", "difficulty": "medium", "final_answer": {"answer": 710.1602, "unit": "kPa"}, "id": "ideal_gas_006159_3.29_418_16.1", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=3.29 mol, T=418 K, and V=16.1 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 3.29 * 8.314 * 418 / 16.1.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 3.29, "temp_k": 418, "volume_l": 16.1}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=1.1 V and R=86.2 ohm.\nFinal: {\"answer\": 0.014, \"unit\": \"W\"}", "dedupe_signature": "51981f2838f2864ed3666b0eafa8fefbf2c17009b1d369bda9f9691bfedc6b33", "difficulty": "easy", "final_answer": {"answer": 0.014, "unit": "W"}, "id": "ohm_power_006161_1.1_86.2", "license": "Apache-2.0", "prompt": "A resistor has resistance 86.2 ohm and voltage 1.1 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=1.1 V and R=86.2 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 86.2, "voltage": 1.1}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.06 y, so each step multiplies y by 1 - h*0.06.\n3. Apply that update for 4 steps and round the final state.\nFinal: {\"answer\": 11.5329, \"unit\": \"state_units\"}", "dedupe_signature": "c5a83878a53bedf03610f7b64fc0f165aaeec20553f135c0b347777fcc901172", "difficulty": "medium", "final_answer": {"answer": 11.5329, "unit": "state_units"}, "id": "euler_decay_006165_17.5_0.06_1.65_4", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.06 y with y(0)=17.5, step size h=1.65, for 4 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.06 y, so each step multiplies y by 1 - h*0.06.\nApply that update for 4 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 17.5, "rate": 0.06, "step": 1.65, "steps": 4}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(5.8)=-18.3 and f(6.9)=-22.15.\n3. The interval width is 1.1.\nFinal: {\"answer\": -22.2475, \"unit\": \"area_units\"}", "dedupe_signature": "27e0f2b6863e9ea3d4f30ac5502b295513127b0d73c7fd2bf5c4b714aae57bd5", "difficulty": "medium", "final_answer": {"answer": -22.2475, "unit": "area_units"}, "id": "trapz_linear_006166_-3.5_2_5.8_6.9", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-3.5x+2 from x=5.8 to x=6.9. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(5.8)=-18.3 and f(6.9)=-22.15.\nThe interval width is 1.1.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 2.0, "slope": -3.5, "x0": 5.8, "x1": 6.9}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.32 and add it to the current value.\nFinal: {\"answer\": [0.91, 1.416, 1.762], \"unit\": \"temperature_units\"}", "dedupe_signature": "03fce35b571e061a5f89a50437b17bb31c20bb5e1e2d377fb4a098e7dbc1099d", "difficulty": "hard", "final_answer": {"answer": [0.91, 1.416, 1.762], "unit": "temperature_units"}, "id": "heat_step_006167_0.32_0.65_0.35_1.8_2.05_1.4", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=0.65, right=1.4; current interior values are [0.35, 1.8, 2.05]. Use r=0.32. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.32 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [0.35, 1.8, 2.05], "left": 0.65, "r": 0.32, "right": 1.4}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kelvin equals Celsius plus 273.15.\n2. Apply the conversion factor directly to the given value.\n3. Compute 180.0 + 273.15.\nFinal: {\"answer\": 453.15, \"unit\": \"K\"}", "dedupe_signature": "5f441c2456e22b1ef7d2babea9e112071d2471b08b3c5ab5a76029a33c1eee7b", "difficulty": "easy", "final_answer": {"answer": 453.15, "unit": "K"}, "id": "unit_convert_006168_c_to_k_180", "license": "Apache-2.0", "prompt": "Convert 180 degC to K. Return the converted value with unit.", "reasoning_trace": "Kelvin equals Celsius plus 273.15.\nApply the conversion factor directly to the given value.\nCompute 180.0 + 273.15.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 180.0}, "verifier": {"formula": "value + 273.15", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=112 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-106.9502, 264.711], \"unit\": \"N\"}", "dedupe_signature": "a04d5c7ca9aeb27b33e7da2b900015cd7cdf6bf2a778b717c552efb47574b844", "difficulty": "medium", "final_answer": {"answer": [-106.9502, 264.711], "unit": "N"}, "id": "vector_components_006169_285.5_112", "license": "Apache-2.0", "prompt": "A vector has magnitude 285.5 N at 112 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=112 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 112, "magnitude": 285.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-4.85, 25.75], \"unit\": \"dimensionless\"}", "dedupe_signature": "3869de63d0fd684e437a0a63dec78006c0bb3afe2467f4c40a01d5f7a97af278", "difficulty": "medium", "final_answer": {"answer": [-4.85, 25.75], "unit": "dimensionless"}, "id": "line_two_point_006170_4.25_17_-4.85_25.75", "license": "Apache-2.0", "prompt": "A line passes through points (4.25, 5.1375) and (17, -56.7). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 4.25, "x2": 17.0, "y1": 5.137500000000003, "y2": -56.69999999999999}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. grams cancel with J/(g*K), and kelvin cancels, leaving joules\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "fdbb8ed4242a4510e0b6b6cb1bdd54505ec21ac530658ebe35ab7a5b99ae56ff", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_006171_consistent_4153435f_792977", "license": "Apache-2.0", "prompt": "In instrument manual case 792977, check dimensional consistency for Q = m * c * DeltaT. The left side has dimensions J and the right side has dimensions J. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\ngrams cancel with J/(g*K), and kelvin cancels, leaving joules\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "Q = m * c * DeltaT"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef threshold_flags_006172(values, threshold):\n    return [value >= threshold for value in values]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"threshold_flags_006172\"}", "dedupe_signature": "ddea48282e0577152215f178c743dd942888d764db7ad8be8e0aba48ea7d2c85", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "threshold_flags_006172"}, "id": "code_006172_threshold_flags_006172", "license": "Apache-2.0", "prompt": "Write a Python function threshold_flags_006172(values, threshold) that returns a list of booleans showing whether each value is greater than or equal to threshold. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "threshold_flags_006172"}, "verifier": {"function": "threshold_flags_006172", "tests": ["assert threshold_flags_006172([1, 2, 3], 2) == [False, True, True]", "assert threshold_flags_006172([], 5) == []", "assert threshold_flags_006172([-1, 0], 0) == [False, True]"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: launch_angle_or_vertical_velocity.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"launch_angle_or_vertical_velocity\"]}", "dedupe_signature": "b9eb5a61924eedc6bfeaa4b53d374650cc7c2ef3d262d509bfbc449c9e941718", "difficulty": "easy", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["launch_angle_or_vertical_velocity"]}, "id": "abstain_006173_launch_angle_or_vertical_velocity", "license": "Apache-2.0", "prompt": "Compute projectile range on level ground. The prompt gives initial speed 20.3 m/s but does not give launch angle or vertical velocity. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: launch_angle_or_vertical_velocity.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["launch_angle_or_vertical_velocity"]}, "verifier": {"missing": ["launch_angle_or_vertical_velocity"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 23.55 kg and a = 12.15 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 286.1325, \"unit\": \"N\"}", "dedupe_signature": "5e0586f81bbf8058da3c2d52fd5cb492f90711ab3659627cec8c0ca1918f2b19", "difficulty": "easy", "final_answer": {"answer": 286.1325, "unit": "N"}, "id": "force_006174_23.55_12.15", "license": "Apache-2.0", "prompt": "A cart has mass 23.55 kg and measured acceleration 12.15 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 23.55 kg and a = 12.15 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 12.15, "mass": 23.55}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 25.2^2 and multiply by 0.5 * 12.85.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 4080.132, \"unit\": \"J\"}", "dedupe_signature": "3820202084b51be803e0149aaa78e35b4e0fd9d5a3cd2a6c8727781ee90d8da3", "difficulty": "easy", "final_answer": {"answer": 4080.132, "unit": "J"}, "id": "ke_006175_12.85_25.2", "license": "Apache-2.0", "prompt": "A body of mass 12.85 kg moves at 25.2 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 25.2^2 and multiply by 0.5 * 12.85.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 12.85, "velocity": 25.2}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=55 degrees through the sine of 2 theta.\n3. Substitute v=40.3 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 155.5704, \"unit\": \"m\"}", "dedupe_signature": "4592ea5ea2417202d8eec5feaf22cd3579ba90730c4322b88d262b2a22379b3a", "difficulty": "medium", "final_answer": {"answer": 155.5704, "unit": "m"}, "id": "projectile_range_006176_40.3_55", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 40.3 m/s and angle 55 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=55 degrees through the sine of 2 theta.\nSubstitute v=40.3 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 55, "gravity": 9.81, "speed": 40.3}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 3.59 * 8.314 * 587 / 44.8.\nFinal: {\"answer\": 391.0791, \"unit\": \"kPa\"}", "dedupe_signature": "9c7eabe4b2e3794b8b78ebfe266dd69b3473f4efb4adb52677b291d64b657549", "difficulty": "medium", "final_answer": {"answer": 391.0791, "unit": "kPa"}, "id": "ideal_gas_006177_3.59_587_44.8", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=3.59 mol, T=587 K, and V=44.8 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 3.59 * 8.314 * 587 / 44.8.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 3.59, "temp_k": 587, "volume_l": 44.8}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=62.2 V and R=184.2 ohm.\nFinal: {\"answer\": 21.0035, \"unit\": \"W\"}", "dedupe_signature": "8d44ca9a9dd086b566fcbaad6f8859df66fae95639157dfaf9ab39014b5348d3", "difficulty": "easy", "final_answer": {"answer": 21.0035, "unit": "W"}, "id": "ohm_power_006179_62.2_184.2", "license": "Apache-2.0", "prompt": "A resistor has resistance 184.2 ohm and voltage 62.2 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=62.2 V and R=184.2 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 184.2, "voltage": 62.2}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=73 mg, t=360 h, and T_half=11 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 0.0, \"unit\": \"mg\"}", "dedupe_signature": "d854358a5a7da4164917631221428c35ae02e90c088435a0b18beff3b9579ff8", "difficulty": "medium", "final_answer": {"answer": 0.0, "unit": "mg"}, "id": "half_life_006180_73_11_360", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 73 mg. Its half-life is 11 hours. How many mg remain after 360 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=73 mg, t=360 h, and T_half=11 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 360.0, "half_life": 11.0, "initial_amount": 73.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 0.07 mol * 44.01 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 3.0807, \"unit\": \"g\"}", "dedupe_signature": "18f7c79d006970f24e790672d9370232750d4055a218c9a9590442672906111d", "difficulty": "medium", "final_answer": {"answer": 3.0807, "unit": "g"}, "id": "stoich_mass_006181_carbon_dioxide_0.07", "license": "Apache-2.0", "prompt": "A sample contains 0.07 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 0.07 mol * 44.01 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "carbon dioxide", "molar_mass": 44.01, "moles": 0.07}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 3755 mL to 3.755 L.\n3. Compute M = 4.18 / 3.755.\nFinal: {\"answer\": 1.1132, \"unit\": \"mol/L\"}", "dedupe_signature": "7d2be3b889e9fcfd2bc12aecf726994a832299eb208fe4d772191742104020a8", "difficulty": "medium", "final_answer": {"answer": 1.1132, "unit": "mol/L"}, "id": "molarity_006182_4.18_3755", "license": "Apache-2.0", "prompt": "A solution contains 4.18 mol of solute in 3755 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 3755 mL to 3.755 L.\nCompute M = 4.18 / 3.755.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 4.18, "volume_ml": 3755}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(4.1)=-7.68 and f(5.4)=-11.32.\n3. The interval width is 1.3.\nFinal: {\"answer\": -12.35, \"unit\": \"area_units\"}", "dedupe_signature": "4fa468db81187a2937864a97c431e4e4fd196cc72a70443b8dbf3ccf7be9f015", "difficulty": "medium", "final_answer": {"answer": -12.35, "unit": "area_units"}, "id": "trapz_linear_006184_-2.8_3.8_4.1_5.4", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-2.8x+3.8 from x=4.1 to x=5.4. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(4.1)=-7.68 and f(5.4)=-11.32.\nThe interval width is 1.3.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 3.8, "slope": -2.8, "x0": 4.1, "x1": 5.3999999999999995}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.42 and add it to the current value.\nFinal: {\"answer\": [0.06, -0.001, -0.54], \"unit\": \"temperature_units\"}", "dedupe_signature": "769df9417d99271c36ac3c263071bbc59d055e0ebd2481f937713523fa9c655c", "difficulty": "hard", "final_answer": {"answer": [0.06, -0.001, -0.54], "unit": "temperature_units"}, "id": "heat_step_006185_0.42_0.6_-0.15_-0.4_0.3_-1.0", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=0.6, right=-1; current interior values are [-0.15, -0.4, 0.3]. Use r=0.42. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.42 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-0.15, -0.4, 0.3], "left": 0.6, "r": 0.42, "right": -1.0}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kelvin equals Celsius plus 273.15.\n2. Apply the conversion factor directly to the given value.\n3. Compute 123.0 + 273.15.\nFinal: {\"answer\": 396.15, \"unit\": \"K\"}", "dedupe_signature": "4ed9559adf97a61f2d7a7149ed926d6fbc14425c32a3df2a7db39d8850eb4073", "difficulty": "easy", "final_answer": {"answer": 396.15, "unit": "K"}, "id": "unit_convert_006186_c_to_k_123", "license": "Apache-2.0", "prompt": "Convert 123 degC to K. Return the converted value with unit.", "reasoning_trace": "Kelvin equals Celsius plus 273.15.\nApply the conversion factor directly to the given value.\nCompute 123.0 + 273.15.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 123.0}, "verifier": {"formula": "value + 273.15", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=112 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-88.5945, 219.279], \"unit\": \"N\"}", "dedupe_signature": "4b31c3cd15ed95fb48d6f8efd04db2e701dc2f6fec4a9c94152de903d8910f6e", "difficulty": "medium", "final_answer": {"answer": [-88.5945, 219.279], "unit": "N"}, "id": "vector_components_006187_236.5_112", "license": "Apache-2.0", "prompt": "A vector has magnitude 236.5 N at 112 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=112 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 112, "magnitude": 236.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-8.0, -24.0], \"unit\": \"dimensionless\"}", "dedupe_signature": "ae325c437c2c458136278af2d3ea958e437f0ba35efe2e9f803b6730999d07f7", "difficulty": "medium", "final_answer": {"answer": [-8.0, -24.0], "unit": "dimensionless"}, "id": "line_two_point_006188_2.25_2.75_-8_-24", "license": "Apache-2.0", "prompt": "A line passes through points (2.25, -42) and (2.75, -46). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 2.25, "x2": 2.75, "y1": -42.0, "y2": -46.0}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. speed squared over acceleration has units of meters\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "3368cb47e0d049f8f2342a217352123fb6d8dcd84d099e67070baf0749447ef4", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_006189_consistent_741d4e34_681747", "license": "Apache-2.0", "prompt": "In simulation spec case 681747, check dimensional consistency for R = v^2 * sin(theta) / g. The left side has dimensions m and the right side has dimensions m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nspeed squared over acceleration has units of meters\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "R = v^2 * sin(theta) / g"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef running_total_006190(values):\n    total = 0\n    out = []\n    for value in values:\n        total += value\n        out.append(total)\n    return out\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"running_total_006190\"}", "dedupe_signature": "3b1aec6e2f057417668c7c3f5ef687e9b3608a9d7aa3b3929ca16c949d066b3e", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "running_total_006190"}, "id": "code_006190_running_total_006190", "license": "Apache-2.0", "prompt": "Write a Python function running_total_006190(values) that returns cumulative sums as a new list. It must not mutate the input list. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "running_total_006190"}, "verifier": {"function": "running_total_006190", "tests": ["assert running_total_006190([1, 2, 3]) == [1, 3, 6]", "xs = [4, -1, 2]; assert running_total_006190(xs) == [4, 3, 5] and xs == [4, -1, 2]", "assert running_total_006190([]) == []"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: left_boundary, right_boundary.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"left_boundary\", \"right_boundary\"]}", "dedupe_signature": "c6cd778723b78e0149e44dd8ae6200f186dcf619b0c10e904043e0f69072ee86", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["left_boundary", "right_boundary"]}, "id": "abstain_006191_left_boundary_right_boundary", "license": "Apache-2.0", "prompt": "Solve the 1D heat equation after one finite-difference step. The prompt gives r=0.3 and interior values [-0.45, 0.05, -1.8], but gives no boundary values. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: left_boundary, right_boundary.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["left_boundary", "right_boundary"]}, "verifier": {"missing": ["left_boundary", "right_boundary"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 19.7 kg and a = 0.75 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 14.775, \"unit\": \"N\"}", "dedupe_signature": "e29be1aa1d8a961af2f16104c593085ca78dae76d71d4c3a6e263515b0cd9c2f", "difficulty": "easy", "final_answer": {"answer": 14.775, "unit": "N"}, "id": "force_006192_19.7_0.75", "license": "Apache-2.0", "prompt": "A cart has mass 19.7 kg and measured acceleration 0.75 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 19.7 kg and a = 0.75 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 0.75, "mass": 19.7}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=18 degrees through the sine of 2 theta.\n3. Substitute v=57.9 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 200.8662, \"unit\": \"m\"}", "dedupe_signature": "45341a71aaeb5d9a62581027257c54b6ab386411a91febce012d0542ad4b99df", "difficulty": "medium", "final_answer": {"answer": 200.8662, "unit": "m"}, "id": "projectile_range_006194_57.9_18", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 57.9 m/s and angle 18 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=18 degrees through the sine of 2 theta.\nSubstitute v=57.9 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 18, "gravity": 9.81, "speed": 57.9}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 2.44 * 8.314 * 590 / 58.0.\nFinal: {\"answer\": 206.3592, \"unit\": \"kPa\"}", "dedupe_signature": "09987f528b9b8a76b24c3113e9808af32ad4236445f9e8b4a08a19cfbeafcde1", "difficulty": "medium", "final_answer": {"answer": 206.3592, "unit": "kPa"}, "id": "ideal_gas_006195_2.44_590_58.0", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=2.44 mol, T=590 K, and V=58.0 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 2.44 * 8.314 * 590 / 58.0.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 2.44, "temp_k": 590, "volume_l": 58.0}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 745 * 3.835 * 31.\nFinal: {\"answer\": 88569.325, \"unit\": \"J\"}", "dedupe_signature": "d3c40168c77d7d4c2c7eae0560f7ae8f36a3ae4dc54ebe9ff22eacf701aa1cb0", "difficulty": "easy", "final_answer": {"answer": 88569.325, "unit": "J"}, "id": "heat_q_006196_745_3.835_31", "license": "Apache-2.0", "prompt": "A 745 g sample has specific heat 3.835 J/(g*K). How much heat is needed to raise its temperature by 31 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 745 * 3.835 * 31.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 31, "heat_capacity": 3.835, "mass_g": 745}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=61.1 V and R=122.2 ohm.\nFinal: {\"answer\": 30.55, \"unit\": \"W\"}", "dedupe_signature": "9df58cc3609f9ea62e75cfe087828b7fabe9105eb20f697c380ce083f054b7fe", "difficulty": "easy", "final_answer": {"answer": 30.55, "unit": "W"}, "id": "ohm_power_006197_61.1_122.2", "license": "Apache-2.0", "prompt": "A resistor has resistance 122.2 ohm and voltage 61.1 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=61.1 V and R=122.2 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 122.2, "voltage": 61.1}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=88.5 mg, t=200.5 h, and T_half=35.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 1.7651, \"unit\": \"mg\"}", "dedupe_signature": "89bf775cee4cb2b9a69cb53705f68f0d50f7fbad45467da895a1cace3e9962e3", "difficulty": "medium", "final_answer": {"answer": 1.7651, "unit": "mg"}, "id": "half_life_006198_88.5_35.5_200.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 88.5 mg. Its half-life is 35.5 hours. How many mg remain after 200.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=88.5 mg, t=200.5 h, and T_half=35.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 200.5, "half_life": 35.5, "initial_amount": 88.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 4845 mL to 4.845 L.\n3. Compute M = 4.31 / 4.845.\nFinal: {\"answer\": 0.8896, \"unit\": \"mol/L\"}", "dedupe_signature": "cd9d2f8c1a1ff858675c1fa1551c4805a5f80307f7cdd5bb3c9dc3d49b0918c7", "difficulty": "medium", "final_answer": {"answer": 0.8896, "unit": "mol/L"}, "id": "molarity_006200_4.31_4845", "license": "Apache-2.0", "prompt": "A solution contains 4.31 mol of solute in 4845 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 4845 mL to 4.845 L.\nCompute M = 4.31 / 4.845.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 4.31, "volume_ml": 4845}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.77 y, so each step multiplies y by 1 - h*0.77.\n3. Apply that update for 10 steps and round the final state.\nFinal: {\"answer\": 0.0001, \"unit\": \"state_units\"}", "dedupe_signature": "45f2baf5f60476ddaa3753f68c9ed11a518857f43ad1cb2ef7806503e9ebdce6", "difficulty": "medium", "final_answer": {"answer": 0.0001, "unit": "state_units"}, "id": "euler_decay_006201_9_0.77_0.9_10", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.77 y with y(0)=9, step size h=0.9, for 10 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.77 y, so each step multiplies y by 1 - h*0.77.\nApply that update for 10 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 9.0, "rate": 0.77, "step": 0.9, "steps": 10}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-5)=-33.9 and f(-2.6)=-20.22.\n3. The interval width is 2.4.\nFinal: {\"answer\": -64.944, \"unit\": \"area_units\"}", "dedupe_signature": "cdd8c725bf791be8ce8ca9823946c9b701e2b43759753235c846e90e8d9db4a4", "difficulty": "medium", "final_answer": {"answer": -64.944, "unit": "area_units"}, "id": "trapz_linear_006202_5.7_-5.4_-5_-2.6", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=5.7x+-5.4 from x=-5 to x=-2.6. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-5)=-33.9 and f(-2.6)=-20.22.\nThe interval width is 2.4.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -5.4, "slope": 5.7, "x0": -5.0, "x1": -2.6}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.36 and add it to the current value.\nFinal: {\"answer\": [-0.036, -0.654, -0.738], \"unit\": \"temperature_units\"}", "dedupe_signature": "74773ec40d3699f9e5c7911f4952440d6aadf869103eb070db6cb6788d261c5f", "difficulty": "hard", "final_answer": {"answer": [-0.036, -0.654, -0.738], "unit": "temperature_units"}, "id": "heat_step_006203_0.36_1.2_-0.9_-0.6_-0.45_-1.1", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.2, right=-1.1; current interior values are [-0.9, -0.6, -0.45]. Use r=0.36. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.36 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-0.9, -0.6, -0.45], "left": 1.2, "r": 0.36, "right": -1.1}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kelvin equals Celsius plus 273.15.\n2. Apply the conversion factor directly to the given value.\n3. Compute -52.5 + 273.15.\nFinal: {\"answer\": 220.65, \"unit\": \"K\"}", "dedupe_signature": "6d223f4541ec3d4f3a90f7274ea2a876f05eb742e171871f3e5f07a0320ad53a", "difficulty": "easy", "final_answer": {"answer": 220.65, "unit": "K"}, "id": "unit_convert_006204_c_to_k_-52.5", "license": "Apache-2.0", "prompt": "Convert -52.5 degC to K. Return the converted value with unit.", "reasoning_trace": "Kelvin equals Celsius plus 273.15.\nApply the conversion factor directly to the given value.\nCompute -52.5 + 273.15.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": -52.5}, "verifier": {"formula": "value + 273.15", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. lever arm times force has torque dimensions\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "4b33355a9ba75301dd7acbb34e81d999a22d8a81df3e047cf2fda6dc80d2de5e", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_006207_consistent_5ca82cb9_962447", "license": "Apache-2.0", "prompt": "In lab notebook case 962447, check dimensional consistency for tau = r * F. The left side has dimensions N*m and the right side has dimensions N*m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nlever arm times force has torque dimensions\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "tau = r * F"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\nimport math\n\ndef unit_vector_006208(x, y):\n    norm = math.hypot(x, y)\n    if norm == 0:\n        raise ValueError('zero vector has no direction')\n    return (x / norm, y / norm)\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"unit_vector_006208\"}", "dedupe_signature": "1b56a28035a761eac347841008ffed5099db507f25cff2aa8eea8b16e811ca91", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "unit_vector_006208"}, "id": "code_006208_unit_vector_006208", "license": "Apache-2.0", "prompt": "Write a Python function unit_vector_006208(x, y) that returns the 2D unit vector as a tuple. Raise ValueError for the zero vector. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "unit_vector_006208"}, "verifier": {"function": "unit_vector_006208", "tests": ["ux, uy = unit_vector_006208(3, 4); assert abs(ux - 0.6) < 1e-12 and abs(uy - 0.8) < 1e-12", "assert unit_vector_006208(0, 5) == (0, 1)", "try:\n    unit_vector_006208(0, 0)\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: rate_constant, number_of_steps.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"rate_constant\", \"number_of_steps\"]}", "dedupe_signature": "54fbd31d693de30eb84682ae924a79640511136d0b6b964d90d018d8e041b6f1", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["rate_constant", "number_of_steps"]}, "id": "abstain_006209_rate_constant_number_of_steps", "license": "Apache-2.0", "prompt": "Use explicit Euler for dy/dt = -k y. The prompt gives y(0)=11.5 and h=0.25, but omits both k and the number of steps. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: rate_constant, number_of_steps.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["rate_constant", "number_of_steps"]}, "verifier": {"missing": ["rate_constant", "number_of_steps"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 8.9 kg and a = 3.7 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 32.93, \"unit\": \"N\"}", "dedupe_signature": "7b45d829861fd4b0d8f3f82a1b27d099bbe891cbd0e43d021655225bd96c57f9", "difficulty": "easy", "final_answer": {"answer": 32.93, "unit": "N"}, "id": "force_006210_8.9_3.7", "license": "Apache-2.0", "prompt": "A cart has mass 8.9 kg and measured acceleration 3.7 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 8.9 kg and a = 3.7 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 3.7, "mass": 8.9}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=8 degrees through the sine of 2 theta.\n3. Substitute v=81.5 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 186.6312, \"unit\": \"m\"}", "dedupe_signature": "fcd7da3adc3c1c3ff774b8840b3f5769630c280031e68c38e5d4e9a3ff1c70ff", "difficulty": "medium", "final_answer": {"answer": 186.6312, "unit": "m"}, "id": "projectile_range_006212_81.5_8", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 81.5 m/s and angle 8 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=8 degrees through the sine of 2 theta.\nSubstitute v=81.5 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 8, "gravity": 9.81, "speed": 81.5}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 4.24 * 8.314 * 345 / 95.9.\nFinal: {\"answer\": 126.8167, \"unit\": \"kPa\"}", "dedupe_signature": "a989a1650c89932a4f027b05d5c43eb8f62c09f05df8e584f13ea0d0fc59b0ac", "difficulty": "medium", "final_answer": {"answer": 126.8167, "unit": "kPa"}, "id": "ideal_gas_006213_4.24_345_95.9", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=4.24 mol, T=345 K, and V=95.9 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 4.24 * 8.314 * 345 / 95.9.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 4.24, "temp_k": 345, "volume_l": 95.9}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=171.8 V and R=111.8 ohm.\nFinal: {\"answer\": 264.0004, \"unit\": \"W\"}", "dedupe_signature": "147e5c5eea65c86156a5cc09114bbc763fe626b6a8c8eea1ac6ebbdd501afae0", "difficulty": "easy", "final_answer": {"answer": 264.0004, "unit": "W"}, "id": "ohm_power_006215_171.8_111.8", "license": "Apache-2.0", "prompt": "A resistor has resistance 111.8 ohm and voltage 171.8 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=171.8 V and R=111.8 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 111.8, "voltage": 171.8}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=20.5 mg, t=134 h, and T_half=41.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 2.1865, \"unit\": \"mg\"}", "dedupe_signature": "2c0725faaf795ca1acf773e25f7130fd8c3fe02c33f8807604aeb245383604ca", "difficulty": "medium", "final_answer": {"answer": 2.1865, "unit": "mg"}, "id": "half_life_006216_20.5_41.5_134", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 20.5 mg. Its half-life is 41.5 hours. How many mg remain after 134 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=20.5 mg, t=134 h, and T_half=41.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 134.0, "half_life": 41.5, "initial_amount": 20.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 7.41 mol * 18.015 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 133.4912, \"unit\": \"g\"}", "dedupe_signature": "8531b4492c5b2e8b0d6e5950c7a1c16c725a8b90131769c5eb55a33827225731", "difficulty": "medium", "final_answer": {"answer": 133.4912, "unit": "g"}, "id": "stoich_mass_006217_water_7.41", "license": "Apache-2.0", "prompt": "A sample contains 7.41 mol of water. Using molar mass 18.015 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 7.41 mol * 18.015 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "water", "molar_mass": 18.015, "moles": 7.41}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 2700 mL to 2.7 L.\n3. Compute M = 0.985 / 2.7.\nFinal: {\"answer\": 0.3648, \"unit\": \"mol/L\"}", "dedupe_signature": "718bef84b36d2eecafd00b55a2d5c6e6432032ee90dce63d578999bee3e4265d", "difficulty": "medium", "final_answer": {"answer": 0.3648, "unit": "mol/L"}, "id": "molarity_006218_0.985_2700", "license": "Apache-2.0", "prompt": "A solution contains 0.985 mol of solute in 2700 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 2700 mL to 2.7 L.\nCompute M = 0.985 / 2.7.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 0.985, "volume_ml": 2700}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.81 y, so each step multiplies y by 1 - h*0.81.\n3. Apply that update for 11 steps and round the final state.\nFinal: {\"answer\": -0.2368, \"unit\": \"state_units\"}", "dedupe_signature": "8e6591f109e5624bab333bd251e4dbdda45c66524e14ae7224d9427a05b8842e", "difficulty": "medium", "final_answer": {"answer": -0.2368, "unit": "state_units"}, "id": "euler_decay_006219_45.5_0.81_2_11", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.81 y with y(0)=45.5, step size h=2, for 11 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.81 y, so each step multiplies y by 1 - h*0.81.\nApply that update for 11 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 45.5, "rate": 0.81, "step": 2.0, "steps": 11}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.28 and add it to the current value.\nFinal: {\"answer\": [0.682, 0.912, 1.328], \"unit\": \"temperature_units\"}", "dedupe_signature": "b7e785dc037f55a73b88c7ec43dc075cac1033a4cd8bc2f8b5c2c53ac89bb08d", "difficulty": "hard", "final_answer": {"answer": [0.682, 0.912, 1.328], "unit": "temperature_units"}, "id": "heat_step_006221_0.28_1.6_-0.2_1.15_1.65_1.0", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.6, right=1; current interior values are [-0.2, 1.15, 1.65]. Use r=0.28. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.28 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-0.2, 1.15, 1.65], "left": 1.6, "r": 0.28, "right": 1.0}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 100 centimeters in one meter.\n2. Apply the conversion factor directly to the given value.\n3. Compute 4853.5 / 100.\nFinal: {\"answer\": 48.535, \"unit\": \"m\"}", "dedupe_signature": "32bd00aa0e10880609f1ed4272dd97401cce5180a6b0a1d7919669a1ef36b972", "difficulty": "easy", "final_answer": {"answer": 48.535, "unit": "m"}, "id": "unit_convert_006222_cm_to_m_4853.5", "license": "Apache-2.0", "prompt": "Convert 4853.5 cm to m. Return the converted value with unit.", "reasoning_trace": "There are 100 centimeters in one meter.\nApply the conversion factor directly to the given value.\nCompute 4853.5 / 100.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 4853.5}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=321 degrees and keep the unit as newtons.\nFinal: {\"answer\": [235.8638, -190.9987], \"unit\": \"N\"}", "dedupe_signature": "e081e64ad069f93f455ae6e8ced41937e88c2127832c051517ee485ca6e28f22", "difficulty": "medium", "final_answer": {"answer": [235.8638, -190.9987], "unit": "N"}, "id": "vector_components_006223_303.5_321", "license": "Apache-2.0", "prompt": "A vector has magnitude 303.5 N at 321 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=321 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 321, "magnitude": 303.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [6.45, -25.0], \"unit\": \"dimensionless\"}", "dedupe_signature": "15e09b792f6210a2d9646184b6851b2e5534ea89650cdea637b251301c7dfed2", "difficulty": "medium", "final_answer": {"answer": [6.45, -25.0], "unit": "dimensionless"}, "id": "line_two_point_006224_19.25_25.25_6.45_-25", "license": "Apache-2.0", "prompt": "A line passes through points (19.25, 99.1625) and (25.25, 137.863). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 19.25, "x2": 25.25, "y1": 99.16250000000001, "y2": 137.8625}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. volt squared divided by ohm is watt\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "5e55813e6f855b84254bbb9892e59472e0fcfa1bd744b9f400a83f9327476dc2", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_006225_consistent_82e93f3d_643001", "license": "Apache-2.0", "prompt": "In field worksheet case 643001, check dimensional consistency for P = V^2 / R. The left side has dimensions W and the right side has dimensions W. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nvolt squared divided by ohm is watt\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "P = V^2 / R"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef finite_differences_006226(values):\n    return [values[i + 1] - values[i] for i in range(len(values) - 1)]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"finite_differences_006226\"}", "dedupe_signature": "4297ff5a2976950dc9e46bc5cba2243f00cd02a6adbccb823c6d65787d0ab759", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "finite_differences_006226"}, "id": "code_006226_finite_differences_006226", "license": "Apache-2.0", "prompt": "Write a Python function finite_differences_006226(values) that returns the list of successive differences values[i+1] - values[i]. It must return [] for fewer than two values. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "finite_differences_006226"}, "verifier": {"function": "finite_differences_006226", "tests": ["assert finite_differences_006226([1, 4, 9, 16]) == [3, 5, 7]", "assert finite_differences_006226([5]) == []", "assert finite_differences_006226([]) == []"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 17.1 kg and a = 0.8 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 13.68, \"unit\": \"N\"}", "dedupe_signature": "893d139dee53dcd785d2610fb609c7c3efc62deecf4d6818d329f30f4f5dd771", "difficulty": "easy", "final_answer": {"answer": 13.68, "unit": "N"}, "id": "force_006228_17.1_0.8", "license": "Apache-2.0", "prompt": "A cart has mass 17.1 kg and measured acceleration 0.8 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 17.1 kg and a = 0.8 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 0.8, "mass": 17.1}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 27.65^2 and multiply by 0.5 * 19.5.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 7454.0944, \"unit\": \"J\"}", "dedupe_signature": "8465710d0ae65eac70a3a2cfb16907eae1b0e2fa47d96719ab0b08c06d20834b", "difficulty": "easy", "final_answer": {"answer": 7454.0944, "unit": "J"}, "id": "ke_006229_19.5_27.65", "license": "Apache-2.0", "prompt": "A body of mass 19.5 kg moves at 27.65 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 27.65^2 and multiply by 0.5 * 19.5.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 19.5, "velocity": 27.65}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=62 degrees through the sine of 2 theta.\n3. Substitute v=16.8 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 23.8519, \"unit\": \"m\"}", "dedupe_signature": "8f5835bb71d033be0e25356b9ef457c697fd3da8bd946acc17a446e214efccd2", "difficulty": "medium", "final_answer": {"answer": 23.8519, "unit": "m"}, "id": "projectile_range_006230_16.8_62", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 16.8 m/s and angle 62 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=62 degrees through the sine of 2 theta.\nSubstitute v=16.8 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 62, "gravity": 9.81, "speed": 16.8}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 360 * 0.985 * 95.\nFinal: {\"answer\": 33687.0, \"unit\": \"J\"}", "dedupe_signature": "343fa8844bb834b11fdb7771b64103f54240ce296124e1ee4a007f4ede11a78d", "difficulty": "easy", "final_answer": {"answer": 33687.0, "unit": "J"}, "id": "heat_q_006232_360_0.985_95", "license": "Apache-2.0", "prompt": "A 360 g sample has specific heat 0.985 J/(g*K). How much heat is needed to raise its temperature by 95 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 360 * 0.985 * 95.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 95, "heat_capacity": 0.985, "mass_g": 360}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=75 V and R=103.6 ohm.\nFinal: {\"answer\": 54.2954, \"unit\": \"W\"}", "dedupe_signature": "0e412e7bc332f07b432a661104d4eb24c19a0f91da00d735b4a4b50f562e0e8e", "difficulty": "easy", "final_answer": {"answer": 54.2954, "unit": "W"}, "id": "ohm_power_006233_75_103.6", "license": "Apache-2.0", "prompt": "A resistor has resistance 103.6 ohm and voltage 75 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=75 V and R=103.6 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 103.6, "voltage": 75.0}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=297 mg, t=62 h, and T_half=12 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 8.2687, \"unit\": \"mg\"}", "dedupe_signature": "c09c6b517099a1da84e73e8d4aa48781e71ce5065aeddaf9338416bd56a0be7a", "difficulty": "medium", "final_answer": {"answer": 8.2687, "unit": "mg"}, "id": "half_life_006234_297_12_62", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 297 mg. Its half-life is 12 hours. How many mg remain after 62 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=297 mg, t=62 h, and T_half=12 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 62.0, "half_life": 12.0, "initial_amount": 297.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 5.46 mol * 44.01 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 240.2946, \"unit\": \"g\"}", "dedupe_signature": "90d0c8ae9de5c95e32b68a67800afea86ace4b163528faec0ddb0abbe9686850", "difficulty": "medium", "final_answer": {"answer": 240.2946, "unit": "g"}, "id": "stoich_mass_006235_carbon_dioxide_5.46", "license": "Apache-2.0", "prompt": "A sample contains 5.46 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 5.46 mol * 44.01 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "carbon dioxide", "molar_mass": 44.01, "moles": 5.46}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 970 mL to 0.97 L.\n3. Compute M = 3.38 / 0.97.\nFinal: {\"answer\": 3.4845, \"unit\": \"mol/L\"}", "dedupe_signature": "ea1f545888afe610a2ea0d70f13ae35a377577d44521ab444ffca19c985daa3d", "difficulty": "medium", "final_answer": {"answer": 3.4845, "unit": "mol/L"}, "id": "molarity_006236_3.38_970", "license": "Apache-2.0", "prompt": "A solution contains 3.38 mol of solute in 970 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 970 mL to 0.97 L.\nCompute M = 3.38 / 0.97.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 3.38, "volume_ml": 970}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.12 y, so each step multiplies y by 1 - h*0.12.\n3. Apply that update for 8 steps and round the final state.\nFinal: {\"answer\": 0.1712, \"unit\": \"state_units\"}", "dedupe_signature": "be6dd340e3aa613c330b6edc24f44d81c20354527a295e4a329116506df291f0", "difficulty": "medium", "final_answer": {"answer": 0.1712, "unit": "state_units"}, "id": "euler_decay_006237_1_0.12_1.65_8", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.12 y with y(0)=1, step size h=1.65, for 8 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.12 y, so each step multiplies y by 1 - h*0.12.\nApply that update for 8 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 1.0, "rate": 0.12, "step": 1.65, "steps": 8}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-5.8)=-34.56 and f(0.9)=0.28.\n3. The interval width is 6.7.\nFinal: {\"answer\": -114.838, \"unit\": \"area_units\"}", "dedupe_signature": "5d4532c228f04a3159073d47d895fe467d1e1b6f9ff6449b7ae56111ff80808f", "difficulty": "medium", "final_answer": {"answer": -114.838, "unit": "area_units"}, "id": "trapz_linear_006238_5.2_-4.4_-5.8_0.9", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=5.2x+-4.4 from x=-5.8 to x=0.9. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-5.8)=-34.56 and f(0.9)=0.28.\nThe interval width is 6.7.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -4.4, "slope": 5.2, "x0": -5.8, "x1": 0.9000000000000004}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 23497.0 / 1000.\nFinal: {\"answer\": 23.497, \"unit\": \"kg\"}", "dedupe_signature": "6504150e3952268a42b54adb289082d9cac0408e31334ef59548b81fce94982b", "difficulty": "easy", "final_answer": {"answer": 23.497, "unit": "kg"}, "id": "unit_convert_006240_g_to_kg_23497", "license": "Apache-2.0", "prompt": "Convert 23497 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 23497.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 23497.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-5.9, -8.5], \"unit\": \"dimensionless\"}", "dedupe_signature": "7627ae9fef36e2ab7a1418d82b4851f7167d11173168a1c6523af8022c968840", "difficulty": "medium", "final_answer": {"answer": [-5.9, -8.5], "unit": "dimensionless"}, "id": "line_two_point_006242_-19.75_-5.5_-5.9_-8.5", "license": "Apache-2.0", "prompt": "A line passes through points (-19.75, 108.025) and (-5.5, 23.95). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -19.75, "x2": -5.5, "y1": 108.025, "y2": 23.950000000000003}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. m*v is momentum, not energy\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "49eb986a9847ebfa2338001aca3a4904dcfa49ddbf9bb554bde303732d6a238b", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_006243_inconsistent_1e14b074_309894", "license": "Apache-2.0", "prompt": "In sensor calibration case 309894, check dimensional consistency for E = m * v. The left side has dimensions kg*m^2/s^2 and the right side has dimensions kg*m/s. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nm*v is momentum, not energy\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "E = m * v"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef finite_differences_006244(values):\n    return [values[i + 1] - values[i] for i in range(len(values) - 1)]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"finite_differences_006244\"}", "dedupe_signature": "e2d08990b32dac7672d3bd757a2cb800be1a621b9d226e81719948ee9ea38e67", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "finite_differences_006244"}, "id": "code_006244_finite_differences_006244", "license": "Apache-2.0", "prompt": "Write a Python function finite_differences_006244(values) that returns the list of successive differences values[i+1] - values[i]. It must return [] for fewer than two values. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "finite_differences_006244"}, "verifier": {"function": "finite_differences_006244", "tests": ["assert finite_differences_006244([1, 4, 9, 16]) == [3, 5, 7]", "assert finite_differences_006244([5]) == []", "assert finite_differences_006244([]) == []"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 1.65 kg and a = 0.55 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 0.9075, \"unit\": \"N\"}", "dedupe_signature": "300ea2db492a4348291a8c9139b90d790ae5871b25636a6ddb5d1491bd23d9bd", "difficulty": "easy", "final_answer": {"answer": 0.9075, "unit": "N"}, "id": "force_006246_1.65_0.55", "license": "Apache-2.0", "prompt": "A cart has mass 1.65 kg and measured acceleration 0.55 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 1.65 kg and a = 0.55 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 0.55, "mass": 1.65}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=13 degrees through the sine of 2 theta.\n3. Substitute v=75 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 251.3596, \"unit\": \"m\"}", "dedupe_signature": "94167021ef5acd51a68b082fcbd426ff02fa3b84a7a684284a944400539f87aa", "difficulty": "medium", "final_answer": {"answer": 251.3596, "unit": "m"}, "id": "projectile_range_006248_75_13", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 75 m/s and angle 13 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=13 degrees through the sine of 2 theta.\nSubstitute v=75 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 13, "gravity": 9.81, "speed": 75.0}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1075 * 3.86 * 16.\nFinal: {\"answer\": 66392.0, \"unit\": \"J\"}", "dedupe_signature": "109bdf30e6a98f098d59b3e1dcd7c0be7ffc63d35db525105859c71996f04103", "difficulty": "easy", "final_answer": {"answer": 66392.0, "unit": "J"}, "id": "heat_q_006250_1075_3.86_16", "license": "Apache-2.0", "prompt": "A 1075 g sample has specific heat 3.86 J/(g*K). How much heat is needed to raise its temperature by 16 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1075 * 3.86 * 16.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 16, "heat_capacity": 3.86, "mass_g": 1075}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=165.3 V and R=41.7 ohm.\nFinal: {\"answer\": 655.254, \"unit\": \"W\"}", "dedupe_signature": "d3f9764cf618b27bb2b5f15167fcbf9a9a91c44f4eb7b2219b9e402179f37cc7", "difficulty": "easy", "final_answer": {"answer": 655.254, "unit": "W"}, "id": "ohm_power_006251_165.3_41.7", "license": "Apache-2.0", "prompt": "A resistor has resistance 41.7 ohm and voltage 165.3 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=165.3 V and R=41.7 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 41.7, "voltage": 165.3}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=577.5 mg, t=15 h, and T_half=81.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 508.3323, \"unit\": \"mg\"}", "dedupe_signature": "4b5409c564958d1d0b6f6b66c2925fa788dd3a61a556ea943980c75d81071e8e", "difficulty": "medium", "final_answer": {"answer": 508.3323, "unit": "mg"}, "id": "half_life_006252_577.5_81.5_15", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 577.5 mg. Its half-life is 81.5 hours. How many mg remain after 15 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=577.5 mg, t=15 h, and T_half=81.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 15.0, "half_life": 81.5, "initial_amount": 577.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 1885 mL to 1.885 L.\n3. Compute M = 2.01 / 1.885.\nFinal: {\"answer\": 1.0663, \"unit\": \"mol/L\"}", "dedupe_signature": "57a8c97702d43ec75ef23e6dc6bbe810fa6a9b6fa3d1752890d93b484bb5e0c8", "difficulty": "medium", "final_answer": {"answer": 1.0663, "unit": "mol/L"}, "id": "molarity_006254_2.01_1885", "license": "Apache-2.0", "prompt": "A solution contains 2.01 mol of solute in 1885 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 1885 mL to 1.885 L.\nCompute M = 2.01 / 1.885.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 2.01, "volume_ml": 1885}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.15 y, so each step multiplies y by 1 - h*0.15.\n3. Apply that update for 10 steps and round the final state.\nFinal: {\"answer\": 6.4823, \"unit\": \"state_units\"}", "dedupe_signature": "9f78c48c56d8a6c9c4b41434359f34f3ecf16e44efeae2b12d2a7b8c09a4afe9", "difficulty": "medium", "final_answer": {"answer": 6.4823, "unit": "state_units"}, "id": "euler_decay_006255_9.5_0.15_0.25_10", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.15 y with y(0)=9.5, step size h=0.25, for 10 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.15 y, so each step multiplies y by 1 - h*0.15.\nApply that update for 10 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 9.5, "rate": 0.15, "step": 0.25, "steps": 10}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(1.9)=-10.49 and f(2.1)=-11.31.\n3. The interval width is 0.2.\nFinal: {\"answer\": -2.18, \"unit\": \"area_units\"}", "dedupe_signature": "41f0b90138b8f9d8fbf492e74132c9c57da684daa7924eca1d05fbb8b01c7801", "difficulty": "medium", "final_answer": {"answer": -2.18, "unit": "area_units"}, "id": "trapz_linear_006256_-4.1_-2.7_1.9_2.1", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-4.1x+-2.7 from x=1.9 to x=2.1. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(1.9)=-10.49 and f(2.1)=-11.31.\nThe interval width is 0.2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -2.7, "slope": -4.1, "x0": 1.9, "x1": 2.1}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.24 and add it to the current value.\nFinal: {\"answer\": [0.83, 0.644, -0.312], \"unit\": \"temperature_units\"}", "dedupe_signature": "d39d5f972c9bdf5622087187937ed875be9195a6c97df76d287568ab0e97a754", "difficulty": "hard", "final_answer": {"answer": [0.83, 0.644, -0.312], "unit": "temperature_units"}, "id": "heat_step_006257_0.24_-0.05_1.25_0.8_-0.3_-1.45", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-0.05, right=-1.45; current interior values are [1.25, 0.8, -0.3]. Use r=0.24. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.24 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [1.25, 0.8, -0.3], "left": -0.05, "r": 0.24, "right": -1.45}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 100 centimeters in one meter.\n2. Apply the conversion factor directly to the given value.\n3. Compute 2887.5 / 100.\nFinal: {\"answer\": 28.875, \"unit\": \"m\"}", "dedupe_signature": "0d2accb755a62f7ab5f64365ec950f314e453459476b9cc4cf04f6e355d41e73", "difficulty": "easy", "final_answer": {"answer": 28.875, "unit": "m"}, "id": "unit_convert_006258_cm_to_m_2887.5", "license": "Apache-2.0", "prompt": "Convert 2887.5 cm to m. Return the converted value with unit.", "reasoning_trace": "There are 100 centimeters in one meter.\nApply the conversion factor directly to the given value.\nCompute 2887.5 / 100.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 2887.5}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-8.05, -20.0], \"unit\": \"dimensionless\"}", "dedupe_signature": "f020d5c7a390fdc0c364cb4e0d1f2434815aef493bf67abb4fd82a4c2a85fb2b", "difficulty": "medium", "final_answer": {"answer": [-8.05, -20.0], "unit": "dimensionless"}, "id": "line_two_point_006260_-11_1.75_-8.05_-20", "license": "Apache-2.0", "prompt": "A line passes through points (-11, 68.55) and (1.75, -34.0875). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -11.0, "x2": 1.75, "y1": 68.55000000000001, "y2": -34.087500000000006}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. m*v is momentum, not energy\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "b3a746a58229df29c980900d3842ee54920834e3a4362b064ab79d5a9651fbd5", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_006261_inconsistent_1e14b074_264683", "license": "Apache-2.0", "prompt": "In field worksheet case 264683, check dimensional consistency for E = m * v. The left side has dimensions kg*m^2/s^2 and the right side has dimensions kg*m/s. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nm*v is momentum, not energy\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "E = m * v"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\nimport math\n\ndef unit_vector_006262(x, y):\n    norm = math.hypot(x, y)\n    if norm == 0:\n        raise ValueError('zero vector has no direction')\n    return (x / norm, y / norm)\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"unit_vector_006262\"}", "dedupe_signature": "b325122922410eaadf445d7086cb56267bf830416b6af0ee59ab2932d5da28fa", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "unit_vector_006262"}, "id": "code_006262_unit_vector_006262", "license": "Apache-2.0", "prompt": "Write a Python function unit_vector_006262(x, y) that returns the 2D unit vector as a tuple. Raise ValueError for the zero vector. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "unit_vector_006262"}, "verifier": {"function": "unit_vector_006262", "tests": ["ux, uy = unit_vector_006262(3, 4); assert abs(ux - 0.6) < 1e-12 and abs(uy - 0.8) < 1e-12", "assert unit_vector_006262(0, 5) == (0, 1)", "try:\n    unit_vector_006262(0, 0)\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: required_fields, allowed_transformations.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"required_fields\", \"allowed_transformations\"]}", "dedupe_signature": "3a2da25ec6e91e02da50ab106f05a122befe6c3f13dc1ef4b74d7e8d2fbe655b", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["required_fields", "allowed_transformations"]}, "id": "abstain_006263_required_fields_allowed_transformations", "license": "Apache-2.0", "prompt": "Write a sanitizer for valid registry experiment records in release 877521, but the prompt does not state which fields are required or which transformations are allowed. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: required_fields, allowed_transformations.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["required_fields", "allowed_transformations"]}, "verifier": {"missing": ["required_fields", "allowed_transformations"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 9.65 kg and a = 15.8 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 152.47, \"unit\": \"N\"}", "dedupe_signature": "7274c2c98f29c194d0ded149603647f88a40a5b52e5e70bedafe85c86bc60732", "difficulty": "easy", "final_answer": {"answer": 152.47, "unit": "N"}, "id": "force_006264_9.65_15.8", "license": "Apache-2.0", "prompt": "A cart has mass 9.65 kg and measured acceleration 15.8 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 9.65 kg and a = 15.8 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 15.8, "mass": 9.65}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 31.95^2 and multiply by 0.5 * 24.65.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 12581.3908, \"unit\": \"J\"}", "dedupe_signature": "86f44681152b4b37a00a178eeae6fe9fd3ca81349d784f88a89e6b7b0d2e647e", "difficulty": "easy", "final_answer": {"answer": 12581.3908, "unit": "J"}, "id": "ke_006265_24.65_31.95", "license": "Apache-2.0", "prompt": "A body of mass 24.65 kg moves at 31.95 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 31.95^2 and multiply by 0.5 * 24.65.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 24.65, "velocity": 31.95}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 2.66 * 8.314 * 250 / 82.6.\nFinal: {\"answer\": 66.9347, \"unit\": \"kPa\"}", "dedupe_signature": "7d18ade372f747b957a7b40f60bf0be37a20e61c433c1308ca1dfd2f057709fb", "difficulty": "medium", "final_answer": {"answer": 66.9347, "unit": "kPa"}, "id": "ideal_gas_006267_2.66_250_82.6", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=2.66 mol, T=250 K, and V=82.6 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 2.66 * 8.314 * 250 / 82.6.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 2.66, "temp_k": 250, "volume_l": 82.6}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1810 * 3.41 * 3.\nFinal: {\"answer\": 18516.3, \"unit\": \"J\"}", "dedupe_signature": "78358b856cbc396b9a506f666c54409fe61fd9696807650590709701e2a4f91d", "difficulty": "easy", "final_answer": {"answer": 18516.3, "unit": "J"}, "id": "heat_q_006268_1810_3.41_3", "license": "Apache-2.0", "prompt": "A 1810 g sample has specific heat 3.41 J/(g*K). How much heat is needed to raise its temperature by 3 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1810 * 3.41 * 3.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 3, "heat_capacity": 3.41, "mass_g": 1810}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=21.3 V and R=100.3 ohm.\nFinal: {\"answer\": 4.5233, \"unit\": \"W\"}", "dedupe_signature": "58ecd0527fa58ffd91a9952c9db961c1c2b18a5e10e6a433704d78ff3806ca8d", "difficulty": "easy", "final_answer": {"answer": 4.5233, "unit": "W"}, "id": "ohm_power_006269_21.3_100.3", "license": "Apache-2.0", "prompt": "A resistor has resistance 100.3 ohm and voltage 21.3 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=21.3 V and R=100.3 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 100.3, "voltage": 21.3}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 6.77 mol * 58.44 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 395.6388, \"unit\": \"g\"}", "dedupe_signature": "54ac600f7b8f6d9e63afcf32b6ac8ebf0804bc7fb16f86fa7f20d10c542ddd1b", "difficulty": "medium", "final_answer": {"answer": 395.6388, "unit": "g"}, "id": "stoich_mass_006271_sodium_chloride_6.77", "license": "Apache-2.0", "prompt": "A sample contains 6.77 mol of sodium chloride. Using molar mass 58.44 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 6.77 mol * 58.44 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "sodium chloride", "molar_mass": 58.44, "moles": 6.77}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 3455 mL to 3.455 L.\n3. Compute M = 2.54 / 3.455.\nFinal: {\"answer\": 0.7352, \"unit\": \"mol/L\"}", "dedupe_signature": "fd33cc7beea4fb8b11583c9a81af70702873439e917bf7ef33c1e69950235c6a", "difficulty": "medium", "final_answer": {"answer": 0.7352, "unit": "mol/L"}, "id": "molarity_006272_2.54_3455", "license": "Apache-2.0", "prompt": "A solution contains 2.54 mol of solute in 3455 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 3455 mL to 3.455 L.\nCompute M = 2.54 / 3.455.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 2.54, "volume_ml": 3455}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.61 y, so each step multiplies y by 1 - h*0.61.\n3. Apply that update for 9 steps and round the final state.\nFinal: {\"answer\": 0.0, \"unit\": \"state_units\"}", "dedupe_signature": "db3ebefef60e4a89d146d64d8303aeb9b6c501a8bb78be41280da5644f5a6ee3", "difficulty": "medium", "final_answer": {"answer": 0.0, "unit": "state_units"}, "id": "euler_decay_006273_58.5_0.61_1.8_9", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.61 y with y(0)=58.5, step size h=1.8, for 9 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.61 y, so each step multiplies y by 1 - h*0.61.\nApply that update for 9 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 58.5, "rate": 0.61, "step": 1.8, "steps": 9}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.48 and add it to the current value.\nFinal: {\"answer\": [0.042, 1.308, -0.072], \"unit\": \"temperature_units\"}", "dedupe_signature": "a53de9aa4680038193c671b173b73f52e87fd8b8122ab32f58afbb3248d969ab", "difficulty": "hard", "final_answer": {"answer": [0.042, 1.308, -0.072], "unit": "temperature_units"}, "id": "heat_step_006275_0.48_1.35_2.85_-1.5_0.0_1.35", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.35, right=1.35; current interior values are [2.85, -1.5, 0.0]. Use r=0.48. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.48 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [2.85, -1.5, 0.0], "left": 1.35, "r": 0.48, "right": 1.35}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 31474.0 / 1000.\nFinal: {\"answer\": 31.474, \"unit\": \"kg\"}", "dedupe_signature": "d4e68e6c03a5637edcd14ece0e14c47b39a47728376fe82b705ceabe606817e9", "difficulty": "easy", "final_answer": {"answer": 31.474, "unit": "kg"}, "id": "unit_convert_006276_g_to_kg_31474", "license": "Apache-2.0", "prompt": "Convert 31474 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 31474.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 31474.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=19 degrees and keep the unit as newtons.\nFinal: {\"answer\": [165.4658, 56.9744], \"unit\": \"N\"}", "dedupe_signature": "c4ce77b1e124ace2f9711158d32056e82320ac47504b7ad790fbd0ef43eb5d9c", "difficulty": "medium", "final_answer": {"answer": [165.4658, 56.9744], "unit": "N"}, "id": "vector_components_006277_175_19", "license": "Apache-2.0", "prompt": "A vector has magnitude 175 N at 19 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=19 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 19, "magnitude": 175.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-6.9, -20.0], \"unit\": \"dimensionless\"}", "dedupe_signature": "310c6dc56ba2959026906390dc5a97a3177aad7b300f730351c21766b2d80f4b", "difficulty": "medium", "final_answer": {"answer": [-6.9, -20.0], "unit": "dimensionless"}, "id": "line_two_point_006278_-0.75_8.75_-6.9_-20", "license": "Apache-2.0", "prompt": "A line passes through points (-0.75, -14.825) and (8.75, -80.375). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -0.75, "x2": 8.75, "y1": -14.825, "y2": -80.375}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. grams cancel with J/(g*K), and kelvin cancels, leaving joules\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "890037a9fe251ef43f13f2accc175c40938b0ad39114f56e40ce043467b57971", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_006279_consistent_4153435f_683720", "license": "Apache-2.0", "prompt": "In field worksheet case 683720, check dimensional consistency for Q = m * c * DeltaT. The left side has dimensions J and the right side has dimensions J. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\ngrams cancel with J/(g*K), and kelvin cancels, leaving joules\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "Q = m * c * DeltaT"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 17.65 kg and a = 2.8 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 49.42, \"unit\": \"N\"}", "dedupe_signature": "f752fb1382550d10e881e3e53acdc26e0c7cb744ee487086d0fe32957bb497e9", "difficulty": "easy", "final_answer": {"answer": 49.42, "unit": "N"}, "id": "force_006282_17.65_2.8", "license": "Apache-2.0", "prompt": "A cart has mass 17.65 kg and measured acceleration 2.8 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 17.65 kg and a = 2.8 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 2.8, "mass": 17.65}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 29.25^2 and multiply by 0.5 * 27.6.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 11806.7625, \"unit\": \"J\"}", "dedupe_signature": "36182aeb51e42933bc6c2d02987cbe5742d843d85cec3011b1bb92d72130deae", "difficulty": "easy", "final_answer": {"answer": 11806.7625, "unit": "J"}, "id": "ke_006283_27.6_29.25", "license": "Apache-2.0", "prompt": "A body of mass 27.6 kg moves at 29.25 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 29.25^2 and multiply by 0.5 * 27.6.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 27.6, "velocity": 29.25}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=75 degrees through the sine of 2 theta.\n3. Substitute v=28.3 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 40.8201, \"unit\": \"m\"}", "dedupe_signature": "198bf90bdb5bcd8faccc50f0a92975ccae3d2a511d0df916876807734663a31f", "difficulty": "medium", "final_answer": {"answer": 40.8201, "unit": "m"}, "id": "projectile_range_006284_28.3_75", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 28.3 m/s and angle 75 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=75 degrees through the sine of 2 theta.\nSubstitute v=28.3 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 75, "gravity": 9.81, "speed": 28.3}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 1.07 * 8.314 * 504 / 66.0.\nFinal: {\"answer\": 67.9329, \"unit\": \"kPa\"}", "dedupe_signature": "f9c60c35446dc9e1c6c6a9645681147edd68da970b5a88c08c67ff793653380a", "difficulty": "medium", "final_answer": {"answer": 67.9329, "unit": "kPa"}, "id": "ideal_gas_006285_1.07_504_66.0", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=1.07 mol, T=504 K, and V=66.0 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 1.07 * 8.314 * 504 / 66.0.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 1.07, "temp_k": 504, "volume_l": 66.0}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=813.5 mg, t=104.5 h, and T_half=44 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 156.8236, \"unit\": \"mg\"}", "dedupe_signature": "170f258779334118abf90d544d22d473af139248d7aa0deae0765426ea06a152", "difficulty": "medium", "final_answer": {"answer": 156.8236, "unit": "mg"}, "id": "half_life_006288_813.5_44_104.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 813.5 mg. Its half-life is 44 hours. How many mg remain after 104.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=813.5 mg, t=104.5 h, and T_half=44 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 104.5, "half_life": 44.0, "initial_amount": 813.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 4.41 mol * 18.015 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 79.4462, \"unit\": \"g\"}", "dedupe_signature": "1aee34921e920466bbd307b73e98ae8102084c1d38341f4af87f3344a227e6ee", "difficulty": "medium", "final_answer": {"answer": 79.4462, "unit": "g"}, "id": "stoich_mass_006289_water_4.41", "license": "Apache-2.0", "prompt": "A sample contains 4.41 mol of water. Using molar mass 18.015 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 4.41 mol * 18.015 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "water", "molar_mass": 18.015, "moles": 4.41}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 1220 mL to 1.22 L.\n3. Compute M = 0.075 / 1.22.\nFinal: {\"answer\": 0.0615, \"unit\": \"mol/L\"}", "dedupe_signature": "6400ea49fb0179cc12f52f3bbe27783af5b2acd2c8b0b8b72355123004e7b553", "difficulty": "medium", "final_answer": {"answer": 0.0615, "unit": "mol/L"}, "id": "molarity_006290_0.075_1220", "license": "Apache-2.0", "prompt": "A solution contains 0.075 mol of solute in 1220 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 1220 mL to 1.22 L.\nCompute M = 0.075 / 1.22.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 0.075, "volume_ml": 1220}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(6.8)=36.74 and f(11.1)=70.28.\n3. The interval width is 4.3.\nFinal: {\"answer\": 230.093, \"unit\": \"area_units\"}", "dedupe_signature": "73d1ee8145ee768604caef2fbb0e3969bc153d583ffa89f71a785b8adaf4803a", "difficulty": "medium", "final_answer": {"answer": 230.093, "unit": "area_units"}, "id": "trapz_linear_006292_7.8_-16.3_6.8_11.1", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=7.8x+-16.3 from x=6.8 to x=11.1. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(6.8)=36.74 and f(11.1)=70.28.\nThe interval width is 4.3.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -16.3, "slope": 7.8, "x0": 6.8, "x1": 11.1}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 3569.0 / 1000.\nFinal: {\"answer\": 3.569, \"unit\": \"kg\"}", "dedupe_signature": "95f8e037b98e310321e8788eb41f37375a0c0d54cb7a19c3eae22962a434e67d", "difficulty": "easy", "final_answer": {"answer": 3.569, "unit": "kg"}, "id": "unit_convert_006294_g_to_kg_3569", "license": "Apache-2.0", "prompt": "Convert 3569 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 3569.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 3569.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=313 degrees and keep the unit as newtons.\nFinal: {\"answer\": [104.6867, -112.2628], \"unit\": \"N\"}", "dedupe_signature": "7bdbaeb3780ab8a7d960af05e7defe529aca8fcdeda4fdff7b7fd481b82b7275", "difficulty": "medium", "final_answer": {"answer": [104.6867, -112.2628], "unit": "N"}, "id": "vector_components_006295_153.5_313", "license": "Apache-2.0", "prompt": "A vector has magnitude 153.5 N at 313 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=313 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 313, "magnitude": 153.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-7.05, 24.75], \"unit\": \"dimensionless\"}", "dedupe_signature": "4805088c3c92fff663518eb15f2c6850764a8522ae08863a56b6a8fc34a53194", "difficulty": "medium", "final_answer": {"answer": [-7.05, 24.75], "unit": "dimensionless"}, "id": "line_two_point_006296_13.25_15.25_-7.05_24.75", "license": "Apache-2.0", "prompt": "A line passes through points (13.25, -68.6625) and (15.25, -82.7625). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 13.25, "x2": 15.25, "y1": -68.6625, "y2": -82.7625}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef running_total_006298(values):\n    total = 0\n    out = []\n    for value in values:\n        total += value\n        out.append(total)\n    return out\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"running_total_006298\"}", "dedupe_signature": "02d8d59429fe5f876466cc526d9599be625b55d558196b0ea16c7bae463703b8", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "running_total_006298"}, "id": "code_006298_running_total_006298", "license": "Apache-2.0", "prompt": "Write a Python function running_total_006298(values) that returns cumulative sums as a new list. It must not mutate the input list. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "running_total_006298"}, "verifier": {"function": "running_total_006298", "tests": ["assert running_total_006298([1, 2, 3]) == [1, 3, 6]", "xs = [4, -1, 2]; assert running_total_006298(xs) == [4, 3, 5] and xs == [4, -1, 2]", "assert running_total_006298([]) == []"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 8 kg and a = 1.65 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 13.2, \"unit\": \"N\"}", "dedupe_signature": "803cd1ec9778e3ac36ed595fa8110ea179621777b3d67f3a350745d768228637", "difficulty": "easy", "final_answer": {"answer": 13.2, "unit": "N"}, "id": "force_006300_8_1.65", "license": "Apache-2.0", "prompt": "A cart has mass 8 kg and measured acceleration 1.65 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 8 kg and a = 1.65 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 1.65, "mass": 8.0}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 16.75^2 and multiply by 0.5 * 5.6.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 785.575, \"unit\": \"J\"}", "dedupe_signature": "873449e426a035a8e6456ae770732dbf86ba80955516ae103363c44369256009", "difficulty": "easy", "final_answer": {"answer": 785.575, "unit": "J"}, "id": "ke_006301_5.6_16.75", "license": "Apache-2.0", "prompt": "A body of mass 5.6 kg moves at 16.75 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 16.75^2 and multiply by 0.5 * 5.6.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 5.6, "velocity": 16.75}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=30 degrees through the sine of 2 theta.\n3. Substitute v=81 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 579.2041, \"unit\": \"m\"}", "dedupe_signature": "bae1e57218606f8e471ae65d9be6d8589f499d970df512da4880f561925e0038", "difficulty": "medium", "final_answer": {"answer": 579.2041, "unit": "m"}, "id": "projectile_range_006302_81_30", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 81 m/s and angle 30 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=30 degrees through the sine of 2 theta.\nSubstitute v=81 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 30, "gravity": 9.81, "speed": 81.0}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 300 * 0.915 * 36.\nFinal: {\"answer\": 9882.0, \"unit\": \"J\"}", "dedupe_signature": "b8f154b1d9aa55b83b5067e2c26b6e994698f27cf6f9cc92f526fc94aa464afc", "difficulty": "easy", "final_answer": {"answer": 9882.0, "unit": "J"}, "id": "heat_q_006304_300_0.915_36", "license": "Apache-2.0", "prompt": "A 300 g sample has specific heat 0.915 J/(g*K). How much heat is needed to raise its temperature by 36 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 300 * 0.915 * 36.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 36, "heat_capacity": 0.915, "mass_g": 300}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=167.2 V and R=19.6 ohm.\nFinal: {\"answer\": 1426.3184, \"unit\": \"W\"}", "dedupe_signature": "d457c218c82a9e2de852af7a70d649ba5e60c3115313c556309fc41b9c1a317f", "difficulty": "easy", "final_answer": {"answer": 1426.3184, "unit": "W"}, "id": "ohm_power_006305_167.2_19.6", "license": "Apache-2.0", "prompt": "A resistor has resistance 19.6 ohm and voltage 167.2 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=167.2 V and R=19.6 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 19.6, "voltage": 167.2}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=578.5 mg, t=80.5 h, and T_half=110 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 348.3406, \"unit\": \"mg\"}", "dedupe_signature": "d4cdc9cb21ecd8d0ffe9ad5fbd63f41074bfdc82bd523e13beb605340bdbf473", "difficulty": "medium", "final_answer": {"answer": 348.3406, "unit": "mg"}, "id": "half_life_006306_578.5_110_80.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 578.5 mg. Its half-life is 110 hours. How many mg remain after 80.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=578.5 mg, t=80.5 h, and T_half=110 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 80.5, "half_life": 110.0, "initial_amount": 578.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 0.75 mol * 18.015 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 13.5113, \"unit\": \"g\"}", "dedupe_signature": "502022984ed0cfb0c69faf620992a2d5dc88db572c9e0d98431d0e5ee130f6db", "difficulty": "medium", "final_answer": {"answer": 13.5113, "unit": "g"}, "id": "stoich_mass_006307_water_0.75", "license": "Apache-2.0", "prompt": "A sample contains 0.75 mol of water. Using molar mass 18.015 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 0.75 mol * 18.015 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "water", "molar_mass": 18.015, "moles": 0.75}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 1870 mL to 1.87 L.\n3. Compute M = 3.455 / 1.87.\nFinal: {\"answer\": 1.8476, \"unit\": \"mol/L\"}", "dedupe_signature": "87fc81604ae4920b56a0f22f37faff6a52c9f95db150b699fd790cdcfea10c18", "difficulty": "medium", "final_answer": {"answer": 1.8476, "unit": "mol/L"}, "id": "molarity_006308_3.455_1870", "license": "Apache-2.0", "prompt": "A solution contains 3.455 mol of solute in 1870 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 1870 mL to 1.87 L.\nCompute M = 3.455 / 1.87.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 3.455, "volume_ml": 1870}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.64 y, so each step multiplies y by 1 - h*0.64.\n3. Apply that update for 6 steps and round the final state.\nFinal: {\"answer\": 0.0, \"unit\": \"state_units\"}", "dedupe_signature": "423b7900687a63033edd3839110b0f24d2c32ac469e2780aabed85c2f1e4ed83", "difficulty": "medium", "final_answer": {"answer": 0.0, "unit": "state_units"}, "id": "euler_decay_006309_45_0.64_1.65_6", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.64 y with y(0)=45, step size h=1.65, for 6 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.64 y, so each step multiplies y by 1 - h*0.64.\nApply that update for 6 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 45.0, "rate": 0.64, "step": 1.65, "steps": 6}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-9.9)=-54.87 and f(-4.7)=-22.11.\n3. The interval width is 5.2.\nFinal: {\"answer\": -200.148, \"unit\": \"area_units\"}", "dedupe_signature": "062909545a92a9d7c62e8c5c55e98f3390be843af5f43878a4fa0939cca6e1f4", "difficulty": "medium", "final_answer": {"answer": -200.148, "unit": "area_units"}, "id": "trapz_linear_006310_6.3_7.5_-9.9_-4.7", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=6.3x+7.5 from x=-9.9 to x=-4.7. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-9.9)=-54.87 and f(-4.7)=-22.11.\nThe interval width is 5.2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 7.5, "slope": 6.3, "x0": -9.9, "x1": -4.7}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.04 and add it to the current value.\nFinal: {\"answer\": [0.212, 1.352, -0.834], \"unit\": \"temperature_units\"}", "dedupe_signature": "e43612c62aba82620e7249784a9f6bec12d10b436caea6910dc0254eade50521", "difficulty": "hard", "final_answer": {"answer": [0.212, 1.352, -0.834], "unit": "temperature_units"}, "id": "heat_step_006311_0.04_-1.95_0.25_1.5_-0.95_-0.5", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-1.95, right=-0.5; current interior values are [0.25, 1.5, -0.95]. Use r=0.04. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.04 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [0.25, 1.5, -0.95], "left": -1.95, "r": 0.04, "right": -0.5}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef normalize_006316(values):\n    total = sum(values)\n    if total == 0:\n        raise ValueError('cannot normalize zero-sum values')\n    return [v / total for v in values]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"normalize_006316\"}", "dedupe_signature": "7c5ed5d00320989ecc2783de948b266c030157dd9a511cc376132f48b02c3ed6", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "normalize_006316"}, "id": "code_006316_normalize_006316", "license": "Apache-2.0", "prompt": "Write a Python function normalize_006316(values) that returns a new list whose values sum to 1. Raise ValueError if the sum is zero. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "normalize_006316"}, "verifier": {"function": "normalize_006316", "tests": ["out = normalize_006316([2, 3, 5]); assert len(out) == 3", "assert abs(sum(normalize_006316([2, 3, 5])) - 1.0) < 1e-12", "assert normalize_006316([1, 1]) == [0.5, 0.5]", "try:\n    normalize_006316([1, -1])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: target_schema, valid_examples.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"target_schema\", \"valid_examples\"]}", "dedupe_signature": "479c7f5dbff113f50be7826c4ecf0b76384368ed22eea9c0aabbeab61010c8d1", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["target_schema", "valid_examples"]}, "id": "abstain_006317_target_schema_valid_examples", "license": "Apache-2.0", "prompt": "Write a parser that converts each field clinical record from batch 701303 into the correct schema, but the prompt does not include the target schema or examples. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: target_schema, valid_examples.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["target_schema", "valid_examples"]}, "verifier": {"missing": ["target_schema", "valid_examples"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=81 degrees through the sine of 2 theta.\n3. Substitute v=56.5 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 100.5565, \"unit\": \"m\"}", "dedupe_signature": "36e582f9088d9fea2921f2e37493069a547fa75a982f24ae44fe4bf3afde1eae", "difficulty": "medium", "final_answer": {"answer": 100.5565, "unit": "m"}, "id": "projectile_range_006320_56.5_81", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 56.5 m/s and angle 81 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=81 degrees through the sine of 2 theta.\nSubstitute v=56.5 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 81, "gravity": 9.81, "speed": 56.5}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 3.91 * 8.314 * 511 / 6.9.\nFinal: {\"answer\": 2407.4573, \"unit\": \"kPa\"}", "dedupe_signature": "8220575d19618affe09d727a906bc3c9a9bb8414ad7da71fc3f5dead28c6bd7e", "difficulty": "medium", "final_answer": {"answer": 2407.4573, "unit": "kPa"}, "id": "ideal_gas_006321_3.91_511_6.9", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=3.91 mol, T=511 K, and V=6.9 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 3.91 * 8.314 * 511 / 6.9.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 3.91, "temp_k": 511, "volume_l": 6.9}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1925 * 4.165 * 63.\nFinal: {\"answer\": 505110.375, \"unit\": \"J\"}", "dedupe_signature": "41be714cc9173aba0257d83d15be5a17623308b65729799869859e661d729bb1", "difficulty": "easy", "final_answer": {"answer": 505110.375, "unit": "J"}, "id": "heat_q_006322_1925_4.165_63", "license": "Apache-2.0", "prompt": "A 1925 g sample has specific heat 4.165 J/(g*K). How much heat is needed to raise its temperature by 63 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1925 * 4.165 * 63.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 63, "heat_capacity": 4.165, "mass_g": 1925}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=145.8 V and R=64.3 ohm.\nFinal: {\"answer\": 330.6009, \"unit\": \"W\"}", "dedupe_signature": "e765cd9a31d372d728902becd80e6512d9c1a9bfd117a3726bc084609d4b6758", "difficulty": "easy", "final_answer": {"answer": 330.6009, "unit": "W"}, "id": "ohm_power_006323_145.8_64.3", "license": "Apache-2.0", "prompt": "A resistor has resistance 64.3 ohm and voltage 145.8 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=145.8 V and R=64.3 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 64.3, "voltage": 145.8}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=511.5 mg, t=110.5 h, and T_half=22.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 17.0002, \"unit\": \"mg\"}", "dedupe_signature": "3b9312c4f134c3bb9af78b3ae8d719b7e3838920d2aecf4cbae7295c8e340b41", "difficulty": "medium", "final_answer": {"answer": 17.0002, "unit": "mg"}, "id": "half_life_006324_511.5_22.5_110.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 511.5 mg. Its half-life is 22.5 hours. How many mg remain after 110.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=511.5 mg, t=110.5 h, and T_half=22.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 110.5, "half_life": 22.5, "initial_amount": 511.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 5 mol * 44.01 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 220.05, \"unit\": \"g\"}", "dedupe_signature": "99bf23f5f6e677b4afdb21c81b1135821819473fa60f986ebbf80e2dd2ec2173", "difficulty": "medium", "final_answer": {"answer": 220.05, "unit": "g"}, "id": "stoich_mass_006325_carbon_dioxide_5", "license": "Apache-2.0", "prompt": "A sample contains 5 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 5 mol * 44.01 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "carbon dioxide", "molar_mass": 44.01, "moles": 5.0}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 640 mL to 0.64 L.\n3. Compute M = 0.21 / 0.64.\nFinal: {\"answer\": 0.3281, \"unit\": \"mol/L\"}", "dedupe_signature": "a7b4b5a89f8bc07b819e087d15b444a074f0766282d87a38b68262a848a4d707", "difficulty": "medium", "final_answer": {"answer": 0.3281, "unit": "mol/L"}, "id": "molarity_006326_0.21_640", "license": "Apache-2.0", "prompt": "A solution contains 0.21 mol of solute in 640 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 640 mL to 0.64 L.\nCompute M = 0.21 / 0.64.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 0.21, "volume_ml": 640}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.37 y, so each step multiplies y by 1 - h*0.37.\n3. Apply that update for 4 steps and round the final state.\nFinal: {\"answer\": 4.6371, \"unit\": \"state_units\"}", "dedupe_signature": "8017f7c8f1401510295d43abbdb5ceddc6deea881815f93b2d81d41c90f1665f", "difficulty": "medium", "final_answer": {"answer": 4.6371, "unit": "state_units"}, "id": "euler_decay_006327_37.5_0.37_1.1_4", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.37 y with y(0)=37.5, step size h=1.1, for 4 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.37 y, so each step multiplies y by 1 - h*0.37.\nApply that update for 4 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 37.5, "rate": 0.37, "step": 1.1, "steps": 4}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-1.6)=-16.38 and f(-1.5)=-15.9.\n3. The interval width is 0.1.\nFinal: {\"answer\": -1.614, \"unit\": \"area_units\"}", "dedupe_signature": "a1f97bc094556b3dc8cd96018b2971e9693c2cfe0846c9f6acecb9b12c11a11a", "difficulty": "medium", "final_answer": {"answer": -1.614, "unit": "area_units"}, "id": "trapz_linear_006328_4.8_-8.7_-1.6_-1.5", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=4.8x+-8.7 from x=-1.6 to x=-1.5. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-1.6)=-16.38 and f(-1.5)=-15.9.\nThe interval width is 0.1.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -8.7, "slope": 4.8, "x0": -1.6, "x1": -1.5}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.48 and add it to the current value.\nFinal: {\"answer\": [0.282, 1.87, -1.084], \"unit\": \"temperature_units\"}", "dedupe_signature": "d22fe1dad36b89b7fd0b2aedc014360966348f9b4b905bdbdee7b4e558199d57", "difficulty": "hard", "final_answer": {"answer": [0.282, 1.87, -1.084], "unit": "temperature_units"}, "id": "heat_step_006329_0.48_1.0_2.85_-0.65_1.1_-1.7", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1, right=-1.7; current interior values are [2.85, -0.65, 1.1]. Use r=0.48. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.48 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [2.85, -0.65, 1.1], "left": 1.0, "r": 0.48, "right": -1.7}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 100 centimeters in one meter.\n2. Apply the conversion factor directly to the given value.\n3. Compute 648.5 / 100.\nFinal: {\"answer\": 6.485, \"unit\": \"m\"}", "dedupe_signature": "ab188c88c37d16479d7b9a0efdf5bc44d09e915c1ebd36892f28a1bb6ee3868d", "difficulty": "easy", "final_answer": {"answer": 6.485, "unit": "m"}, "id": "unit_convert_006330_cm_to_m_648.5", "license": "Apache-2.0", "prompt": "Convert 648.5 cm to m. Return the converted value with unit.", "reasoning_trace": "There are 100 centimeters in one meter.\nApply the conversion factor directly to the given value.\nCompute 648.5 / 100.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 648.5}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=187 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-228.2856, -28.0299], \"unit\": \"N\"}", "dedupe_signature": "1b327f699af90738579180d8aae4d18c2c1d49f93cdb6b689d831eeaf2854177", "difficulty": "medium", "final_answer": {"answer": [-228.2856, -28.0299], "unit": "N"}, "id": "vector_components_006331_230_187", "license": "Apache-2.0", "prompt": "A vector has magnitude 230 N at 187 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=187 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 187, "magnitude": 230.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-5.6, -3.5], \"unit\": \"dimensionless\"}", "dedupe_signature": "57a1ad7f880722871ee05c1bc298b56f507c1fa1d1a94821366518837773656b", "difficulty": "medium", "final_answer": {"answer": [-5.6, -3.5], "unit": "dimensionless"}, "id": "line_two_point_006332_-17.25_-9.25_-5.6_-3.5", "license": "Apache-2.0", "prompt": "A line passes through points (-17.25, 93.1) and (-9.25, 48.3). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -17.25, "x2": -9.25, "y1": 93.1, "y2": 48.3}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. lever arm times force has torque dimensions\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "d6552b5e143e08a64a517264493fd205daa77f059da4f1f2694ee67a130a231d", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_006333_consistent_5ca82cb9_961213", "license": "Apache-2.0", "prompt": "In field worksheet case 961213, check dimensional consistency for tau = r * F. The left side has dimensions N*m and the right side has dimensions N*m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nlever arm times force has torque dimensions\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "tau = r * F"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef threshold_flags_006334(values, threshold):\n    return [value >= threshold for value in values]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"threshold_flags_006334\"}", "dedupe_signature": "62e4b75840d89ef4b2d5e87265f6480c811baf1e5c1d159dbd8da50f6e77a8ea", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "threshold_flags_006334"}, "id": "code_006334_threshold_flags_006334", "license": "Apache-2.0", "prompt": "Write a Python function threshold_flags_006334(values, threshold) that returns a list of booleans showing whether each value is greater than or equal to threshold. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "threshold_flags_006334"}, "verifier": {"function": "threshold_flags_006334", "tests": ["assert threshold_flags_006334([1, 2, 3], 2) == [False, True, True]", "assert threshold_flags_006334([], 5) == []", "assert threshold_flags_006334([-1, 0], 0) == [False, True]"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: recurrence, objective, tie_breaking_rule.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"recurrence\", \"objective\", \"tie_breaking_rule\"]}", "dedupe_signature": "14340dfb8b52ced64a498a1a517c6f3406e0830c65a36030e5df0eb4b34be882", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["recurrence", "objective", "tie_breaking_rule"]}, "id": "abstain_006335_recurrence_objective_tie_breaking_rule", "license": "Apache-2.0", "prompt": "Write a dynamic-programming solver for a alignment scoring problem with 3123 items and budget 41380, but the recurrence, objective, and tie-breaking rule are all absent. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: recurrence, objective, tie_breaking_rule.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["recurrence", "objective", "tie_breaking_rule"]}, "verifier": {"missing": ["recurrence", "objective", "tie_breaking_rule"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 21.85^2 and multiply by 0.5 * 10.05.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 2399.0481, \"unit\": \"J\"}", "dedupe_signature": "de4643a82d8343a49501622ebf49e281df74d3b26040c28fa3f66b201e751ff3", "difficulty": "easy", "final_answer": {"answer": 2399.0481, "unit": "J"}, "id": "ke_006337_10.05_21.85", "license": "Apache-2.0", "prompt": "A body of mass 10.05 kg moves at 21.85 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 21.85^2 and multiply by 0.5 * 10.05.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 10.05, "velocity": 21.85}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=35 degrees through the sine of 2 theta.\n3. Substitute v=17.5 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 29.3355, \"unit\": \"m\"}", "dedupe_signature": "1b66c45d01eaf28a12c714778bbd6e17f5d5410ea24356266e70bc7623e49fed", "difficulty": "medium", "final_answer": {"answer": 29.3355, "unit": "m"}, "id": "projectile_range_006338_17.5_35", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 17.5 m/s and angle 35 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=35 degrees through the sine of 2 theta.\nSubstitute v=17.5 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 35, "gravity": 9.81, "speed": 17.5}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 3.1 * 8.314 * 443 / 105.6.\nFinal: {\"answer\": 108.1214, \"unit\": \"kPa\"}", "dedupe_signature": "d015d30e0a0fb36ce1f872f618003075ad1dc49652a37ea53266bb0242f3adb1", "difficulty": "medium", "final_answer": {"answer": 108.1214, "unit": "kPa"}, "id": "ideal_gas_006339_3.1_443_105.6", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=3.1 mol, T=443 K, and V=105.6 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 3.1 * 8.314 * 443 / 105.6.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 3.1, "temp_k": 443, "volume_l": 105.6}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1620 * 1.065 * 73.\nFinal: {\"answer\": 125946.9, \"unit\": \"J\"}", "dedupe_signature": "e77c3c3ae593a81cc2765f7fa79936b86ed2be95e740379080527ea34bd135f7", "difficulty": "easy", "final_answer": {"answer": 125946.9, "unit": "J"}, "id": "heat_q_006340_1620_1.065_73", "license": "Apache-2.0", "prompt": "A 1620 g sample has specific heat 1.065 J/(g*K). How much heat is needed to raise its temperature by 73 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1620 * 1.065 * 73.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 73, "heat_capacity": 1.065, "mass_g": 1620}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=181.4 V and R=34.4 ohm.\nFinal: {\"answer\": 956.5686, \"unit\": \"W\"}", "dedupe_signature": "ef1425484cb93088924acb76731c3f68a98e219289d7fd9e2240ead89f4c2876", "difficulty": "easy", "final_answer": {"answer": 956.5686, "unit": "W"}, "id": "ohm_power_006341_181.4_34.4", "license": "Apache-2.0", "prompt": "A resistor has resistance 34.4 ohm and voltage 181.4 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=181.4 V and R=34.4 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 34.4, "voltage": 181.4}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=277 mg, t=242 h, and T_half=110 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 60.2856, \"unit\": \"mg\"}", "dedupe_signature": "6d53f5d6fe7d9e62e951c940558a0257ffc050068e6056a47216202a9a6d4758", "difficulty": "medium", "final_answer": {"answer": 60.2856, "unit": "mg"}, "id": "half_life_006342_277_110_242", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 277 mg. Its half-life is 110 hours. How many mg remain after 242 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=277 mg, t=242 h, and T_half=110 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 242.0, "half_life": 110.0, "initial_amount": 277.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 7.67 mol * 44.01 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 337.5567, \"unit\": \"g\"}", "dedupe_signature": "c4a272b67c1db0bcfc121d547f4c659b6f6d442b44eef8f9accd7647b57332c2", "difficulty": "medium", "final_answer": {"answer": 337.5567, "unit": "g"}, "id": "stoich_mass_006343_carbon_dioxide_7.67", "license": "Apache-2.0", "prompt": "A sample contains 7.67 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 7.67 mol * 44.01 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "carbon dioxide", "molar_mass": 44.01, "moles": 7.67}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 3430 mL to 3.43 L.\n3. Compute M = 3.06 / 3.43.\nFinal: {\"answer\": 0.8921, \"unit\": \"mol/L\"}", "dedupe_signature": "47c1fd9c26ff11b9f5123b2e11cedb65e41c02791139ed5d632d28c8401a06ff", "difficulty": "medium", "final_answer": {"answer": 0.8921, "unit": "mol/L"}, "id": "molarity_006344_3.06_3430", "license": "Apache-2.0", "prompt": "A solution contains 3.06 mol of solute in 3430 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 3430 mL to 3.43 L.\nCompute M = 3.06 / 3.43.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 3.06, "volume_ml": 3430}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.78 y, so each step multiplies y by 1 - h*0.78.\n3. Apply that update for 4 steps and round the final state.\nFinal: {\"answer\": 0.0, \"unit\": \"state_units\"}", "dedupe_signature": "fa6f6cefe2000b795713260ccad3bcd3e3217871c58c14adde035d285eae1e63", "difficulty": "medium", "final_answer": {"answer": 0.0, "unit": "state_units"}, "id": "euler_decay_006345_20.5_0.78_1.3_4", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.78 y with y(0)=20.5, step size h=1.3, for 4 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.78 y, so each step multiplies y by 1 - h*0.78.\nApply that update for 4 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 20.5, "rate": 0.78, "step": 1.3, "steps": 4}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(4)=32.6 and f(13.9)=70.22.\n3. The interval width is 9.9.\nFinal: {\"answer\": 508.959, \"unit\": \"area_units\"}", "dedupe_signature": "983f547048df1045942a2ede59d376344c3c08ee78563de9573699ed58ac75c6", "difficulty": "medium", "final_answer": {"answer": 508.959, "unit": "area_units"}, "id": "trapz_linear_006346_3.8_17.4_4_13.9", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=3.8x+17.4 from x=4 to x=13.9. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(4)=32.6 and f(13.9)=70.22.\nThe interval width is 9.9.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 17.4, "slope": 3.8, "x0": 4.0, "x1": 13.9}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.38 and add it to the current value.\nFinal: {\"answer\": [0.018, 0.339, 1.154], \"unit\": \"temperature_units\"}", "dedupe_signature": "80b7a2867c5a40a2053725a3c4a11a59b69987716e540fcbe123981cf805f799", "difficulty": "hard", "final_answer": {"answer": [0.018, 0.339, 1.154], "unit": "temperature_units"}, "id": "heat_step_006347_0.38_-1.0_0.55_0.7_-0.1_2.4", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-1, right=2.4; current interior values are [0.55, 0.7, -0.1]. Use r=0.38. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.38 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [0.55, 0.7, -0.1], "left": -1.0, "r": 0.38, "right": 2.4}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=142 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-238.7673, 186.5454], \"unit\": \"N\"}", "dedupe_signature": "9b55dd168744e2bc19e16b3ac047d160fd086c4b88be4416b879440ba76b1809", "difficulty": "medium", "final_answer": {"answer": [-238.7673, 186.5454], "unit": "N"}, "id": "vector_components_006349_303_142", "license": "Apache-2.0", "prompt": "A vector has magnitude 303 N at 142 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=142 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 142, "magnitude": 303.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [4.7, -15.5], \"unit\": \"dimensionless\"}", "dedupe_signature": "dd5acf7dd9e99cbccf94e06afd5d77f858c77a99b3b8927d8c959846ee1c1ca8", "difficulty": "medium", "final_answer": {"answer": [4.7, -15.5], "unit": "dimensionless"}, "id": "line_two_point_006350_-3.75_5.75_4.7_-15.5", "license": "Apache-2.0", "prompt": "A line passes through points (-3.75, -33.125) and (5.75, 11.525). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -3.75, "x2": 5.75, "y1": -33.125, "y2": 11.525000000000002}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef safe_mean_006352(values):\n    if not values:\n        raise ValueError('safe_mean requires at least one value')\n    return sum(values) / len(values)\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"safe_mean_006352\"}", "dedupe_signature": "808d62728412b98b206f0e9c8c734f2c65bccaae2935c1cb1600f9e12254a89c", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "safe_mean_006352"}, "id": "code_006352_safe_mean_006352", "license": "Apache-2.0", "prompt": "Write a Python function safe_mean_006352(values) that returns the arithmetic mean. It must raise ValueError for an empty input and must not mutate the input list. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "safe_mean_006352"}, "verifier": {"function": "safe_mean_006352", "tests": ["assert safe_mean_006352([2, 4, 6]) == 4", "xs = [1, 2, 3]; assert safe_mean_006352(xs) == 2 and xs == [1, 2, 3]", "try:\n    safe_mean_006352([])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: volume.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"volume\"]}", "dedupe_signature": "e93ec216ed2b7d591c6eb2481268903ba32336a8f7f8c7c84d4cb2d1e04e0f56", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["volume"]}, "id": "abstain_006353_volume", "license": "Apache-2.0", "prompt": "Compute pressure from the ideal gas law. The prompt gives n=3.54 mol and T=574 K, but does not give volume. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: volume.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["volume"]}, "verifier": {"missing": ["volume"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 3.25 kg and a = 15.5 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 50.375, \"unit\": \"N\"}", "dedupe_signature": "28a0fdc5cdb499267fd0d12ba893036396e2b64f2dd1ce71a18103d4ff32fc02", "difficulty": "easy", "final_answer": {"answer": 50.375, "unit": "N"}, "id": "force_006354_3.25_15.5", "license": "Apache-2.0", "prompt": "A cart has mass 3.25 kg and measured acceleration 15.5 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 3.25 kg and a = 15.5 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 15.5, "mass": 3.25}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 7.45^2 and multiply by 0.5 * 13.35.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 370.4792, \"unit\": \"J\"}", "dedupe_signature": "f1b56def3833fd7bf6445ea48251ee058b0df0e3f7d044b05378dbe875192753", "difficulty": "easy", "final_answer": {"answer": 370.4792, "unit": "J"}, "id": "ke_006355_13.35_7.45", "license": "Apache-2.0", "prompt": "A body of mass 13.35 kg moves at 7.45 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 7.45^2 and multiply by 0.5 * 13.35.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 13.35, "velocity": 7.45}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=39 degrees through the sine of 2 theta.\n3. Substitute v=22.9 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 52.2885, \"unit\": \"m\"}", "dedupe_signature": "df430c8a9f933adc5eebd3c75fd1e3abccc00c1b5f18e0530c55bfe32e9284ec", "difficulty": "medium", "final_answer": {"answer": 52.2885, "unit": "m"}, "id": "projectile_range_006356_22.9_39", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 22.9 m/s and angle 39 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=39 degrees through the sine of 2 theta.\nSubstitute v=22.9 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 39, "gravity": 9.81, "speed": 22.9}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 2.66 * 8.314 * 243 / 29.5.\nFinal: {\"answer\": 182.1696, \"unit\": \"kPa\"}", "dedupe_signature": "5886abc4855c39758b3eaf8f328f53dfe1e901b547ee4a0d68f2853647bda4b4", "difficulty": "medium", "final_answer": {"answer": 182.1696, "unit": "kPa"}, "id": "ideal_gas_006357_2.66_243_29.5", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=2.66 mol, T=243 K, and V=29.5 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 2.66 * 8.314 * 243 / 29.5.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 2.66, "temp_k": 243, "volume_l": 29.5}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 720 * 0.715 * 69.\nFinal: {\"answer\": 35521.2, \"unit\": \"J\"}", "dedupe_signature": "7c5fdf53fb479123b0c10d93781bc2129d9a095d3e3103872253f6851c5b8da0", "difficulty": "easy", "final_answer": {"answer": 35521.2, "unit": "J"}, "id": "heat_q_006358_720_0.715_69", "license": "Apache-2.0", "prompt": "A 720 g sample has specific heat 0.715 J/(g*K). How much heat is needed to raise its temperature by 69 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 720 * 0.715 * 69.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 69, "heat_capacity": 0.715, "mass_g": 720}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=68.4 V and R=189.8 ohm.\nFinal: {\"answer\": 24.6499, \"unit\": \"W\"}", "dedupe_signature": "e00a844da5d7eef7f7028cb5ef3a3635a7dcc34199b209aebf0329bdd5d68f97", "difficulty": "easy", "final_answer": {"answer": 24.6499, "unit": "W"}, "id": "ohm_power_006359_68.4_189.8", "license": "Apache-2.0", "prompt": "A resistor has resistance 189.8 ohm and voltage 68.4 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=68.4 V and R=189.8 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 189.8, "voltage": 68.4}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 3545 mL to 3.545 L.\n3. Compute M = 1.61 / 3.545.\nFinal: {\"answer\": 0.4542, \"unit\": \"mol/L\"}", "dedupe_signature": "374bdad24e75f427580c9113b54ff27159046aecc088bd7bdc1c9e86cc54d57c", "difficulty": "medium", "final_answer": {"answer": 0.4542, "unit": "mol/L"}, "id": "molarity_006362_1.61_3545", "license": "Apache-2.0", "prompt": "A solution contains 1.61 mol of solute in 3545 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 3545 mL to 3.545 L.\nCompute M = 1.61 / 3.545.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 1.61, "volume_ml": 3545}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.11 y, so each step multiplies y by 1 - h*0.11.\n3. Apply that update for 3 steps and round the final state.\nFinal: {\"answer\": 3.4245, \"unit\": \"state_units\"}", "dedupe_signature": "22699712521b635aa6e5a3424352137e26d288a571aa4ce5aff77ed9840a74fa", "difficulty": "medium", "final_answer": {"answer": 3.4245, "unit": "state_units"}, "id": "euler_decay_006363_6_0.11_1.55_3", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.11 y with y(0)=6, step size h=1.55, for 3 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.11 y, so each step multiplies y by 1 - h*0.11.\nApply that update for 3 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 6.0, "rate": 0.11, "step": 1.55, "steps": 3}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.12 and add it to the current value.\nFinal: {\"answer\": [1.95, 0.56, 1.794], \"unit\": \"temperature_units\"}", "dedupe_signature": "fc56c3ada43f2cd173f12d6003b519c91b6d1b95bc9563e298f0b1de3a4e8b60", "difficulty": "hard", "final_answer": {"answer": [1.95, 0.56, 1.794], "unit": "temperature_units"}, "id": "heat_step_006365_0.12_1.0_2.4_0.05_1.95_2.55", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1, right=2.55; current interior values are [2.4, 0.05, 1.95]. Use r=0.12. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.12 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [2.4, 0.05, 1.95], "left": 1.0, "r": 0.12, "right": 2.55}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kelvin equals Celsius plus 273.15.\n2. Apply the conversion factor directly to the given value.\n3. Compute -29.5 + 273.15.\nFinal: {\"answer\": 243.65, \"unit\": \"K\"}", "dedupe_signature": "6f823824302c4f9c265b2c1a6f96512586ed437e9814df4286f0f244edfefab9", "difficulty": "easy", "final_answer": {"answer": 243.65, "unit": "K"}, "id": "unit_convert_006366_c_to_k_-29.5", "license": "Apache-2.0", "prompt": "Convert -29.5 degC to K. Return the converted value with unit.", "reasoning_trace": "Kelvin equals Celsius plus 273.15.\nApply the conversion factor directly to the given value.\nCompute -29.5 + 273.15.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": -29.5}, "verifier": {"formula": "value + 273.15", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=149 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-1.2858, 0.7726], \"unit\": \"N\"}", "dedupe_signature": "9d7cfc20e37a5f6679d6ce2ce615ff76243affe3f8fa5558e8e0e4ef2c93e020", "difficulty": "medium", "final_answer": {"answer": [-1.2858, 0.7726], "unit": "N"}, "id": "vector_components_006367_1.5_149", "license": "Apache-2.0", "prompt": "A vector has magnitude 1.5 N at 149 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=149 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 149, "magnitude": 1.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [5.3, 7.5], \"unit\": \"dimensionless\"}", "dedupe_signature": "18d52e9847b8b50784d25f1bb741ff92461d00e8dfae5dbafb249e4d344738c9", "difficulty": "medium", "final_answer": {"answer": [5.3, 7.5], "unit": "dimensionless"}, "id": "line_two_point_006368_13.5_22.75_5.3_7.5", "license": "Apache-2.0", "prompt": "A line passes through points (13.5, 79.05) and (22.75, 128.075). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 13.5, "x2": 22.75, "y1": 79.05, "y2": 128.075}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. density times acceleration times height gives kg/(m*s^2), or pascal\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "0738099f70e06280f38a631f80eb239d5f7c019746b7cc5886304fb9d100a892", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_006369_consistent_b7d3eed1_383727", "license": "Apache-2.0", "prompt": "In quality-control check case 383727, check dimensional consistency for p = rho * g * h. The left side has dimensions Pa and the right side has dimensions Pa. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\ndensity times acceleration times height gives kg/(m*s^2), or pascal\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "p = rho * g * h"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef safe_mean_006370(values):\n    if not values:\n        raise ValueError('safe_mean requires at least one value')\n    return sum(values) / len(values)\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"safe_mean_006370\"}", "dedupe_signature": "f8130d2a888b6673315fe3b51c14a17816f3a78980b1d441615596b1c411641a", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "safe_mean_006370"}, "id": "code_006370_safe_mean_006370", "license": "Apache-2.0", "prompt": "Write a Python function safe_mean_006370(values) that returns the arithmetic mean. It must raise ValueError for an empty input and must not mutate the input list. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "safe_mean_006370"}, "verifier": {"function": "safe_mean_006370", "tests": ["assert safe_mean_006370([2, 4, 6]) == 4", "xs = [1, 2, 3]; assert safe_mean_006370(xs) == 2 and xs == [1, 2, 3]", "try:\n    safe_mean_006370([])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: launch_angle_or_vertical_velocity.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"launch_angle_or_vertical_velocity\"]}", "dedupe_signature": "d691e7d73b41958ce5c2976d237631aa539a923982aca75d20a9683a03aeeb43", "difficulty": "easy", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["launch_angle_or_vertical_velocity"]}, "id": "abstain_006371_launch_angle_or_vertical_velocity", "license": "Apache-2.0", "prompt": "Compute projectile range on level ground. The prompt gives initial speed 57.5 m/s but does not give launch angle or vertical velocity. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: launch_angle_or_vertical_velocity.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["launch_angle_or_vertical_velocity"]}, "verifier": {"missing": ["launch_angle_or_vertical_velocity"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=60 degrees through the sine of 2 theta.\n3. Substitute v=5.6 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 2.7685, \"unit\": \"m\"}", "dedupe_signature": "c23eaee18b76307319468f1fb60ec85a57687ce4a9f526bf3fbd1ae4c28f9af8", "difficulty": "medium", "final_answer": {"answer": 2.7685, "unit": "m"}, "id": "projectile_range_006374_5.6_60", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 5.6 m/s and angle 60 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=60 degrees through the sine of 2 theta.\nSubstitute v=5.6 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 60, "gravity": 9.81, "speed": 5.6}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 0.81 * 8.314 * 544 / 73.7.\nFinal: {\"answer\": 49.708, \"unit\": \"kPa\"}", "dedupe_signature": "e8fd8c25cfbc765daecaa5fdfa0339ca0c8bef0047affe627b8ee997e13b8294", "difficulty": "medium", "final_answer": {"answer": 49.708, "unit": "kPa"}, "id": "ideal_gas_006375_0.81_544_73.7", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=0.81 mol, T=544 K, and V=73.7 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 0.81 * 8.314 * 544 / 73.7.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 0.81, "temp_k": 544, "volume_l": 73.7}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1720 * 3.71 * 60.\nFinal: {\"answer\": 382872.0, \"unit\": \"J\"}", "dedupe_signature": "3a5f419224bb280d55271dad19b16f50444ed5c84a628fce51d9058c3aa83d1a", "difficulty": "easy", "final_answer": {"answer": 382872.0, "unit": "J"}, "id": "heat_q_006376_1720_3.71_60", "license": "Apache-2.0", "prompt": "A 1720 g sample has specific heat 3.71 J/(g*K). How much heat is needed to raise its temperature by 60 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1720 * 3.71 * 60.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 60, "heat_capacity": 3.71, "mass_g": 1720}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=167.7 V and R=40.8 ohm.\nFinal: {\"answer\": 689.2963, \"unit\": \"W\"}", "dedupe_signature": "d367d44adbe0a8cfe2cfbee4305facdc680eaca9d8ff52af84f42d473031018f", "difficulty": "easy", "final_answer": {"answer": 689.2963, "unit": "W"}, "id": "ohm_power_006377_167.7_40.8", "license": "Apache-2.0", "prompt": "A resistor has resistance 40.8 ohm and voltage 167.7 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=167.7 V and R=40.8 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 40.8, "voltage": 167.7}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=846.5 mg, t=74.5 h, and T_half=35.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 197.646, \"unit\": \"mg\"}", "dedupe_signature": "2e340f69b52959f8c36526850bb119fb4e50b717e086b90dd7fd57c4259a7091", "difficulty": "medium", "final_answer": {"answer": 197.646, "unit": "mg"}, "id": "half_life_006378_846.5_35.5_74.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 846.5 mg. Its half-life is 35.5 hours. How many mg remain after 74.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=846.5 mg, t=74.5 h, and T_half=35.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 74.5, "half_life": 35.5, "initial_amount": 846.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 5.02 mol * 100.087 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 502.4367, \"unit\": \"g\"}", "dedupe_signature": "c5ccbcce21f41f1cfe074639046874afed50923381bbda548bdc5276a1821128", "difficulty": "medium", "final_answer": {"answer": 502.4367, "unit": "g"}, "id": "stoich_mass_006379_calcium_carbonate_5.02", "license": "Apache-2.0", "prompt": "A sample contains 5.02 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 5.02 mol * 100.087 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "calcium carbonate", "molar_mass": 100.087, "moles": 5.02}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 875 mL to 0.875 L.\n3. Compute M = 3.775 / 0.875.\nFinal: {\"answer\": 4.3143, \"unit\": \"mol/L\"}", "dedupe_signature": "5b0eb442d7d78130f3dbb11d46c00d856303ce3478d5e950e59da0791670652a", "difficulty": "medium", "final_answer": {"answer": 4.3143, "unit": "mol/L"}, "id": "molarity_006380_3.775_875", "license": "Apache-2.0", "prompt": "A solution contains 3.775 mol of solute in 875 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 875 mL to 0.875 L.\nCompute M = 3.775 / 0.875.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 3.775, "volume_ml": 875}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.2 y, so each step multiplies y by 1 - h*0.2.\n3. Apply that update for 10 steps and round the final state.\nFinal: {\"answer\": 0.2116, \"unit\": \"state_units\"}", "dedupe_signature": "d6ebd093cf2229ebad3a7cbf9a304c92b66689d4451ca0c89b6e126f79cc5d3d", "difficulty": "medium", "final_answer": {"answer": 0.2116, "unit": "state_units"}, "id": "euler_decay_006381_35_0.2_2_10", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.2 y with y(0)=35, step size h=2, for 10 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.2 y, so each step multiplies y by 1 - h*0.2.\nApply that update for 10 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 35.0, "rate": 0.2, "step": 2.0, "steps": 10}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(1.8)=9.08 and f(10.4)=14.24.\n3. The interval width is 8.6.\nFinal: {\"answer\": 100.276, \"unit\": \"area_units\"}", "dedupe_signature": "c7cb7057f8e304e305988791c2de5869034102f60959c6421405967318141e15", "difficulty": "medium", "final_answer": {"answer": 100.276, "unit": "area_units"}, "id": "trapz_linear_006382_0.6_8_1.8_10.4", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=0.6x+8 from x=1.8 to x=10.4. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(1.8)=9.08 and f(10.4)=14.24.\nThe interval width is 8.6.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 8.0, "slope": 0.6, "x0": 1.8, "x1": 10.4}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kelvin equals Celsius plus 273.15.\n2. Apply the conversion factor directly to the given value.\n3. Compute -77.5 + 273.15.\nFinal: {\"answer\": 195.65, \"unit\": \"K\"}", "dedupe_signature": "92d8973939fc17d27c574697d41ea3ba751c5e3d4bb98ffd7fe6bbab4bd5aeae", "difficulty": "easy", "final_answer": {"answer": 195.65, "unit": "K"}, "id": "unit_convert_006384_c_to_k_-77.5", "license": "Apache-2.0", "prompt": "Convert -77.5 degC to K. Return the converted value with unit.", "reasoning_trace": "Kelvin equals Celsius plus 273.15.\nApply the conversion factor directly to the given value.\nCompute -77.5 + 273.15.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": -77.5}, "verifier": {"formula": "value + 273.15", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=59 degrees and keep the unit as newtons.\nFinal: {\"answer\": [137.0001, 228.0065], \"unit\": \"N\"}", "dedupe_signature": "5027e8a7034a6916bf9604943bec68090485e0e333cae5892b3447b0d163e016", "difficulty": "medium", "final_answer": {"answer": [137.0001, 228.0065], "unit": "N"}, "id": "vector_components_006385_266_59", "license": "Apache-2.0", "prompt": "A vector has magnitude 266 N at 59 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=59 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 59, "magnitude": 266.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [4.2, 0.5], \"unit\": \"dimensionless\"}", "dedupe_signature": "24da67e71819ee843c70d014a3133e92797046a21b66e69902627190a2755440", "difficulty": "medium", "final_answer": {"answer": [4.2, 0.5], "unit": "dimensionless"}, "id": "line_two_point_006386_2_8_4.2_0.5", "license": "Apache-2.0", "prompt": "A line passes through points (2, 8.9) and (8, 34.1). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 2.0, "x2": 8.0, "y1": 8.9, "y2": 34.1}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. lever arm times force has torque dimensions\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "4a7b4d3b753869ef259b0853f9d404fdf7652e31499fa2af43024f7074866b59", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_006387_consistent_5ca82cb9_554753", "license": "Apache-2.0", "prompt": "In model card equation case 554753, check dimensional consistency for tau = r * F. The left side has dimensions N*m and the right side has dimensions N*m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nlever arm times force has torque dimensions\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "tau = r * F"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 4.72 * 8.314 * 600 / 50.0.\nFinal: {\"answer\": 470.905, \"unit\": \"kPa\"}", "dedupe_signature": "924831bcd3b409038e73d8a592f35ae1856dec8e9480b1f746fad6a132550fea", "difficulty": "medium", "final_answer": {"answer": 470.905, "unit": "kPa"}, "id": "ideal_gas_006393_4.72_600_50.0", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=4.72 mol, T=600 K, and V=50.0 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 4.72 * 8.314 * 600 / 50.0.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 4.72, "temp_k": 600, "volume_l": 50.0}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1950 * 1.475 * 53.\nFinal: {\"answer\": 152441.25, \"unit\": \"J\"}", "dedupe_signature": "f617dfbe409a99325f6b303b21046e3308befba19a2dda406f2e4f254e03ca1f", "difficulty": "easy", "final_answer": {"answer": 152441.25, "unit": "J"}, "id": "heat_q_006394_1950_1.475_53", "license": "Apache-2.0", "prompt": "A 1950 g sample has specific heat 1.475 J/(g*K). How much heat is needed to raise its temperature by 53 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1950 * 1.475 * 53.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 53, "heat_capacity": 1.475, "mass_g": 1950}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=733 mg, t=86 h, and T_half=22 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 48.7922, \"unit\": \"mg\"}", "dedupe_signature": "a6ccb8249c7366b2762fc590b7056def1a62c29062b461ef05d44498b7e833c5", "difficulty": "medium", "final_answer": {"answer": 48.7922, "unit": "mg"}, "id": "half_life_006396_733_22_86", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 733 mg. Its half-life is 22 hours. How many mg remain after 86 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=733 mg, t=86 h, and T_half=22 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 86.0, "half_life": 22.0, "initial_amount": 733.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 6.95 mol * 44.01 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 305.8695, \"unit\": \"g\"}", "dedupe_signature": "fba8313eebcc976858fa3e8bba81cb0b6402a090e7d026b7d2a94637166d4620", "difficulty": "medium", "final_answer": {"answer": 305.8695, "unit": "g"}, "id": "stoich_mass_006397_carbon_dioxide_6.95", "license": "Apache-2.0", "prompt": "A sample contains 6.95 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 6.95 mol * 44.01 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "carbon dioxide", "molar_mass": 44.01, "moles": 6.95}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 2290 mL to 2.29 L.\n3. Compute M = 2.57 / 2.29.\nFinal: {\"answer\": 1.1223, \"unit\": \"mol/L\"}", "dedupe_signature": "dc2f9c18813211b2429bcaacd698b75d80556dd7924aa8d54dbfc419fac3c9f8", "difficulty": "medium", "final_answer": {"answer": 1.1223, "unit": "mol/L"}, "id": "molarity_006398_2.57_2290", "license": "Apache-2.0", "prompt": "A solution contains 2.57 mol of solute in 2290 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 2290 mL to 2.29 L.\nCompute M = 2.57 / 2.29.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 2.57, "volume_ml": 2290}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.42 y, so each step multiplies y by 1 - h*0.42.\n3. Apply that update for 5 steps and round the final state.\nFinal: {\"answer\": 5.244, \"unit\": \"state_units\"}", "dedupe_signature": "d2c1b5570bcca8cb73d8654334bf092ec7118c9a357e1a92eab0a08ac579c6c8", "difficulty": "medium", "final_answer": {"answer": 5.244, "unit": "state_units"}, "id": "euler_decay_006399_19.5_0.42_0.55_5", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.42 y with y(0)=19.5, step size h=0.55, for 5 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.42 y, so each step multiplies y by 1 - h*0.42.\nApply that update for 5 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 19.5, "rate": 0.42, "step": 0.55, "steps": 5}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(4.9)=-18.99 and f(5.6)=-21.86.\n3. The interval width is 0.7.\nFinal: {\"answer\": -14.2975, \"unit\": \"area_units\"}", "dedupe_signature": "ffd8519207afca0c12abbbdb00ee441cbfc4a5613f3bb490ce116844218ed1cb", "difficulty": "medium", "final_answer": {"answer": -14.2975, "unit": "area_units"}, "id": "trapz_linear_006400_-4.1_1.1_4.9_5.6", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-4.1x+1.1 from x=4.9 to x=5.6. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(4.9)=-18.99 and f(5.6)=-21.86.\nThe interval width is 0.7.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 1.1, "slope": -4.1, "x0": 4.9, "x1": 5.6000000000000005}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.02 and add it to the current value.\nFinal: {\"answer\": [2.451, -0.977, -1.01], \"unit\": \"temperature_units\"}", "dedupe_signature": "c4475b12ab3af4039168707fbcdd6b8435c6070958e2fedb52719c8a6b705f41", "difficulty": "hard", "final_answer": {"answer": [2.451, -0.977, -1.01], "unit": "temperature_units"}, "id": "heat_step_006401_0.02_-1.2_2.6_-1.05_-1.05_0.95", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-1.2, right=0.95; current interior values are [2.6, -1.05, -1.05]. Use r=0.02. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.02 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [2.6, -1.05, -1.05], "left": -1.2, "r": 0.02, "right": 0.95}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 28739.0 / 1000.\nFinal: {\"answer\": 28.739, \"unit\": \"kg\"}", "dedupe_signature": "f9114bfba87b2fe027d6b0e8911257d694f468532ab9f4f55e094ef255de971d", "difficulty": "easy", "final_answer": {"answer": 28.739, "unit": "kg"}, "id": "unit_convert_006402_g_to_kg_28739", "license": "Apache-2.0", "prompt": "Convert 28739 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 28739.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 28739.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=247 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-22.467, -52.929], \"unit\": \"N\"}", "dedupe_signature": "01f2af0008f1d6bd084d69233a8a8b976341bcda650b76f7f8d70b89cb3cea0a", "difficulty": "medium", "final_answer": {"answer": [-22.467, -52.929], "unit": "N"}, "id": "vector_components_006403_57.5_247", "license": "Apache-2.0", "prompt": "A vector has magnitude 57.5 N at 247 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=247 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 247, "magnitude": 57.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-5.9, 10.0], \"unit\": \"dimensionless\"}", "dedupe_signature": "425056c28fd5c1f32ce1ce254d76b9910d3c1c8f3ec80f6e05858661b7fbea7e", "difficulty": "medium", "final_answer": {"answer": [-5.9, 10.0], "unit": "dimensionless"}, "id": "line_two_point_006404_17.5_28.5_-5.9_10", "license": "Apache-2.0", "prompt": "A line passes through points (17.5, -93.25) and (28.5, -158.15). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 17.5, "x2": 28.5, "y1": -93.25, "y2": -158.15}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: left_boundary, right_boundary.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"left_boundary\", \"right_boundary\"]}", "dedupe_signature": "a5426d9c58ff964e5a9dec656119835993547c1a1321d67310a6ca722b7d2e43", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["left_boundary", "right_boundary"]}, "id": "abstain_006407_left_boundary_right_boundary", "license": "Apache-2.0", "prompt": "Solve the 1D heat equation after one finite-difference step. The prompt gives r=0.28 and interior values [0.15, -1.05, 2.45], but gives no boundary values. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: left_boundary, right_boundary.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["left_boundary", "right_boundary"]}, "verifier": {"missing": ["left_boundary", "right_boundary"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 12.9 kg and a = 3.1 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 39.99, \"unit\": \"N\"}", "dedupe_signature": "f30224f874bcda0177000aec7c6c46bc0fcb8654fde6904103c3a39ec4649bfd", "difficulty": "easy", "final_answer": {"answer": 39.99, "unit": "N"}, "id": "force_006408_12.9_3.1", "license": "Apache-2.0", "prompt": "A cart has mass 12.9 kg and measured acceleration 3.1 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 12.9 kg and a = 3.1 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 3.1, "mass": 12.9}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 42.85^2 and multiply by 0.5 * 23.15.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 21253.1179, \"unit\": \"J\"}", "dedupe_signature": "1a23b3dd6818f02e1db65e5ed4a23674d95da05d05a44344953d873ca63fe9ae", "difficulty": "easy", "final_answer": {"answer": 21253.1179, "unit": "J"}, "id": "ke_006409_23.15_42.85", "license": "Apache-2.0", "prompt": "A body of mass 23.15 kg moves at 42.85 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 42.85^2 and multiply by 0.5 * 23.15.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 23.15, "velocity": 42.85}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=57 degrees through the sine of 2 theta.\n3. Substitute v=54.6 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 277.6172, \"unit\": \"m\"}", "dedupe_signature": "bd9aacf4fb83854bce87e0fd800be8f9c2e19a9e9f2b2d255db2b97da29c8d4b", "difficulty": "medium", "final_answer": {"answer": 277.6172, "unit": "m"}, "id": "projectile_range_006410_54.6_57", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 54.6 m/s and angle 57 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=57 degrees through the sine of 2 theta.\nSubstitute v=54.6 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 57, "gravity": 9.81, "speed": 54.6}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 2.73 * 8.314 * 334 / 33.8.\nFinal: {\"answer\": 224.2861, \"unit\": \"kPa\"}", "dedupe_signature": "06616c026640f8d47ab8927634a3e655bbd31ec9d5471fcf84c7e31ba0c35dfe", "difficulty": "medium", "final_answer": {"answer": 224.2861, "unit": "kPa"}, "id": "ideal_gas_006411_2.73_334_33.8", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=2.73 mol, T=334 K, and V=33.8 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 2.73 * 8.314 * 334 / 33.8.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 2.73, "temp_k": 334, "volume_l": 33.8}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1665 * 4.675 * 1.\nFinal: {\"answer\": 7783.875, \"unit\": \"J\"}", "dedupe_signature": "1f3a091d38fedef84f3cdf7c6401a06cd1936395a380fdc174a350da964ba4c4", "difficulty": "easy", "final_answer": {"answer": 7783.875, "unit": "J"}, "id": "heat_q_006412_1665_4.675_1", "license": "Apache-2.0", "prompt": "A 1665 g sample has specific heat 4.675 J/(g*K). How much heat is needed to raise its temperature by 1 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1665 * 4.675 * 1.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 1, "heat_capacity": 4.675, "mass_g": 1665}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=75.9 V and R=118.6 ohm.\nFinal: {\"answer\": 48.5734, \"unit\": \"W\"}", "dedupe_signature": "f9715f7354f2aaf629849473f8ba7da1e07bb06784d4cb20a247ca467a6ff703", "difficulty": "easy", "final_answer": {"answer": 48.5734, "unit": "W"}, "id": "ohm_power_006413_75.9_118.6", "license": "Apache-2.0", "prompt": "A resistor has resistance 118.6 ohm and voltage 75.9 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=75.9 V and R=118.6 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 118.6, "voltage": 75.9}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 0.86 mol * 58.44 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 50.2584, \"unit\": \"g\"}", "dedupe_signature": "d6a0bc3f78cf69009a5b2be732f7ce67fd90706e640d1c804b8e24024d28217b", "difficulty": "medium", "final_answer": {"answer": 50.2584, "unit": "g"}, "id": "stoich_mass_006415_sodium_chloride_0.86", "license": "Apache-2.0", "prompt": "A sample contains 0.86 mol of sodium chloride. Using molar mass 58.44 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 0.86 mol * 58.44 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "sodium chloride", "molar_mass": 58.44, "moles": 0.86}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 50 mL to 0.05 L.\n3. Compute M = 2.85 / 0.05.\nFinal: {\"answer\": 57.0, \"unit\": \"mol/L\"}", "dedupe_signature": "f1f2005f9e7a412e5e1efc24e131330af055842852a9ca9953f7539d2b49ba67", "difficulty": "medium", "final_answer": {"answer": 57.0, "unit": "mol/L"}, "id": "molarity_006416_2.85_50", "license": "Apache-2.0", "prompt": "A solution contains 2.85 mol of solute in 50 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 50 mL to 0.05 L.\nCompute M = 2.85 / 0.05.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 2.85, "volume_ml": 50}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.53 y, so each step multiplies y by 1 - h*0.53.\n3. Apply that update for 5 steps and round the final state.\nFinal: {\"answer\": 0.0001, \"unit\": \"state_units\"}", "dedupe_signature": "64bc2e6e99d61408f8d1bcdda51b237efbc1c323bdfbea1de4391e628ff71c43", "difficulty": "medium", "final_answer": {"answer": 0.0001, "unit": "state_units"}, "id": "euler_decay_006417_53.5_0.53_1.75_5", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.53 y with y(0)=53.5, step size h=1.75, for 5 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.53 y, so each step multiplies y by 1 - h*0.53.\nApply that update for 5 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 53.5, "rate": 0.53, "step": 1.75, "steps": 5}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(2)=-13.1 and f(9.7)=-65.46.\n3. The interval width is 7.7.\nFinal: {\"answer\": -302.456, \"unit\": \"area_units\"}", "dedupe_signature": "dc771848d1d477c61b4fcb40ffd34b0bf51da1888059be2b38b8235998d0fa17", "difficulty": "medium", "final_answer": {"answer": -302.456, "unit": "area_units"}, "id": "trapz_linear_006418_-6.8_0.5_2_9.7", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-6.8x+0.5 from x=2 to x=9.7. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(2)=-13.1 and f(9.7)=-65.46.\nThe interval width is 7.7.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 0.5, "slope": -6.8, "x0": 2.0, "x1": 9.7}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.44 and add it to the current value.\nFinal: {\"answer\": [0.676, 1.328, -0.488], \"unit\": \"temperature_units\"}", "dedupe_signature": "18cd0f76817212b597821ba6ca80fc9e76de0aa182ff683dac756624d99e9a23", "difficulty": "hard", "final_answer": {"answer": [0.676, 1.328, -0.488], "unit": "temperature_units"}, "id": "heat_step_006419_0.44_2.65_1.05_-1.4_2.35_-0.35", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=2.65, right=-0.35; current interior values are [1.05, -1.4, 2.35]. Use r=0.44. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.44 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [1.05, -1.4, 2.35], "left": 2.65, "r": 0.44, "right": -0.35}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [6.4, 4.75], \"unit\": \"dimensionless\"}", "dedupe_signature": "6c9db653407689bca6139d44a26a78f6e22bcc34f1ca62e88e79c287d3e81d0a", "difficulty": "medium", "final_answer": {"answer": [6.4, 4.75], "unit": "dimensionless"}, "id": "line_two_point_006422_4.5_4.75_6.4_4.75", "license": "Apache-2.0", "prompt": "A line passes through points (4.5, 33.55) and (4.75, 35.15). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 4.5, "x2": 4.75, "y1": 33.55, "y2": 35.150000000000006}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. velocity times time gives distance, not acceleration\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "ed464e08adbed65b918fa512e1ec853145e46e134f1fcbc52118947355161d91", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_006423_inconsistent_7481c798_283655", "license": "Apache-2.0", "prompt": "In instrument manual case 283655, check dimensional consistency for a = v * t. The left side has dimensions m/s^2 and the right side has dimensions m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nvelocity times time gives distance, not acceleration\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "a = v * t"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef center_values_006424(values):\n    if not values:\n        raise ValueError('center_values requires at least one value')\n    mean = sum(values) / len(values)\n    return [value - mean for value in values]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"center_values_006424\"}", "dedupe_signature": "5153237115362ed42512188b8efc5d27d408a79dbc85f1f3a7dcac9ff13f13f9", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "center_values_006424"}, "id": "code_006424_center_values_006424", "license": "Apache-2.0", "prompt": "Write a Python function center_values_006424(values) that subtracts the arithmetic mean from each value and returns a new list. Raise ValueError for an empty input. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "center_values_006424"}, "verifier": {"function": "center_values_006424", "tests": ["out = center_values_006424([1, 2, 3]); assert out == [-1, 0, 1]", "assert center_values_006424([5]) == [0]", "try:\n    center_values_006424([])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: launch_angle_or_vertical_velocity.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"launch_angle_or_vertical_velocity\"]}", "dedupe_signature": "af4a2e88053a14aecf4986ab3f149a957828428758d4e932f8c58e3eeb15badd", "difficulty": "easy", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["launch_angle_or_vertical_velocity"]}, "id": "abstain_006425_launch_angle_or_vertical_velocity", "license": "Apache-2.0", "prompt": "Compute projectile range on level ground. The prompt gives initial speed 10.7 m/s but does not give launch angle or vertical velocity. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: launch_angle_or_vertical_velocity.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["launch_angle_or_vertical_velocity"]}, "verifier": {"missing": ["launch_angle_or_vertical_velocity"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 6.3 kg and a = 1 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 6.3, \"unit\": \"N\"}", "dedupe_signature": "44e8cb9a5f6ab15a05c60238350ebaac6f0eb19dc0d75fc7bcb6ee61a69566f4", "difficulty": "easy", "final_answer": {"answer": 6.3, "unit": "N"}, "id": "force_006426_6.3_1", "license": "Apache-2.0", "prompt": "A cart has mass 6.3 kg and measured acceleration 1 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 6.3 kg and a = 1 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 1.0, "mass": 6.3}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=66 degrees through the sine of 2 theta.\n3. Substitute v=79.9 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 483.613, \"unit\": \"m\"}", "dedupe_signature": "d6e7045d3c087a49f4d01804220e8d593cf8cf4bb3a79de5f2e6d1c5919c93ef", "difficulty": "medium", "final_answer": {"answer": 483.613, "unit": "m"}, "id": "projectile_range_006428_79.9_66", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 79.9 m/s and angle 66 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=66 degrees through the sine of 2 theta.\nSubstitute v=79.9 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 66, "gravity": 9.81, "speed": 79.9}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 3.84 * 8.314 * 263 / 114.3.\nFinal: {\"answer\": 73.46, \"unit\": \"kPa\"}", "dedupe_signature": "09bf629736278fd9f67a28a00104069c1e556636e8f95c682617119daab0319d", "difficulty": "medium", "final_answer": {"answer": 73.46, "unit": "kPa"}, "id": "ideal_gas_006429_3.84_263_114.3", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=3.84 mol, T=263 K, and V=114.3 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 3.84 * 8.314 * 263 / 114.3.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 3.84, "temp_k": 263, "volume_l": 114.3}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 760 * 4.385 * 83.\nFinal: {\"answer\": 276605.8, \"unit\": \"J\"}", "dedupe_signature": "9d281e2ab4c2345cb763d3276d79b503ba049e38172fe9baf2c68e4dbb2921c3", "difficulty": "easy", "final_answer": {"answer": 276605.8, "unit": "J"}, "id": "heat_q_006430_760_4.385_83", "license": "Apache-2.0", "prompt": "A 760 g sample has specific heat 4.385 J/(g*K). How much heat is needed to raise its temperature by 83 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 760 * 4.385 * 83.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 83, "heat_capacity": 4.385, "mass_g": 760}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=162.1 V and R=168 ohm.\nFinal: {\"answer\": 156.4072, \"unit\": \"W\"}", "dedupe_signature": "03eae1978a8f5f7bdfb7574d8cfec3dfee83b94f63a436d68ab1d5382a87c2a6", "difficulty": "easy", "final_answer": {"answer": 156.4072, "unit": "W"}, "id": "ohm_power_006431_162.1_168", "license": "Apache-2.0", "prompt": "A resistor has resistance 168 ohm and voltage 162.1 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=162.1 V and R=168 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 168.0, "voltage": 162.1}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 2.23 mol * 180.156 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 401.7479, \"unit\": \"g\"}", "dedupe_signature": "06fce04f9b6eb22e5cde472f7bd7e8971f65f749f7c0b4243f060384a00c40e8", "difficulty": "medium", "final_answer": {"answer": 401.7479, "unit": "g"}, "id": "stoich_mass_006433_glucose_2.23", "license": "Apache-2.0", "prompt": "A sample contains 2.23 mol of glucose. Using molar mass 180.156 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 2.23 mol * 180.156 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "glucose", "molar_mass": 180.156, "moles": 2.23}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 2300 mL to 2.3 L.\n3. Compute M = 4.115 / 2.3.\nFinal: {\"answer\": 1.7891, \"unit\": \"mol/L\"}", "dedupe_signature": "036d1dafd49c7621e4d438da76973121fa254416f0aa508fe5d9b808b0ed9f24", "difficulty": "medium", "final_answer": {"answer": 1.7891, "unit": "mol/L"}, "id": "molarity_006434_4.115_2300", "license": "Apache-2.0", "prompt": "A solution contains 4.115 mol of solute in 2300 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 2300 mL to 2.3 L.\nCompute M = 4.115 / 2.3.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 4.115, "volume_ml": 2300}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.47 y, so each step multiplies y by 1 - h*0.47.\n3. Apply that update for 3 steps and round the final state.\nFinal: {\"answer\": 39.351, \"unit\": \"state_units\"}", "dedupe_signature": "7aafa7f31bea5b5748272a82e510752bea028b03443c9f74e57899fce04fa245", "difficulty": "medium", "final_answer": {"answer": 39.351, "unit": "state_units"}, "id": "euler_decay_006435_73.5_0.47_0.4_3", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.47 y with y(0)=73.5, step size h=0.4, for 3 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.47 y, so each step multiplies y by 1 - h*0.47.\nApply that update for 3 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 73.5, "rate": 0.47, "step": 0.4, "steps": 3}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-6.4)=-20.46 and f(-5)=-12.9.\n3. The interval width is 1.4.\nFinal: {\"answer\": -23.352, \"unit\": \"area_units\"}", "dedupe_signature": "c7f8e108933e2597f04a050de5c0dd59cbdf63a7ed25e7166ebd402a15e61b58", "difficulty": "medium", "final_answer": {"answer": -23.352, "unit": "area_units"}, "id": "trapz_linear_006436_5.4_14.1_-6.4_-5", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=5.4x+14.1 from x=-6.4 to x=-5. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-6.4)=-20.46 and f(-5)=-12.9.\nThe interval width is 1.4.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 14.1, "slope": 5.4, "x0": -6.4, "x1": -5.0}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.38 and add it to the current value.\nFinal: {\"answer\": [1.657, 1.316, 0.79], \"unit\": \"temperature_units\"}", "dedupe_signature": "9dd02e3f0611914505a0990707deacf85762ea967deceacc2b0c033d6204b997", "difficulty": "hard", "final_answer": {"answer": [1.657, 1.316, 0.79], "unit": "temperature_units"}, "id": "heat_step_006437_0.38_0.75_2.55_2.0_-0.35_0.3", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=0.75, right=0.3; current interior values are [2.55, 2.0, -0.35]. Use r=0.38. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.38 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [2.55, 2.0, -0.35], "left": 0.75, "r": 0.38, "right": 0.3}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=33 degrees and keep the unit as newtons.\nFinal: {\"answer\": [64.997, 42.2095], \"unit\": \"N\"}", "dedupe_signature": "3ce03d61bea2a92fabff3a5ca302b2094cd46c6cf0fc89b811524766473279c0", "difficulty": "medium", "final_answer": {"answer": [64.997, 42.2095], "unit": "N"}, "id": "vector_components_006439_77.5_33", "license": "Apache-2.0", "prompt": "A vector has magnitude 77.5 N at 33 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=33 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 33, "magnitude": 77.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. velocity divided by time is acceleration\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "dc989dd11331214ebdfb5646c79c0f21f2257dfa3b1da51a7269711b0c608688", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_006441_inconsistent_c1271127_833475", "license": "Apache-2.0", "prompt": "In simulation spec case 833475, check dimensional consistency for x = v / t. The left side has dimensions m and the right side has dimensions m/s^2. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nvelocity divided by time is acceleration\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "x = v / t"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef center_values_006442(values):\n    if not values:\n        raise ValueError('center_values requires at least one value')\n    mean = sum(values) / len(values)\n    return [value - mean for value in values]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"center_values_006442\"}", "dedupe_signature": "595c5e3595cb6bf44c6f3348f65ce743e8a57b513871f76f4207ded3cbf52675", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "center_values_006442"}, "id": "code_006442_center_values_006442", "license": "Apache-2.0", "prompt": "Write a Python function center_values_006442(values) that subtracts the arithmetic mean from each value and returns a new list. Raise ValueError for an empty input. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "center_values_006442"}, "verifier": {"function": "center_values_006442", "tests": ["out = center_values_006442([1, 2, 3]); assert out == [-1, 0, 1]", "assert center_values_006442([5]) == [0]", "try:\n    center_values_006442([])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: volume.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"volume\"]}", "dedupe_signature": "36f64dc77898ee7fa5267317450c059be790ffb328e25e210fe4f4063fc3702c", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["volume"]}, "id": "abstain_006443_volume", "license": "Apache-2.0", "prompt": "Compute pressure from the ideal gas law. The prompt gives n=2.18 mol and T=244 K, but does not give volume. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: volume.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["volume"]}, "verifier": {"missing": ["volume"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 14.65 kg and a = 10.7 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 156.755, \"unit\": \"N\"}", "dedupe_signature": "25bf90329c0c13c3d99d1b1a13c3650d655cd783d69cd28bd0f52a9d661351fe", "difficulty": "easy", "final_answer": {"answer": 156.755, "unit": "N"}, "id": "force_006444_14.65_10.7", "license": "Apache-2.0", "prompt": "A cart has mass 14.65 kg and measured acceleration 10.7 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 14.65 kg and a = 10.7 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 10.7, "mass": 14.65}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 25.75^2 and multiply by 0.5 * 15.7.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 5205.0406, \"unit\": \"J\"}", "dedupe_signature": "a30b4ef7f745881cd4da7eab12feead757ad9059a59b4343ddc0e13365cf5b03", "difficulty": "easy", "final_answer": {"answer": 5205.0406, "unit": "J"}, "id": "ke_006445_15.7_25.75", "license": "Apache-2.0", "prompt": "A body of mass 15.7 kg moves at 25.75 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 25.75^2 and multiply by 0.5 * 15.7.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 15.7, "velocity": 25.75}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=63 degrees through the sine of 2 theta.\n3. Substitute v=42.2 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 146.8634, \"unit\": \"m\"}", "dedupe_signature": "9f1ab337dd5180b519a5a77c1633866ad3eabeeb8078349c011c6ceeab269bbf", "difficulty": "medium", "final_answer": {"answer": 146.8634, "unit": "m"}, "id": "projectile_range_006446_42.2_63", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 42.2 m/s and angle 63 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=63 degrees through the sine of 2 theta.\nSubstitute v=42.2 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 63, "gravity": 9.81, "speed": 42.2}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 2.24 * 8.314 * 285 / 92.3.\nFinal: {\"answer\": 57.5044, \"unit\": \"kPa\"}", "dedupe_signature": "d986c46558d33c08e01a85a4d6fc36a47b9cd1b39b2537ff05c5b1f58026ce42", "difficulty": "medium", "final_answer": {"answer": 57.5044, "unit": "kPa"}, "id": "ideal_gas_006447_2.24_285_92.3", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=2.24 mol, T=285 K, and V=92.3 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 2.24 * 8.314 * 285 / 92.3.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 2.24, "temp_k": 285, "volume_l": 92.3}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 150 * 4.305 * 32.\nFinal: {\"answer\": 20664.0, \"unit\": \"J\"}", "dedupe_signature": "8591161ee3b529eac2bde0dd31279adc828f818848308aa9eb38c75e9d5ff069", "difficulty": "easy", "final_answer": {"answer": 20664.0, "unit": "J"}, "id": "heat_q_006448_150_4.305_32", "license": "Apache-2.0", "prompt": "A 150 g sample has specific heat 4.305 J/(g*K). How much heat is needed to raise its temperature by 32 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 150 * 4.305 * 32.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 32, "heat_capacity": 4.305, "mass_g": 150}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=142.5 V and R=185.6 ohm.\nFinal: {\"answer\": 109.4087, \"unit\": \"W\"}", "dedupe_signature": "d971e1656d24ad0b507f96977fa3349a77dbe9bf730606b7a3c709e58af310ac", "difficulty": "easy", "final_answer": {"answer": 109.4087, "unit": "W"}, "id": "ohm_power_006449_142.5_185.6", "license": "Apache-2.0", "prompt": "A resistor has resistance 185.6 ohm and voltage 142.5 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=142.5 V and R=185.6 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 185.6, "voltage": 142.5}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=17.5 mg, t=132 h, and T_half=93 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 6.5429, \"unit\": \"mg\"}", "dedupe_signature": "8c3ec1718f2da688b5f249c236e73891842daa3546d72f578972fd6f719d4e1b", "difficulty": "medium", "final_answer": {"answer": 6.5429, "unit": "mg"}, "id": "half_life_006450_17.5_93_132", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 17.5 mg. Its half-life is 93 hours. How many mg remain after 132 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=17.5 mg, t=132 h, and T_half=93 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 132.0, "half_life": 93.0, "initial_amount": 17.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 2.85 mol * 44.01 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 125.4285, \"unit\": \"g\"}", "dedupe_signature": "60e7d6b588e6ebef9ac4866f302bf9d58da21101ee102f1f18a213d51fee5bc8", "difficulty": "medium", "final_answer": {"answer": 125.4285, "unit": "g"}, "id": "stoich_mass_006451_carbon_dioxide_2.85", "license": "Apache-2.0", "prompt": "A sample contains 2.85 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 2.85 mol * 44.01 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "carbon dioxide", "molar_mass": 44.01, "moles": 2.85}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 4715 mL to 4.715 L.\n3. Compute M = 4.255 / 4.715.\nFinal: {\"answer\": 0.9024, \"unit\": \"mol/L\"}", "dedupe_signature": "99d2a53b5fe521b8e88b27f73d9dca068b6fa77a28583e897a59fd69af0452a2", "difficulty": "medium", "final_answer": {"answer": 0.9024, "unit": "mol/L"}, "id": "molarity_006452_4.255_4715", "license": "Apache-2.0", "prompt": "A solution contains 4.255 mol of solute in 4715 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 4715 mL to 4.715 L.\nCompute M = 4.255 / 4.715.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 4.255, "volume_ml": 4715}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-1)=-23 and f(0.2)=-14.48.\n3. The interval width is 1.2.\nFinal: {\"answer\": -22.488, \"unit\": \"area_units\"}", "dedupe_signature": "be54384b0c6db1e9b86a9df79e05cade170ddc9f3b997d6e1d83a98fdf6ab9f6", "difficulty": "medium", "final_answer": {"answer": -22.488, "unit": "area_units"}, "id": "trapz_linear_006454_7.1_-15.9_-1_0.2", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=7.1x+-15.9 from x=-1 to x=0.2. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-1)=-23 and f(0.2)=-14.48.\nThe interval width is 1.2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -15.9, "slope": 7.1, "x0": -1.0, "x1": 0.19999999999999996}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.16 and add it to the current value.\nFinal: {\"answer\": [1.76, -0.098, 1.932], \"unit\": \"temperature_units\"}", "dedupe_signature": "9a9060b92df4d112e2054bbd0d2d12b424eadbac266c15cdd292b969b529ee6e", "difficulty": "hard", "final_answer": {"answer": [1.76, -0.098, 1.932], "unit": "temperature_units"}, "id": "heat_step_006455_0.16_2.9_2.2_-1.25_2.5_2.7", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=2.9, right=2.7; current interior values are [2.2, -1.25, 2.5]. Use r=0.16. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.16 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [2.2, -1.25, 2.5], "left": 2.9, "r": 0.16, "right": 2.7}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 3097.0 / 1000.\nFinal: {\"answer\": 3.097, \"unit\": \"kg\"}", "dedupe_signature": "6e3135e781abc6cf82ca141a49a21ca23f7160f188726f68a3a468fd599839bb", "difficulty": "easy", "final_answer": {"answer": 3.097, "unit": "kg"}, "id": "unit_convert_006456_g_to_kg_3097", "license": "Apache-2.0", "prompt": "Convert 3097 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 3097.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 3097.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=72 degrees and keep the unit as newtons.\nFinal: {\"answer\": [84.6707, 260.5895], \"unit\": \"N\"}", "dedupe_signature": "b0460d2f2d9226858c63cbd0a765d110dca3452eb62695718fbb2749613b9291", "difficulty": "medium", "final_answer": {"answer": [84.6707, 260.5895], "unit": "N"}, "id": "vector_components_006457_274_72", "license": "Apache-2.0", "prompt": "A vector has magnitude 274 N at 72 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=72 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 72, "magnitude": 274.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [1.25, -2.25], \"unit\": \"dimensionless\"}", "dedupe_signature": "bbaef62752b0685845847b523e48e44873df8dc53539cf7c26fc2b6ef5e2abcd", "difficulty": "medium", "final_answer": {"answer": [1.25, -2.25], "unit": "dimensionless"}, "id": "line_two_point_006458_7.75_19.25_1.25_-2.25", "license": "Apache-2.0", "prompt": "A line passes through points (7.75, 7.4375) and (19.25, 21.8125). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 7.75, "x2": 19.25, "y1": 7.4375, "y2": 21.8125}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. density times acceleration times height gives kg/(m*s^2), or pascal\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "c4fb0d52df9e8aa6e97f91dd69c141dc8b9485faf08f21c91dfb030679397c02", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_006459_consistent_b7d3eed1_607251", "license": "Apache-2.0", "prompt": "In simulation spec case 607251, check dimensional consistency for p = rho * g * h. The left side has dimensions Pa and the right side has dimensions Pa. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\ndensity times acceleration times height gives kg/(m*s^2), or pascal\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "p = rho * g * h"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef clamp_006460(x, lo, hi):\n    if lo > hi:\n        raise ValueError('lo must be <= hi')\n    return min(max(x, lo), hi)\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"clamp_006460\"}", "dedupe_signature": "b154d9222b8bc0672eaa8fb55212f3ad80a60f3157433e2ef1b88fcf6a01325b", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "clamp_006460"}, "id": "code_006460_clamp_006460", "license": "Apache-2.0", "prompt": "Write a Python function clamp_006460(x, lo, hi) that clips x into the inclusive interval [lo, hi]. It must raise ValueError if lo > hi. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "clamp_006460"}, "verifier": {"function": "clamp_006460", "tests": ["assert clamp_006460(5, 0, 10) == 5", "assert clamp_006460(-2, 0, 10) == 0", "assert clamp_006460(12, 0, 10) == 10", "try:\n    clamp_006460(1, 3, 2)\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: rate_constant, number_of_steps.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"rate_constant\", \"number_of_steps\"]}", "dedupe_signature": "b005c5a9e87a766a02d53e05adad4af0b2f66915b891eefcc9e73bab82d13a96", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["rate_constant", "number_of_steps"]}, "id": "abstain_006461_rate_constant_number_of_steps", "license": "Apache-2.0", "prompt": "Use explicit Euler for dy/dt = -k y. The prompt gives y(0)=68.5 and h=0.7, but omits both k and the number of steps. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: rate_constant, number_of_steps.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["rate_constant", "number_of_steps"]}, "verifier": {"missing": ["rate_constant", "number_of_steps"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 43.4^2 and multiply by 0.5 * 0.55.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 517.979, \"unit\": \"J\"}", "dedupe_signature": "deff0a0a703b6e56a44b6cb192a17d63f5ec6f0f1a5886dc4872891a43e63b42", "difficulty": "easy", "final_answer": {"answer": 517.979, "unit": "J"}, "id": "ke_006463_0.55_43.4", "license": "Apache-2.0", "prompt": "A body of mass 0.55 kg moves at 43.4 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 43.4^2 and multiply by 0.5 * 0.55.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 0.55, "velocity": 43.4}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 3.9 * 8.314 * 514 / 83.6.\nFinal: {\"answer\": 199.357, \"unit\": \"kPa\"}", "dedupe_signature": "a46bfc5d704fe507189092b7da8dacc7d2c8b2aaeee0738fca44d90f434ed1d6", "difficulty": "medium", "final_answer": {"answer": 199.357, "unit": "kPa"}, "id": "ideal_gas_006465_3.9_514_83.6", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=3.9 mol, T=514 K, and V=83.6 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 3.9 * 8.314 * 514 / 83.6.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 3.9, "temp_k": 514, "volume_l": 83.6}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 985 * 3.94 * 4.\nFinal: {\"answer\": 15523.6, \"unit\": \"J\"}", "dedupe_signature": "0d8a4c5180228f77872a4425525ea290d789c7aaa93f32c7cc9a4abd90953398", "difficulty": "easy", "final_answer": {"answer": 15523.6, "unit": "J"}, "id": "heat_q_006466_985_3.94_4", "license": "Apache-2.0", "prompt": "A 985 g sample has specific heat 3.94 J/(g*K). How much heat is needed to raise its temperature by 4 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 985 * 3.94 * 4.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 4, "heat_capacity": 3.94, "mass_g": 985}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=174.4 V and R=147.1 ohm.\nFinal: {\"answer\": 206.7666, \"unit\": \"W\"}", "dedupe_signature": "64c5495235bb1735107030125d5df400cdc408024d14c9e978f60775f0dd2662", "difficulty": "easy", "final_answer": {"answer": 206.7666, "unit": "W"}, "id": "ohm_power_006467_174.4_147.1", "license": "Apache-2.0", "prompt": "A resistor has resistance 147.1 ohm and voltage 174.4 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=174.4 V and R=147.1 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 147.1, "voltage": 174.4}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=43.5 mg, t=15 h, and T_half=24 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 28.2063, \"unit\": \"mg\"}", "dedupe_signature": "1bee4433dd984e8935716e0e0783172893f86982a653da961bf9fc2a8176d6f1", "difficulty": "medium", "final_answer": {"answer": 28.2063, "unit": "mg"}, "id": "half_life_006468_43.5_24_15", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 43.5 mg. Its half-life is 24 hours. How many mg remain after 15 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=43.5 mg, t=15 h, and T_half=24 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 15.0, "half_life": 24.0, "initial_amount": 43.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 3.56 mol * 58.44 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 208.0464, \"unit\": \"g\"}", "dedupe_signature": "3e642042737eea36d00b0a177f935600b7b096fff833ff00420a2f1c51b9f2ec", "difficulty": "medium", "final_answer": {"answer": 208.0464, "unit": "g"}, "id": "stoich_mass_006469_sodium_chloride_3.56", "license": "Apache-2.0", "prompt": "A sample contains 3.56 mol of sodium chloride. Using molar mass 58.44 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 3.56 mol * 58.44 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "sodium chloride", "molar_mass": 58.44, "moles": 3.56}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 4310 mL to 4.31 L.\n3. Compute M = 4.285 / 4.31.\nFinal: {\"answer\": 0.9942, \"unit\": \"mol/L\"}", "dedupe_signature": "b9638a6554854fa4b4d45241ae6a1e5a04c5a8d748a84f7fd3c4f2d560955fdd", "difficulty": "medium", "final_answer": {"answer": 0.9942, "unit": "mol/L"}, "id": "molarity_006470_4.285_4310", "license": "Apache-2.0", "prompt": "A solution contains 4.285 mol of solute in 4310 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 4310 mL to 4.31 L.\nCompute M = 4.285 / 4.31.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 4.285, "volume_ml": 4310}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.71 y, so each step multiplies y by 1 - h*0.71.\n3. Apply that update for 4 steps and round the final state.\nFinal: {\"answer\": 0.8837, \"unit\": \"state_units\"}", "dedupe_signature": "8a0a4db268ba13ef0af8cf3a1ef61e6da055f17744484c702702c91ca4483a70", "difficulty": "medium", "final_answer": {"answer": 0.8837, "unit": "state_units"}, "id": "euler_decay_006471_18.5_0.71_0.75_4", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.71 y with y(0)=18.5, step size h=0.75, for 4 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.71 y, so each step multiplies y by 1 - h*0.71.\nApply that update for 4 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 18.5, "rate": 0.71, "step": 0.75, "steps": 4}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(4.1)=-12.05 and f(7.7)=-24.65.\n3. The interval width is 3.6.\nFinal: {\"answer\": -66.06, \"unit\": \"area_units\"}", "dedupe_signature": "677f959a87c86d6f3e26330a58d86706b86c9c06ac4276a35e446ca88d0d0ce1", "difficulty": "medium", "final_answer": {"answer": -66.06, "unit": "area_units"}, "id": "trapz_linear_006472_-3.5_2.3_4.1_7.7", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-3.5x+2.3 from x=4.1 to x=7.7. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(4.1)=-12.05 and f(7.7)=-24.65.\nThe interval width is 3.6.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 2.3, "slope": -3.5, "x0": 4.1, "x1": 7.699999999999999}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.36 and add it to the current value.\nFinal: {\"answer\": [0.428, -0.646, -0.032], \"unit\": \"temperature_units\"}", "dedupe_signature": "712c127491bbed277a53167339edfa0339187cc17ac37f19e1a86041c7dda5ee", "difficulty": "hard", "final_answer": {"answer": [0.428, -0.646, -0.032], "unit": "temperature_units"}, "id": "heat_step_006473_0.36_1.95_0.5_-1.15_-1.4_2.15", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.95, right=2.15; current interior values are [0.5, -1.15, -1.4]. Use r=0.36. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.36 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [0.5, -1.15, -1.4], "left": 1.95, "r": 0.36, "right": 2.15}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kelvin equals Celsius plus 273.15.\n2. Apply the conversion factor directly to the given value.\n3. Compute 225.0 + 273.15.\nFinal: {\"answer\": 498.15, \"unit\": \"K\"}", "dedupe_signature": "0fe2d0b507df6314c138193178465921e019b7a64155b5e0e708bdd22eabda2c", "difficulty": "easy", "final_answer": {"answer": 498.15, "unit": "K"}, "id": "unit_convert_006474_c_to_k_225", "license": "Apache-2.0", "prompt": "Convert 225 degC to K. Return the converted value with unit.", "reasoning_trace": "Kelvin equals Celsius plus 273.15.\nApply the conversion factor directly to the given value.\nCompute 225.0 + 273.15.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 225.0}, "verifier": {"formula": "value + 273.15", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=18 degrees and keep the unit as newtons.\nFinal: {\"answer\": [295.303, 95.9498], \"unit\": \"N\"}", "dedupe_signature": "b33e894a7edc1dbde389ab61b3b06677d5adc011b52d317283a1462ea3a45733", "difficulty": "medium", "final_answer": {"answer": [295.303, 95.9498], "unit": "N"}, "id": "vector_components_006475_310.5_18", "license": "Apache-2.0", "prompt": "A vector has magnitude 310.5 N at 18 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=18 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 18, "magnitude": 310.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-8.85, -18.0], \"unit\": \"dimensionless\"}", "dedupe_signature": "f22b56bda8bd97e996056877c09a54cbc5a474b79bd907c35180614a3e85b856", "difficulty": "medium", "final_answer": {"answer": [-8.85, -18.0], "unit": "dimensionless"}, "id": "line_two_point_006476_-10.5_-9.5_-8.85_-18", "license": "Apache-2.0", "prompt": "A line passes through points (-10.5, 74.925) and (-9.5, 66.075). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -10.5, "x2": -9.5, "y1": 74.925, "y2": 66.075}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. mass times acceleration has newton dimensions\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "8f04773089c0800fbc3de76f6450de46c7c3ca0cd1a46f9c6371c4ca338fbbd3", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_006477_consistent_03f5e041_258430", "license": "Apache-2.0", "prompt": "In field worksheet case 258430, check dimensional consistency for F = m * a. The left side has dimensions kg*m/s^2 and the right side has dimensions kg*m/s^2. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nmass times acceleration has newton dimensions\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "F = m * a"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef clamp_006478(x, lo, hi):\n    if lo > hi:\n        raise ValueError('lo must be <= hi')\n    return min(max(x, lo), hi)\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"clamp_006478\"}", "dedupe_signature": "9728c27105ec29dcd475b0f09ee43ccd76e69dd25e6d18223a01afc69e3b81ab", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "clamp_006478"}, "id": "code_006478_clamp_006478", "license": "Apache-2.0", "prompt": "Write a Python function clamp_006478(x, lo, hi) that clips x into the inclusive interval [lo, hi]. It must raise ValueError if lo > hi. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "clamp_006478"}, "verifier": {"function": "clamp_006478", "tests": ["assert clamp_006478(5, 0, 10) == 5", "assert clamp_006478(-2, 0, 10) == 0", "assert clamp_006478(12, 0, 10) == 10", "try:\n    clamp_006478(1, 3, 2)\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: required_fields, allowed_transformations.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"required_fields\", \"allowed_transformations\"]}", "dedupe_signature": "a76d3c34d6510314b198dc718f6e78f8bba0c8e44cf65fe45d3239630b4776fb", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["required_fields", "allowed_transformations"]}, "id": "abstain_006479_required_fields_allowed_transformations", "license": "Apache-2.0", "prompt": "Write a sanitizer for valid mobile ledger records in release 281656, but the prompt does not state which fields are required or which transformations are allowed. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: required_fields, allowed_transformations.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["required_fields", "allowed_transformations"]}, "verifier": {"missing": ["required_fields", "allowed_transformations"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 17.5 kg and a = 8.25 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 144.375, \"unit\": \"N\"}", "dedupe_signature": "c8f43e979191a0832bc58b982ba8248d50bf61c629e8f6fd5c24446cab3cbae9", "difficulty": "easy", "final_answer": {"answer": 144.375, "unit": "N"}, "id": "force_006480_17.5_8.25", "license": "Apache-2.0", "prompt": "A cart has mass 17.5 kg and measured acceleration 8.25 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 17.5 kg and a = 8.25 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 8.25, "mass": 17.5}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 13.25^2 and multiply by 0.5 * 9.05.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 794.4203, \"unit\": \"J\"}", "dedupe_signature": "7e2bf8cde4b90ae4cd1361222b324f5e35328be5588dc24b680bc899568b5677", "difficulty": "easy", "final_answer": {"answer": 794.4203, "unit": "J"}, "id": "ke_006481_9.05_13.25", "license": "Apache-2.0", "prompt": "A body of mass 9.05 kg moves at 13.25 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 13.25^2 and multiply by 0.5 * 9.05.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 9.05, "velocity": 13.25}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=41 degrees through the sine of 2 theta.\n3. Substitute v=55 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 305.3579, \"unit\": \"m\"}", "dedupe_signature": "74e63777b6b7e338f3baf935c6b33b4884804fd031113b66b0d6db4ef21d5fbb", "difficulty": "medium", "final_answer": {"answer": 305.3579, "unit": "m"}, "id": "projectile_range_006482_55_41", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 55 m/s and angle 41 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=41 degrees through the sine of 2 theta.\nSubstitute v=55 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 41, "gravity": 9.81, "speed": 55.0}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 2.14 * 8.314 * 253 / 26.4.\nFinal: {\"answer\": 170.5063, \"unit\": \"kPa\"}", "dedupe_signature": "e6f0d5cd800c4cff70515cc7b0a7c00ef7bd2907c7c88afb9a535c80ddd80a8f", "difficulty": "medium", "final_answer": {"answer": 170.5063, "unit": "kPa"}, "id": "ideal_gas_006483_2.14_253_26.4", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=2.14 mol, T=253 K, and V=26.4 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 2.14 * 8.314 * 253 / 26.4.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 2.14, "temp_k": 253, "volume_l": 26.4}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1960 * 2.45 * 111.\nFinal: {\"answer\": 533022.0, \"unit\": \"J\"}", "dedupe_signature": "c3a13ca96e72275f9d89afded3ab0bffeaad0d10969445dcea6d522dfdae30cb", "difficulty": "easy", "final_answer": {"answer": 533022.0, "unit": "J"}, "id": "heat_q_006484_1960_2.45_111", "license": "Apache-2.0", "prompt": "A 1960 g sample has specific heat 2.45 J/(g*K). How much heat is needed to raise its temperature by 111 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1960 * 2.45 * 111.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 111, "heat_capacity": 2.45, "mass_g": 1960}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=86.2 V and R=31.8 ohm.\nFinal: {\"answer\": 233.6616, \"unit\": \"W\"}", "dedupe_signature": "bb29c15a443b1c3ca7b3ca3d40ee3d31ee0b9e7e6c7fc75e7f8663966f6f5daf", "difficulty": "easy", "final_answer": {"answer": 233.6616, "unit": "W"}, "id": "ohm_power_006485_86.2_31.8", "license": "Apache-2.0", "prompt": "A resistor has resistance 31.8 ohm and voltage 86.2 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=86.2 V and R=31.8 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 31.8, "voltage": 86.2}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=185 mg, t=293 h, and T_half=53 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 4.0085, \"unit\": \"mg\"}", "dedupe_signature": "eafcd40e258c704cc2f49dd022eb89798f28206b89feef316c70cdc9e4c28a03", "difficulty": "medium", "final_answer": {"answer": 4.0085, "unit": "mg"}, "id": "half_life_006486_185_53_293", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 185 mg. Its half-life is 53 hours. How many mg remain after 293 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=185 mg, t=293 h, and T_half=53 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 293.0, "half_life": 53.0, "initial_amount": 185.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 2.4 mol * 100.087 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 240.2088, \"unit\": \"g\"}", "dedupe_signature": "9c6edf9ab2846ee6915ac8113039cf24522b53d8e3325e800c47aef6a7804e4c", "difficulty": "medium", "final_answer": {"answer": 240.2088, "unit": "g"}, "id": "stoich_mass_006487_calcium_carbonate_2.4", "license": "Apache-2.0", "prompt": "A sample contains 2.4 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 2.4 mol * 100.087 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "calcium carbonate", "molar_mass": 100.087, "moles": 2.4}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 3645 mL to 3.645 L.\n3. Compute M = 3.545 / 3.645.\nFinal: {\"answer\": 0.9726, \"unit\": \"mol/L\"}", "dedupe_signature": "b71c270bb44669f4f13211f3bc2877ef39b9610d1dccc04f4bfe2c89b2083e94", "difficulty": "medium", "final_answer": {"answer": 0.9726, "unit": "mol/L"}, "id": "molarity_006488_3.545_3645", "license": "Apache-2.0", "prompt": "A solution contains 3.545 mol of solute in 3645 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 3645 mL to 3.645 L.\nCompute M = 3.545 / 3.645.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 3.545, "volume_ml": 3645}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.71 y, so each step multiplies y by 1 - h*0.71.\n3. Apply that update for 8 steps and round the final state.\nFinal: {\"answer\": 0.0125, \"unit\": \"state_units\"}", "dedupe_signature": "de3dcd45c380029f2e5cca3ec12ed5166895d6576eada8ad10ed6c6e2985cd05", "difficulty": "medium", "final_answer": {"answer": 0.0125, "unit": "state_units"}, "id": "euler_decay_006489_5.5_0.71_0.75_8", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.71 y with y(0)=5.5, step size h=0.75, for 8 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.71 y, so each step multiplies y by 1 - h*0.71.\nApply that update for 8 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 5.5, "rate": 0.71, "step": 0.75, "steps": 8}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(3.7)=13.91 and f(11)=38.\n3. The interval width is 7.3.\nFinal: {\"answer\": 189.4715, \"unit\": \"area_units\"}", "dedupe_signature": "0c088f0684e580a609d0ade52cdc28bcdd4c8cf366d29f22c6aa7a82b52d9f86", "difficulty": "medium", "final_answer": {"answer": 189.4715, "unit": "area_units"}, "id": "trapz_linear_006490_3.3_1.7_3.7_11", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=3.3x+1.7 from x=3.7 to x=11. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(3.7)=13.91 and f(11)=38.\nThe interval width is 7.3.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 1.7, "slope": 3.3, "x0": 3.7, "x1": 11.0}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.24 and add it to the current value.\nFinal: {\"answer\": [0.942, 0.922, 0.102], \"unit\": \"temperature_units\"}", "dedupe_signature": "f2ca64dc736aa4122380ff5897324230794f4208eeb00b697ffbe4b0cd56e81c", "difficulty": "hard", "final_answer": {"answer": [0.942, 0.922, 0.102], "unit": "temperature_units"}, "id": "heat_step_006491_0.24_0.9_0.45_2.05_-1.05_0.65", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=0.9, right=0.65; current interior values are [0.45, 2.05, -1.05]. Use r=0.24. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.24 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [0.45, 2.05, -1.05], "left": 0.9, "r": 0.24, "right": 0.65}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kelvin equals Celsius plus 273.15.\n2. Apply the conversion factor directly to the given value.\n3. Compute 46.0 + 273.15.\nFinal: {\"answer\": 319.15, \"unit\": \"K\"}", "dedupe_signature": "05bbab275f67f8eb07ecea3adb4c26e6ed177ab0ab6cdaade35f906b4f5b5a8b", "difficulty": "easy", "final_answer": {"answer": 319.15, "unit": "K"}, "id": "unit_convert_006492_c_to_k_46", "license": "Apache-2.0", "prompt": "Convert 46 degC to K. Return the converted value with unit.", "reasoning_trace": "Kelvin equals Celsius plus 273.15.\nApply the conversion factor directly to the given value.\nCompute 46.0 + 273.15.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 46.0}, "verifier": {"formula": "value + 273.15", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=226 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-56.962, -58.9859], \"unit\": \"N\"}", "dedupe_signature": "1384c20076c9f75e1b7a388af3d0ca9527d4500206b8daf2f723df040b75135c", "difficulty": "medium", "final_answer": {"answer": [-56.962, -58.9859], "unit": "N"}, "id": "vector_components_006493_82_226", "license": "Apache-2.0", "prompt": "A vector has magnitude 82 N at 226 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=226 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 226, "magnitude": 82.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-8.8, 7.75], \"unit\": \"dimensionless\"}", "dedupe_signature": "fc08fda67c1e98f7bf2b5c4abb01188b941edf2d8ca1773f68ce84a759bc45d3", "difficulty": "medium", "final_answer": {"answer": [-8.8, 7.75], "unit": "dimensionless"}, "id": "line_two_point_006494_-7.25_6.75_-8.8_7.75", "license": "Apache-2.0", "prompt": "A line passes through points (-7.25, 71.55) and (6.75, -51.65). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -7.25, "x2": 6.75, "y1": 71.55000000000001, "y2": -51.650000000000006}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. amount times volume is not concentration\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "efa9b54107fc431b2382508bfffc1a0139714fa68e5209eb24f7585d4916d0e9", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_006495_inconsistent_74ac0b02_440140", "license": "Apache-2.0", "prompt": "In sensor calibration case 440140, check dimensional consistency for C = n * V. The left side has dimensions mol/L and the right side has dimensions mol*L. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\namount times volume is not concentration\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "C = n * V"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef finite_differences_006496(values):\n    return [values[i + 1] - values[i] for i in range(len(values) - 1)]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"finite_differences_006496\"}", "dedupe_signature": "6cb57654c7b6c4db330195ac9d602cecec9734b3e58a4339ac0a78487fe53e57", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "finite_differences_006496"}, "id": "code_006496_finite_differences_006496", "license": "Apache-2.0", "prompt": "Write a Python function finite_differences_006496(values) that returns the list of successive differences values[i+1] - values[i]. It must return [] for fewer than two values. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "finite_differences_006496"}, "verifier": {"function": "finite_differences_006496", "tests": ["assert finite_differences_006496([1, 4, 9, 16]) == [3, 5, 7]", "assert finite_differences_006496([5]) == []", "assert finite_differences_006496([]) == []"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 9.35 kg and a = 0.8 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 7.48, \"unit\": \"N\"}", "dedupe_signature": "8d831ccefa3049d0fcc677256bd84b9ce04c5a155095a2a2f07a9a205429f6dc", "difficulty": "easy", "final_answer": {"answer": 7.48, "unit": "N"}, "id": "force_006498_9.35_0.8", "license": "Apache-2.0", "prompt": "A cart has mass 9.35 kg and measured acceleration 0.8 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 9.35 kg and a = 0.8 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 0.8, "mass": 9.35}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 6.7^2 and multiply by 0.5 * 26.4.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 592.548, \"unit\": \"J\"}", "dedupe_signature": "865d2e65c0173965c6dabd3434b74fc6528e483a586b6ed0314787d74773b7af", "difficulty": "easy", "final_answer": {"answer": 592.548, "unit": "J"}, "id": "ke_006499_26.4_6.7", "license": "Apache-2.0", "prompt": "A body of mass 26.4 kg moves at 6.7 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 6.7^2 and multiply by 0.5 * 26.4.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 26.4, "velocity": 6.7}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=38 degrees through the sine of 2 theta.\n3. Substitute v=33.8 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 112.9974, \"unit\": \"m\"}", "dedupe_signature": "ad8fa5d89ffe4d8ddfea755431ebc61cf0ba95f6cb704f16f7ce5ed82edb74a7", "difficulty": "medium", "final_answer": {"answer": 112.9974, "unit": "m"}, "id": "projectile_range_006500_33.8_38", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 33.8 m/s and angle 38 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=38 degrees through the sine of 2 theta.\nSubstitute v=33.8 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 38, "gravity": 9.81, "speed": 33.8}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 155 * 3.71 * 27.\nFinal: {\"answer\": 15526.35, \"unit\": \"J\"}", "dedupe_signature": "6da094b609b809be9f451f4331b51dfd3bca4212e17e2dd54b1ceb3dd143145b", "difficulty": "easy", "final_answer": {"answer": 15526.35, "unit": "J"}, "id": "heat_q_006502_155_3.71_27", "license": "Apache-2.0", "prompt": "A 155 g sample has specific heat 3.71 J/(g*K). How much heat is needed to raise its temperature by 27 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 155 * 3.71 * 27.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 27, "heat_capacity": 3.71, "mass_g": 155}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=3.3 V and R=58 ohm.\nFinal: {\"answer\": 0.1878, \"unit\": \"W\"}", "dedupe_signature": "8ad8345866cc0af4387dea9b32a47c03d73a3c3cba875d5c8c2cbfa8952e072d", "difficulty": "easy", "final_answer": {"answer": 0.1878, "unit": "W"}, "id": "ohm_power_006503_3.3_58", "license": "Apache-2.0", "prompt": "A resistor has resistance 58 ohm and voltage 3.3 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=3.3 V and R=58 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 58.0, "voltage": 3.3}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 4.02 mol * 58.44 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 234.9288, \"unit\": \"g\"}", "dedupe_signature": "fd9fb395a99eceab098072e6dbc64d27c9416b6570f5f186d234058be1eecde8", "difficulty": "medium", "final_answer": {"answer": 234.9288, "unit": "g"}, "id": "stoich_mass_006505_sodium_chloride_4.02", "license": "Apache-2.0", "prompt": "A sample contains 4.02 mol of sodium chloride. Using molar mass 58.44 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 4.02 mol * 58.44 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "sodium chloride", "molar_mass": 58.44, "moles": 4.02}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 1590 mL to 1.59 L.\n3. Compute M = 1.74 / 1.59.\nFinal: {\"answer\": 1.0943, \"unit\": \"mol/L\"}", "dedupe_signature": "3eb008f2f74ae32848dcda641419ee95a83b2f7f479efa29b75a284ccb19c0d4", "difficulty": "medium", "final_answer": {"answer": 1.0943, "unit": "mol/L"}, "id": "molarity_006506_1.74_1590", "license": "Apache-2.0", "prompt": "A solution contains 1.74 mol of solute in 1590 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 1590 mL to 1.59 L.\nCompute M = 1.74 / 1.59.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 1.74, "volume_ml": 1590}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.21 y, so each step multiplies y by 1 - h*0.21.\n3. Apply that update for 5 steps and round the final state.\nFinal: {\"answer\": 0.6092, \"unit\": \"state_units\"}", "dedupe_signature": "90c40cb3f994a5b39848e638498c6ef3c0a68f55b7b4a2e384988cf9863535d5", "difficulty": "medium", "final_answer": {"answer": 0.6092, "unit": "state_units"}, "id": "euler_decay_006507_3_0.21_1.3_5", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.21 y with y(0)=3, step size h=1.3, for 5 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.21 y, so each step multiplies y by 1 - h*0.21.\nApply that update for 5 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 3.0, "rate": 0.21, "step": 1.3, "steps": 5}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.14 and add it to the current value.\nFinal: {\"answer\": [0.982, 0.404, 1.55], \"unit\": \"temperature_units\"}", "dedupe_signature": "bfd229c87a254bbb209dabc839311fec3afc20026530143fc3fd980aa8b7cc22", "difficulty": "hard", "final_answer": {"answer": [0.982, 0.404, 1.55], "unit": "temperature_units"}, "id": "heat_step_006509_0.14_1.2_1.15_-0.1_2.25_-0.4", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.2, right=-0.4; current interior values are [1.15, -0.1, 2.25]. Use r=0.14. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.14 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [1.15, -0.1, 2.25], "left": 1.2, "r": 0.14, "right": -0.4}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kelvin equals Celsius plus 273.15.\n2. Apply the conversion factor directly to the given value.\n3. Compute 28.5 + 273.15.\nFinal: {\"answer\": 301.65, \"unit\": \"K\"}", "dedupe_signature": "f532063b724edb44dfffeaa0159335694ddf647effc63b7a11d0bd4791c1ef0d", "difficulty": "easy", "final_answer": {"answer": 301.65, "unit": "K"}, "id": "unit_convert_006510_c_to_k_28.5", "license": "Apache-2.0", "prompt": "Convert 28.5 degC to K. Return the converted value with unit.", "reasoning_trace": "Kelvin equals Celsius plus 273.15.\nApply the conversion factor directly to the given value.\nCompute 28.5 + 273.15.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 28.5}, "verifier": {"formula": "value + 273.15", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=214 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-371.8234, -250.798], \"unit\": \"N\"}", "dedupe_signature": "0a1033a4ade77b9556fa2057be21d1a74bbadccbe393dbf636e4b6cd7369dc4e", "difficulty": "medium", "final_answer": {"answer": [-371.8234, -250.798], "unit": "N"}, "id": "vector_components_006511_448.5_214", "license": "Apache-2.0", "prompt": "A vector has magnitude 448.5 N at 214 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=214 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 214, "magnitude": 448.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. coulomb per second is ampere\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "2a3bcee75237c9c1d10af432a1220954a45f651887b9225fa59066b8fe01b536", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_006513_consistent_8b38953d_342687", "license": "Apache-2.0", "prompt": "In student derivation case 342687, check dimensional consistency for I = Q / t. The left side has dimensions A and the right side has dimensions A. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\ncoulomb per second is ampere\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "I = Q / t"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef weighted_sum_006514(values, weights):\n    if len(values) != len(weights):\n        raise ValueError('length mismatch')\n    return sum(value * weight for value, weight in zip(values, weights))\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"weighted_sum_006514\"}", "dedupe_signature": "d37a93a0a6e7987c6ec1337d38c3bc6b3338d8a85c2f1a3eec1a66d1ac88fd6e", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "weighted_sum_006514"}, "id": "code_006514_weighted_sum_006514", "license": "Apache-2.0", "prompt": "Write a Python function weighted_sum_006514(values, weights) that returns sum(value*weight). Raise ValueError when the two inputs have different lengths. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "weighted_sum_006514"}, "verifier": {"function": "weighted_sum_006514", "tests": ["assert weighted_sum_006514([2, 3], [4, 5]) == 23", "assert weighted_sum_006514([], []) == 0", "try:\n    weighted_sum_006514([1], [1, 2])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: target_schema, valid_examples.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"target_schema\", \"valid_examples\"]}", "dedupe_signature": "466ca51b5d10c7cb20526f0f2bdb807ebf21c236ce76a12c838e0315bd66ee54", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["target_schema", "valid_examples"]}, "id": "abstain_006515_target_schema_valid_examples", "license": "Apache-2.0", "prompt": "Write a parser that converts each registry ledger record from batch 149509 into the correct schema, but the prompt does not include the target schema or examples. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: target_schema, valid_examples.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["target_schema", "valid_examples"]}, "verifier": {"missing": ["target_schema", "valid_examples"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 18.55 kg and a = 12.3 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 228.165, \"unit\": \"N\"}", "dedupe_signature": "5026efd6bb5426a6d994e223a9aa2963ddd44f4a4372440ef471ee6fac7027ab", "difficulty": "easy", "final_answer": {"answer": 228.165, "unit": "N"}, "id": "force_006516_18.55_12.3", "license": "Apache-2.0", "prompt": "A cart has mass 18.55 kg and measured acceleration 12.3 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 18.55 kg and a = 12.3 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 12.3, "mass": 18.55}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 18.4^2 and multiply by 0.5 * 4.1.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 694.048, \"unit\": \"J\"}", "dedupe_signature": "69fcdbb18b49ec5180c97579ca32e06e8154dcd25c5345d08e43ef78d95bc941", "difficulty": "easy", "final_answer": {"answer": 694.048, "unit": "J"}, "id": "ke_006517_4.1_18.4", "license": "Apache-2.0", "prompt": "A body of mass 4.1 kg moves at 18.4 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 18.4^2 and multiply by 0.5 * 4.1.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 4.1, "velocity": 18.4}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 3.31 * 8.314 * 318 / 64.9.\nFinal: {\"answer\": 134.8405, \"unit\": \"kPa\"}", "dedupe_signature": "67fecf79a29601974228135be933a22b3a4ef0c4631cd6e02cc292261dcc71d3", "difficulty": "medium", "final_answer": {"answer": 134.8405, "unit": "kPa"}, "id": "ideal_gas_006519_3.31_318_64.9", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=3.31 mol, T=318 K, and V=64.9 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 3.31 * 8.314 * 318 / 64.9.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 3.31, "temp_k": 318, "volume_l": 64.9}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1465 * 2.085 * 43.\nFinal: {\"answer\": 131344.575, \"unit\": \"J\"}", "dedupe_signature": "af0ddeb2ea7242367313bee1ecfb7e89e2e7d60c13fb233f129222245bbb76a5", "difficulty": "easy", "final_answer": {"answer": 131344.575, "unit": "J"}, "id": "heat_q_006520_1465_2.085_43", "license": "Apache-2.0", "prompt": "A 1465 g sample has specific heat 2.085 J/(g*K). How much heat is needed to raise its temperature by 43 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1465 * 2.085 * 43.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 43, "heat_capacity": 2.085, "mass_g": 1465}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 1685 mL to 1.685 L.\n3. Compute M = 2.44 / 1.685.\nFinal: {\"answer\": 1.4481, \"unit\": \"mol/L\"}", "dedupe_signature": "4112b89c21ec8895cb1300ea53b3464565fcf7a178426623b5b3657662a2560a", "difficulty": "medium", "final_answer": {"answer": 1.4481, "unit": "mol/L"}, "id": "molarity_006524_2.44_1685", "license": "Apache-2.0", "prompt": "A solution contains 2.44 mol of solute in 1685 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 1685 mL to 1.685 L.\nCompute M = 2.44 / 1.685.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 2.44, "volume_ml": 1685}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.48 and add it to the current value.\nFinal: {\"answer\": [0.156, 0.73, -0.958], \"unit\": \"temperature_units\"}", "dedupe_signature": "ed2206536e24257e2a81ab7e660fc9b92f00b2bc2facd12349629f0a9ce45383", "difficulty": "hard", "final_answer": {"answer": [0.156, 0.73, -0.958], "unit": "temperature_units"}, "id": "heat_step_006527_0.48_0.7_-0.3_-0.35_1.85_-1.8", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=0.7, right=-1.8; current interior values are [-0.3, -0.35, 1.85]. Use r=0.48. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.48 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-0.3, -0.35, 1.85], "left": 0.7, "r": 0.48, "right": -1.8}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 100 centimeters in one meter.\n2. Apply the conversion factor directly to the given value.\n3. Compute 4816.5 / 100.\nFinal: {\"answer\": 48.165, \"unit\": \"m\"}", "dedupe_signature": "30d496577cfbc9766f0c8bdad8f2e8e948399a81d909b48ec8a74b554fbbaa4e", "difficulty": "easy", "final_answer": {"answer": 48.165, "unit": "m"}, "id": "unit_convert_006528_cm_to_m_4816.5", "license": "Apache-2.0", "prompt": "Convert 4816.5 cm to m. Return the converted value with unit.", "reasoning_trace": "There are 100 centimeters in one meter.\nApply the conversion factor directly to the given value.\nCompute 4816.5 / 100.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 4816.5}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [6.85, 13.25], \"unit\": \"dimensionless\"}", "dedupe_signature": "9a04e8705453483dfc48e790e141942e3d06275b56cc37942acff0abea44e4cd", "difficulty": "medium", "final_answer": {"answer": [6.85, 13.25], "unit": "dimensionless"}, "id": "line_two_point_006530_8.75_23.5_6.85_13.25", "license": "Apache-2.0", "prompt": "A line passes through points (8.75, 73.1875) and (23.5, 174.225). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 8.75, "x2": 23.5, "y1": 73.1875, "y2": 174.225}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. lever arm times force has torque dimensions\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "f4305356bf80e3597c7ceaa23ce0c64c5c9b4be8c3e038b8d63eac91ddc0ad05", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_006531_consistent_5ca82cb9_113903", "license": "Apache-2.0", "prompt": "In simulation spec case 113903, check dimensional consistency for tau = r * F. The left side has dimensions N*m and the right side has dimensions N*m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nlever arm times force has torque dimensions\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "tau = r * F"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef center_values_006532(values):\n    if not values:\n        raise ValueError('center_values requires at least one value')\n    mean = sum(values) / len(values)\n    return [value - mean for value in values]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"center_values_006532\"}", "dedupe_signature": "694a656ce7532e5b5fe1225763aa1d6453bcfedba3ccb047c1e8bf9037844e5d", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "center_values_006532"}, "id": "code_006532_center_values_006532", "license": "Apache-2.0", "prompt": "Write a Python function center_values_006532(values) that subtracts the arithmetic mean from each value and returns a new list. Raise ValueError for an empty input. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "center_values_006532"}, "verifier": {"function": "center_values_006532", "tests": ["out = center_values_006532([1, 2, 3]); assert out == [-1, 0, 1]", "assert center_values_006532([5]) == [0]", "try:\n    center_values_006532([])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: recurrence, objective, tie_breaking_rule.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"recurrence\", \"objective\", \"tie_breaking_rule\"]}", "dedupe_signature": "e86d53cc62d5c5f982282d436cab654354041976e563f05d0a8daed7d0be3526", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["recurrence", "objective", "tie_breaking_rule"]}, "id": "abstain_006533_recurrence_objective_tie_breaking_rule", "license": "Apache-2.0", "prompt": "Write a dynamic-programming solver for a routing scoring problem with 2450 items and budget 61715, but the recurrence, objective, and tie-breaking rule are all absent. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: recurrence, objective, tie_breaking_rule.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["recurrence", "objective", "tie_breaking_rule"]}, "verifier": {"missing": ["recurrence", "objective", "tie_breaking_rule"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 16.25 kg and a = 0.25 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 4.0625, \"unit\": \"N\"}", "dedupe_signature": "77562fc361f444349041196891ba7efaf59c859e156d528fb9896440af576bc9", "difficulty": "easy", "final_answer": {"answer": 4.0625, "unit": "N"}, "id": "force_006534_16.25_0.25", "license": "Apache-2.0", "prompt": "A cart has mass 16.25 kg and measured acceleration 0.25 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 16.25 kg and a = 0.25 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 0.25, "mass": 16.25}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 0.7^2 and multiply by 0.5 * 20.4.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 4.998, \"unit\": \"J\"}", "dedupe_signature": "1a7ed265e31cc9473a8640f6c550ae1631477791611226c27711d0bcf6064a92", "difficulty": "easy", "final_answer": {"answer": 4.998, "unit": "J"}, "id": "ke_006535_20.4_0.7", "license": "Apache-2.0", "prompt": "A body of mass 20.4 kg moves at 0.7 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 0.7^2 and multiply by 0.5 * 20.4.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 20.4, "velocity": 0.7}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 1.18 * 8.314 * 332 / 26.8.\nFinal: {\"answer\": 121.5333, \"unit\": \"kPa\"}", "dedupe_signature": "7ef13ea72cdb935161c841875f2acec04305521f212c533833b667ef1f68686f", "difficulty": "medium", "final_answer": {"answer": 121.5333, "unit": "kPa"}, "id": "ideal_gas_006537_1.18_332_26.8", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=1.18 mol, T=332 K, and V=26.8 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 1.18 * 8.314 * 332 / 26.8.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 1.18, "temp_k": 332, "volume_l": 26.8}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 635 * 3.505 * 20.\nFinal: {\"answer\": 44513.5, \"unit\": \"J\"}", "dedupe_signature": "828e740efffe914d1603d940feb94439790191faa8f29f25be0bc7d393835599", "difficulty": "easy", "final_answer": {"answer": 44513.5, "unit": "J"}, "id": "heat_q_006538_635_3.505_20", "license": "Apache-2.0", "prompt": "A 635 g sample has specific heat 3.505 J/(g*K). How much heat is needed to raise its temperature by 20 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 635 * 3.505 * 20.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 20, "heat_capacity": 3.505, "mass_g": 635}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=123.4 V and R=20.4 ohm.\nFinal: {\"answer\": 746.449, \"unit\": \"W\"}", "dedupe_signature": "52ea9666011dc7a5a76f78f360b4eaadb8508be711bb72fa6a1aec2faaa58630", "difficulty": "easy", "final_answer": {"answer": 746.449, "unit": "W"}, "id": "ohm_power_006539_123.4_20.4", "license": "Apache-2.0", "prompt": "A resistor has resistance 20.4 ohm and voltage 123.4 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=123.4 V and R=20.4 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 20.4, "voltage": 123.4}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=358 mg, t=224 h, and T_half=30 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 2.0239, \"unit\": \"mg\"}", "dedupe_signature": "7ae822a1b4e99bc4a25db4dbf2685538b2d9dc927af7bcdb8aff30d12966a2a0", "difficulty": "medium", "final_answer": {"answer": 2.0239, "unit": "mg"}, "id": "half_life_006540_358_30_224", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 358 mg. Its half-life is 30 hours. How many mg remain after 224 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=358 mg, t=224 h, and T_half=30 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 224.0, "half_life": 30.0, "initial_amount": 358.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 6.99 mol * 18.015 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 125.9249, \"unit\": \"g\"}", "dedupe_signature": "dc275b9cef92fd3eb8f71cdb0370c6450daaee3cbc19f19489ea71dc1b2bacee", "difficulty": "medium", "final_answer": {"answer": 125.9249, "unit": "g"}, "id": "stoich_mass_006541_water_6.99", "license": "Apache-2.0", "prompt": "A sample contains 6.99 mol of water. Using molar mass 18.015 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 6.99 mol * 18.015 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "water", "molar_mass": 18.015, "moles": 6.99}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 3225 mL to 3.225 L.\n3. Compute M = 4.675 / 3.225.\nFinal: {\"answer\": 1.4496, \"unit\": \"mol/L\"}", "dedupe_signature": "8e9590f73a8bc8b60d9216225bd0381d34419913c10803826bb5e3ae95245957", "difficulty": "medium", "final_answer": {"answer": 1.4496, "unit": "mol/L"}, "id": "molarity_006542_4.675_3225", "license": "Apache-2.0", "prompt": "A solution contains 4.675 mol of solute in 3225 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 3225 mL to 3.225 L.\nCompute M = 4.675 / 3.225.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 4.675, "volume_ml": 3225}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.77 y, so each step multiplies y by 1 - h*0.77.\n3. Apply that update for 10 steps and round the final state.\nFinal: {\"answer\": 0.0002, \"unit\": \"state_units\"}", "dedupe_signature": "52166f6ab94c44571ae5531918a57a308406b153bcff2a0e30a8705fb9635fd2", "difficulty": "medium", "final_answer": {"answer": 0.0002, "unit": "state_units"}, "id": "euler_decay_006543_26.5_0.77_0.9_10", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.77 y with y(0)=26.5, step size h=0.9, for 10 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.77 y, so each step multiplies y by 1 - h*0.77.\nApply that update for 10 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 26.5, "rate": 0.77, "step": 0.9, "steps": 10}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(0.3)=-14.27 and f(5.6)=-19.04.\n3. The interval width is 5.3.\nFinal: {\"answer\": -88.2715, \"unit\": \"area_units\"}", "dedupe_signature": "8e676d3420e5eeec3dda05108076979599d1ded65bc1a329dd7297f043f78453", "difficulty": "medium", "final_answer": {"answer": -88.2715, "unit": "area_units"}, "id": "trapz_linear_006544_-0.9_-14_0.3_5.6", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-0.9x+-14 from x=0.3 to x=5.6. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(0.3)=-14.27 and f(5.6)=-19.04.\nThe interval width is 5.3.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -14.0, "slope": -0.9, "x0": 0.3, "x1": 5.6}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.48 and add it to the current value.\nFinal: {\"answer\": [1.048, 0.52, 1.87], \"unit\": \"temperature_units\"}", "dedupe_signature": "c2f8b7e9c2a9c702a4772a05980e7282b3770703a365fbd81249a0924b47e722", "difficulty": "hard", "final_answer": {"answer": [1.048, 0.52, 1.87], "unit": "temperature_units"}, "id": "heat_step_006545_0.48_0.75_-2.0_1.6_2.95_2.05", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=0.75, right=2.05; current interior values are [-2.0, 1.6, 2.95]. Use r=0.48. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.48 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-2.0, 1.6, 2.95], "left": 0.75, "r": 0.48, "right": 2.05}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 100 centimeters in one meter.\n2. Apply the conversion factor directly to the given value.\n3. Compute 800.0 / 100.\nFinal: {\"answer\": 8.0, \"unit\": \"m\"}", "dedupe_signature": "d21a144162dac4bcef10632d7dce95d174e6be22df60c7d1f0f5ae170a37af6c", "difficulty": "easy", "final_answer": {"answer": 8.0, "unit": "m"}, "id": "unit_convert_006546_cm_to_m_800", "license": "Apache-2.0", "prompt": "Convert 800 cm to m. Return the converted value with unit.", "reasoning_trace": "There are 100 centimeters in one meter.\nApply the conversion factor directly to the given value.\nCompute 800.0 / 100.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 800.0}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=40 degrees and keep the unit as newtons.\nFinal: {\"answer\": [158.9542, 133.3784], \"unit\": \"N\"}", "dedupe_signature": "0034b0a7ec631fd241a1d8908f665cadf6e84936fe9867b378950e309d8882ed", "difficulty": "medium", "final_answer": {"answer": [158.9542, 133.3784], "unit": "N"}, "id": "vector_components_006547_207.5_40", "license": "Apache-2.0", "prompt": "A vector has magnitude 207.5 N at 40 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=40 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 40, "magnitude": 207.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-2.85, -13.5], \"unit\": \"dimensionless\"}", "dedupe_signature": "42f3ccd4d02690daf03d5adb468a53afb9619c0a88d4a86480174cdd125a5241", "difficulty": "medium", "final_answer": {"answer": [-2.85, -13.5], "unit": "dimensionless"}, "id": "line_two_point_006548_4_8_-2.85_-13.5", "license": "Apache-2.0", "prompt": "A line passes through points (4, -24.9) and (8, -36.3). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 4.0, "x2": 8.0, "y1": -24.9, "y2": -36.3}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef normalize_006550(values):\n    total = sum(values)\n    if total == 0:\n        raise ValueError('cannot normalize zero-sum values')\n    return [v / total for v in values]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"normalize_006550\"}", "dedupe_signature": "48ebdc978a2be5558a80f185c53d66f246fd0334249e0d2aaa4acc50d3537856", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "normalize_006550"}, "id": "code_006550_normalize_006550", "license": "Apache-2.0", "prompt": "Write a Python function normalize_006550(values) that returns a new list whose values sum to 1. Raise ValueError if the sum is zero. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "normalize_006550"}, "verifier": {"function": "normalize_006550", "tests": ["out = normalize_006550([2, 3, 5]); assert len(out) == 3", "assert abs(sum(normalize_006550([2, 3, 5])) - 1.0) < 1e-12", "assert normalize_006550([1, 1]) == [0.5, 0.5]", "try:\n    normalize_006550([1, -1])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: rate_constant, number_of_steps.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"rate_constant\", \"number_of_steps\"]}", "dedupe_signature": "9c6bdaf187d21791c9937206023baeb8e7e480bea9008a70f921cfeb5ca6b1b3", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["rate_constant", "number_of_steps"]}, "id": "abstain_006551_rate_constant_number_of_steps", "license": "Apache-2.0", "prompt": "Use explicit Euler for dy/dt = -k y. The prompt gives y(0)=13 and h=0.6, but omits both k and the number of steps. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: rate_constant, number_of_steps.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["rate_constant", "number_of_steps"]}, "verifier": {"missing": ["rate_constant", "number_of_steps"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 12.35^2 and multiply by 0.5 * 29.1.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 2219.2024, \"unit\": \"J\"}", "dedupe_signature": "a4e0cc42e4467126fb9736cdd4b158dc4cc112cff3e122903824f55508f53d26", "difficulty": "easy", "final_answer": {"answer": 2219.2024, "unit": "J"}, "id": "ke_006553_29.1_12.35", "license": "Apache-2.0", "prompt": "A body of mass 29.1 kg moves at 12.35 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 12.35^2 and multiply by 0.5 * 29.1.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 29.1, "velocity": 12.35}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 4.85 * 8.314 * 439 / 75.1.\nFinal: {\"answer\": 235.7091, \"unit\": \"kPa\"}", "dedupe_signature": "d5a08087f1a1ef94d1cea3213d73097e50130fffd7fecefa94026d7d553c826d", "difficulty": "medium", "final_answer": {"answer": 235.7091, "unit": "kPa"}, "id": "ideal_gas_006555_4.85_439_75.1", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=4.85 mol, T=439 K, and V=75.1 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 4.85 * 8.314 * 439 / 75.1.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 4.85, "temp_k": 439, "volume_l": 75.1}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 235 * 2.235 * 87.\nFinal: {\"answer\": 45694.575, \"unit\": \"J\"}", "dedupe_signature": "427bfb50f35a2b29b970adecbede59e80673000f9464867bc56bc1c0edff99a8", "difficulty": "easy", "final_answer": {"answer": 45694.575, "unit": "J"}, "id": "heat_q_006556_235_2.235_87", "license": "Apache-2.0", "prompt": "A 235 g sample has specific heat 2.235 J/(g*K). How much heat is needed to raise its temperature by 87 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 235 * 2.235 * 87.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 87, "heat_capacity": 2.235, "mass_g": 235}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=96.7 V and R=189.9 ohm.\nFinal: {\"answer\": 49.2411, \"unit\": \"W\"}", "dedupe_signature": "b73b79e3bb0461e89877c945116473f9eb6a0a8ccca9d1d199f033604e904813", "difficulty": "easy", "final_answer": {"answer": 49.2411, "unit": "W"}, "id": "ohm_power_006557_96.7_189.9", "license": "Apache-2.0", "prompt": "A resistor has resistance 189.9 ohm and voltage 96.7 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=96.7 V and R=189.9 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 189.9, "voltage": 96.7}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=200 mg, t=244.5 h, and T_half=5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 0.0, \"unit\": \"mg\"}", "dedupe_signature": "2de6b6e54689763563012799347435b17642b34581168baeaaa8c4060b83ea9b", "difficulty": "medium", "final_answer": {"answer": 0.0, "unit": "mg"}, "id": "half_life_006558_200_5_244.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 200 mg. Its half-life is 5 hours. How many mg remain after 244.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=200 mg, t=244.5 h, and T_half=5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 244.5, "half_life": 5.0, "initial_amount": 200.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 7.15 mol * 100.087 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 715.6221, \"unit\": \"g\"}", "dedupe_signature": "123b26d3397bb3b5f398da69be2d6e1b27f7831f73ebe5e9648929dd72fdb992", "difficulty": "medium", "final_answer": {"answer": 715.6221, "unit": "g"}, "id": "stoich_mass_006559_calcium_carbonate_7.15", "license": "Apache-2.0", "prompt": "A sample contains 7.15 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 7.15 mol * 100.087 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "calcium carbonate", "molar_mass": 100.087, "moles": 7.15}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 370 mL to 0.37 L.\n3. Compute M = 2.73 / 0.37.\nFinal: {\"answer\": 7.3784, \"unit\": \"mol/L\"}", "dedupe_signature": "033a40f3196fc49119ac8688016d896da0a74d5b8a9f09f66a54a32a13a7a10c", "difficulty": "medium", "final_answer": {"answer": 7.3784, "unit": "mol/L"}, "id": "molarity_006560_2.73_370", "license": "Apache-2.0", "prompt": "A solution contains 2.73 mol of solute in 370 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 370 mL to 0.37 L.\nCompute M = 2.73 / 0.37.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 2.73, "volume_ml": 370}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(5.9)=-61.43 and f(10.1)=-93.77.\n3. The interval width is 4.2.\nFinal: {\"answer\": -325.92, \"unit\": \"area_units\"}", "dedupe_signature": "996821418e2a187c3ae1974866809d1049a998ed3f7af24bb7d4a55497f7616b", "difficulty": "medium", "final_answer": {"answer": -325.92, "unit": "area_units"}, "id": "trapz_linear_006562_-7.7_-16_5.9_10.1", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-7.7x+-16 from x=5.9 to x=10.1. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(5.9)=-61.43 and f(10.1)=-93.77.\nThe interval width is 4.2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -16.0, "slope": -7.7, "x0": 5.9, "x1": 10.100000000000001}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.06 and add it to the current value.\nFinal: {\"answer\": [0.416, -1.624, 0.186], \"unit\": \"temperature_units\"}", "dedupe_signature": "19846f3f1e6f74df5ba9c5a06f6f2e70329ee6f7b140d637835ce0f7a18eb2fb", "difficulty": "hard", "final_answer": {"answer": [0.416, -1.624, 0.186], "unit": "temperature_units"}, "id": "heat_step_006563_0.06_-0.7_0.65_-1.9_0.15_2.8", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-0.7, right=2.8; current interior values are [0.65, -1.9, 0.15]. Use r=0.06. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.06 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [0.65, -1.9, 0.15], "left": -0.7, "r": 0.06, "right": 2.8}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 100 centimeters in one meter.\n2. Apply the conversion factor directly to the given value.\n3. Compute 4468.5 / 100.\nFinal: {\"answer\": 44.685, \"unit\": \"m\"}", "dedupe_signature": "319e5ab1ca2ca94a2190fa6da046cacb08a230cded19cf98000c6370630c5067", "difficulty": "easy", "final_answer": {"answer": 44.685, "unit": "m"}, "id": "unit_convert_006564_cm_to_m_4468.5", "license": "Apache-2.0", "prompt": "Convert 4468.5 cm to m. Return the converted value with unit.", "reasoning_trace": "There are 100 centimeters in one meter.\nApply the conversion factor directly to the given value.\nCompute 4468.5 / 100.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 4468.5}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=31 degrees and keep the unit as newtons.\nFinal: {\"answer\": [33.4295, 20.0865], \"unit\": \"N\"}", "dedupe_signature": "4418916fcfac00f2e25af71242bbcae0195fee45b6b7009a39ce40d4bb690836", "difficulty": "medium", "final_answer": {"answer": [33.4295, 20.0865], "unit": "N"}, "id": "vector_components_006565_39_31", "license": "Apache-2.0", "prompt": "A vector has magnitude 39 N at 31 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=31 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 31, "magnitude": 39.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. lever arm times force has torque dimensions\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "d5a2caaeb3c1dcadc314d8d45d1fa6f6c9bb834478d63efeffd290a2b6fff9fd", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_006567_consistent_5ca82cb9_777541", "license": "Apache-2.0", "prompt": "In instrument manual case 777541, check dimensional consistency for tau = r * F. The left side has dimensions N*m and the right side has dimensions N*m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nlever arm times force has torque dimensions\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "tau = r * F"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef running_total_006568(values):\n    total = 0\n    out = []\n    for value in values:\n        total += value\n        out.append(total)\n    return out\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"running_total_006568\"}", "dedupe_signature": "f84e30067afc19957672a88ef5eb854a05041dbd4cc54af8d72cd6a968c5b417", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "running_total_006568"}, "id": "code_006568_running_total_006568", "license": "Apache-2.0", "prompt": "Write a Python function running_total_006568(values) that returns cumulative sums as a new list. It must not mutate the input list. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "running_total_006568"}, "verifier": {"function": "running_total_006568", "tests": ["assert running_total_006568([1, 2, 3]) == [1, 3, 6]", "xs = [4, -1, 2]; assert running_total_006568(xs) == [4, 3, 5] and xs == [4, -1, 2]", "assert running_total_006568([]) == []"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: recurrence, objective, tie_breaking_rule.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"recurrence\", \"objective\", \"tie_breaking_rule\"]}", "dedupe_signature": "cfa751c4ad263f42961f7a3eeb412c32be267b24c3389ff5d9e0e2f2bb49b0c8", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["recurrence", "objective", "tie_breaking_rule"]}, "id": "abstain_006569_recurrence_objective_tie_breaking_rule", "license": "Apache-2.0", "prompt": "Write a dynamic-programming solver for a allocation scoring problem with 2203 items and budget 99015, but the recurrence, objective, and tie-breaking rule are all absent. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: recurrence, objective, tie_breaking_rule.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["recurrence", "objective", "tie_breaking_rule"]}, "verifier": {"missing": ["recurrence", "objective", "tie_breaking_rule"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 9.55 kg and a = 7.95 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 75.9225, \"unit\": \"N\"}", "dedupe_signature": "c3d412c1f96906431b3aaded4cdd15258aa7fe87a379f8d5731171659884f3bd", "difficulty": "easy", "final_answer": {"answer": 75.9225, "unit": "N"}, "id": "force_006570_9.55_7.95", "license": "Apache-2.0", "prompt": "A cart has mass 9.55 kg and measured acceleration 7.95 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 9.55 kg and a = 7.95 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 7.95, "mass": 9.55}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 10.95^2 and multiply by 0.5 * 13.7.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 821.3321, \"unit\": \"J\"}", "dedupe_signature": "d1357698a6b9be31d80239db3f988f1be99ce6267b9aed7d76664cdf1e04df27", "difficulty": "easy", "final_answer": {"answer": 821.3321, "unit": "J"}, "id": "ke_006571_13.7_10.95", "license": "Apache-2.0", "prompt": "A body of mass 13.7 kg moves at 10.95 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 10.95^2 and multiply by 0.5 * 13.7.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 13.7, "velocity": 10.95}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 5.33 * 8.314 * 277 / 60.8.\nFinal: {\"answer\": 201.8894, \"unit\": \"kPa\"}", "dedupe_signature": "655eff9b3a8c3e5dc4210472c41d893aa6e2dcddc9beb29c56584f69a903d526", "difficulty": "medium", "final_answer": {"answer": 201.8894, "unit": "kPa"}, "id": "ideal_gas_006573_5.33_277_60.8", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=5.33 mol, T=277 K, and V=60.8 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 5.33 * 8.314 * 277 / 60.8.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 5.33, "temp_k": 277, "volume_l": 60.8}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 275 * 2.955 * 84.\nFinal: {\"answer\": 68260.5, \"unit\": \"J\"}", "dedupe_signature": "c5faa1c17e5c824d308e2708b9b778fb6f2e9914dae69dc187f3a76d873c8466", "difficulty": "easy", "final_answer": {"answer": 68260.5, "unit": "J"}, "id": "heat_q_006574_275_2.955_84", "license": "Apache-2.0", "prompt": "A 275 g sample has specific heat 2.955 J/(g*K). How much heat is needed to raise its temperature by 84 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 275 * 2.955 * 84.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 84, "heat_capacity": 2.955, "mass_g": 275}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=741.5 mg, t=173.5 h, and T_half=59 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 96.5781, \"unit\": \"mg\"}", "dedupe_signature": "eec840c1b856c89f30281069233d2bb6909bfcb98caa88cb2e8d744d2e793111", "difficulty": "medium", "final_answer": {"answer": 96.5781, "unit": "mg"}, "id": "half_life_006576_741.5_59_173.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 741.5 mg. Its half-life is 59 hours. How many mg remain after 173.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=741.5 mg, t=173.5 h, and T_half=59 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 173.5, "half_life": 59.0, "initial_amount": 741.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 1.81 mol * 18.015 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 32.6072, \"unit\": \"g\"}", "dedupe_signature": "ee96d4f157d8e4bf40d8d920b9053664ba25e0d771277c8e6a7fc672caa42637", "difficulty": "medium", "final_answer": {"answer": 32.6072, "unit": "g"}, "id": "stoich_mass_006577_water_1.81", "license": "Apache-2.0", "prompt": "A sample contains 1.81 mol of water. Using molar mass 18.015 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 1.81 mol * 18.015 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "water", "molar_mass": 18.015, "moles": 1.81}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 3450 mL to 3.45 L.\n3. Compute M = 3.78 / 3.45.\nFinal: {\"answer\": 1.0957, \"unit\": \"mol/L\"}", "dedupe_signature": "6134d065b571c83555d1edb1a9d13a525828f1b301d8e08cf18347627cfe7237", "difficulty": "medium", "final_answer": {"answer": 1.0957, "unit": "mol/L"}, "id": "molarity_006578_3.78_3450", "license": "Apache-2.0", "prompt": "A solution contains 3.78 mol of solute in 3450 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 3450 mL to 3.45 L.\nCompute M = 3.78 / 3.45.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 3.78, "volume_ml": 3450}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.29 y, so each step multiplies y by 1 - h*0.29.\n3. Apply that update for 7 steps and round the final state.\nFinal: {\"answer\": 11.5875, \"unit\": \"state_units\"}", "dedupe_signature": "e6d9ac624ae973d9acddf6fb93613f034380b6c494a62a467378938470073ffb", "difficulty": "medium", "final_answer": {"answer": 11.5875, "unit": "state_units"}, "id": "euler_decay_006579_50_0.29_0.65_7", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.29 y with y(0)=50, step size h=0.65, for 7 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.29 y, so each step multiplies y by 1 - h*0.29.\nApply that update for 7 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 50.0, "rate": 0.29, "step": 0.65, "steps": 7}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(1.5)=15.5 and f(7)=43.\n3. The interval width is 5.5.\nFinal: {\"answer\": 160.875, \"unit\": \"area_units\"}", "dedupe_signature": "d62d5ce2115594f36c78002a261f7dd267711e568883fcc19a38c48210875b47", "difficulty": "medium", "final_answer": {"answer": 160.875, "unit": "area_units"}, "id": "trapz_linear_006580_5_8_1.5_7", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=5x+8 from x=1.5 to x=7. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(1.5)=15.5 and f(7)=43.\nThe interval width is 5.5.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 8.0, "slope": 5.0, "x0": 1.5, "x1": 7.0}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.44 and add it to the current value.\nFinal: {\"answer\": [0.614, -0.094, -1.02], \"unit\": \"temperature_units\"}", "dedupe_signature": "1df7763f3e28d976ed39b5071b5264ead5c3799a3fb5900f868ad0e12736a266", "difficulty": "hard", "final_answer": {"answer": [0.614, -0.094, -1.02], "unit": "temperature_units"}, "id": "heat_step_006581_0.44_2.15_1.45_-1.15_-1.35_-0.8", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=2.15, right=-0.8; current interior values are [1.45, -1.15, -1.35]. Use r=0.44. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.44 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [1.45, -1.15, -1.35], "left": 2.15, "r": 0.44, "right": -0.8}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 11568.0 / 1000.\nFinal: {\"answer\": 11.568, \"unit\": \"kg\"}", "dedupe_signature": "edc188e2d0d54d150e1ba2cc2c6af4a6bb0d96c32c3c4484f7cfa62d1121d954", "difficulty": "easy", "final_answer": {"answer": 11.568, "unit": "kg"}, "id": "unit_convert_006582_g_to_kg_11568", "license": "Apache-2.0", "prompt": "Convert 11568 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 11568.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 11568.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=228 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-212.7835, -236.3201], \"unit\": \"N\"}", "dedupe_signature": "3e647e1376ad69ce0358c4e4ec7321eec9d81fe3b37fceb5da6250b9c9cae9a8", "difficulty": "medium", "final_answer": {"answer": [-212.7835, -236.3201], "unit": "N"}, "id": "vector_components_006583_318_228", "license": "Apache-2.0", "prompt": "A vector has magnitude 318 N at 228 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=228 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 228, "magnitude": 318.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-9.45, -10.0], \"unit\": \"dimensionless\"}", "dedupe_signature": "e7ad446afe579e054ecba66fa998816bd207878ff36055b4b25e85c579ae619d", "difficulty": "medium", "final_answer": {"answer": [-9.45, -10.0], "unit": "dimensionless"}, "id": "line_two_point_006584_9_21.5_-9.45_-10", "license": "Apache-2.0", "prompt": "A line passes through points (9, -95.05) and (21.5, -213.175). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 9.0, "x2": 21.5, "y1": -95.05, "y2": -213.17499999999998}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef pairwise_ratios_006586(numerators, denominators):\n    if len(numerators) != len(denominators):\n        raise ValueError('length mismatch')\n    out = []\n    for numerator, denominator in zip(numerators, denominators):\n        if denominator == 0:\n            raise ValueError('zero denominator')\n        out.append(numerator / denominator)\n    return out\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"pairwise_ratios_006586\"}", "dedupe_signature": "bb9a3021f00647e1e39c0c69bd1130f66fcbf561ed8b5f893bf59362a7e623a5", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "pairwise_ratios_006586"}, "id": "code_006586_pairwise_ratios_006586", "license": "Apache-2.0", "prompt": "Write a Python function pairwise_ratios_006586(numerators, denominators) that returns a list of n/d values. Raise ValueError if lengths differ or any denominator is zero. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "pairwise_ratios_006586"}, "verifier": {"function": "pairwise_ratios_006586", "tests": ["assert pairwise_ratios_006586([2, 9], [4, 3]) == [0.5, 3.0]", "try:\n    pairwise_ratios_006586([1], [0])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass", "try:\n    pairwise_ratios_006586([1, 2], [1])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 18.8 kg and a = 8.25 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 155.1, \"unit\": \"N\"}", "dedupe_signature": "e11fef39bb4602ead05dd37a08654b5b3536a32f44b71c5d0f8141e479ef05fd", "difficulty": "easy", "final_answer": {"answer": 155.1, "unit": "N"}, "id": "force_006588_18.8_8.25", "license": "Apache-2.0", "prompt": "A cart has mass 18.8 kg and measured acceleration 8.25 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 18.8 kg and a = 8.25 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 8.25, "mass": 18.8}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=42 degrees through the sine of 2 theta.\n3. Substitute v=23.1 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 54.0965, \"unit\": \"m\"}", "dedupe_signature": "b5c08facc9df0e382c4d5131be799439754c2f926113647cbc36c0fa69182e46", "difficulty": "medium", "final_answer": {"answer": 54.0965, "unit": "m"}, "id": "projectile_range_006590_23.1_42", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 23.1 m/s and angle 42 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=42 degrees through the sine of 2 theta.\nSubstitute v=23.1 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 42, "gravity": 9.81, "speed": 23.1}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 750 * 2.04 * 99.\nFinal: {\"answer\": 151470.0, \"unit\": \"J\"}", "dedupe_signature": "020c21e80b0f8c0d1141de66e06084c0bfb63ab7afff6461e9369c229672ee04", "difficulty": "easy", "final_answer": {"answer": 151470.0, "unit": "J"}, "id": "heat_q_006592_750_2.04_99", "license": "Apache-2.0", "prompt": "A 750 g sample has specific heat 2.04 J/(g*K). How much heat is needed to raise its temperature by 99 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 750 * 2.04 * 99.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 99, "heat_capacity": 2.04, "mass_g": 750}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=202.4 V and R=54.5 ohm.\nFinal: {\"answer\": 751.6653, \"unit\": \"W\"}", "dedupe_signature": "ac1801be3b600147c2a4ef8ebd0b888111b794cfedf03a193e7997d3429f1d39", "difficulty": "easy", "final_answer": {"answer": 751.6653, "unit": "W"}, "id": "ohm_power_006593_202.4_54.5", "license": "Apache-2.0", "prompt": "A resistor has resistance 54.5 ohm and voltage 202.4 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=202.4 V and R=54.5 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 54.5, "voltage": 202.4}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 5.09 mol * 18.015 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 91.6963, \"unit\": \"g\"}", "dedupe_signature": "6d8c268d7680a0e91410498107285d3c38076442b81b7fe2fb2242137367eef6", "difficulty": "medium", "final_answer": {"answer": 91.6963, "unit": "g"}, "id": "stoich_mass_006595_water_5.09", "license": "Apache-2.0", "prompt": "A sample contains 5.09 mol of water. Using molar mass 18.015 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 5.09 mol * 18.015 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "water", "molar_mass": 18.015, "moles": 5.09}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(2.8)=24.34 and f(7.2)=56.46.\n3. The interval width is 4.4.\nFinal: {\"answer\": 177.76, \"unit\": \"area_units\"}", "dedupe_signature": "723b99f338dfcabe4a0b8fe4c3a9d64e6be5f615f719d57fd77f959715dafa86", "difficulty": "medium", "final_answer": {"answer": 177.76, "unit": "area_units"}, "id": "trapz_linear_006598_7.3_3.9_2.8_7.2", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=7.3x+3.9 from x=2.8 to x=7.2. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(2.8)=24.34 and f(7.2)=56.46.\nThe interval width is 4.4.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 3.9, "slope": 7.3, "x0": 2.8, "x1": 7.2}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.28 and add it to the current value.\nFinal: {\"answer\": [0.592, 0.956, 1.826], \"unit\": \"temperature_units\"}", "dedupe_signature": "3632d1b9fbf287b521dcbb7f4e63f51f0431267c8ecaaa931d6b72de946864ab", "difficulty": "hard", "final_answer": {"answer": [0.592, 0.956, 1.826], "unit": "temperature_units"}, "id": "heat_step_006599_0.28_1.7_-1.2_2.3_1.0_2.65", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.7, right=2.65; current interior values are [-1.2, 2.3, 1.0]. Use r=0.28. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.28 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-1.2, 2.3, 1.0], "left": 1.7, "r": 0.28, "right": 2.65}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 100 centimeters in one meter.\n2. Apply the conversion factor directly to the given value.\n3. Compute 3702.5 / 100.\nFinal: {\"answer\": 37.025, \"unit\": \"m\"}", "dedupe_signature": "634a223098590ead7f3b0641564f1016d005f74d372ae0c981050e9696b6855e", "difficulty": "easy", "final_answer": {"answer": 37.025, "unit": "m"}, "id": "unit_convert_006600_cm_to_m_3702.5", "license": "Apache-2.0", "prompt": "Convert 3702.5 cm to m. Return the converted value with unit.", "reasoning_trace": "There are 100 centimeters in one meter.\nApply the conversion factor directly to the given value.\nCompute 3702.5 / 100.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 3702.5}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=303 degrees and keep the unit as newtons.\nFinal: {\"answer\": [21.5132, -33.1275], \"unit\": \"N\"}", "dedupe_signature": "45bf1ed7b5f4babd6c82328a170a11118a5f2849679e388464c5b1e710fad533", "difficulty": "medium", "final_answer": {"answer": [21.5132, -33.1275], "unit": "N"}, "id": "vector_components_006601_39.5_303", "license": "Apache-2.0", "prompt": "A vector has magnitude 39.5 N at 303 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=303 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 303, "magnitude": 39.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [5.75, -14.75], \"unit\": \"dimensionless\"}", "dedupe_signature": "7fe1e7241d9971ce7b670a735cf1e14df058490fee12cfb12dec5ff4aaacb541", "difficulty": "medium", "final_answer": {"answer": [5.75, -14.75], "unit": "dimensionless"}, "id": "line_two_point_006602_-1.75_4.75_5.75_-14.75", "license": "Apache-2.0", "prompt": "A line passes through points (-1.75, -24.8125) and (4.75, 12.5625). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -1.75, "x2": 4.75, "y1": -24.8125, "y2": 12.5625}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef clamp_006604(x, lo, hi):\n    if lo > hi:\n        raise ValueError('lo must be <= hi')\n    return min(max(x, lo), hi)\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"clamp_006604\"}", "dedupe_signature": "4495620b0b2d408555a4dafa6e47d0c743542f9ec6dd0629949e802d29c72968", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "clamp_006604"}, "id": "code_006604_clamp_006604", "license": "Apache-2.0", "prompt": "Write a Python function clamp_006604(x, lo, hi) that clips x into the inclusive interval [lo, hi]. It must raise ValueError if lo > hi. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "clamp_006604"}, "verifier": {"function": "clamp_006604", "tests": ["assert clamp_006604(5, 0, 10) == 5", "assert clamp_006604(-2, 0, 10) == 0", "assert clamp_006604(12, 0, 10) == 10", "try:\n    clamp_006604(1, 3, 2)\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: target_schema, valid_examples.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"target_schema\", \"valid_examples\"]}", "dedupe_signature": "e9870e0abe4a9c638859fc164e7af6ba21b605ed6bc2aacc5fe223e9f9f87eba", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["target_schema", "valid_examples"]}, "id": "abstain_006605_target_schema_valid_examples", "license": "Apache-2.0", "prompt": "Write a parser that converts each laboratory sensor record from batch 13602 into the correct schema, but the prompt does not include the target schema or examples. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: target_schema, valid_examples.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["target_schema", "valid_examples"]}, "verifier": {"missing": ["target_schema", "valid_examples"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 6.7 kg and a = 12.25 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 82.075, \"unit\": \"N\"}", "dedupe_signature": "a023e2608b22d522ae552f7e6a92e77cdc4f500b3a405dfaef83e0e540c2d44f", "difficulty": "easy", "final_answer": {"answer": 82.075, "unit": "N"}, "id": "force_006606_6.7_12.25", "license": "Apache-2.0", "prompt": "A cart has mass 6.7 kg and measured acceleration 12.25 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 6.7 kg and a = 12.25 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 12.25, "mass": 6.7}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 20.15^2 and multiply by 0.5 * 10.8.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 2192.5215, \"unit\": \"J\"}", "dedupe_signature": "565e61227869572e56bf65ebd58993e7ce77fea003d3754fa05599c1f43a4f9b", "difficulty": "easy", "final_answer": {"answer": 2192.5215, "unit": "J"}, "id": "ke_006607_10.8_20.15", "license": "Apache-2.0", "prompt": "A body of mass 10.8 kg moves at 20.15 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 20.15^2 and multiply by 0.5 * 10.8.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 10.8, "velocity": 20.15}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=85 degrees through the sine of 2 theta.\n3. Substitute v=71 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 89.2314, \"unit\": \"m\"}", "dedupe_signature": "5614e81ee94dcf72f9ef4dbf4aa39e47ecc617a2cd468157c9adc37c82395769", "difficulty": "medium", "final_answer": {"answer": 89.2314, "unit": "m"}, "id": "projectile_range_006608_71_85", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 71 m/s and angle 85 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=85 degrees through the sine of 2 theta.\nSubstitute v=71 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 85, "gravity": 9.81, "speed": 71.0}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 1.79 * 8.314 * 559 / 67.5.\nFinal: {\"answer\": 123.2455, \"unit\": \"kPa\"}", "dedupe_signature": "b4ea064365e36462b42a7da8fb78be4a9d67a12acec19b04a5a6aa8604395ac8", "difficulty": "medium", "final_answer": {"answer": 123.2455, "unit": "kPa"}, "id": "ideal_gas_006609_1.79_559_67.5", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=1.79 mol, T=559 K, and V=67.5 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 1.79 * 8.314 * 559 / 67.5.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 1.79, "temp_k": 559, "volume_l": 67.5}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 505 * 2.82 * 37.\nFinal: {\"answer\": 52691.7, \"unit\": \"J\"}", "dedupe_signature": "b6caf44e3652779225dcffa4e5c0d8b632029effeb826d94e78a738711dce0ef", "difficulty": "easy", "final_answer": {"answer": 52691.7, "unit": "J"}, "id": "heat_q_006610_505_2.82_37", "license": "Apache-2.0", "prompt": "A 505 g sample has specific heat 2.82 J/(g*K). How much heat is needed to raise its temperature by 37 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 505 * 2.82 * 37.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 37, "heat_capacity": 2.82, "mass_g": 505}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 3.72 mol * 44.01 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 163.7172, \"unit\": \"g\"}", "dedupe_signature": "9ff4a1f4424143972206c252ffdfbc8b252baa70cfdb40cd0706e719f78dad23", "difficulty": "medium", "final_answer": {"answer": 163.7172, "unit": "g"}, "id": "stoich_mass_006613_carbon_dioxide_3.72", "license": "Apache-2.0", "prompt": "A sample contains 3.72 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 3.72 mol * 44.01 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "carbon dioxide", "molar_mass": 44.01, "moles": 3.72}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 4165 mL to 4.165 L.\n3. Compute M = 2.35 / 4.165.\nFinal: {\"answer\": 0.5642, \"unit\": \"mol/L\"}", "dedupe_signature": "4daa6d489d6e7e27e9e531ca06e888c35579e8c7f7f4b64d06e2ccf635193dd4", "difficulty": "medium", "final_answer": {"answer": 0.5642, "unit": "mol/L"}, "id": "molarity_006614_2.35_4165", "license": "Apache-2.0", "prompt": "A solution contains 2.35 mol of solute in 4165 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 4165 mL to 4.165 L.\nCompute M = 2.35 / 4.165.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 2.35, "volume_ml": 4165}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.51 y, so each step multiplies y by 1 - h*0.51.\n3. Apply that update for 7 steps and round the final state.\nFinal: {\"answer\": 0.004, \"unit\": \"state_units\"}", "dedupe_signature": "f2236def4b1d42042918545349638ff2d810de0796c219a20338b898fa154fc5", "difficulty": "medium", "final_answer": {"answer": 0.004, "unit": "state_units"}, "id": "euler_decay_006615_25.5_0.51_1.4_7", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.51 y with y(0)=25.5, step size h=1.4, for 7 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.51 y, so each step multiplies y by 1 - h*0.51.\nApply that update for 7 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 25.5, "rate": 0.51, "step": 1.4, "steps": 7}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.02 and add it to the current value.\nFinal: {\"answer\": [-1.389, 2.154, 1.254], \"unit\": \"temperature_units\"}", "dedupe_signature": "7b0b75c882cb4d94d93abe1ee36feea4edaa7590a5114c14e5ca35fbc529a48a", "difficulty": "hard", "final_answer": {"answer": [-1.389, 2.154, 1.254], "unit": "temperature_units"}, "id": "heat_step_006617_0.02_2.7_-1.55_2.25_1.25_0.45", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=2.7, right=0.45; current interior values are [-1.55, 2.25, 1.25]. Use r=0.02. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.02 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-1.55, 2.25, 1.25], "left": 2.7, "r": 0.02, "right": 0.45}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kelvin equals Celsius plus 273.15.\n2. Apply the conversion factor directly to the given value.\n3. Compute 134.5 + 273.15.\nFinal: {\"answer\": 407.65, \"unit\": \"K\"}", "dedupe_signature": "e9e541ec4e9e356937bc26277bcb0e66bb4c886f1377c8f7202c26983f2bd330", "difficulty": "easy", "final_answer": {"answer": 407.65, "unit": "K"}, "id": "unit_convert_006618_c_to_k_134.5", "license": "Apache-2.0", "prompt": "Convert 134.5 degC to K. Return the converted value with unit.", "reasoning_trace": "Kelvin equals Celsius plus 273.15.\nApply the conversion factor directly to the given value.\nCompute 134.5 + 273.15.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 134.5}, "verifier": {"formula": "value + 273.15", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=214 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-120.625, -81.3626], \"unit\": \"N\"}", "dedupe_signature": "20e7864858ca31b4e00ed464c2ca3086102a5f1dc00a994184dacc256e9342ab", "difficulty": "medium", "final_answer": {"answer": [-120.625, -81.3626], "unit": "N"}, "id": "vector_components_006619_145.5_214", "license": "Apache-2.0", "prompt": "A vector has magnitude 145.5 N at 214 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=214 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 214, "magnitude": 145.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-8.55, -19.5], \"unit\": \"dimensionless\"}", "dedupe_signature": "2bf5958bee8df6a5bab9fe875520bb06f0cbee03471c001cfccb6209fe68c8e8", "difficulty": "medium", "final_answer": {"answer": [-8.55, -19.5], "unit": "dimensionless"}, "id": "line_two_point_006620_2_9.25_-8.55_-19.5", "license": "Apache-2.0", "prompt": "A line passes through points (2, -36.6) and (9.25, -98.5875). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 2.0, "x2": 9.25, "y1": -36.6, "y2": -98.5875}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. coulomb per second is ampere\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "5d8052ed92372f7a7848766431c653d44318b4cfe89c3eb89cde64e681927328", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_006621_consistent_8b38953d_791740", "license": "Apache-2.0", "prompt": "In model card equation case 791740, check dimensional consistency for I = Q / t. The left side has dimensions A and the right side has dimensions A. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\ncoulomb per second is ampere\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "I = Q / t"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\nimport math\n\ndef unit_vector_006622(x, y):\n    norm = math.hypot(x, y)\n    if norm == 0:\n        raise ValueError('zero vector has no direction')\n    return (x / norm, y / norm)\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"unit_vector_006622\"}", "dedupe_signature": "f4cff406c957bdb522069c43f62d8c59615a10d7c806e45d7cf5d3541fce0b20", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "unit_vector_006622"}, "id": "code_006622_unit_vector_006622", "license": "Apache-2.0", "prompt": "Write a Python function unit_vector_006622(x, y) that returns the 2D unit vector as a tuple. Raise ValueError for the zero vector. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "unit_vector_006622"}, "verifier": {"function": "unit_vector_006622", "tests": ["ux, uy = unit_vector_006622(3, 4); assert abs(ux - 0.6) < 1e-12 and abs(uy - 0.8) < 1e-12", "assert unit_vector_006622(0, 5) == (0, 1)", "try:\n    unit_vector_006622(0, 0)\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: required_fields, allowed_transformations.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"required_fields\", \"allowed_transformations\"]}", "dedupe_signature": "d5a808a98eab6d81af0c40e9458d18c6559aee7725c961963a8e155a9b35ecf8", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["required_fields", "allowed_transformations"]}, "id": "abstain_006623_required_fields_allowed_transformations", "license": "Apache-2.0", "prompt": "Write a sanitizer for valid laboratory survey records in release 208030, but the prompt does not state which fields are required or which transformations are allowed. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: required_fields, allowed_transformations.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["required_fields", "allowed_transformations"]}, "verifier": {"missing": ["required_fields", "allowed_transformations"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 24.95 kg and a = 9.05 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 225.7975, \"unit\": \"N\"}", "dedupe_signature": "5c22799cb111ea8a71004dd234426866de4967d3da5dffb632c80ce529ff3896", "difficulty": "easy", "final_answer": {"answer": 225.7975, "unit": "N"}, "id": "force_006624_24.95_9.05", "license": "Apache-2.0", "prompt": "A cart has mass 24.95 kg and measured acceleration 9.05 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 24.95 kg and a = 9.05 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 9.05, "mass": 24.95}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 1.6^2 and multiply by 0.5 * 9.35.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 11.968, \"unit\": \"J\"}", "dedupe_signature": "479910be4a7f133051ac30426d2db4b639e7752a1ff2529ddc59a1b9b119e68a", "difficulty": "easy", "final_answer": {"answer": 11.968, "unit": "J"}, "id": "ke_006625_9.35_1.6", "license": "Apache-2.0", "prompt": "A body of mass 9.35 kg moves at 1.6 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 1.6^2 and multiply by 0.5 * 9.35.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 9.35, "velocity": 1.6}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=79 degrees through the sine of 2 theta.\n3. Substitute v=40.8 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 63.5663, \"unit\": \"m\"}", "dedupe_signature": "191f99abdd67eb5be4c1a6cecb8d466d346fdd4c7b0b81f403fac7f4b6656e2f", "difficulty": "medium", "final_answer": {"answer": 63.5663, "unit": "m"}, "id": "projectile_range_006626_40.8_79", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 40.8 m/s and angle 79 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=79 degrees through the sine of 2 theta.\nSubstitute v=40.8 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 79, "gravity": 9.81, "speed": 40.8}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 5.46 * 8.314 * 474 / 31.0.\nFinal: {\"answer\": 694.0956, \"unit\": \"kPa\"}", "dedupe_signature": "d1d2882f69bbdb45c16a43dde456cd8ca37a0c52f4b0bbe3cdfe9f65ac52a920", "difficulty": "medium", "final_answer": {"answer": 694.0956, "unit": "kPa"}, "id": "ideal_gas_006627_5.46_474_31.0", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=5.46 mol, T=474 K, and V=31.0 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 5.46 * 8.314 * 474 / 31.0.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 5.46, "temp_k": 474, "volume_l": 31.0}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1920 * 3.275 * 19.\nFinal: {\"answer\": 119472.0, \"unit\": \"J\"}", "dedupe_signature": "e3aaf1bf6016fbe986ddcb47ed3c5d7ec8afed0781a3bb7079df8b4a13f83a78", "difficulty": "easy", "final_answer": {"answer": 119472.0, "unit": "J"}, "id": "heat_q_006628_1920_3.275_19", "license": "Apache-2.0", "prompt": "A 1920 g sample has specific heat 3.275 J/(g*K). How much heat is needed to raise its temperature by 19 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1920 * 3.275 * 19.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 19, "heat_capacity": 3.275, "mass_g": 1920}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=750 mg, t=329.5 h, and T_half=59.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 16.1441, \"unit\": \"mg\"}", "dedupe_signature": "91df45ceaf9db71124fe837f40b6f3288deee1c91dfdfa0d2af78f9303335b38", "difficulty": "medium", "final_answer": {"answer": 16.1441, "unit": "mg"}, "id": "half_life_006630_750_59.5_329.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 750 mg. Its half-life is 59.5 hours. How many mg remain after 329.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=750 mg, t=329.5 h, and T_half=59.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 329.5, "half_life": 59.5, "initial_amount": 750.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 7.28 mol * 100.087 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 728.6334, \"unit\": \"g\"}", "dedupe_signature": "2debc678edf849159805a69a90d9f60c36e8646ea3572d73280340b953fe1956", "difficulty": "medium", "final_answer": {"answer": 728.6334, "unit": "g"}, "id": "stoich_mass_006631_calcium_carbonate_7.28", "license": "Apache-2.0", "prompt": "A sample contains 7.28 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 7.28 mol * 100.087 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "calcium carbonate", "molar_mass": 100.087, "moles": 7.28}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 4760 mL to 4.76 L.\n3. Compute M = 4.56 / 4.76.\nFinal: {\"answer\": 0.958, \"unit\": \"mol/L\"}", "dedupe_signature": "eb28daeba7c186535cf620e5bd90279396d46a311a6ba97fe3e065031625ba7a", "difficulty": "medium", "final_answer": {"answer": 0.958, "unit": "mol/L"}, "id": "molarity_006632_4.56_4760", "license": "Apache-2.0", "prompt": "A solution contains 4.56 mol of solute in 4760 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 4760 mL to 4.76 L.\nCompute M = 4.56 / 4.76.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 4.56, "volume_ml": 4760}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(0)=-19 and f(3.6)=-44.2.\n3. The interval width is 3.6.\nFinal: {\"answer\": -113.76, \"unit\": \"area_units\"}", "dedupe_signature": "fb4401fc7fc41733e18d8b1c6e97ecfff1f87c67a205e06394399cea2395622e", "difficulty": "medium", "final_answer": {"answer": -113.76, "unit": "area_units"}, "id": "trapz_linear_006634_-7_-19_0_3.6", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-7x+-19 from x=0 to x=3.6. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(0)=-19 and f(3.6)=-44.2.\nThe interval width is 3.6.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -19.0, "slope": -7.0, "x0": 0.0, "x1": 3.6}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.14 and add it to the current value.\nFinal: {\"answer\": [0.959, -0.088, 0.394], \"unit\": \"temperature_units\"}", "dedupe_signature": "474fdbc05ca496a3383fbbb7b4e1125a795767812fdcc8cde9f922f2e6a7b8d4", "difficulty": "hard", "final_answer": {"answer": [0.959, -0.088, 0.394], "unit": "temperature_units"}, "id": "heat_step_006635_0.14_-1.6_1.75_-0.55_0.45_1.05", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-1.6, right=1.05; current interior values are [1.75, -0.55, 0.45]. Use r=0.14. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.14 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [1.75, -0.55, 0.45], "left": -1.6, "r": 0.14, "right": 1.05}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 27536.0 / 1000.\nFinal: {\"answer\": 27.536, \"unit\": \"kg\"}", "dedupe_signature": "1df4ebe8a52e267a728e814dadbacc432f6d9b11e2ac91885e12003682c4b336", "difficulty": "easy", "final_answer": {"answer": 27.536, "unit": "kg"}, "id": "unit_convert_006636_g_to_kg_27536", "license": "Apache-2.0", "prompt": "Convert 27536 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 27536.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 27536.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=178 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-36.4778, 1.2738], \"unit\": \"N\"}", "dedupe_signature": "6d3d63523b69cf622112343ddebf9c459dd885c499ea0ffac7f559b4800590e4", "difficulty": "medium", "final_answer": {"answer": [-36.4778, 1.2738], "unit": "N"}, "id": "vector_components_006637_36.5_178", "license": "Apache-2.0", "prompt": "A vector has magnitude 36.5 N at 178 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=178 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 178, "magnitude": 36.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-7.3, -22.75], \"unit\": \"dimensionless\"}", "dedupe_signature": "271934c695ddaccd23d5e44a3b93ed1fa5841ea98af5c7cc5c4df1ab301e9448", "difficulty": "medium", "final_answer": {"answer": [-7.3, -22.75], "unit": "dimensionless"}, "id": "line_two_point_006638_-2.5_2.75_-7.3_-22.75", "license": "Apache-2.0", "prompt": "A line passes through points (-2.5, -4.5) and (2.75, -42.825). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -2.5, "x2": 2.75, "y1": -4.5, "y2": -42.825}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. density times acceleration times height gives kg/(m*s^2), or pascal\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "dd3912928b7136ca7a70eb64253b14fbefdfad704a57a5b8a1104f593ae55ded", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_006639_consistent_b7d3eed1_125157", "license": "Apache-2.0", "prompt": "In model card equation case 125157, check dimensional consistency for p = rho * g * h. The left side has dimensions Pa and the right side has dimensions Pa. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\ndensity times acceleration times height gives kg/(m*s^2), or pascal\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "p = rho * g * h"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef finite_differences_006640(values):\n    return [values[i + 1] - values[i] for i in range(len(values) - 1)]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"finite_differences_006640\"}", "dedupe_signature": "3a09bb843fd4792f33a222d5b09e6ba15c97322a0d0bcd88cc5714e1c3ad932f", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "finite_differences_006640"}, "id": "code_006640_finite_differences_006640", "license": "Apache-2.0", "prompt": "Write a Python function finite_differences_006640(values) that returns the list of successive differences values[i+1] - values[i]. It must return [] for fewer than two values. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "finite_differences_006640"}, "verifier": {"function": "finite_differences_006640", "tests": ["assert finite_differences_006640([1, 4, 9, 16]) == [3, 5, 7]", "assert finite_differences_006640([5]) == []", "assert finite_differences_006640([]) == []"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: launch_angle_or_vertical_velocity.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"launch_angle_or_vertical_velocity\"]}", "dedupe_signature": "468c9619a336c1e69ed9fb7ae977905e793c634e2b8401c25c2463f055c37289", "difficulty": "easy", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["launch_angle_or_vertical_velocity"]}, "id": "abstain_006641_launch_angle_or_vertical_velocity", "license": "Apache-2.0", "prompt": "Compute projectile range on level ground. The prompt gives initial speed 44.5 m/s but does not give launch angle or vertical velocity. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: launch_angle_or_vertical_velocity.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["launch_angle_or_vertical_velocity"]}, "verifier": {"missing": ["launch_angle_or_vertical_velocity"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 6.15 kg and a = 15.1 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 92.865, \"unit\": \"N\"}", "dedupe_signature": "e2588156cb2b8c92f056ddfbb93bb0e0a2ba4bb0b358cc86366d3a7a821015b0", "difficulty": "easy", "final_answer": {"answer": 92.865, "unit": "N"}, "id": "force_006642_6.15_15.1", "license": "Apache-2.0", "prompt": "A cart has mass 6.15 kg and measured acceleration 15.1 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 6.15 kg and a = 15.1 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 15.1, "mass": 6.15}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 31.95^2 and multiply by 0.5 * 28.8.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 14699.556, \"unit\": \"J\"}", "dedupe_signature": "0bff5a260a2f0433f59795fb3435a5b26bb4866cda0151b19fddc056ad5bce33", "difficulty": "easy", "final_answer": {"answer": 14699.556, "unit": "J"}, "id": "ke_006643_28.8_31.95", "license": "Apache-2.0", "prompt": "A body of mass 28.8 kg moves at 31.95 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 31.95^2 and multiply by 0.5 * 28.8.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 28.8, "velocity": 31.95}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=47 degrees through the sine of 2 theta.\n3. Substitute v=20.3 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 41.9048, \"unit\": \"m\"}", "dedupe_signature": "8f4350c3d04220c56f0ecc39cb82cc9dd9b9f26e37305ed344798b1695b514b0", "difficulty": "medium", "final_answer": {"answer": 41.9048, "unit": "m"}, "id": "projectile_range_006644_20.3_47", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 20.3 m/s and angle 47 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=47 degrees through the sine of 2 theta.\nSubstitute v=20.3 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 47, "gravity": 9.81, "speed": 20.3}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 4.16 * 8.314 * 277 / 14.1.\nFinal: {\"answer\": 679.4602, \"unit\": \"kPa\"}", "dedupe_signature": "b28239713b79023bed8eb612d6d666b9b5bca6d9ad67925dcc85b71519849701", "difficulty": "medium", "final_answer": {"answer": 679.4602, "unit": "kPa"}, "id": "ideal_gas_006645_4.16_277_14.1", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=4.16 mol, T=277 K, and V=14.1 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 4.16 * 8.314 * 277 / 14.1.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 4.16, "temp_k": 277, "volume_l": 14.1}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=198.7 V and R=118.5 ohm.\nFinal: {\"answer\": 333.1788, \"unit\": \"W\"}", "dedupe_signature": "d03aefc60aa97de0c1cc4476c8b8af21d8d44e1edf874195d447c7ed9f3b7674", "difficulty": "easy", "final_answer": {"answer": 333.1788, "unit": "W"}, "id": "ohm_power_006647_198.7_118.5", "license": "Apache-2.0", "prompt": "A resistor has resistance 118.5 ohm and voltage 198.7 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=198.7 V and R=118.5 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 118.5, "voltage": 198.7}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 6.69 mol * 58.44 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 390.9636, \"unit\": \"g\"}", "dedupe_signature": "a999ffa5cba87c32565e2418a5dbdc258cf575e7246ef3550488e0eb8d4a86f5", "difficulty": "medium", "final_answer": {"answer": 390.9636, "unit": "g"}, "id": "stoich_mass_006649_sodium_chloride_6.69", "license": "Apache-2.0", "prompt": "A sample contains 6.69 mol of sodium chloride. Using molar mass 58.44 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 6.69 mol * 58.44 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "sodium chloride", "molar_mass": 58.44, "moles": 6.69}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 3885 mL to 3.885 L.\n3. Compute M = 4.95 / 3.885.\nFinal: {\"answer\": 1.2741, \"unit\": \"mol/L\"}", "dedupe_signature": "9934987a821eeb6e837082b9fe856f9c239ec299311806acb93598e41138cd82", "difficulty": "medium", "final_answer": {"answer": 1.2741, "unit": "mol/L"}, "id": "molarity_006650_4.95_3885", "license": "Apache-2.0", "prompt": "A solution contains 4.95 mol of solute in 3885 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 3885 mL to 3.885 L.\nCompute M = 4.95 / 3.885.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 4.95, "volume_ml": 3885}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.63 y, so each step multiplies y by 1 - h*0.63.\n3. Apply that update for 7 steps and round the final state.\nFinal: {\"answer\": 0.0076, \"unit\": \"state_units\"}", "dedupe_signature": "170ff1d0f6c6320d6ce6f918d270ab5ad1df022c7754dfd058459316fe8472bf", "difficulty": "medium", "final_answer": {"answer": 0.0076, "unit": "state_units"}, "id": "euler_decay_006651_15_0.63_1.05_7", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.63 y with y(0)=15, step size h=1.05, for 7 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.63 y, so each step multiplies y by 1 - h*0.63.\nApply that update for 7 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 15.0, "rate": 0.63, "step": 1.05, "steps": 7}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.2 and add it to the current value.\nFinal: {\"answer\": [1.01, 1.63, 0.54], \"unit\": \"temperature_units\"}", "dedupe_signature": "4328175b20670fc040f5dc8434a6612e3db54045ac9f625c681e2e480978ea1e", "difficulty": "hard", "final_answer": {"answer": [1.01, 1.63, 0.54], "unit": "temperature_units"}, "id": "heat_step_006653_0.2_-1.7_1.4_2.55_-0.9_2.85", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-1.7, right=2.85; current interior values are [1.4, 2.55, -0.9]. Use r=0.2. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.2 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [1.4, 2.55, -0.9], "left": -1.7, "r": 0.2, "right": 2.85}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 100 centimeters in one meter.\n2. Apply the conversion factor directly to the given value.\n3. Compute 2386.5 / 100.\nFinal: {\"answer\": 23.865, \"unit\": \"m\"}", "dedupe_signature": "4b91901407fbd016099d6d4a59b41b8af55860aafae7502242557344dc3b7f00", "difficulty": "easy", "final_answer": {"answer": 23.865, "unit": "m"}, "id": "unit_convert_006654_cm_to_m_2386.5", "license": "Apache-2.0", "prompt": "Convert 2386.5 cm to m. Return the converted value with unit.", "reasoning_trace": "There are 100 centimeters in one meter.\nApply the conversion factor directly to the given value.\nCompute 2386.5 / 100.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 2386.5}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=328 degrees and keep the unit as newtons.\nFinal: {\"answer\": [312.0817, -195.0103], \"unit\": \"N\"}", "dedupe_signature": "6c0984b663748d6558a0ca5e22e823c0c9fb082939b7b200491a90dec070c97d", "difficulty": "medium", "final_answer": {"answer": [312.0817, -195.0103], "unit": "N"}, "id": "vector_components_006655_368_328", "license": "Apache-2.0", "prompt": "A vector has magnitude 368 N at 328 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=328 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 328, "magnitude": 368.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. mass times acceleration has newton dimensions\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "321427834c410c2e218c5bddc15cfb9f79ae87b142b9c461729a42fb075fd953", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_006657_consistent_03f5e041_799716", "license": "Apache-2.0", "prompt": "In field worksheet case 799716, check dimensional consistency for F = m * a. The left side has dimensions kg*m/s^2 and the right side has dimensions kg*m/s^2. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nmass times acceleration has newton dimensions\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "F = m * a"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef normalize_006658(values):\n    total = sum(values)\n    if total == 0:\n        raise ValueError('cannot normalize zero-sum values')\n    return [v / total for v in values]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"normalize_006658\"}", "dedupe_signature": "164e03700d3429c6d7351fe26a45aa3c7a626314c64b25fa4d464d8c6cb9a698", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "normalize_006658"}, "id": "code_006658_normalize_006658", "license": "Apache-2.0", "prompt": "Write a Python function normalize_006658(values) that returns a new list whose values sum to 1. Raise ValueError if the sum is zero. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "normalize_006658"}, "verifier": {"function": "normalize_006658", "tests": ["out = normalize_006658([2, 3, 5]); assert len(out) == 3", "assert abs(sum(normalize_006658([2, 3, 5])) - 1.0) < 1e-12", "assert normalize_006658([1, 1]) == [0.5, 0.5]", "try:\n    normalize_006658([1, -1])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: target_schema, valid_examples.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"target_schema\", \"valid_examples\"]}", "dedupe_signature": "e82513e09fef58c709892deca99dbaf08372a5e066c564db05a9d6fa8c34e614", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["target_schema", "valid_examples"]}, "id": "abstain_006659_target_schema_valid_examples", "license": "Apache-2.0", "prompt": "Write a parser that converts each mobile clinical record from batch 951128 into the correct schema, but the prompt does not include the target schema or examples. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: target_schema, valid_examples.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["target_schema", "valid_examples"]}, "verifier": {"missing": ["target_schema", "valid_examples"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 11.65^2 and multiply by 0.5 * 24.45.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 1659.2076, \"unit\": \"J\"}", "dedupe_signature": "ef803bff732139159b9f6963672eaa947e3d2ed7b13a8d1758d4509e3104783e", "difficulty": "easy", "final_answer": {"answer": 1659.2076, "unit": "J"}, "id": "ke_006661_24.45_11.65", "license": "Apache-2.0", "prompt": "A body of mass 24.45 kg moves at 11.65 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 11.65^2 and multiply by 0.5 * 24.45.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 24.45, "velocity": 11.65}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 1.75 * 8.314 * 601 / 36.4.\nFinal: {\"answer\": 240.2266, \"unit\": \"kPa\"}", "dedupe_signature": "b03dabf4c908357c879e9cfd4c16b450b6a23ee96d3d74889cc27aa59642d050", "difficulty": "medium", "final_answer": {"answer": 240.2266, "unit": "kPa"}, "id": "ideal_gas_006663_1.75_601_36.4", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=1.75 mol, T=601 K, and V=36.4 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 1.75 * 8.314 * 601 / 36.4.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 1.75, "temp_k": 601, "volume_l": 36.4}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 695 * 1.375 * 94.\nFinal: {\"answer\": 89828.75, \"unit\": \"J\"}", "dedupe_signature": "5db3ab28bab191ed362d43f403fa1902d631a0ec6118a33f7cd53aaadacefe90", "difficulty": "easy", "final_answer": {"answer": 89828.75, "unit": "J"}, "id": "heat_q_006664_695_1.375_94", "license": "Apache-2.0", "prompt": "A 695 g sample has specific heat 1.375 J/(g*K). How much heat is needed to raise its temperature by 94 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 695 * 1.375 * 94.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 94, "heat_capacity": 1.375, "mass_g": 695}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=192.1 V and R=39 ohm.\nFinal: {\"answer\": 946.2156, \"unit\": \"W\"}", "dedupe_signature": "eb231f368782cebf1d3b49b94203484212f9391fa13e25c0f7f9893f9fdf6544", "difficulty": "easy", "final_answer": {"answer": 946.2156, "unit": "W"}, "id": "ohm_power_006665_192.1_39", "license": "Apache-2.0", "prompt": "A resistor has resistance 39 ohm and voltage 192.1 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=192.1 V and R=39 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 39.0, "voltage": 192.1}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=538 mg, t=23 h, and T_half=43 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 371.3353, \"unit\": \"mg\"}", "dedupe_signature": "8341903e827e8a82cf6b7c8535a6860dad109c631550a270fac6d93ddae2b69d", "difficulty": "medium", "final_answer": {"answer": 371.3353, "unit": "mg"}, "id": "half_life_006666_538_43_23", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 538 mg. Its half-life is 43 hours. How many mg remain after 23 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=538 mg, t=23 h, and T_half=43 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 23.0, "half_life": 43.0, "initial_amount": 538.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -1 y, so each step multiplies y by 1 - h*1.\n3. Apply that update for 7 steps and round the final state.\nFinal: {\"answer\": -0.6858, \"unit\": \"state_units\"}", "dedupe_signature": "6f8bee53025d4756fbc52c4677b0297b993a0e822faef38ecb10629118d21ca7", "difficulty": "medium", "final_answer": {"answer": -0.6858, "unit": "state_units"}, "id": "euler_decay_006669_24.5_1_1.6_7", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -1 y with y(0)=24.5, step size h=1.6, for 7 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -1 y, so each step multiplies y by 1 - h*1.\nApply that update for 7 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 24.5, "rate": 1.0, "step": 1.6, "steps": 7}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(7.4)=13.76 and f(8.6)=19.04.\n3. The interval width is 1.2.\nFinal: {\"answer\": 19.68, \"unit\": \"area_units\"}", "dedupe_signature": "cd8df556f0fe330decf3ef3269a0640d32b8db8b0c53b904010f24039b60a7c6", "difficulty": "medium", "final_answer": {"answer": 19.68, "unit": "area_units"}, "id": "trapz_linear_006670_4.4_-18.8_7.4_8.6", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=4.4x+-18.8 from x=7.4 to x=8.6. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(7.4)=13.76 and f(8.6)=19.04.\nThe interval width is 1.2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -18.8, "slope": 4.4, "x0": 7.4, "x1": 8.6}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kelvin equals Celsius plus 273.15.\n2. Apply the conversion factor directly to the given value.\n3. Compute -30.0 + 273.15.\nFinal: {\"answer\": 243.15, \"unit\": \"K\"}", "dedupe_signature": "6fc1f9ec3a7fa97da9121e6b94153ad58afbeeb06219138c83271592b6e6a276", "difficulty": "easy", "final_answer": {"answer": 243.15, "unit": "K"}, "id": "unit_convert_006672_c_to_k_-30", "license": "Apache-2.0", "prompt": "Convert -30 degC to K. Return the converted value with unit.", "reasoning_trace": "Kelvin equals Celsius plus 273.15.\nApply the conversion factor directly to the given value.\nCompute -30.0 + 273.15.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": -30.0}, "verifier": {"formula": "value + 273.15", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=11 degrees and keep the unit as newtons.\nFinal: {\"answer\": [213.9947, 41.5964], \"unit\": \"N\"}", "dedupe_signature": "73a70cf92515155d9cce133023788b324118d5dcc3fc463f4f499900b34b13e3", "difficulty": "medium", "final_answer": {"answer": [213.9947, 41.5964], "unit": "N"}, "id": "vector_components_006673_218_11", "license": "Apache-2.0", "prompt": "A vector has magnitude 218 N at 11 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=11 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 11, "magnitude": 218.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [3.35, -3.5], \"unit\": \"dimensionless\"}", "dedupe_signature": "845e1c72eab2f0d132b81ed1776125dc45b84e742d501bad18fd196012cf45ef", "difficulty": "medium", "final_answer": {"answer": [3.35, -3.5], "unit": "dimensionless"}, "id": "line_two_point_006674_10.25_18.75_3.35_-3.5", "license": "Apache-2.0", "prompt": "A line passes through points (10.25, 30.8375) and (18.75, 59.3125). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 10.25, "x2": 18.75, "y1": 30.8375, "y2": 59.3125}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. energy divided by length is force, not spring constant\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "446e2f8acc04f5a566651366f9ee6d6fffaac32ba2459fda81d50a1cd3194796", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_006675_inconsistent_56040f5d_517571", "license": "Apache-2.0", "prompt": "In field worksheet case 517571, check dimensional consistency for k = E / x. The left side has dimensions N/m and the right side has dimensions J/m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nenergy divided by length is force, not spring constant\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "k = E / x"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef weighted_sum_006676(values, weights):\n    if len(values) != len(weights):\n        raise ValueError('length mismatch')\n    return sum(value * weight for value, weight in zip(values, weights))\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"weighted_sum_006676\"}", "dedupe_signature": "e3118c4828c393ca0a156af2ee64f56783b0e5cf5359b9226415646b579a02af", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "weighted_sum_006676"}, "id": "code_006676_weighted_sum_006676", "license": "Apache-2.0", "prompt": "Write a Python function weighted_sum_006676(values, weights) that returns sum(value*weight). Raise ValueError when the two inputs have different lengths. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "weighted_sum_006676"}, "verifier": {"function": "weighted_sum_006676", "tests": ["assert weighted_sum_006676([2, 3], [4, 5]) == 23", "assert weighted_sum_006676([], []) == 0", "try:\n    weighted_sum_006676([1], [1, 2])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: launch_angle_or_vertical_velocity.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"launch_angle_or_vertical_velocity\"]}", "dedupe_signature": "ee378ad7c22b82e9f70e01fd2ac58f1c2757f2780b0511c048afda745c2c7215", "difficulty": "easy", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["launch_angle_or_vertical_velocity"]}, "id": "abstain_006677_launch_angle_or_vertical_velocity", "license": "Apache-2.0", "prompt": "Compute projectile range on level ground. The prompt gives initial speed 43.4 m/s but does not give launch angle or vertical velocity. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: launch_angle_or_vertical_velocity.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["launch_angle_or_vertical_velocity"]}, "verifier": {"missing": ["launch_angle_or_vertical_velocity"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 7.35 kg and a = 2.45 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 18.0075, \"unit\": \"N\"}", "dedupe_signature": "a8dd8ea050cd14c2201a2403dde87d2929af9a9ab12cbbb0703723e9adee9d0b", "difficulty": "easy", "final_answer": {"answer": 18.0075, "unit": "N"}, "id": "force_006678_7.35_2.45", "license": "Apache-2.0", "prompt": "A cart has mass 7.35 kg and measured acceleration 2.45 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 7.35 kg and a = 2.45 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 2.45, "mass": 7.35}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 30.9^2 and multiply by 0.5 * 23.5.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 11219.0175, \"unit\": \"J\"}", "dedupe_signature": "bff82fe170be2225e6e04d8544fbb84bc9a11f3400999df4a2fed26acd1e89b3", "difficulty": "easy", "final_answer": {"answer": 11219.0175, "unit": "J"}, "id": "ke_006679_23.5_30.9", "license": "Apache-2.0", "prompt": "A body of mass 23.5 kg moves at 30.9 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 30.9^2 and multiply by 0.5 * 23.5.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 23.5, "velocity": 30.9}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=68 degrees through the sine of 2 theta.\n3. Substitute v=53.1 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 199.6601, \"unit\": \"m\"}", "dedupe_signature": "6ec6ca4d7826c3c7848e90cd5b11f2ef766df370196ab1338beca25d8d34b056", "difficulty": "medium", "final_answer": {"answer": 199.6601, "unit": "m"}, "id": "projectile_range_006680_53.1_68", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 53.1 m/s and angle 68 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=68 degrees through the sine of 2 theta.\nSubstitute v=53.1 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 68, "gravity": 9.81, "speed": 53.1}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1575 * 2.785 * 6.\nFinal: {\"answer\": 26318.25, \"unit\": \"J\"}", "dedupe_signature": "57f5664c87744e03ef15a75529824ca91d2b965674bc6e3e38a42b4badf24ea7", "difficulty": "easy", "final_answer": {"answer": 26318.25, "unit": "J"}, "id": "heat_q_006682_1575_2.785_6", "license": "Apache-2.0", "prompt": "A 1575 g sample has specific heat 2.785 J/(g*K). How much heat is needed to raise its temperature by 6 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1575 * 2.785 * 6.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 6, "heat_capacity": 2.785, "mass_g": 1575}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=125 V and R=33.9 ohm.\nFinal: {\"answer\": 460.9145, \"unit\": \"W\"}", "dedupe_signature": "79c40d076015248ce9045f0bf2b9d52903861d5d310df05030c139317fd243a4", "difficulty": "easy", "final_answer": {"answer": 460.9145, "unit": "W"}, "id": "ohm_power_006683_125_33.9", "license": "Apache-2.0", "prompt": "A resistor has resistance 33.9 ohm and voltage 125 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=125 V and R=33.9 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 33.9, "voltage": 125.0}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 3.16 mol * 100.087 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 316.2749, \"unit\": \"g\"}", "dedupe_signature": "3bbc8563894705fcf274c7a90ecf91178a3ea90c838f3f783e3edf6a8c1d4f72", "difficulty": "medium", "final_answer": {"answer": 316.2749, "unit": "g"}, "id": "stoich_mass_006685_calcium_carbonate_3.16", "license": "Apache-2.0", "prompt": "A sample contains 3.16 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 3.16 mol * 100.087 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "calcium carbonate", "molar_mass": 100.087, "moles": 3.16}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 2015 mL to 2.015 L.\n3. Compute M = 4.655 / 2.015.\nFinal: {\"answer\": 2.3102, \"unit\": \"mol/L\"}", "dedupe_signature": "fd77f84d6749179238d1f866d6589b261be12e9f8e74a266121009187a0947b1", "difficulty": "medium", "final_answer": {"answer": 2.3102, "unit": "mol/L"}, "id": "molarity_006686_4.655_2015", "license": "Apache-2.0", "prompt": "A solution contains 4.655 mol of solute in 2015 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 2015 mL to 2.015 L.\nCompute M = 4.655 / 2.015.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 4.655, "volume_ml": 2015}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.83 y, so each step multiplies y by 1 - h*0.83.\n3. Apply that update for 12 steps and round the final state.\nFinal: {\"answer\": 0.0027, \"unit\": \"state_units\"}", "dedupe_signature": "cab048845f1d6ca43c2571ca71ae0632ea30515e6e1a5b73cda3264fb4d9e266", "difficulty": "medium", "final_answer": {"answer": 0.0027, "unit": "state_units"}, "id": "euler_decay_006687_36_0.83_1.75_12", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.83 y with y(0)=36, step size h=1.75, for 12 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.83 y, so each step multiplies y by 1 - h*0.83.\nApply that update for 12 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 36.0, "rate": 0.83, "step": 1.75, "steps": 12}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-1.1)=10.58 and f(7.3)=37.46.\n3. The interval width is 8.4.\nFinal: {\"answer\": 201.768, \"unit\": \"area_units\"}", "dedupe_signature": "7e427ce84acde148a8d26e6d54b1c98ae804a275a082890eb0b0abffcf327cd5", "difficulty": "medium", "final_answer": {"answer": 201.768, "unit": "area_units"}, "id": "trapz_linear_006688_3.2_14.1_-1.1_7.3", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=3.2x+14.1 from x=-1.1 to x=7.3. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-1.1)=10.58 and f(7.3)=37.46.\nThe interval width is 8.4.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 14.1, "slope": 3.2, "x0": -1.1, "x1": 7.300000000000001}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.26 and add it to the current value.\nFinal: {\"answer\": [1.061, 0.95, 0.912], \"unit\": \"temperature_units\"}", "dedupe_signature": "a94e62ac23c5c980d363fc6f0d2fe9375e1798405279adb511176f8a9c0594c0", "difficulty": "hard", "final_answer": {"answer": [1.061, 0.95, 0.912], "unit": "temperature_units"}, "id": "heat_step_006689_0.26_0.0_2.4_-0.35_1.9_0.35", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=0, right=0.35; current interior values are [2.4, -0.35, 1.9]. Use r=0.26. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.26 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [2.4, -0.35, 1.9], "left": 0.0, "r": 0.26, "right": 0.35}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=225 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-13.0815, -13.0815], \"unit\": \"N\"}", "dedupe_signature": "4b88a116e4cebe98916378b7e889ae8baaf4f18e724ebb9b38e676c02fa59e54", "difficulty": "medium", "final_answer": {"answer": [-13.0815, -13.0815], "unit": "N"}, "id": "vector_components_006691_18.5_225", "license": "Apache-2.0", "prompt": "A vector has magnitude 18.5 N at 225 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=225 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 225, "magnitude": 18.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. amount times volume is not concentration\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "6f6b10f00cfa0a9f16a6047bd5d3b291ee571561da3ba6e5754cdd69e41bbb5b", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_006693_inconsistent_74ac0b02_682808", "license": "Apache-2.0", "prompt": "In quality-control check case 682808, check dimensional consistency for C = n * V. The left side has dimensions mol/L and the right side has dimensions mol*L. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\namount times volume is not concentration\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "C = n * V"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\nimport math\n\ndef unit_vector_006694(x, y):\n    norm = math.hypot(x, y)\n    if norm == 0:\n        raise ValueError('zero vector has no direction')\n    return (x / norm, y / norm)\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"unit_vector_006694\"}", "dedupe_signature": "e47c87dca900307d44381770f378351cb934b395952c1e6ed9f3a1338fc0541b", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "unit_vector_006694"}, "id": "code_006694_unit_vector_006694", "license": "Apache-2.0", "prompt": "Write a Python function unit_vector_006694(x, y) that returns the 2D unit vector as a tuple. Raise ValueError for the zero vector. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "unit_vector_006694"}, "verifier": {"function": "unit_vector_006694", "tests": ["ux, uy = unit_vector_006694(3, 4); assert abs(ux - 0.6) < 1e-12 and abs(uy - 0.8) < 1e-12", "assert unit_vector_006694(0, 5) == (0, 1)", "try:\n    unit_vector_006694(0, 0)\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: recurrence, objective, tie_breaking_rule.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"recurrence\", \"objective\", \"tie_breaking_rule\"]}", "dedupe_signature": "3a11b119351840572006f28cc5ab115b40f5c88fccff363475091c6943ded4dd", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["recurrence", "objective", "tie_breaking_rule"]}, "id": "abstain_006695_recurrence_objective_tie_breaking_rule", "license": "Apache-2.0", "prompt": "Write a dynamic-programming solver for a routing scoring problem with 3026 items and budget 80945, but the recurrence, objective, and tie-breaking rule are all absent. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: recurrence, objective, tie_breaking_rule.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["recurrence", "objective", "tie_breaking_rule"]}, "verifier": {"missing": ["recurrence", "objective", "tie_breaking_rule"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 20.55 kg and a = 12 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 246.6, \"unit\": \"N\"}", "dedupe_signature": "64778225330f8dc3c80b9ebd75e4af97541a1a1d603d04e691ae08b1ffeeee29", "difficulty": "easy", "final_answer": {"answer": 246.6, "unit": "N"}, "id": "force_006696_20.55_12", "license": "Apache-2.0", "prompt": "A cart has mass 20.55 kg and measured acceleration 12 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 20.55 kg and a = 12 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 12.0, "mass": 20.55}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 18.4^2 and multiply by 0.5 * 9.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 1523.52, \"unit\": \"J\"}", "dedupe_signature": "d964a229c6f147738c108597dc873c499eab32ed3f07fda6ee3e99e51672971d", "difficulty": "easy", "final_answer": {"answer": 1523.52, "unit": "J"}, "id": "ke_006697_9_18.4", "license": "Apache-2.0", "prompt": "A body of mass 9 kg moves at 18.4 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 18.4^2 and multiply by 0.5 * 9.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 9.0, "velocity": 18.4}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=19 degrees through the sine of 2 theta.\n3. Substitute v=80.2 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 403.6656, \"unit\": \"m\"}", "dedupe_signature": "0e29c9c76f3aa2f47d0e8168f72e945cda996274491f3e715d266c5f61b92a46", "difficulty": "medium", "final_answer": {"answer": 403.6656, "unit": "m"}, "id": "projectile_range_006698_80.2_19", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 80.2 m/s and angle 19 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=19 degrees through the sine of 2 theta.\nSubstitute v=80.2 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 19, "gravity": 9.81, "speed": 80.2}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 5.21 * 8.314 * 519 / 16.8.\nFinal: {\"answer\": 1338.1531, \"unit\": \"kPa\"}", "dedupe_signature": "6f176595ddca5d61bf209dbc5ae0f542082c520767ab84bc54f023b32eeb482f", "difficulty": "medium", "final_answer": {"answer": 1338.1531, "unit": "kPa"}, "id": "ideal_gas_006699_5.21_519_16.8", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=5.21 mol, T=519 K, and V=16.8 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 5.21 * 8.314 * 519 / 16.8.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 5.21, "temp_k": 519, "volume_l": 16.8}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1315 * 0.895 * 108.\nFinal: {\"answer\": 127107.9, \"unit\": \"J\"}", "dedupe_signature": "cb3230c12ed87bfa6ca122e0bd76eaaeaaf3d60fdac3d00f5c10438bc04c3107", "difficulty": "easy", "final_answer": {"answer": 127107.9, "unit": "J"}, "id": "heat_q_006700_1315_0.895_108", "license": "Apache-2.0", "prompt": "A 1315 g sample has specific heat 0.895 J/(g*K). How much heat is needed to raise its temperature by 108 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1315 * 0.895 * 108.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 108, "heat_capacity": 0.895, "mass_g": 1315}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=59.7 V and R=44.3 ohm.\nFinal: {\"answer\": 80.4535, \"unit\": \"W\"}", "dedupe_signature": "ca57955e72208d2409207c7f4ad1bfdc2dea34227da28490c23a427690ef2fb6", "difficulty": "easy", "final_answer": {"answer": 80.4535, "unit": "W"}, "id": "ohm_power_006701_59.7_44.3", "license": "Apache-2.0", "prompt": "A resistor has resistance 44.3 ohm and voltage 59.7 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=59.7 V and R=44.3 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 44.3, "voltage": 59.7}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=604 mg, t=201.5 h, and T_half=106.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 162.7356, \"unit\": \"mg\"}", "dedupe_signature": "ff95658bec218109f132638fe09773f6e9f35cb16436eb28f9336ddf38bd8139", "difficulty": "medium", "final_answer": {"answer": 162.7356, "unit": "mg"}, "id": "half_life_006702_604_106.5_201.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 604 mg. Its half-life is 106.5 hours. How many mg remain after 201.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=604 mg, t=201.5 h, and T_half=106.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 201.5, "half_life": 106.5, "initial_amount": 604.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 0.97 mol * 58.44 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 56.6868, \"unit\": \"g\"}", "dedupe_signature": "4aa8878d185c7e5925d106faf3c497bc4cc46b1503cdf615c06ae8fcb5c927dd", "difficulty": "medium", "final_answer": {"answer": 56.6868, "unit": "g"}, "id": "stoich_mass_006703_sodium_chloride_0.97", "license": "Apache-2.0", "prompt": "A sample contains 0.97 mol of sodium chloride. Using molar mass 58.44 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 0.97 mol * 58.44 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "sodium chloride", "molar_mass": 58.44, "moles": 0.97}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 4860 mL to 4.86 L.\n3. Compute M = 2.055 / 4.86.\nFinal: {\"answer\": 0.4228, \"unit\": \"mol/L\"}", "dedupe_signature": "6913c7427c6ab0b91e422cf18a6219f9e75a1f129a85c56b9d251a4a4bd63b8d", "difficulty": "medium", "final_answer": {"answer": 0.4228, "unit": "mol/L"}, "id": "molarity_006704_2.055_4860", "license": "Apache-2.0", "prompt": "A solution contains 2.055 mol of solute in 4860 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 4860 mL to 4.86 L.\nCompute M = 2.055 / 4.86.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 2.055, "volume_ml": 4860}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.14 y, so each step multiplies y by 1 - h*0.14.\n3. Apply that update for 5 steps and round the final state.\nFinal: {\"answer\": 22.3705, \"unit\": \"state_units\"}", "dedupe_signature": "93864eb3ce012bd8cabcb1820093998a92c7c9f0b6ad9eacfbf4e55451d9eaf8", "difficulty": "medium", "final_answer": {"answer": 22.3705, "unit": "state_units"}, "id": "euler_decay_006705_79.5_0.14_1.6_5", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.14 y with y(0)=79.5, step size h=1.6, for 5 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.14 y, so each step multiplies y by 1 - h*0.14.\nApply that update for 5 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 79.5, "rate": 0.14, "step": 1.6, "steps": 5}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-4.5)=-6.05 and f(0.9)=-5.51.\n3. The interval width is 5.4.\nFinal: {\"answer\": -31.212, \"unit\": \"area_units\"}", "dedupe_signature": "78f5fb10fcde4259b5314a1c131a04eb40ed541d68c2c41bc2f72f95d52f6b25", "difficulty": "medium", "final_answer": {"answer": -31.212, "unit": "area_units"}, "id": "trapz_linear_006706_0.1_-5.6_-4.5_0.9", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=0.1x+-5.6 from x=-4.5 to x=0.9. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-4.5)=-6.05 and f(0.9)=-5.51.\nThe interval width is 5.4.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -5.6, "slope": 0.1, "x0": -4.5, "x1": 0.9000000000000004}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 17717.0 / 1000.\nFinal: {\"answer\": 17.717, \"unit\": \"kg\"}", "dedupe_signature": "6f4a36cc2cbe27584f788449f5cc988151eca5ebc1eac73689cbcd8d3b6d2149", "difficulty": "easy", "final_answer": {"answer": 17.717, "unit": "kg"}, "id": "unit_convert_006708_g_to_kg_17717", "license": "Apache-2.0", "prompt": "Convert 17717 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 17717.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 17717.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=310 degrees and keep the unit as newtons.\nFinal: {\"answer\": [49.816, -59.3684], \"unit\": \"N\"}", "dedupe_signature": "97dc6b990d95249031e5743e089d0473efb04b61105a173757c3f2129bc30f1d", "difficulty": "medium", "final_answer": {"answer": [49.816, -59.3684], "unit": "N"}, "id": "vector_components_006709_77.5_310", "license": "Apache-2.0", "prompt": "A vector has magnitude 77.5 N at 310 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=310 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 310, "magnitude": 77.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-6.75, -2.25], \"unit\": \"dimensionless\"}", "dedupe_signature": "bc11b8636a0f2d65363a634ab21a214817f979cce1c797cd7084fceefb653078", "difficulty": "medium", "final_answer": {"answer": [-6.75, -2.25], "unit": "dimensionless"}, "id": "line_two_point_006710_-4_-1_-6.75_-2.25", "license": "Apache-2.0", "prompt": "A line passes through points (-4, 24.75) and (-1, 4.5). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -4.0, "x2": -1.0, "y1": 24.75, "y2": 4.5}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. density times acceleration times height gives kg/(m*s^2), or pascal\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "5cd327323638649bc60af672ce7c0d3382453b8883c5c269539af1054b7f8193", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_006711_consistent_b7d3eed1_67778", "license": "Apache-2.0", "prompt": "In instrument manual case 67778, check dimensional consistency for p = rho * g * h. The left side has dimensions Pa and the right side has dimensions Pa. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\ndensity times acceleration times height gives kg/(m*s^2), or pascal\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "p = rho * g * h"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef pairwise_ratios_006712(numerators, denominators):\n    if len(numerators) != len(denominators):\n        raise ValueError('length mismatch')\n    out = []\n    for numerator, denominator in zip(numerators, denominators):\n        if denominator == 0:\n            raise ValueError('zero denominator')\n        out.append(numerator / denominator)\n    return out\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"pairwise_ratios_006712\"}", "dedupe_signature": "074bc2a3d0cc9053ece671f79525d39504eab72c62670c153fc65cd41ec7f6cf", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "pairwise_ratios_006712"}, "id": "code_006712_pairwise_ratios_006712", "license": "Apache-2.0", "prompt": "Write a Python function pairwise_ratios_006712(numerators, denominators) that returns a list of n/d values. Raise ValueError if lengths differ or any denominator is zero. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "pairwise_ratios_006712"}, "verifier": {"function": "pairwise_ratios_006712", "tests": ["assert pairwise_ratios_006712([2, 9], [4, 3]) == [0.5, 3.0]", "try:\n    pairwise_ratios_006712([1], [0])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass", "try:\n    pairwise_ratios_006712([1, 2], [1])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: left_boundary, right_boundary.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"left_boundary\", \"right_boundary\"]}", "dedupe_signature": "0593c1e1aedc2008a4f71fbc0001fafc3227b576d57ba3b2a7c61c324dfedddf", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["left_boundary", "right_boundary"]}, "id": "abstain_006713_left_boundary_right_boundary", "license": "Apache-2.0", "prompt": "Solve the 1D heat equation after one finite-difference step. The prompt gives r=0.1 and interior values [0.4, 0.85, 1.6], but gives no boundary values. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: left_boundary, right_boundary.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["left_boundary", "right_boundary"]}, "verifier": {"missing": ["left_boundary", "right_boundary"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 19.65 kg and a = 15.3 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 300.645, \"unit\": \"N\"}", "dedupe_signature": "06772f0aa6d5edee4dc76db95814c433a124a4aa76eb704d604d73a80be1238c", "difficulty": "easy", "final_answer": {"answer": 300.645, "unit": "N"}, "id": "force_006714_19.65_15.3", "license": "Apache-2.0", "prompt": "A cart has mass 19.65 kg and measured acceleration 15.3 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 19.65 kg and a = 15.3 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 15.3, "mass": 19.65}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=35 degrees through the sine of 2 theta.\n3. Substitute v=50.3 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 242.3554, \"unit\": \"m\"}", "dedupe_signature": "3a9a1a7790320088f7bcd38b24b10a427d68cafa832fdd444e595abebd609394", "difficulty": "medium", "final_answer": {"answer": 242.3554, "unit": "m"}, "id": "projectile_range_006716_50.3_35", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 50.3 m/s and angle 35 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=35 degrees through the sine of 2 theta.\nSubstitute v=50.3 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 35, "gravity": 9.81, "speed": 50.3}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 5.83 * 8.314 * 412 / 24.4.\nFinal: {\"answer\": 818.4383, \"unit\": \"kPa\"}", "dedupe_signature": "6ba6f9555bebd59dc384d54cc91285b30addf491e50c7ec53f4a299123f6099d", "difficulty": "medium", "final_answer": {"answer": 818.4383, "unit": "kPa"}, "id": "ideal_gas_006717_5.83_412_24.4", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=5.83 mol, T=412 K, and V=24.4 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 5.83 * 8.314 * 412 / 24.4.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 5.83, "temp_k": 412, "volume_l": 24.4}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 740 * 2.095 * 56.\nFinal: {\"answer\": 86816.8, \"unit\": \"J\"}", "dedupe_signature": "0c17670226abce1d2b99cf2321ff8c80f2251c10c1719abc75003194c3c63e32", "difficulty": "easy", "final_answer": {"answer": 86816.8, "unit": "J"}, "id": "heat_q_006718_740_2.095_56", "license": "Apache-2.0", "prompt": "A 740 g sample has specific heat 2.095 J/(g*K). How much heat is needed to raise its temperature by 56 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 740 * 2.095 * 56.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 56, "heat_capacity": 2.095, "mass_g": 740}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=222.3 V and R=8.3 ohm.\nFinal: {\"answer\": 5953.8904, \"unit\": \"W\"}", "dedupe_signature": "9161a346360e032214f9be2910779392c1612e84575ac0d88e6983832b3f41a9", "difficulty": "easy", "final_answer": {"answer": 5953.8904, "unit": "W"}, "id": "ohm_power_006719_222.3_8.3", "license": "Apache-2.0", "prompt": "A resistor has resistance 8.3 ohm and voltage 222.3 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=222.3 V and R=8.3 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 8.3, "voltage": 222.3}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=837.5 mg, t=26.5 h, and T_half=108.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 707.0683, \"unit\": \"mg\"}", "dedupe_signature": "15c3a071073df526a98a1f5e53907ce512dc920c9d6b0bd2c679cd2ed0cab83e", "difficulty": "medium", "final_answer": {"answer": 707.0683, "unit": "mg"}, "id": "half_life_006720_837.5_108.5_26.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 837.5 mg. Its half-life is 108.5 hours. How many mg remain after 26.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=837.5 mg, t=26.5 h, and T_half=108.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 26.5, "half_life": 108.5, "initial_amount": 837.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 0.37 mol * 18.015 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 6.6656, \"unit\": \"g\"}", "dedupe_signature": "b028255b9a8a450f3c66e93a576ba8401cb5bfeeac739149cda9c6882c3737f6", "difficulty": "medium", "final_answer": {"answer": 6.6656, "unit": "g"}, "id": "stoich_mass_006721_water_0.37", "license": "Apache-2.0", "prompt": "A sample contains 0.37 mol of water. Using molar mass 18.015 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 0.37 mol * 18.015 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "water", "molar_mass": 18.015, "moles": 0.37}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 4435 mL to 4.435 L.\n3. Compute M = 3.51 / 4.435.\nFinal: {\"answer\": 0.7914, \"unit\": \"mol/L\"}", "dedupe_signature": "0920a5c0acaa63c98eba573dec656ff9b4d2f80a4a323fc4013181e9d44e2f0d", "difficulty": "medium", "final_answer": {"answer": 0.7914, "unit": "mol/L"}, "id": "molarity_006722_3.51_4435", "license": "Apache-2.0", "prompt": "A solution contains 3.51 mol of solute in 4435 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 4435 mL to 4.435 L.\nCompute M = 3.51 / 4.435.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 3.51, "volume_ml": 4435}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(2)=13.3 and f(7.1)=22.48.\n3. The interval width is 5.1.\nFinal: {\"answer\": 91.239, \"unit\": \"area_units\"}", "dedupe_signature": "514face2d4f809cdefa568c3605ecdbcccc3e81d93addd237b29d302967fd1d7", "difficulty": "medium", "final_answer": {"answer": 91.239, "unit": "area_units"}, "id": "trapz_linear_006724_1.8_9.7_2_7.1", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=1.8x+9.7 from x=2 to x=7.1. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(2)=13.3 and f(7.1)=22.48.\nThe interval width is 5.1.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 9.7, "slope": 1.8, "x0": 2.0, "x1": 7.1}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.44 and add it to the current value.\nFinal: {\"answer\": [0.768, 0.308, 1.472], \"unit\": \"temperature_units\"}", "dedupe_signature": "87a3daeb0705d2c7acf1a9cc4f20b260675f828bf87a7ea60cdf2a995932f753", "difficulty": "hard", "final_answer": {"answer": [0.768, 0.308, 1.472], "unit": "temperature_units"}, "id": "heat_step_006725_0.44_1.95_-0.75_0.0_1.45_2.95", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.95, right=2.95; current interior values are [-0.75, 0.0, 1.45]. Use r=0.44. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.44 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-0.75, 0.0, 1.45], "left": 1.95, "r": 0.44, "right": 2.95}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 3790.0 / 1000.\nFinal: {\"answer\": 3.79, \"unit\": \"kg\"}", "dedupe_signature": "92953163ed4a84e654cf94e40252588aa76e842e8d1105242181036cb54b7f54", "difficulty": "easy", "final_answer": {"answer": 3.79, "unit": "kg"}, "id": "unit_convert_006726_g_to_kg_3790", "license": "Apache-2.0", "prompt": "Convert 3790 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 3790.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 3790.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=15 degrees and keep the unit as newtons.\nFinal: {\"answer\": [370.9155, 99.3865], \"unit\": \"N\"}", "dedupe_signature": "bca719c618aa2d36add85c0b887faa259f07fdaec1b7d255c4fc1662ff03e7a2", "difficulty": "medium", "final_answer": {"answer": [370.9155, 99.3865], "unit": "N"}, "id": "vector_components_006727_384_15", "license": "Apache-2.0", "prompt": "A vector has magnitude 384 N at 15 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=15 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 15, "magnitude": 384.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. energy divided by length is force, not spring constant\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "9c699dc019a1eadc1063109868bdea1db2dde091d22ae6431b77dd52a3e17b2b", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_006729_inconsistent_56040f5d_437754", "license": "Apache-2.0", "prompt": "In instrument manual case 437754, check dimensional consistency for k = E / x. The left side has dimensions N/m and the right side has dimensions J/m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nenergy divided by length is force, not spring constant\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "k = E / x"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef weighted_sum_006730(values, weights):\n    if len(values) != len(weights):\n        raise ValueError('length mismatch')\n    return sum(value * weight for value, weight in zip(values, weights))\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"weighted_sum_006730\"}", "dedupe_signature": "03b046ab1f79bd18f58eb87fcc4ba3a2176f1ca3a54473f179c310aea6e00c49", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "weighted_sum_006730"}, "id": "code_006730_weighted_sum_006730", "license": "Apache-2.0", "prompt": "Write a Python function weighted_sum_006730(values, weights) that returns sum(value*weight). Raise ValueError when the two inputs have different lengths. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "weighted_sum_006730"}, "verifier": {"function": "weighted_sum_006730", "tests": ["assert weighted_sum_006730([2, 3], [4, 5]) == 23", "assert weighted_sum_006730([], []) == 0", "try:\n    weighted_sum_006730([1], [1, 2])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: rate_constant, number_of_steps.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"rate_constant\", \"number_of_steps\"]}", "dedupe_signature": "dd26f118b757e9ec5839b247cffee573c6518ec03662639bc9605ddca9971b8e", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["rate_constant", "number_of_steps"]}, "id": "abstain_006731_rate_constant_number_of_steps", "license": "Apache-2.0", "prompt": "Use explicit Euler for dy/dt = -k y. The prompt gives y(0)=18 and h=1.9, but omits both k and the number of steps. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: rate_constant, number_of_steps.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["rate_constant", "number_of_steps"]}, "verifier": {"missing": ["rate_constant", "number_of_steps"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 10.6 kg and a = 12.9 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 136.74, \"unit\": \"N\"}", "dedupe_signature": "008e0bc1c701c52eb1a9ec90449a3fd5113a2005759b275a4b8ba970394443ab", "difficulty": "easy", "final_answer": {"answer": 136.74, "unit": "N"}, "id": "force_006732_10.6_12.9", "license": "Apache-2.0", "prompt": "A cart has mass 10.6 kg and measured acceleration 12.9 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 10.6 kg and a = 12.9 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 12.9, "mass": 10.6}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 5.65^2 and multiply by 0.5 * 22.25.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 355.1378, \"unit\": \"J\"}", "dedupe_signature": "bebc023e2e60ef7c069cfef11825db928032034777ec2e804de2965a031aac2a", "difficulty": "easy", "final_answer": {"answer": 355.1378, "unit": "J"}, "id": "ke_006733_22.25_5.65", "license": "Apache-2.0", "prompt": "A body of mass 22.25 kg moves at 5.65 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 5.65^2 and multiply by 0.5 * 22.25.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 22.25, "velocity": 5.65}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=58 degrees through the sine of 2 theta.\n3. Substitute v=83.1 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 632.6933, \"unit\": \"m\"}", "dedupe_signature": "d3ef6826d05e247a5ac022f13a5dffcda8200bc4aab6f35431e3c9682c459a20", "difficulty": "medium", "final_answer": {"answer": 632.6933, "unit": "m"}, "id": "projectile_range_006734_83.1_58", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 83.1 m/s and angle 58 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=58 degrees through the sine of 2 theta.\nSubstitute v=83.1 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 58, "gravity": 9.81, "speed": 83.1}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 3.34 * 8.314 * 530 / 99.6.\nFinal: {\"answer\": 147.7655, \"unit\": \"kPa\"}", "dedupe_signature": "9d0dc4af474b6303aaeb7695832378544722acab9ec9869d20bcadfe840f2278", "difficulty": "medium", "final_answer": {"answer": 147.7655, "unit": "kPa"}, "id": "ideal_gas_006735_3.34_530_99.6", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=3.34 mol, T=530 K, and V=99.6 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 3.34 * 8.314 * 530 / 99.6.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 3.34, "temp_k": 530, "volume_l": 99.6}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1425 * 4.93 * 31.\nFinal: {\"answer\": 217782.75, \"unit\": \"J\"}", "dedupe_signature": "3867450175e0dea06c0e74082bbdda4775c00257225d7a4c313b40bbf73cec89", "difficulty": "easy", "final_answer": {"answer": 217782.75, "unit": "J"}, "id": "heat_q_006736_1425_4.93_31", "license": "Apache-2.0", "prompt": "A 1425 g sample has specific heat 4.93 J/(g*K). How much heat is needed to raise its temperature by 31 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1425 * 4.93 * 31.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 31, "heat_capacity": 4.93, "mass_g": 1425}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=182.9 V and R=36.8 ohm.\nFinal: {\"answer\": 909.0329, \"unit\": \"W\"}", "dedupe_signature": "37eff574834e390b6349ad09d8ae5984d388967f90bc95f800e4d67acba7e501", "difficulty": "easy", "final_answer": {"answer": 909.0329, "unit": "W"}, "id": "ohm_power_006737_182.9_36.8", "license": "Apache-2.0", "prompt": "A resistor has resistance 36.8 ohm and voltage 182.9 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=182.9 V and R=36.8 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 36.8, "voltage": 182.9}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 7.51 mol * 44.01 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 330.5151, \"unit\": \"g\"}", "dedupe_signature": "6b85558c7dc918780d55c2a3c4839904f2e1fce6c46bc0e5f94f2de5472d6365", "difficulty": "medium", "final_answer": {"answer": 330.5151, "unit": "g"}, "id": "stoich_mass_006739_carbon_dioxide_7.51", "license": "Apache-2.0", "prompt": "A sample contains 7.51 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 7.51 mol * 44.01 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "carbon dioxide", "molar_mass": 44.01, "moles": 7.51}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 3350 mL to 3.35 L.\n3. Compute M = 3.48 / 3.35.\nFinal: {\"answer\": 1.0388, \"unit\": \"mol/L\"}", "dedupe_signature": "8ca21bcb391d13a06c16265576fbf677b7793fc743e43729f09cdbeed2e82151", "difficulty": "medium", "final_answer": {"answer": 1.0388, "unit": "mol/L"}, "id": "molarity_006740_3.48_3350", "license": "Apache-2.0", "prompt": "A solution contains 3.48 mol of solute in 3350 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 3350 mL to 3.35 L.\nCompute M = 3.48 / 3.35.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 3.48, "volume_ml": 3350}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.94 y, so each step multiplies y by 1 - h*0.94.\n3. Apply that update for 8 steps and round the final state.\nFinal: {\"answer\": 0.0529, \"unit\": \"state_units\"}", "dedupe_signature": "893e6cfc06874018d89b6574c61c617f2bb651320fbb11cda9adbafd0e9bec61", "difficulty": "medium", "final_answer": {"answer": 0.0529, "unit": "state_units"}, "id": "euler_decay_006741_40.5_0.94_0.6_8", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.94 y with y(0)=40.5, step size h=0.6, for 8 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.94 y, so each step multiplies y by 1 - h*0.94.\nApply that update for 8 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 40.5, "rate": 0.94, "step": 0.6, "steps": 8}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.32 and add it to the current value.\nFinal: {\"answer\": [1.87, 1.75, 1.978], \"unit\": \"temperature_units\"}", "dedupe_signature": "54d82dd46e8491e0b77802f4cb4f507afe07f66f76607ad2bea7862f4ad37783", "difficulty": "hard", "final_answer": {"answer": [1.87, 1.75, 1.978], "unit": "temperature_units"}, "id": "heat_step_006743_0.32_1.55_1.55_2.55_1.05_2.45", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.55, right=2.45; current interior values are [1.55, 2.55, 1.05]. Use r=0.32. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.32 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [1.55, 2.55, 1.05], "left": 1.55, "r": 0.32, "right": 2.45}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 43213.0 / 1000.\nFinal: {\"answer\": 43.213, \"unit\": \"kg\"}", "dedupe_signature": "a638efc43d0a18d832567be345f1bd1cafaca13aa86bdf0b10bc9570a8a6a993", "difficulty": "easy", "final_answer": {"answer": 43.213, "unit": "kg"}, "id": "unit_convert_006744_g_to_kg_43213", "license": "Apache-2.0", "prompt": "Convert 43213 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 43213.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 43213.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=19 degrees and keep the unit as newtons.\nFinal: {\"answer\": [401.3726, 138.2037], \"unit\": \"N\"}", "dedupe_signature": "ee4862a3e229976d1fe10c492477d703b2c43964e8346c337231fb6d806ce236", "difficulty": "medium", "final_answer": {"answer": [401.3726, 138.2037], "unit": "N"}, "id": "vector_components_006745_424.5_19", "license": "Apache-2.0", "prompt": "A vector has magnitude 424.5 N at 19 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=19 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 19, "magnitude": 424.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. speed squared over acceleration has units of meters\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "72d95ebec84525f77eda7222fe20b077f37ecaa0a710d032246d17f297508425", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_006747_consistent_741d4e34_731468", "license": "Apache-2.0", "prompt": "In student derivation case 731468, check dimensional consistency for R = v^2 * sin(theta) / g. The left side has dimensions m and the right side has dimensions m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nspeed squared over acceleration has units of meters\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "R = v^2 * sin(theta) / g"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef center_values_006748(values):\n    if not values:\n        raise ValueError('center_values requires at least one value')\n    mean = sum(values) / len(values)\n    return [value - mean for value in values]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"center_values_006748\"}", "dedupe_signature": "c88fa1434b5962dc93b7c1b5829b54ed6ea54259dd49dc2b447249f8c6d04b34", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "center_values_006748"}, "id": "code_006748_center_values_006748", "license": "Apache-2.0", "prompt": "Write a Python function center_values_006748(values) that subtracts the arithmetic mean from each value and returns a new list. Raise ValueError for an empty input. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "center_values_006748"}, "verifier": {"function": "center_values_006748", "tests": ["out = center_values_006748([1, 2, 3]); assert out == [-1, 0, 1]", "assert center_values_006748([5]) == [0]", "try:\n    center_values_006748([])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: recurrence, objective, tie_breaking_rule.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"recurrence\", \"objective\", \"tie_breaking_rule\"]}", "dedupe_signature": "082203aba86f92a0f15156aa1ad5395f6aae4c92ac34c5b693b2cdfb7214d6c5", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["recurrence", "objective", "tie_breaking_rule"]}, "id": "abstain_006749_recurrence_objective_tie_breaking_rule", "license": "Apache-2.0", "prompt": "Write a dynamic-programming solver for a allocation scoring problem with 280 items and budget 60470, but the recurrence, objective, and tie-breaking rule are all absent. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: recurrence, objective, tie_breaking_rule.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["recurrence", "objective", "tie_breaking_rule"]}, "verifier": {"missing": ["recurrence", "objective", "tie_breaking_rule"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 16.95 kg and a = 1.45 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 24.5775, \"unit\": \"N\"}", "dedupe_signature": "a89e2b19038a762e60b7012cd0abcb8f9218f106b3c269fecffb6164c4eb1bfe", "difficulty": "easy", "final_answer": {"answer": 24.5775, "unit": "N"}, "id": "force_006750_16.95_1.45", "license": "Apache-2.0", "prompt": "A cart has mass 16.95 kg and measured acceleration 1.45 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 16.95 kg and a = 1.45 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 1.45, "mass": 16.95}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=11 degrees through the sine of 2 theta.\n3. Substitute v=80 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 244.3917, \"unit\": \"m\"}", "dedupe_signature": "09e69ff53e2f90ff8dcfe901f46a907d4b575cdc29d4893bd28db070d4fed685", "difficulty": "medium", "final_answer": {"answer": 244.3917, "unit": "m"}, "id": "projectile_range_006752_80_11", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 80 m/s and angle 11 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=11 degrees through the sine of 2 theta.\nSubstitute v=80 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 11, "gravity": 9.81, "speed": 80.0}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 375 * 1.645 * 39.\nFinal: {\"answer\": 24058.125, \"unit\": \"J\"}", "dedupe_signature": "f8056991b22d6c36b02ffd1353ba58d36c7d19f27d80fb0acf96bfda2a6e1499", "difficulty": "easy", "final_answer": {"answer": 24058.125, "unit": "J"}, "id": "heat_q_006754_375_1.645_39", "license": "Apache-2.0", "prompt": "A 375 g sample has specific heat 1.645 J/(g*K). How much heat is needed to raise its temperature by 39 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 375 * 1.645 * 39.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 39, "heat_capacity": 1.645, "mass_g": 375}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=40.5 V and R=189.5 ohm.\nFinal: {\"answer\": 8.6557, \"unit\": \"W\"}", "dedupe_signature": "4b7a75a8f2b549c0d4608b86fc9da321ee451ce0e1cc15d7eea2be748d61a7be", "difficulty": "easy", "final_answer": {"answer": 8.6557, "unit": "W"}, "id": "ohm_power_006755_40.5_189.5", "license": "Apache-2.0", "prompt": "A resistor has resistance 189.5 ohm and voltage 40.5 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=40.5 V and R=189.5 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 189.5, "voltage": 40.5}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=885 mg, t=295.5 h, and T_half=17 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 0.0052, \"unit\": \"mg\"}", "dedupe_signature": "4f46249c262435a0c8f4be3de9041956dba07ac6ae760f7db21fffec67d71f63", "difficulty": "medium", "final_answer": {"answer": 0.0052, "unit": "mg"}, "id": "half_life_006756_885_17_295.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 885 mg. Its half-life is 17 hours. How many mg remain after 295.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=885 mg, t=295.5 h, and T_half=17 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 295.5, "half_life": 17.0, "initial_amount": 885.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 2560 mL to 2.56 L.\n3. Compute M = 3.405 / 2.56.\nFinal: {\"answer\": 1.3301, \"unit\": \"mol/L\"}", "dedupe_signature": "ec6ead6a3753f8c35357827426392aa10546385f8a4119f7fa706510482870b7", "difficulty": "medium", "final_answer": {"answer": 1.3301, "unit": "mol/L"}, "id": "molarity_006758_3.405_2560", "license": "Apache-2.0", "prompt": "A solution contains 3.405 mol of solute in 2560 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 2560 mL to 2.56 L.\nCompute M = 3.405 / 2.56.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 3.405, "volume_ml": 2560}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.56 y, so each step multiplies y by 1 - h*0.56.\n3. Apply that update for 10 steps and round the final state.\nFinal: {\"answer\": 0.0, \"unit\": \"state_units\"}", "dedupe_signature": "ca9b9fd57dc835eeff42230af2643f0c6f9c403a7d05452b0c79871938bc1e65", "difficulty": "medium", "final_answer": {"answer": 0.0, "unit": "state_units"}, "id": "euler_decay_006759_49_0.56_1.75_10", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.56 y with y(0)=49, step size h=1.75, for 10 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.56 y, so each step multiplies y by 1 - h*0.56.\nApply that update for 10 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 49.0, "rate": 0.56, "step": 1.75, "steps": 10}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.06 and add it to the current value.\nFinal: {\"answer\": [0.176, 0.615, 1.091], \"unit\": \"temperature_units\"}", "dedupe_signature": "e141ea031f24e8bad295558dd7ae9254047c1fd0051888c802a674ca2dfe9820", "difficulty": "hard", "final_answer": {"answer": [0.176, 0.615, 1.091], "unit": "temperature_units"}, "id": "heat_step_006761_0.06_-0.6_0.2_0.6_1.25_-0.75", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-0.6, right=-0.75; current interior values are [0.2, 0.6, 1.25]. Use r=0.06. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.06 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [0.2, 0.6, 1.25], "left": -0.6, "r": 0.06, "right": -0.75}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=281 degrees and keep the unit as newtons.\nFinal: {\"answer\": [75.465, -388.2336], \"unit\": \"N\"}", "dedupe_signature": "0bdf474dca995a8eb663c2df6414dc466dac6b63b5b5c29c637e348de9730cf4", "difficulty": "medium", "final_answer": {"answer": [75.465, -388.2336], "unit": "N"}, "id": "vector_components_006763_395.5_281", "license": "Apache-2.0", "prompt": "A vector has magnitude 395.5 N at 281 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=281 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 281, "magnitude": 395.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-6.1, 0.75], \"unit\": \"dimensionless\"}", "dedupe_signature": "9613fbc48926eae79d2e82830ac233fb55acda5736d1fa0c11de7445e433eeda", "difficulty": "medium", "final_answer": {"answer": [-6.1, 0.75], "unit": "dimensionless"}, "id": "line_two_point_006764_-15_-8.25_-6.1_0.75", "license": "Apache-2.0", "prompt": "A line passes through points (-15, 92.25) and (-8.25, 51.075). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -15.0, "x2": -8.25, "y1": 92.25, "y2": 51.074999999999996}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. lever arm times force has torque dimensions\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "b4c03b8739a4d8138feb042f9fe8a36716bcd975a7cea001dbfe9fce53c7b81d", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_006765_consistent_5ca82cb9_79857", "license": "Apache-2.0", "prompt": "In field worksheet case 79857, check dimensional consistency for tau = r * F. The left side has dimensions N*m and the right side has dimensions N*m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nlever arm times force has torque dimensions\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "tau = r * F"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef safe_mean_006766(values):\n    if not values:\n        raise ValueError('safe_mean requires at least one value')\n    return sum(values) / len(values)\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"safe_mean_006766\"}", "dedupe_signature": "36cde3c9f16df249c9e0173b17d840393d93493198e0648828b96e738f36db61", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "safe_mean_006766"}, "id": "code_006766_safe_mean_006766", "license": "Apache-2.0", "prompt": "Write a Python function safe_mean_006766(values) that returns the arithmetic mean. It must raise ValueError for an empty input and must not mutate the input list. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "safe_mean_006766"}, "verifier": {"function": "safe_mean_006766", "tests": ["assert safe_mean_006766([2, 4, 6]) == 4", "xs = [1, 2, 3]; assert safe_mean_006766(xs) == 2 and xs == [1, 2, 3]", "try:\n    safe_mean_006766([])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: left_boundary, right_boundary.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"left_boundary\", \"right_boundary\"]}", "dedupe_signature": "abf80695fb30085ec38ab3aea9e0541447873c839e839e2e9eecc5b97e55002a", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["left_boundary", "right_boundary"]}, "id": "abstain_006767_left_boundary_right_boundary", "license": "Apache-2.0", "prompt": "Solve the 1D heat equation after one finite-difference step. The prompt gives r=0.46 and interior values [0.5, -2.0, 1.1], but gives no boundary values. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: left_boundary, right_boundary.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["left_boundary", "right_boundary"]}, "verifier": {"missing": ["left_boundary", "right_boundary"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 15.8 kg and a = 9.45 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 149.31, \"unit\": \"N\"}", "dedupe_signature": "5bf7fcbfe27696144f1456ddfce7ccffaa58f343be9825210cfd4b6e6d566299", "difficulty": "easy", "final_answer": {"answer": 149.31, "unit": "N"}, "id": "force_006768_15.8_9.45", "license": "Apache-2.0", "prompt": "A cart has mass 15.8 kg and measured acceleration 9.45 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 15.8 kg and a = 9.45 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 9.45, "mass": 15.8}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=54 degrees through the sine of 2 theta.\n3. Substitute v=59.6 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 344.3736, \"unit\": \"m\"}", "dedupe_signature": "b52df2e410bdbf687bcd475b0ae900d655b1911a77e6869e67b40c61c925ab3f", "difficulty": "medium", "final_answer": {"answer": 344.3736, "unit": "m"}, "id": "projectile_range_006770_59.6_54", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 59.6 m/s and angle 54 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=54 degrees through the sine of 2 theta.\nSubstitute v=59.6 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 54, "gravity": 9.81, "speed": 59.6}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 5.09 * 8.314 * 370 / 31.6.\nFinal: {\"answer\": 495.4986, \"unit\": \"kPa\"}", "dedupe_signature": "cc53ad61eab32ffcdc7b4d6f3b8cf5f30c8ea1d99a92f6fde93804f83b7bbc6d", "difficulty": "medium", "final_answer": {"answer": 495.4986, "unit": "kPa"}, "id": "ideal_gas_006771_5.09_370_31.6", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=5.09 mol, T=370 K, and V=31.6 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 5.09 * 8.314 * 370 / 31.6.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 5.09, "temp_k": 370, "volume_l": 31.6}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 840 * 3.97 * 106.\nFinal: {\"answer\": 353488.8, \"unit\": \"J\"}", "dedupe_signature": "7feb02b75749355662241bef916785451888d1b9a43f7ad21928aeec3b4e1ae9", "difficulty": "easy", "final_answer": {"answer": 353488.8, "unit": "J"}, "id": "heat_q_006772_840_3.97_106", "license": "Apache-2.0", "prompt": "A 840 g sample has specific heat 3.97 J/(g*K). How much heat is needed to raise its temperature by 106 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 840 * 3.97 * 106.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 106, "heat_capacity": 3.97, "mass_g": 840}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=22.9 V and R=59 ohm.\nFinal: {\"answer\": 8.8883, \"unit\": \"W\"}", "dedupe_signature": "2450928c35a83053149f701b68ee7f57eb245e8b463a7106b1dbafb73a4e5944", "difficulty": "easy", "final_answer": {"answer": 8.8883, "unit": "W"}, "id": "ohm_power_006773_22.9_59", "license": "Apache-2.0", "prompt": "A resistor has resistance 59 ohm and voltage 22.9 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=22.9 V and R=59 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 59.0, "voltage": 22.9}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=18 mg, t=72.5 h, and T_half=76 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 9.2919, \"unit\": \"mg\"}", "dedupe_signature": "219e366ef5aec7a64f194cc08ef33bf2bd0a65ed333593c7ff5ad98c957545a6", "difficulty": "medium", "final_answer": {"answer": 9.2919, "unit": "mg"}, "id": "half_life_006774_18_76_72.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 18 mg. Its half-life is 76 hours. How many mg remain after 72.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=18 mg, t=72.5 h, and T_half=76 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 72.5, "half_life": 76.0, "initial_amount": 18.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 2940 mL to 2.94 L.\n3. Compute M = 4.98 / 2.94.\nFinal: {\"answer\": 1.6939, \"unit\": \"mol/L\"}", "dedupe_signature": "15c1d1f89ad6cbd72a13a2ccfb2e821299ceab4e90d491013e99d8297d90f544", "difficulty": "medium", "final_answer": {"answer": 1.6939, "unit": "mol/L"}, "id": "molarity_006776_4.98_2940", "license": "Apache-2.0", "prompt": "A solution contains 4.98 mol of solute in 2940 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 2940 mL to 2.94 L.\nCompute M = 4.98 / 2.94.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 4.98, "volume_ml": 2940}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.32 y, so each step multiplies y by 1 - h*0.32.\n3. Apply that update for 11 steps and round the final state.\nFinal: {\"answer\": 0.0035, \"unit\": \"state_units\"}", "dedupe_signature": "c17aa963392dcc58847e93f92176e15878acfbfa2a99dd49e4b5426cec1ad7bb", "difficulty": "medium", "final_answer": {"answer": 0.0035, "unit": "state_units"}, "id": "euler_decay_006777_68_0.32_1.85_11", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.32 y with y(0)=68, step size h=1.85, for 11 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.32 y, so each step multiplies y by 1 - h*0.32.\nApply that update for 11 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 68.0, "rate": 0.32, "step": 1.85, "steps": 11}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(0.5)=10.4 and f(7.5)=-33.\n3. The interval width is 7.\nFinal: {\"answer\": -79.1, \"unit\": \"area_units\"}", "dedupe_signature": "59dcc2a7e9d4d59d27e2ede3e0682e50e61e0ff8add27a4b4aae64b8cd3e74ce", "difficulty": "medium", "final_answer": {"answer": -79.1, "unit": "area_units"}, "id": "trapz_linear_006778_-6.2_13.5_0.5_7.5", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-6.2x+13.5 from x=0.5 to x=7.5. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(0.5)=10.4 and f(7.5)=-33.\nThe interval width is 7.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 13.5, "slope": -6.2, "x0": 0.5, "x1": 7.5}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.38 and add it to the current value.\nFinal: {\"answer\": [0.524, 1.18, -0.421], \"unit\": \"temperature_units\"}", "dedupe_signature": "8fac43faee4335c6bcec129eb52f97be808b8d91a656113312ad3b65fc51fab9", "difficulty": "hard", "final_answer": {"answer": [0.524, 1.18, -0.421], "unit": "temperature_units"}, "id": "heat_step_006779_0.38_0.55_1.55_-0.15_1.65_-2.0", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=0.55, right=-2; current interior values are [1.55, -0.15, 1.65]. Use r=0.38. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.38 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [1.55, -0.15, 1.65], "left": 0.55, "r": 0.38, "right": -2.0}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=272 degrees and keep the unit as newtons.\nFinal: {\"answer\": [1.8846, -53.9671], \"unit\": \"N\"}", "dedupe_signature": "1beacfc3edfd108c5eda7fc1189adbb92452661e047fde6811859231aca2e6d1", "difficulty": "medium", "final_answer": {"answer": [1.8846, -53.9671], "unit": "N"}, "id": "vector_components_006781_54_272", "license": "Apache-2.0", "prompt": "A vector has magnitude 54 N at 272 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=272 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 272, "magnitude": 54.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [4.35, 0.5], \"unit\": \"dimensionless\"}", "dedupe_signature": "8e17b6d03700d926140854a8f52dfb6b2cdbc91d985f31e64170250f01f94d39", "difficulty": "medium", "final_answer": {"answer": [4.35, 0.5], "unit": "dimensionless"}, "id": "line_two_point_006782_4_7.5_4.35_0.5", "license": "Apache-2.0", "prompt": "A line passes through points (4, 17.9) and (7.5, 33.125). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 4.0, "x2": 7.5, "y1": 17.9, "y2": 33.125}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. velocity divided by time is acceleration\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "992d2f96aad92b7f543cafcecd3b26b4044419408a5faf9551d469eefd4281d1", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_006783_inconsistent_c1271127_895028", "license": "Apache-2.0", "prompt": "In simulation spec case 895028, check dimensional consistency for x = v / t. The left side has dimensions m and the right side has dimensions m/s^2. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nvelocity divided by time is acceleration\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "x = v / t"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef normalize_006784(values):\n    total = sum(values)\n    if total == 0:\n        raise ValueError('cannot normalize zero-sum values')\n    return [v / total for v in values]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"normalize_006784\"}", "dedupe_signature": "981d50ca0c601d32cb2bafae1e5e7000b709b649aaf75b91904505cacb6ea6ca", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "normalize_006784"}, "id": "code_006784_normalize_006784", "license": "Apache-2.0", "prompt": "Write a Python function normalize_006784(values) that returns a new list whose values sum to 1. Raise ValueError if the sum is zero. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "normalize_006784"}, "verifier": {"function": "normalize_006784", "tests": ["out = normalize_006784([2, 3, 5]); assert len(out) == 3", "assert abs(sum(normalize_006784([2, 3, 5])) - 1.0) < 1e-12", "assert normalize_006784([1, 1]) == [0.5, 0.5]", "try:\n    normalize_006784([1, -1])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: left_boundary, right_boundary.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"left_boundary\", \"right_boundary\"]}", "dedupe_signature": "b66f50fb5288a5f671a3b949615b059439b9fefedc36821a3f5b8c3b34dc032a", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["left_boundary", "right_boundary"]}, "id": "abstain_006785_left_boundary_right_boundary", "license": "Apache-2.0", "prompt": "Solve the 1D heat equation after one finite-difference step. The prompt gives r=0.22 and interior values [2.2, 0.25, 1.4], but gives no boundary values. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: left_boundary, right_boundary.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["left_boundary", "right_boundary"]}, "verifier": {"missing": ["left_boundary", "right_boundary"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 6.3 kg and a = 13.2 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 83.16, \"unit\": \"N\"}", "dedupe_signature": "f9c92f3dc974c2f738332cb807bb03a24a2ae9fda179818ece725b3dca5f2d37", "difficulty": "easy", "final_answer": {"answer": 83.16, "unit": "N"}, "id": "force_006786_6.3_13.2", "license": "Apache-2.0", "prompt": "A cart has mass 6.3 kg and measured acceleration 13.2 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 6.3 kg and a = 13.2 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 13.2, "mass": 6.3}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 23.75^2 and multiply by 0.5 * 8.9.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 2510.0781, \"unit\": \"J\"}", "dedupe_signature": "e18e86930707d5a9fcbb741bac0bd2961368948ae3d928b22bb96d8b454417c7", "difficulty": "easy", "final_answer": {"answer": 2510.0781, "unit": "J"}, "id": "ke_006787_8.9_23.75", "license": "Apache-2.0", "prompt": "A body of mass 8.9 kg moves at 23.75 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 23.75^2 and multiply by 0.5 * 8.9.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 8.9, "velocity": 23.75}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=38 degrees through the sine of 2 theta.\n3. Substitute v=26.5 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 69.4587, \"unit\": \"m\"}", "dedupe_signature": "8e3b18e3bfe5e9a1cbaa8fccd927f73c92694378ea3789b23a66fc7345cefc25", "difficulty": "medium", "final_answer": {"answer": 69.4587, "unit": "m"}, "id": "projectile_range_006788_26.5_38", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 26.5 m/s and angle 38 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=38 degrees through the sine of 2 theta.\nSubstitute v=26.5 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 38, "gravity": 9.81, "speed": 26.5}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 3.93 * 8.314 * 460 / 111.9.\nFinal: {\"answer\": 134.3168, \"unit\": \"kPa\"}", "dedupe_signature": "ba70f79ef38da46ee5a758c8cd93abfb1118288c31f3191e15d32062b3a68139", "difficulty": "medium", "final_answer": {"answer": 134.3168, "unit": "kPa"}, "id": "ideal_gas_006789_3.93_460_111.9", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=3.93 mol, T=460 K, and V=111.9 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 3.93 * 8.314 * 460 / 111.9.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 3.93, "temp_k": 460, "volume_l": 111.9}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1570 * 3.065 * 48.\nFinal: {\"answer\": 230978.4, \"unit\": \"J\"}", "dedupe_signature": "83d00420426e117418d0ba817fe2d96594c3f6102de2f149e9cc1fd32ca38163", "difficulty": "easy", "final_answer": {"answer": 230978.4, "unit": "J"}, "id": "heat_q_006790_1570_3.065_48", "license": "Apache-2.0", "prompt": "A 1570 g sample has specific heat 3.065 J/(g*K). How much heat is needed to raise its temperature by 48 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1570 * 3.065 * 48.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 48, "heat_capacity": 3.065, "mass_g": 1570}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=66.5 V and R=199.9 ohm.\nFinal: {\"answer\": 22.1223, \"unit\": \"W\"}", "dedupe_signature": "355e0cfff8a0a9c7571f05dc69f72ea88d4c60ac4b7f1cfd5af49552f9804bbc", "difficulty": "easy", "final_answer": {"answer": 22.1223, "unit": "W"}, "id": "ohm_power_006791_66.5_199.9", "license": "Apache-2.0", "prompt": "A resistor has resistance 199.9 ohm and voltage 66.5 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=66.5 V and R=199.9 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 199.9, "voltage": 66.5}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=207 mg, t=71 h, and T_half=49 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 75.82, \"unit\": \"mg\"}", "dedupe_signature": "8337cd11f56f3bad4ebbf74e0c6aa4011ab25266d08c289a73fb31babf58620e", "difficulty": "medium", "final_answer": {"answer": 75.82, "unit": "mg"}, "id": "half_life_006792_207_49_71", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 207 mg. Its half-life is 49 hours. How many mg remain after 71 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=207 mg, t=71 h, and T_half=49 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 71.0, "half_life": 49.0, "initial_amount": 207.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 4.06 mol * 44.01 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 178.6806, \"unit\": \"g\"}", "dedupe_signature": "c2578f0accf16b9e12bfa5d7bb8ef076d6c6711ab12883756b6ff4a7760a3b96", "difficulty": "medium", "final_answer": {"answer": 178.6806, "unit": "g"}, "id": "stoich_mass_006793_carbon_dioxide_4.06", "license": "Apache-2.0", "prompt": "A sample contains 4.06 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 4.06 mol * 44.01 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "carbon dioxide", "molar_mass": 44.01, "moles": 4.06}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 420 mL to 0.42 L.\n3. Compute M = 0.875 / 0.42.\nFinal: {\"answer\": 2.0833, \"unit\": \"mol/L\"}", "dedupe_signature": "7123697167241b3e9f076d50698eb79b3a205dc498d288d96c5c8d62d6a3e5dc", "difficulty": "medium", "final_answer": {"answer": 2.0833, "unit": "mol/L"}, "id": "molarity_006794_0.875_420", "license": "Apache-2.0", "prompt": "A solution contains 0.875 mol of solute in 420 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 420 mL to 0.42 L.\nCompute M = 0.875 / 0.42.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 0.875, "volume_ml": 420}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(9.1)=-62.58 and f(17)=-124.2.\n3. The interval width is 7.9.\nFinal: {\"answer\": -737.781, \"unit\": \"area_units\"}", "dedupe_signature": "d0b2775d7a2ea6fc44d6738624c8121f461a6a27523a16b9f6047d8ab8840faa", "difficulty": "medium", "final_answer": {"answer": -737.781, "unit": "area_units"}, "id": "trapz_linear_006796_-7.8_8.4_9.1_17", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-7.8x+8.4 from x=9.1 to x=17. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(9.1)=-62.58 and f(17)=-124.2.\nThe interval width is 7.9.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 8.4, "slope": -7.8, "x0": 9.1, "x1": 17.0}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 100 centimeters in one meter.\n2. Apply the conversion factor directly to the given value.\n3. Compute 4204.0 / 100.\nFinal: {\"answer\": 42.04, \"unit\": \"m\"}", "dedupe_signature": "0f4b44cb14505165e1595297c63fb16e1b69302440c703a005cebb9adb474696", "difficulty": "easy", "final_answer": {"answer": 42.04, "unit": "m"}, "id": "unit_convert_006798_cm_to_m_4204", "license": "Apache-2.0", "prompt": "Convert 4204 cm to m. Return the converted value with unit.", "reasoning_trace": "There are 100 centimeters in one meter.\nApply the conversion factor directly to the given value.\nCompute 4204.0 / 100.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 4204.0}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=278 degrees and keep the unit as newtons.\nFinal: {\"answer\": [26.93, -191.6169], \"unit\": \"N\"}", "dedupe_signature": "0a8ce185af3209f787b1335d4a02e6cea28b393dacbcef55b0d53f0c3ee78a56", "difficulty": "medium", "final_answer": {"answer": [26.93, -191.6169], "unit": "N"}, "id": "vector_components_006799_193.5_278", "license": "Apache-2.0", "prompt": "A vector has magnitude 193.5 N at 278 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=278 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 278, "magnitude": 193.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [5.6, -12.75], \"unit\": \"dimensionless\"}", "dedupe_signature": "a7799eef490332e1a12eb64877e9260f32edb05ea1db1d2d0dd5034003050f4a", "difficulty": "medium", "final_answer": {"answer": [5.6, -12.75], "unit": "dimensionless"}, "id": "line_two_point_006800_9.75_14_5.6_-12.75", "license": "Apache-2.0", "prompt": "A line passes through points (9.75, 41.85) and (14, 65.65). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 9.75, "x2": 14.0, "y1": 41.849999999999994, "y2": 65.64999999999999}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. energy divided by length is force, not spring constant\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "9b8ed8b3c1f14177b6b146c9b36520cae175453931cc627975dea4f0fae8cf43", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_006801_inconsistent_56040f5d_133967", "license": "Apache-2.0", "prompt": "In student derivation case 133967, check dimensional consistency for k = E / x. The left side has dimensions N/m and the right side has dimensions J/m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nenergy divided by length is force, not spring constant\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "k = E / x"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\nimport math\n\ndef unit_vector_006802(x, y):\n    norm = math.hypot(x, y)\n    if norm == 0:\n        raise ValueError('zero vector has no direction')\n    return (x / norm, y / norm)\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"unit_vector_006802\"}", "dedupe_signature": "7f735fe0242b65df14644450fc30cc840998719c657fa20197180b174edd6322", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "unit_vector_006802"}, "id": "code_006802_unit_vector_006802", "license": "Apache-2.0", "prompt": "Write a Python function unit_vector_006802(x, y) that returns the 2D unit vector as a tuple. Raise ValueError for the zero vector. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "unit_vector_006802"}, "verifier": {"function": "unit_vector_006802", "tests": ["ux, uy = unit_vector_006802(3, 4); assert abs(ux - 0.6) < 1e-12 and abs(uy - 0.8) < 1e-12", "assert unit_vector_006802(0, 5) == (0, 1)", "try:\n    unit_vector_006802(0, 0)\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: required_fields, allowed_transformations.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"required_fields\", \"allowed_transformations\"]}", "dedupe_signature": "f48cbea9845ab44885ac2790b733b2db30ae5a09b69c5d96fda0ea4db5d92727", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["required_fields", "allowed_transformations"]}, "id": "abstain_006803_required_fields_allowed_transformations", "license": "Apache-2.0", "prompt": "Write a sanitizer for valid warehouse survey records in release 812789, but the prompt does not state which fields are required or which transformations are allowed. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: required_fields, allowed_transformations.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["required_fields", "allowed_transformations"]}, "verifier": {"missing": ["required_fields", "allowed_transformations"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 18.8 kg and a = 12.3 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 231.24, \"unit\": \"N\"}", "dedupe_signature": "c9f5dcf417e24c80368f0faefa7f2520a4f40bf46a7296a986f65d627e2d64f4", "difficulty": "easy", "final_answer": {"answer": 231.24, "unit": "N"}, "id": "force_006804_18.8_12.3", "license": "Apache-2.0", "prompt": "A cart has mass 18.8 kg and measured acceleration 12.3 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 18.8 kg and a = 12.3 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 12.3, "mass": 18.8}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 30.3^2 and multiply by 0.5 * 26.25.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 12049.9312, \"unit\": \"J\"}", "dedupe_signature": "a9c7178ac1c2902b1d9855fc72a46ac6d5c3fb1d62b1832eea1b35f051cb20b5", "difficulty": "easy", "final_answer": {"answer": 12049.9312, "unit": "J"}, "id": "ke_006805_26.25_30.3", "license": "Apache-2.0", "prompt": "A body of mass 26.25 kg moves at 30.3 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 30.3^2 and multiply by 0.5 * 26.25.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 26.25, "velocity": 30.3}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=39 degrees through the sine of 2 theta.\n3. Substitute v=26.6 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 70.5503, \"unit\": \"m\"}", "dedupe_signature": "31269fab719ff92c5071639dcc506e6525d073fff31edbf52fc7991a7bae773b", "difficulty": "medium", "final_answer": {"answer": 70.5503, "unit": "m"}, "id": "projectile_range_006806_26.6_39", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 26.6 m/s and angle 39 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=39 degrees through the sine of 2 theta.\nSubstitute v=26.6 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 39, "gravity": 9.81, "speed": 26.6}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 3.12 * 8.314 * 564 / 82.6.\nFinal: {\"answer\": 177.1184, \"unit\": \"kPa\"}", "dedupe_signature": "45f45457ad91e00c4785984cb844302f1e5e67ea31bda3638215320bb846db6f", "difficulty": "medium", "final_answer": {"answer": 177.1184, "unit": "kPa"}, "id": "ideal_gas_006807_3.12_564_82.6", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=3.12 mol, T=564 K, and V=82.6 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 3.12 * 8.314 * 564 / 82.6.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 3.12, "temp_k": 564, "volume_l": 82.6}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 845 * 3.065 * 83.\nFinal: {\"answer\": 214963.775, \"unit\": \"J\"}", "dedupe_signature": "732e95cbab06cffeb8ee1e7dc530589ac07d6616a984fd63f299819a6bcdc398", "difficulty": "easy", "final_answer": {"answer": 214963.775, "unit": "J"}, "id": "heat_q_006808_845_3.065_83", "license": "Apache-2.0", "prompt": "A 845 g sample has specific heat 3.065 J/(g*K). How much heat is needed to raise its temperature by 83 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 845 * 3.065 * 83.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 83, "heat_capacity": 3.065, "mass_g": 845}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=219 mg, t=303 h, and T_half=75.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 13.5624, \"unit\": \"mg\"}", "dedupe_signature": "af5de9cdfbd02a4d24671d42cf657d1af153b76d27f0d2ba71710e8ef5a8bae6", "difficulty": "medium", "final_answer": {"answer": 13.5624, "unit": "mg"}, "id": "half_life_006810_219_75.5_303", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 219 mg. Its half-life is 75.5 hours. How many mg remain after 303 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=219 mg, t=303 h, and T_half=75.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 303.0, "half_life": 75.5, "initial_amount": 219.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 2.84 mol * 58.44 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 165.9696, \"unit\": \"g\"}", "dedupe_signature": "8d48647574382ad167d507a5d0ad74b82903787c4f6746f958a34c3486ee77ae", "difficulty": "medium", "final_answer": {"answer": 165.9696, "unit": "g"}, "id": "stoich_mass_006811_sodium_chloride_2.84", "license": "Apache-2.0", "prompt": "A sample contains 2.84 mol of sodium chloride. Using molar mass 58.44 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 2.84 mol * 58.44 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "sodium chloride", "molar_mass": 58.44, "moles": 2.84}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 3800 mL to 3.8 L.\n3. Compute M = 3.82 / 3.8.\nFinal: {\"answer\": 1.0053, \"unit\": \"mol/L\"}", "dedupe_signature": "4c45eb43b82387fc77d4c03811e949a8800e9f01fe211364e27a400970dc5ebb", "difficulty": "medium", "final_answer": {"answer": 1.0053, "unit": "mol/L"}, "id": "molarity_006812_3.82_3800", "license": "Apache-2.0", "prompt": "A solution contains 3.82 mol of solute in 3800 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 3800 mL to 3.8 L.\nCompute M = 3.82 / 3.8.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 3.82, "volume_ml": 3800}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.71 y, so each step multiplies y by 1 - h*0.71.\n3. Apply that update for 10 steps and round the final state.\nFinal: {\"answer\": 0.0, \"unit\": \"state_units\"}", "dedupe_signature": "c09c8dc53755881b1e9f291deb27b494e9532b1e982c5eb225ea2f34213820d6", "difficulty": "medium", "final_answer": {"answer": 0.0, "unit": "state_units"}, "id": "euler_decay_006813_75.5_0.71_1.35_10", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.71 y with y(0)=75.5, step size h=1.35, for 10 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.71 y, so each step multiplies y by 1 - h*0.71.\nApply that update for 10 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 75.5, "rate": 0.71, "step": 1.35, "steps": 10}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(2.6)=8.06 and f(3.8)=3.98.\n3. The interval width is 1.2.\nFinal: {\"answer\": 7.224, \"unit\": \"area_units\"}", "dedupe_signature": "26f175f57b121950a7f8902ec0e437200b328860a13db9005676fa04e2147699", "difficulty": "medium", "final_answer": {"answer": 7.224, "unit": "area_units"}, "id": "trapz_linear_006814_-3.4_16.9_2.6_3.8", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-3.4x+16.9 from x=2.6 to x=3.8. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(2.6)=8.06 and f(3.8)=3.98.\nThe interval width is 1.2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 16.9, "slope": -3.4, "x0": 2.6, "x1": 3.8}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 2061.0 / 1000.\nFinal: {\"answer\": 2.061, \"unit\": \"kg\"}", "dedupe_signature": "1dd118591ea6425eb8208d876c038b59c77ae09eed3823d982696cd1fb420a85", "difficulty": "easy", "final_answer": {"answer": 2.061, "unit": "kg"}, "id": "unit_convert_006816_g_to_kg_2061", "license": "Apache-2.0", "prompt": "Convert 2061 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 2061.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 2061.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=356 degrees and keep the unit as newtons.\nFinal: {\"answer\": [197.0189, -13.7769], \"unit\": \"N\"}", "dedupe_signature": "c4438c7128c7d107acc50ad9a26f34cb6e540844059b474e6fb95f503f7653e3", "difficulty": "medium", "final_answer": {"answer": [197.0189, -13.7769], "unit": "N"}, "id": "vector_components_006817_197.5_356", "license": "Apache-2.0", "prompt": "A vector has magnitude 197.5 N at 356 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=356 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 356, "magnitude": 197.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: left_boundary, right_boundary.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"left_boundary\", \"right_boundary\"]}", "dedupe_signature": "30dd2cb374fe38233a5efa27b3b199c09c82e7dd659029a13f6ceb9b9454f265", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["left_boundary", "right_boundary"]}, "id": "abstain_006821_left_boundary_right_boundary", "license": "Apache-2.0", "prompt": "Solve the 1D heat equation after one finite-difference step. The prompt gives r=0.12 and interior values [-1.9, 2.55, 2.75], but gives no boundary values. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: left_boundary, right_boundary.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["left_boundary", "right_boundary"]}, "verifier": {"missing": ["left_boundary", "right_boundary"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 16 kg and a = 13.05 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 208.8, \"unit\": \"N\"}", "dedupe_signature": "faf7debb07c7bb44f2a64ff124220f5f0de0e7872a791b2d0b62e435f31ea09d", "difficulty": "easy", "final_answer": {"answer": 208.8, "unit": "N"}, "id": "force_006822_16_13.05", "license": "Apache-2.0", "prompt": "A cart has mass 16 kg and measured acceleration 13.05 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 16 kg and a = 13.05 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 13.05, "mass": 16.0}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 10.25^2 and multiply by 0.5 * 8.85.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 464.9016, \"unit\": \"J\"}", "dedupe_signature": "785e09fb689a299d2f5aa3a1ecf281c45e6b0f05a3dd9fff0faf2b95f5910000", "difficulty": "easy", "final_answer": {"answer": 464.9016, "unit": "J"}, "id": "ke_006823_8.85_10.25", "license": "Apache-2.0", "prompt": "A body of mass 8.85 kg moves at 10.25 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 10.25^2 and multiply by 0.5 * 8.85.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 8.85, "velocity": 10.25}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=28 degrees through the sine of 2 theta.\n3. Substitute v=30.9 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 80.6905, \"unit\": \"m\"}", "dedupe_signature": "0a5b9a4685886e1e1f10c7ba902e2407ad5253b8b00cfef2a17dd3201156d5c2", "difficulty": "medium", "final_answer": {"answer": 80.6905, "unit": "m"}, "id": "projectile_range_006824_30.9_28", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 30.9 m/s and angle 28 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=28 degrees through the sine of 2 theta.\nSubstitute v=30.9 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 28, "gravity": 9.81, "speed": 30.9}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 2.51 * 8.314 * 609 / 111.5.\nFinal: {\"answer\": 113.9793, \"unit\": \"kPa\"}", "dedupe_signature": "4e595a5042d4616464dceec38b796b8304409e42b124cb14d527d458426f6e7f", "difficulty": "medium", "final_answer": {"answer": 113.9793, "unit": "kPa"}, "id": "ideal_gas_006825_2.51_609_111.5", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=2.51 mol, T=609 K, and V=111.5 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 2.51 * 8.314 * 609 / 111.5.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 2.51, "temp_k": 609, "volume_l": 111.5}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 545 * 3.66 * 103.\nFinal: {\"answer\": 205454.1, \"unit\": \"J\"}", "dedupe_signature": "d78cf172ea18abb1dbd001e741dc8be7160ab9c0fa1f8cef5105b8ee7159021d", "difficulty": "easy", "final_answer": {"answer": 205454.1, "unit": "J"}, "id": "heat_q_006826_545_3.66_103", "license": "Apache-2.0", "prompt": "A 545 g sample has specific heat 3.66 J/(g*K). How much heat is needed to raise its temperature by 103 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 545 * 3.66 * 103.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 103, "heat_capacity": 3.66, "mass_g": 545}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=110.5 V and R=101.2 ohm.\nFinal: {\"answer\": 120.6546, \"unit\": \"W\"}", "dedupe_signature": "b96ab64c87d0d4736c0595772d20d3396b7bd70ad830d1ab9de1e4b0586344ad", "difficulty": "easy", "final_answer": {"answer": 120.6546, "unit": "W"}, "id": "ohm_power_006827_110.5_101.2", "license": "Apache-2.0", "prompt": "A resistor has resistance 101.2 ohm and voltage 110.5 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=110.5 V and R=101.2 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 101.2, "voltage": 110.5}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 6.73 mol * 18.015 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 121.241, \"unit\": \"g\"}", "dedupe_signature": "906314ef05bbc1d621a921eccb95641f98bbf8751606b7ead3d7e8be3cefaf0c", "difficulty": "medium", "final_answer": {"answer": 121.241, "unit": "g"}, "id": "stoich_mass_006829_water_6.73", "license": "Apache-2.0", "prompt": "A sample contains 6.73 mol of water. Using molar mass 18.015 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 6.73 mol * 18.015 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "water", "molar_mass": 18.015, "moles": 6.73}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 520 mL to 0.52 L.\n3. Compute M = 3.245 / 0.52.\nFinal: {\"answer\": 6.2404, \"unit\": \"mol/L\"}", "dedupe_signature": "249d29e78f5630093618c19066228f19fd1011e5511d2dd7fba21a7002137315", "difficulty": "medium", "final_answer": {"answer": 6.2404, "unit": "mol/L"}, "id": "molarity_006830_3.245_520", "license": "Apache-2.0", "prompt": "A solution contains 3.245 mol of solute in 520 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 520 mL to 0.52 L.\nCompute M = 3.245 / 0.52.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 3.245, "volume_ml": 520}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.17 y, so each step multiplies y by 1 - h*0.17.\n3. Apply that update for 4 steps and round the final state.\nFinal: {\"answer\": 21.7293, \"unit\": \"state_units\"}", "dedupe_signature": "0c9a3cccb6ae2f80cfc2a736e5c0ccb794e025bcf419fb726775b76cbdfd5aad", "difficulty": "medium", "final_answer": {"answer": 21.7293, "unit": "state_units"}, "id": "euler_decay_006831_31_0.17_0.5_4", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.17 y with y(0)=31, step size h=0.5, for 4 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.17 y, so each step multiplies y by 1 - h*0.17.\nApply that update for 4 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 31.0, "rate": 0.17, "step": 0.5, "steps": 4}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-4.1)=-12.18 and f(3.2)=44.76.\n3. The interval width is 7.3.\nFinal: {\"answer\": 118.917, \"unit\": \"area_units\"}", "dedupe_signature": "16fd29b83f62b4515e2f5f31819f8dec047d8d0ee9a479d48b9f75610cc04f4f", "difficulty": "medium", "final_answer": {"answer": 118.917, "unit": "area_units"}, "id": "trapz_linear_006832_7.8_19.8_-4.1_3.2", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=7.8x+19.8 from x=-4.1 to x=3.2. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-4.1)=-12.18 and f(3.2)=44.76.\nThe interval width is 7.3.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 19.8, "slope": 7.8, "x0": -4.1, "x1": 3.2}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.3 and add it to the current value.\nFinal: {\"answer\": [1.775, 1.665, 0.83], \"unit\": \"temperature_units\"}", "dedupe_signature": "b838b8702a9d5915413a7324bdbb15b314adddd82590c0ba5a45fc2fa7689972", "difficulty": "hard", "final_answer": {"answer": [1.775, 1.665, 0.83], "unit": "temperature_units"}, "id": "heat_step_006833_0.3_0.2_2.15_2.85_-0.4_0.45", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=0.2, right=0.45; current interior values are [2.15, 2.85, -0.4]. Use r=0.3. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.3 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [2.15, 2.85, -0.4], "left": 0.2, "r": 0.3, "right": 0.45}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kelvin equals Celsius plus 273.15.\n2. Apply the conversion factor directly to the given value.\n3. Compute 71.0 + 273.15.\nFinal: {\"answer\": 344.15, \"unit\": \"K\"}", "dedupe_signature": "9a9b558f13866eaec528b3c14bbfe1676ffb8abcdb1d1f826d21de47b9d6090a", "difficulty": "easy", "final_answer": {"answer": 344.15, "unit": "K"}, "id": "unit_convert_006834_c_to_k_71", "license": "Apache-2.0", "prompt": "Convert 71 degC to K. Return the converted value with unit.", "reasoning_trace": "Kelvin equals Celsius plus 273.15.\nApply the conversion factor directly to the given value.\nCompute 71.0 + 273.15.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 71.0}, "verifier": {"formula": "value + 273.15", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=344 degrees and keep the unit as newtons.\nFinal: {\"answer\": [162.4532, -46.5827], \"unit\": \"N\"}", "dedupe_signature": "5b5226256795240138613b0db015335c2b816563a9292aec91bedd10bb8b43c8", "difficulty": "medium", "final_answer": {"answer": [162.4532, -46.5827], "unit": "N"}, "id": "vector_components_006835_169_344", "license": "Apache-2.0", "prompt": "A vector has magnitude 169 N at 344 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=344 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 344, "magnitude": 169.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. coulomb per second is ampere\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "2badfcc0e70ba3b02f0ba1362596488b574c4b45c2ce345682edec996b714fc6", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_006837_consistent_8b38953d_236577", "license": "Apache-2.0", "prompt": "In student derivation case 236577, check dimensional consistency for I = Q / t. The left side has dimensions A and the right side has dimensions A. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\ncoulomb per second is ampere\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "I = Q / t"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef clamp_006838(x, lo, hi):\n    if lo > hi:\n        raise ValueError('lo must be <= hi')\n    return min(max(x, lo), hi)\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"clamp_006838\"}", "dedupe_signature": "0afb7723351c32cb5de60bd956e09d6afd7fac1c02a9f80269772fd4c70075ba", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "clamp_006838"}, "id": "code_006838_clamp_006838", "license": "Apache-2.0", "prompt": "Write a Python function clamp_006838(x, lo, hi) that clips x into the inclusive interval [lo, hi]. It must raise ValueError if lo > hi. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "clamp_006838"}, "verifier": {"function": "clamp_006838", "tests": ["assert clamp_006838(5, 0, 10) == 5", "assert clamp_006838(-2, 0, 10) == 0", "assert clamp_006838(12, 0, 10) == 10", "try:\n    clamp_006838(1, 3, 2)\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: recurrence, objective, tie_breaking_rule.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"recurrence\", \"objective\", \"tie_breaking_rule\"]}", "dedupe_signature": "7559d0ede62a9b7890a6ccae7b4be6ac1af166496683331857c770c4e67c288b", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["recurrence", "objective", "tie_breaking_rule"]}, "id": "abstain_006839_recurrence_objective_tie_breaking_rule", "license": "Apache-2.0", "prompt": "Write a dynamic-programming solver for a allocation scoring problem with 55 items and budget 71985, but the recurrence, objective, and tie-breaking rule are all absent. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: recurrence, objective, tie_breaking_rule.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["recurrence", "objective", "tie_breaking_rule"]}, "verifier": {"missing": ["recurrence", "objective", "tie_breaking_rule"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 3.95 kg and a = 2.8 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 11.06, \"unit\": \"N\"}", "dedupe_signature": "bc55efc8fb1327db452d5b6b81f19148626bf02d3e8d0838a610db5af93caeb6", "difficulty": "easy", "final_answer": {"answer": 11.06, "unit": "N"}, "id": "force_006840_3.95_2.8", "license": "Apache-2.0", "prompt": "A cart has mass 3.95 kg and measured acceleration 2.8 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 3.95 kg and a = 2.8 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 2.8, "mass": 3.95}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 31.1^2 and multiply by 0.5 * 16.1.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 7786.0405, \"unit\": \"J\"}", "dedupe_signature": "c3df8fb9d2cf966655a93ed663b9f08c973cef1b8c46d4a52c7bec8b732fcf99", "difficulty": "easy", "final_answer": {"answer": 7786.0405, "unit": "J"}, "id": "ke_006841_16.1_31.1", "license": "Apache-2.0", "prompt": "A body of mass 16.1 kg moves at 31.1 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 31.1^2 and multiply by 0.5 * 16.1.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 16.1, "velocity": 31.1}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=6 degrees through the sine of 2 theta.\n3. Substitute v=66.5 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 93.7245, \"unit\": \"m\"}", "dedupe_signature": "fc6fd0de35b3e277af7f5606e16c1aeff9bb5946e43aab7b49084588388522c6", "difficulty": "medium", "final_answer": {"answer": 93.7245, "unit": "m"}, "id": "projectile_range_006842_66.5_6", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 66.5 m/s and angle 6 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=6 degrees through the sine of 2 theta.\nSubstitute v=66.5 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 6, "gravity": 9.81, "speed": 66.5}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 3.05 * 8.314 * 567 / 118.5.\nFinal: {\"answer\": 121.3318, \"unit\": \"kPa\"}", "dedupe_signature": "539a211f328413834a9088c730a2e0b38774c50f455637dd06de4a8d0329a310", "difficulty": "medium", "final_answer": {"answer": 121.3318, "unit": "kPa"}, "id": "ideal_gas_006843_3.05_567_118.5", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=3.05 mol, T=567 K, and V=118.5 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 3.05 * 8.314 * 567 / 118.5.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 3.05, "temp_k": 567, "volume_l": 118.5}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1955 * 1.085 * 21.\nFinal: {\"answer\": 44544.675, \"unit\": \"J\"}", "dedupe_signature": "b0fa048efa7186e635580acb7bf29ecc3164fee3fc4913afd31a217c98a20068", "difficulty": "easy", "final_answer": {"answer": 44544.675, "unit": "J"}, "id": "heat_q_006844_1955_1.085_21", "license": "Apache-2.0", "prompt": "A 1955 g sample has specific heat 1.085 J/(g*K). How much heat is needed to raise its temperature by 21 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1955 * 1.085 * 21.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 21, "heat_capacity": 1.085, "mass_g": 1955}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=931 mg, t=219.5 h, and T_half=7 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 0.0, \"unit\": \"mg\"}", "dedupe_signature": "cac4d8f3eecfe8e2137c3c566c66f22b4f20ad0dcf3cbab2edd56545bb0b5ee8", "difficulty": "medium", "final_answer": {"answer": 0.0, "unit": "mg"}, "id": "half_life_006846_931_7_219.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 931 mg. Its half-life is 7 hours. How many mg remain after 219.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=931 mg, t=219.5 h, and T_half=7 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 219.5, "half_life": 7.0, "initial_amount": 931.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 0.59 mol * 44.01 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 25.9659, \"unit\": \"g\"}", "dedupe_signature": "2b756ecf351062c9ed0570fc32b4f9212cb40807f5de1e29846d54d58f5f7c11", "difficulty": "medium", "final_answer": {"answer": 25.9659, "unit": "g"}, "id": "stoich_mass_006847_carbon_dioxide_0.59", "license": "Apache-2.0", "prompt": "A sample contains 0.59 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 0.59 mol * 44.01 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "carbon dioxide", "molar_mass": 44.01, "moles": 0.59}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 820 mL to 0.82 L.\n3. Compute M = 2.625 / 0.82.\nFinal: {\"answer\": 3.2012, \"unit\": \"mol/L\"}", "dedupe_signature": "3e0674f8cf45b65cee148a4255d0a3685b7465cb5cdd49e637e87886ec1f0bf6", "difficulty": "medium", "final_answer": {"answer": 3.2012, "unit": "mol/L"}, "id": "molarity_006848_2.625_820", "license": "Apache-2.0", "prompt": "A solution contains 2.625 mol of solute in 820 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 820 mL to 0.82 L.\nCompute M = 2.625 / 0.82.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 2.625, "volume_ml": 820}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.62 y, so each step multiplies y by 1 - h*0.62.\n3. Apply that update for 2 steps and round the final state.\nFinal: {\"answer\": 0.2926, \"unit\": \"state_units\"}", "dedupe_signature": "39d17f6541022d6082e27c31cfd779869249897e6c3266363ae11d5c158b481e", "difficulty": "medium", "final_answer": {"answer": 0.2926, "unit": "state_units"}, "id": "euler_decay_006849_40.5_0.62_1.75_2", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.62 y with y(0)=40.5, step size h=1.75, for 2 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.62 y, so each step multiplies y by 1 - h*0.62.\nApply that update for 2 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 40.5, "rate": 0.62, "step": 1.75, "steps": 2}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(5.2)=34.72 and f(6.5)=42.65.\n3. The interval width is 1.3.\nFinal: {\"answer\": 50.2905, \"unit\": \"area_units\"}", "dedupe_signature": "2efba7065ac7a9d16a1d5a4ab6b886b01679a2711a99f4e50cf4a0945ce5e0ca", "difficulty": "medium", "final_answer": {"answer": 50.2905, "unit": "area_units"}, "id": "trapz_linear_006850_6.1_3_5.2_6.5", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=6.1x+3 from x=5.2 to x=6.5. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(5.2)=34.72 and f(6.5)=42.65.\nThe interval width is 1.3.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 3.0, "slope": 6.1, "x0": 5.2, "x1": 6.5}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 100 centimeters in one meter.\n2. Apply the conversion factor directly to the given value.\n3. Compute 347.0 / 100.\nFinal: {\"answer\": 3.47, \"unit\": \"m\"}", "dedupe_signature": "f529d1a7fc3203c41d65119ea823e0cebf3dd02d9884bc4d224920a0d8004ca4", "difficulty": "easy", "final_answer": {"answer": 3.47, "unit": "m"}, "id": "unit_convert_006852_cm_to_m_347", "license": "Apache-2.0", "prompt": "Convert 347 cm to m. Return the converted value with unit.", "reasoning_trace": "There are 100 centimeters in one meter.\nApply the conversion factor directly to the given value.\nCompute 347.0 / 100.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 347.0}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=59 degrees and keep the unit as newtons.\nFinal: {\"answer\": [134.1674, 223.2921], \"unit\": \"N\"}", "dedupe_signature": "e983cbb870e147ada73edc93dccf8900e5475daac66961da6f0a20648c463071", "difficulty": "medium", "final_answer": {"answer": [134.1674, 223.2921], "unit": "N"}, "id": "vector_components_006853_260.5_59", "license": "Apache-2.0", "prompt": "A vector has magnitude 260.5 N at 59 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=59 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 59, "magnitude": 260.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-7.85, -15.75], \"unit\": \"dimensionless\"}", "dedupe_signature": "df3556569b58cc3cb7442ae90ea3b87f79d783e21c8b25cff2b7257ec0c6b761", "difficulty": "medium", "final_answer": {"answer": [-7.85, -15.75], "unit": "dimensionless"}, "id": "line_two_point_006854_-3.25_8.75_-7.85_-15.75", "license": "Apache-2.0", "prompt": "A line passes through points (-3.25, 9.7625) and (8.75, -84.4375). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -3.25, "x2": 8.75, "y1": 9.7625, "y2": -84.4375}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. velocity times time gives distance, not acceleration\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "23403a6ab5d4f3d140db302e4512b1d54343b4c463f0ecc44589ac19c4b6c064", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_006855_inconsistent_7481c798_29471", "license": "Apache-2.0", "prompt": "In instrument manual case 29471, check dimensional consistency for a = v * t. The left side has dimensions m/s^2 and the right side has dimensions m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nvelocity times time gives distance, not acceleration\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "a = v * t"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 1.9 kg and a = 10.15 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 19.285, \"unit\": \"N\"}", "dedupe_signature": "a4f8b6b6df89427aa678c35e6d7bb8ab3fe8738315eee4e9d422058a785b2e77", "difficulty": "easy", "final_answer": {"answer": 19.285, "unit": "N"}, "id": "force_006858_1.9_10.15", "license": "Apache-2.0", "prompt": "A cart has mass 1.9 kg and measured acceleration 10.15 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 1.9 kg and a = 10.15 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 10.15, "mass": 1.9}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 41.65^2 and multiply by 0.5 * 8.4.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 7285.8345, \"unit\": \"J\"}", "dedupe_signature": "6098bc67f815f17bad0d47c3697bef17a2ae92a2aa83c0b3eb051d01ca8966e9", "difficulty": "easy", "final_answer": {"answer": 7285.8345, "unit": "J"}, "id": "ke_006859_8.4_41.65", "license": "Apache-2.0", "prompt": "A body of mass 8.4 kg moves at 41.65 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 41.65^2 and multiply by 0.5 * 8.4.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 8.4, "velocity": 41.65}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 0.76 * 8.314 * 352 / 28.1.\nFinal: {\"answer\": 79.1516, \"unit\": \"kPa\"}", "dedupe_signature": "2fca339dce3092f21051b1c3b50cef9c158fad1435d8095333bd62cbdfcb0803", "difficulty": "medium", "final_answer": {"answer": 79.1516, "unit": "kPa"}, "id": "ideal_gas_006861_0.76_352_28.1", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=0.76 mol, T=352 K, and V=28.1 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 0.76 * 8.314 * 352 / 28.1.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 0.76, "temp_k": 352, "volume_l": 28.1}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=58.7 V and R=107.7 ohm.\nFinal: {\"answer\": 31.9934, \"unit\": \"W\"}", "dedupe_signature": "29327d63189e0f048eec5a0204a319f47cf9d216830cb3166ce97c8445fe53ad", "difficulty": "easy", "final_answer": {"answer": 31.9934, "unit": "W"}, "id": "ohm_power_006863_58.7_107.7", "license": "Apache-2.0", "prompt": "A resistor has resistance 107.7 ohm and voltage 58.7 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=58.7 V and R=107.7 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 107.7, "voltage": 58.7}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=865 mg, t=70.5 h, and T_half=75 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 450.8664, \"unit\": \"mg\"}", "dedupe_signature": "a3b1ac599895b93c1165f59f01d8b3b2a38d4d4e23884efef136cf0737724d69", "difficulty": "medium", "final_answer": {"answer": 450.8664, "unit": "mg"}, "id": "half_life_006864_865_75_70.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 865 mg. Its half-life is 75 hours. How many mg remain after 70.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=865 mg, t=70.5 h, and T_half=75 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 70.5, "half_life": 75.0, "initial_amount": 865.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 4740 mL to 4.74 L.\n3. Compute M = 3.69 / 4.74.\nFinal: {\"answer\": 0.7785, \"unit\": \"mol/L\"}", "dedupe_signature": "ab4cebb3ee9bcd92dea782ebf60bd65d72b4502a6e07b64a763bff9aea07be07", "difficulty": "medium", "final_answer": {"answer": 0.7785, "unit": "mol/L"}, "id": "molarity_006866_3.69_4740", "license": "Apache-2.0", "prompt": "A solution contains 3.69 mol of solute in 4740 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 4740 mL to 4.74 L.\nCompute M = 3.69 / 4.74.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 3.69, "volume_ml": 4740}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.43 y, so each step multiplies y by 1 - h*0.43.\n3. Apply that update for 3 steps and round the final state.\nFinal: {\"answer\": 5.2366, \"unit\": \"state_units\"}", "dedupe_signature": "72c0e7ff3df0eac822f86cf10c0f4f0972757693daeab670e5ed23eb9bdcbc68", "difficulty": "medium", "final_answer": {"answer": 5.2366, "unit": "state_units"}, "id": "euler_decay_006867_20.5_0.43_0.85_3", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.43 y with y(0)=20.5, step size h=0.85, for 3 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.43 y, so each step multiplies y by 1 - h*0.43.\nApply that update for 3 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 20.5, "rate": 0.43, "step": 0.85, "steps": 3}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-4.8)=11.2 and f(-4.1)=7.\n3. The interval width is 0.7.\nFinal: {\"answer\": 6.37, \"unit\": \"area_units\"}", "dedupe_signature": "508f975d5fa62720bdf8d56c61e797fd05a6d7613f5860bdba7b15a770e16b7b", "difficulty": "medium", "final_answer": {"answer": 6.37, "unit": "area_units"}, "id": "trapz_linear_006868_-6_-17.6_-4.8_-4.1", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-6x+-17.6 from x=-4.8 to x=-4.1. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-4.8)=11.2 and f(-4.1)=7.\nThe interval width is 0.7.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -17.6, "slope": -6.0, "x0": -4.8, "x1": -4.1}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.04 and add it to the current value.\nFinal: {\"answer\": [-0.392, 0.248, 0.852], \"unit\": \"temperature_units\"}", "dedupe_signature": "4cfd15ad16b08937df18d0c4e1a947b574761294ff01b89b27863d8e4d39ac2b", "difficulty": "hard", "final_answer": {"answer": [-0.392, 0.248, 0.852], "unit": "temperature_units"}, "id": "heat_step_006869_0.04_1.45_-0.5_0.25_0.95_-0.8", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.45, right=-0.8; current interior values are [-0.5, 0.25, 0.95]. Use r=0.04. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.04 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-0.5, 0.25, 0.95], "left": 1.45, "r": 0.04, "right": -0.8}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 6540.0 / 1000.\nFinal: {\"answer\": 6.54, \"unit\": \"kg\"}", "dedupe_signature": "0968910ccc381cdca24e90b98a008e87cbc43b99844d19a4509d2568f4249b07", "difficulty": "easy", "final_answer": {"answer": 6.54, "unit": "kg"}, "id": "unit_convert_006870_g_to_kg_6540", "license": "Apache-2.0", "prompt": "Convert 6540 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 6540.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 6540.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=79 degrees and keep the unit as newtons.\nFinal: {\"answer\": [26.9995, 138.9002], \"unit\": \"N\"}", "dedupe_signature": "b0aecce9f427f481b18e04c219e5740c5d065678b99dc8d1528a089d6823e131", "difficulty": "medium", "final_answer": {"answer": [26.9995, 138.9002], "unit": "N"}, "id": "vector_components_006871_141.5_79", "license": "Apache-2.0", "prompt": "A vector has magnitude 141.5 N at 79 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=79 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 79, "magnitude": 141.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [0.05, -26.0], \"unit\": \"dimensionless\"}", "dedupe_signature": "a55f2ac6555c4013b730e396c57c809e8a5ee90c027bbfd516d26a28eef90adb", "difficulty": "medium", "final_answer": {"answer": [0.05, -26.0], "unit": "dimensionless"}, "id": "line_two_point_006872_18.75_19_0.05_-26", "license": "Apache-2.0", "prompt": "A line passes through points (18.75, -25.0625) and (19, -25.05). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 18.75, "x2": 19.0, "y1": -25.0625, "y2": -25.05}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. m*v is momentum, not energy\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "6c89269a5f7852b51c7c96af4fabf20f3c0559b5337a5248cdc49b4c05062a1c", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_006873_inconsistent_1e14b074_864168", "license": "Apache-2.0", "prompt": "In lab notebook case 864168, check dimensional consistency for E = m * v. The left side has dimensions kg*m^2/s^2 and the right side has dimensions kg*m/s. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nm*v is momentum, not energy\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "E = m * v"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: left_boundary, right_boundary.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"left_boundary\", \"right_boundary\"]}", "dedupe_signature": "509dd06ba2b79246e0846aab7acd5c5bf9534de6592e3778ebf5f199542dfd59", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["left_boundary", "right_boundary"]}, "id": "abstain_006875_left_boundary_right_boundary", "license": "Apache-2.0", "prompt": "Solve the 1D heat equation after one finite-difference step. The prompt gives r=0.28 and interior values [-0.85, -1.45, 0.75], but gives no boundary values. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: left_boundary, right_boundary.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["left_boundary", "right_boundary"]}, "verifier": {"missing": ["left_boundary", "right_boundary"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 21.35 kg and a = 2.2 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 46.97, \"unit\": \"N\"}", "dedupe_signature": "f556efb1da5f8c479868b329300e9d203e56bb0f5c615608b0fc8c7a787c8155", "difficulty": "easy", "final_answer": {"answer": 46.97, "unit": "N"}, "id": "force_006876_21.35_2.2", "license": "Apache-2.0", "prompt": "A cart has mass 21.35 kg and measured acceleration 2.2 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 21.35 kg and a = 2.2 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 2.2, "mass": 21.35}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 30.95^2 and multiply by 0.5 * 12.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 5747.415, \"unit\": \"J\"}", "dedupe_signature": "8b459a3200670cd3e02abd0cfb3b1953d7c55dac367503b5877225190cb929d9", "difficulty": "easy", "final_answer": {"answer": 5747.415, "unit": "J"}, "id": "ke_006877_12_30.95", "license": "Apache-2.0", "prompt": "A body of mass 12 kg moves at 30.95 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 30.95^2 and multiply by 0.5 * 12.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 12.0, "velocity": 30.95}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1355 * 4.165 * 28.\nFinal: {\"answer\": 158020.1, \"unit\": \"J\"}", "dedupe_signature": "468c37d97ffd84806dfbbe8b777e6aa3cac68967c063fc709f4d41a5c80ad52c", "difficulty": "easy", "final_answer": {"answer": 158020.1, "unit": "J"}, "id": "heat_q_006880_1355_4.165_28", "license": "Apache-2.0", "prompt": "A 1355 g sample has specific heat 4.165 J/(g*K). How much heat is needed to raise its temperature by 28 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1355 * 4.165 * 28.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 28, "heat_capacity": 4.165, "mass_g": 1355}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=140 V and R=140.2 ohm.\nFinal: {\"answer\": 139.8003, \"unit\": \"W\"}", "dedupe_signature": "876aee6422e3dca43d380f8345bcbbe25ceb94d8b67c9f23b834b124c9a22c4f", "difficulty": "easy", "final_answer": {"answer": 139.8003, "unit": "W"}, "id": "ohm_power_006881_140_140.2", "license": "Apache-2.0", "prompt": "A resistor has resistance 140.2 ohm and voltage 140 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=140 V and R=140.2 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 140.2, "voltage": 140.0}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=961.5 mg, t=43.5 h, and T_half=12 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 77.932, \"unit\": \"mg\"}", "dedupe_signature": "c315d1ee132bcd0353b719d28ce77540f4c9405678ebd3d50632ec6f893687e7", "difficulty": "medium", "final_answer": {"answer": 77.932, "unit": "mg"}, "id": "half_life_006882_961.5_12_43.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 961.5 mg. Its half-life is 12 hours. How many mg remain after 43.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=961.5 mg, t=43.5 h, and T_half=12 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 43.5, "half_life": 12.0, "initial_amount": 961.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 2.64 mol * 18.015 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 47.5596, \"unit\": \"g\"}", "dedupe_signature": "c37e9238d4b4d8e00e97503c60410295e9521eea5d5d3db0c6ae4e75d0825ca5", "difficulty": "medium", "final_answer": {"answer": 47.5596, "unit": "g"}, "id": "stoich_mass_006883_water_2.64", "license": "Apache-2.0", "prompt": "A sample contains 2.64 mol of water. Using molar mass 18.015 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 2.64 mol * 18.015 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "water", "molar_mass": 18.015, "moles": 2.64}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 1335 mL to 1.335 L.\n3. Compute M = 2.94 / 1.335.\nFinal: {\"answer\": 2.2022, \"unit\": \"mol/L\"}", "dedupe_signature": "e6e52a266b0474f135b53e292dd6b9bbecafe2df065559c7bdc732f1bd10c13d", "difficulty": "medium", "final_answer": {"answer": 2.2022, "unit": "mol/L"}, "id": "molarity_006884_2.94_1335", "license": "Apache-2.0", "prompt": "A solution contains 2.94 mol of solute in 1335 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 1335 mL to 1.335 L.\nCompute M = 2.94 / 1.335.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 2.94, "volume_ml": 1335}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.17 y, so each step multiplies y by 1 - h*0.17.\n3. Apply that update for 5 steps and round the final state.\nFinal: {\"answer\": 4.8289, \"unit\": \"state_units\"}", "dedupe_signature": "8453643d83c756f92067ca7a845b137dfbcfe5c0fb035b6bbab82fee02e6ddfd", "difficulty": "medium", "final_answer": {"answer": 4.8289, "unit": "state_units"}, "id": "euler_decay_006885_6_0.17_0.25_5", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.17 y with y(0)=6, step size h=0.25, for 5 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.17 y, so each step multiplies y by 1 - h*0.17.\nApply that update for 5 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 6.0, "rate": 0.17, "step": 0.25, "steps": 5}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.32 and add it to the current value.\nFinal: {\"answer\": [0.248, -0.424, -1.438], \"unit\": \"temperature_units\"}", "dedupe_signature": "9973fb46da700a7c6fe10ab59adb32e411322ac9f46b82e0dda7890476ae3cf3", "difficulty": "hard", "final_answer": {"answer": [0.248, -0.424, -1.438], "unit": "temperature_units"}, "id": "heat_step_006887_0.32_0.15_1.8_-1.4_-1.55_-1.35", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=0.15, right=-1.35; current interior values are [1.8, -1.4, -1.55]. Use r=0.32. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.32 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [1.8, -1.4, -1.55], "left": 0.15, "r": 0.32, "right": -1.35}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 100 centimeters in one meter.\n2. Apply the conversion factor directly to the given value.\n3. Compute 726.0 / 100.\nFinal: {\"answer\": 7.26, \"unit\": \"m\"}", "dedupe_signature": "c0df7c6954899627ffc1b9a2a4507b20412dd95e66885ae9e8b7240685a0e9b0", "difficulty": "easy", "final_answer": {"answer": 7.26, "unit": "m"}, "id": "unit_convert_006888_cm_to_m_726", "license": "Apache-2.0", "prompt": "Convert 726 cm to m. Return the converted value with unit.", "reasoning_trace": "There are 100 centimeters in one meter.\nApply the conversion factor directly to the given value.\nCompute 726.0 / 100.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 726.0}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=88 degrees and keep the unit as newtons.\nFinal: {\"answer\": [10.086, 288.8239], \"unit\": \"N\"}", "dedupe_signature": "c848caab534b3e6c570bffc74eea3f11640f7a9fe85ed6030ac1207a07ec3acf", "difficulty": "medium", "final_answer": {"answer": [10.086, 288.8239], "unit": "N"}, "id": "vector_components_006889_289_88", "license": "Apache-2.0", "prompt": "A vector has magnitude 289 N at 88 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=88 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 88, "magnitude": 289.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-2.1, -6.5], \"unit\": \"dimensionless\"}", "dedupe_signature": "e026faf67539218ff50bb7e85c3cf1c3fa4805f132253236b6af40bb6987c375", "difficulty": "medium", "final_answer": {"answer": [-2.1, -6.5], "unit": "dimensionless"}, "id": "line_two_point_006890_-10_1_-2.1_-6.5", "license": "Apache-2.0", "prompt": "A line passes through points (-10, 14.5) and (1, -8.6). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -10.0, "x2": 1.0, "y1": 14.5, "y2": -8.6}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. velocity times time gives distance, not acceleration\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "0085eb6c65a540072cb4ff62fb6b43b5ce6bc66a224047d82d61a0390d8a449c", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_006891_inconsistent_7481c798_628513", "license": "Apache-2.0", "prompt": "In lab notebook case 628513, check dimensional consistency for a = v * t. The left side has dimensions m/s^2 and the right side has dimensions m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nvelocity times time gives distance, not acceleration\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "a = v * t"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef clamp_006892(x, lo, hi):\n    if lo > hi:\n        raise ValueError('lo must be <= hi')\n    return min(max(x, lo), hi)\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"clamp_006892\"}", "dedupe_signature": "fa87c1786aa1781f08b5f175981c58e1a851495445997d5b92a69b40f2b05a2f", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "clamp_006892"}, "id": "code_006892_clamp_006892", "license": "Apache-2.0", "prompt": "Write a Python function clamp_006892(x, lo, hi) that clips x into the inclusive interval [lo, hi]. It must raise ValueError if lo > hi. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "clamp_006892"}, "verifier": {"function": "clamp_006892", "tests": ["assert clamp_006892(5, 0, 10) == 5", "assert clamp_006892(-2, 0, 10) == 0", "assert clamp_006892(12, 0, 10) == 10", "try:\n    clamp_006892(1, 3, 2)\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 17.25 kg and a = 5.9 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 101.775, \"unit\": \"N\"}", "dedupe_signature": "01ab86496c6abb1a541f648133661ba13371ee5cadd49f3caec4b7b6d6db89ba", "difficulty": "easy", "final_answer": {"answer": 101.775, "unit": "N"}, "id": "force_006894_17.25_5.9", "license": "Apache-2.0", "prompt": "A cart has mass 17.25 kg and measured acceleration 5.9 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 17.25 kg and a = 5.9 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 5.9, "mass": 17.25}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 33.2^2 and multiply by 0.5 * 4.35.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 2397.372, \"unit\": \"J\"}", "dedupe_signature": "278e8f8ebf8425a4fd28dedb8c212e9303f57bb2a39cf3fdd6153948c544655c", "difficulty": "easy", "final_answer": {"answer": 2397.372, "unit": "J"}, "id": "ke_006895_4.35_33.2", "license": "Apache-2.0", "prompt": "A body of mass 4.35 kg moves at 33.2 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 33.2^2 and multiply by 0.5 * 4.35.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 4.35, "velocity": 33.2}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1230 * 3.495 * 33.\nFinal: {\"answer\": 141862.05, \"unit\": \"J\"}", "dedupe_signature": "388066ee7b7a628035b3a07f6bbc503b770e00703ffe929eee844a0ac379f646", "difficulty": "easy", "final_answer": {"answer": 141862.05, "unit": "J"}, "id": "heat_q_006898_1230_3.495_33", "license": "Apache-2.0", "prompt": "A 1230 g sample has specific heat 3.495 J/(g*K). How much heat is needed to raise its temperature by 33 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1230 * 3.495 * 33.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 33, "heat_capacity": 3.495, "mass_g": 1230}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=85.4 V and R=18.5 ohm.\nFinal: {\"answer\": 394.2249, \"unit\": \"W\"}", "dedupe_signature": "ab3346780f6e789bf0f5b6dc9d01ed63091ac1375c69b0371e18f838a4cbd63e", "difficulty": "easy", "final_answer": {"answer": 394.2249, "unit": "W"}, "id": "ohm_power_006899_85.4_18.5", "license": "Apache-2.0", "prompt": "A resistor has resistance 18.5 ohm and voltage 85.4 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=85.4 V and R=18.5 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 18.5, "voltage": 85.4}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=788 mg, t=105.5 h, and T_half=87.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 341.6411, \"unit\": \"mg\"}", "dedupe_signature": "be64326db3fad2516026f79abb45ce69a7c540b3bd7ff60493d7e96df171485d", "difficulty": "medium", "final_answer": {"answer": 341.6411, "unit": "mg"}, "id": "half_life_006900_788_87.5_105.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 788 mg. Its half-life is 87.5 hours. How many mg remain after 105.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=788 mg, t=105.5 h, and T_half=87.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 105.5, "half_life": 87.5, "initial_amount": 788.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 7.79 mol * 18.015 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 140.3368, \"unit\": \"g\"}", "dedupe_signature": "4e8fe2f8dbb6e86169a2a33af7741c9a7ad786ff086f42fab1c7db554cf03cd3", "difficulty": "medium", "final_answer": {"answer": 140.3368, "unit": "g"}, "id": "stoich_mass_006901_water_7.79", "license": "Apache-2.0", "prompt": "A sample contains 7.79 mol of water. Using molar mass 18.015 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 7.79 mol * 18.015 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "water", "molar_mass": 18.015, "moles": 7.79}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 945 mL to 0.945 L.\n3. Compute M = 2.11 / 0.945.\nFinal: {\"answer\": 2.2328, \"unit\": \"mol/L\"}", "dedupe_signature": "f8cc9a3fc66a2e80f21b47d9b2c7fc8a72b89a779d14004e74725757b5724ed5", "difficulty": "medium", "final_answer": {"answer": 2.2328, "unit": "mol/L"}, "id": "molarity_006902_2.11_945", "license": "Apache-2.0", "prompt": "A solution contains 2.11 mol of solute in 945 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 945 mL to 0.945 L.\nCompute M = 2.11 / 0.945.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 2.11, "volume_ml": 945}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-2.3)=19.98 and f(2.9)=1.26.\n3. The interval width is 5.2.\nFinal: {\"answer\": 55.224, \"unit\": \"area_units\"}", "dedupe_signature": "dea9d421c69f2acfa7570584e3cf08e51258d08038c76b1ac48e1edcecaf1940", "difficulty": "medium", "final_answer": {"answer": 55.224, "unit": "area_units"}, "id": "trapz_linear_006904_-3.6_11.7_-2.3_2.9", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-3.6x+11.7 from x=-2.3 to x=2.9. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-2.3)=19.98 and f(2.9)=1.26.\nThe interval width is 5.2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 11.7, "slope": -3.6, "x0": -2.3, "x1": 2.9000000000000004}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.06 and add it to the current value.\nFinal: {\"answer\": [-0.891, -1.094, 1.111], \"unit\": \"temperature_units\"}", "dedupe_signature": "42ee3ea86841053931e7deb0ba916082edacd4176274e46098650b75336a4c64", "difficulty": "hard", "final_answer": {"answer": [-0.891, -1.094, 1.111], "unit": "temperature_units"}, "id": "heat_step_006905_0.06_1.8_-1.05_-1.25_1.15_2.9", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.8, right=2.9; current interior values are [-1.05, -1.25, 1.15]. Use r=0.06. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.06 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-1.05, -1.25, 1.15], "left": 1.8, "r": 0.06, "right": 2.9}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 24238.0 / 1000.\nFinal: {\"answer\": 24.238, \"unit\": \"kg\"}", "dedupe_signature": "46cfd16e65d894ecee997f6824230211c2d9fa6a6ab246d69becb313237f4330", "difficulty": "easy", "final_answer": {"answer": 24.238, "unit": "kg"}, "id": "unit_convert_006906_g_to_kg_24238", "license": "Apache-2.0", "prompt": "Convert 24238 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 24238.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 24238.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-4.6, -2.75], \"unit\": \"dimensionless\"}", "dedupe_signature": "42a382592f2a149529fc036ed89dd3b7d28359717b7e24dc8ced42948d8bc7e8", "difficulty": "medium", "final_answer": {"answer": [-4.6, -2.75], "unit": "dimensionless"}, "id": "line_two_point_006908_14_16.5_-4.6_-2.75", "license": "Apache-2.0", "prompt": "A line passes through points (14, -67.15) and (16.5, -78.65). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 14.0, "x2": 16.5, "y1": -67.14999999999999, "y2": -78.64999999999999}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\nimport math\n\ndef unit_vector_006910(x, y):\n    norm = math.hypot(x, y)\n    if norm == 0:\n        raise ValueError('zero vector has no direction')\n    return (x / norm, y / norm)\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"unit_vector_006910\"}", "dedupe_signature": "764d344c7a87bb6801ed7210297770591c3c95233a2e6c4f77a8b3b2a69131bd", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "unit_vector_006910"}, "id": "code_006910_unit_vector_006910", "license": "Apache-2.0", "prompt": "Write a Python function unit_vector_006910(x, y) that returns the 2D unit vector as a tuple. Raise ValueError for the zero vector. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "unit_vector_006910"}, "verifier": {"function": "unit_vector_006910", "tests": ["ux, uy = unit_vector_006910(3, 4); assert abs(ux - 0.6) < 1e-12 and abs(uy - 0.8) < 1e-12", "assert unit_vector_006910(0, 5) == (0, 1)", "try:\n    unit_vector_006910(0, 0)\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 26.85^2 and multiply by 0.5 * 19.3.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 6956.9021, \"unit\": \"J\"}", "dedupe_signature": "dc8d57d336f4f537da946a3eb3df7f8f3206c0c1876ceaaa69421b8e9c4861de", "difficulty": "easy", "final_answer": {"answer": 6956.9021, "unit": "J"}, "id": "ke_006913_19.3_26.85", "license": "Apache-2.0", "prompt": "A body of mass 19.3 kg moves at 26.85 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 26.85^2 and multiply by 0.5 * 19.3.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 19.3, "velocity": 26.85}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=9 degrees through the sine of 2 theta.\n3. Substitute v=53.7 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 90.8368, \"unit\": \"m\"}", "dedupe_signature": "8354580da3192b4096deccbf77336018daa7989735b600aceda7840cde18913e", "difficulty": "medium", "final_answer": {"answer": 90.8368, "unit": "m"}, "id": "projectile_range_006914_53.7_9", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 53.7 m/s and angle 9 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=9 degrees through the sine of 2 theta.\nSubstitute v=53.7 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 9, "gravity": 9.81, "speed": 53.7}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 4.62 * 8.314 * 559 / 92.5.\nFinal: {\"answer\": 232.1251, \"unit\": \"kPa\"}", "dedupe_signature": "5ff5947c58deef8cc51c5a59745e43b6d846b7a781caef2e2896d675f28e17e9", "difficulty": "medium", "final_answer": {"answer": 232.1251, "unit": "kPa"}, "id": "ideal_gas_006915_4.62_559_92.5", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=4.62 mol, T=559 K, and V=92.5 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 4.62 * 8.314 * 559 / 92.5.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 4.62, "temp_k": 559, "volume_l": 92.5}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 525 * 3.35 * 92.\nFinal: {\"answer\": 161805.0, \"unit\": \"J\"}", "dedupe_signature": "0feb1afb5ad9451590fc1e20d4233a35e0b4a99a1157b6570b9a056e235ee069", "difficulty": "easy", "final_answer": {"answer": 161805.0, "unit": "J"}, "id": "heat_q_006916_525_3.35_92", "license": "Apache-2.0", "prompt": "A 525 g sample has specific heat 3.35 J/(g*K). How much heat is needed to raise its temperature by 92 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 525 * 3.35 * 92.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 92, "heat_capacity": 3.35, "mass_g": 525}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=127.4 V and R=144.3 ohm.\nFinal: {\"answer\": 112.4793, \"unit\": \"W\"}", "dedupe_signature": "3c19edbc96db23d84f60afd98273cb1804b97f131346a4afad010db972838446", "difficulty": "easy", "final_answer": {"answer": 112.4793, "unit": "W"}, "id": "ohm_power_006917_127.4_144.3", "license": "Apache-2.0", "prompt": "A resistor has resistance 144.3 ohm and voltage 127.4 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=127.4 V and R=144.3 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 144.3, "voltage": 127.4}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=417.5 mg, t=42.5 h, and T_half=73.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 279.635, \"unit\": \"mg\"}", "dedupe_signature": "7a32edfb2ecd0c076ef64c51d4ef856e829a954f264d94e03235c27abe586994", "difficulty": "medium", "final_answer": {"answer": 279.635, "unit": "mg"}, "id": "half_life_006918_417.5_73.5_42.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 417.5 mg. Its half-life is 73.5 hours. How many mg remain after 42.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=417.5 mg, t=42.5 h, and T_half=73.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 42.5, "half_life": 73.5, "initial_amount": 417.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 6.44 mol * 58.44 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 376.3536, \"unit\": \"g\"}", "dedupe_signature": "fd7953946a316a5a6bd0a4c40af8f9c8b5565ad67f85265eedde06b7d7d093a7", "difficulty": "medium", "final_answer": {"answer": 376.3536, "unit": "g"}, "id": "stoich_mass_006919_sodium_chloride_6.44", "license": "Apache-2.0", "prompt": "A sample contains 6.44 mol of sodium chloride. Using molar mass 58.44 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 6.44 mol * 58.44 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "sodium chloride", "molar_mass": 58.44, "moles": 6.44}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.5 y, so each step multiplies y by 1 - h*0.5.\n3. Apply that update for 12 steps and round the final state.\nFinal: {\"answer\": 0.0, \"unit\": \"state_units\"}", "dedupe_signature": "924ed7544a111f7595be9cf655817e4f8002a537195961fe8e728d687ca1fd8f", "difficulty": "medium", "final_answer": {"answer": 0.0, "unit": "state_units"}, "id": "euler_decay_006921_24.5_0.5_1.5_12", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.5 y with y(0)=24.5, step size h=1.5, for 12 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.5 y, so each step multiplies y by 1 - h*0.5.\nApply that update for 12 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 24.5, "rate": 0.5, "step": 1.5, "steps": 12}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(3.1)=-27.96 and f(12.4)=-89.34.\n3. The interval width is 9.3.\nFinal: {\"answer\": -545.445, \"unit\": \"area_units\"}", "dedupe_signature": "6f678a65ba0ee62f64ef826a718524f378dc4f4477131aeda931760ae6dcffb3", "difficulty": "medium", "final_answer": {"answer": -545.445, "unit": "area_units"}, "id": "trapz_linear_006922_-6.6_-7.5_3.1_12.4", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-6.6x+-7.5 from x=3.1 to x=12.4. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(3.1)=-27.96 and f(12.4)=-89.34.\nThe interval width is 9.3.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -7.5, "slope": -6.6, "x0": 3.1, "x1": 12.4}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.02 and add it to the current value.\nFinal: {\"answer\": [2.326, 1.601, 0.863], \"unit\": \"temperature_units\"}", "dedupe_signature": "7eb2c59b635d1b491ecd2722e5cc5bd41e615f143b77e585e018e49edac40cb9", "difficulty": "hard", "final_answer": {"answer": [2.326, 1.601, 0.863], "unit": "temperature_units"}, "id": "heat_step_006923_0.02_1.9_2.35_1.6_0.9_-1.65", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.9, right=-1.65; current interior values are [2.35, 1.6, 0.9]. Use r=0.02. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.02 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [2.35, 1.6, 0.9], "left": 1.9, "r": 0.02, "right": -1.65}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 100 centimeters in one meter.\n2. Apply the conversion factor directly to the given value.\n3. Compute 370.0 / 100.\nFinal: {\"answer\": 3.7, \"unit\": \"m\"}", "dedupe_signature": "b6a5969ddc09145875c471a5f415c1fe6ee2d021f663a7150a9e0aa3174aeda8", "difficulty": "easy", "final_answer": {"answer": 3.7, "unit": "m"}, "id": "unit_convert_006924_cm_to_m_370", "license": "Apache-2.0", "prompt": "Convert 370 cm to m. Return the converted value with unit.", "reasoning_trace": "There are 100 centimeters in one meter.\nApply the conversion factor directly to the given value.\nCompute 370.0 / 100.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 370.0}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=316 degrees and keep the unit as newtons.\nFinal: {\"answer\": [254.2866, -245.5617], \"unit\": \"N\"}", "dedupe_signature": "fa55668e552e5c15fc9e214ff9cd86abf88f31ebc2352fc22d951061b40babcd", "difficulty": "medium", "final_answer": {"answer": [254.2866, -245.5617], "unit": "N"}, "id": "vector_components_006925_353.5_316", "license": "Apache-2.0", "prompt": "A vector has magnitude 353.5 N at 316 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=316 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 316, "magnitude": 353.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-0.6, 7.5], \"unit\": \"dimensionless\"}", "dedupe_signature": "f69486cdaae0a74e84a45168434fd0e23b1ead4dcb8ff3539bf6d2276fc0d9f4", "difficulty": "medium", "final_answer": {"answer": [-0.6, 7.5], "unit": "dimensionless"}, "id": "line_two_point_006926_8_8.25_-0.6_7.5", "license": "Apache-2.0", "prompt": "A line passes through points (8, 2.7) and (8.25, 2.55). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 8.0, "x2": 8.25, "y1": 2.7, "y2": 2.55}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. amount times volume is not concentration\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "2bf7d70a5b469a348e3f3a8aefe607f9df54f932bb37d6335b02ea92e57bdd60", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_006927_inconsistent_74ac0b02_243692", "license": "Apache-2.0", "prompt": "In quality-control check case 243692, check dimensional consistency for C = n * V. The left side has dimensions mol/L and the right side has dimensions mol*L. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\namount times volume is not concentration\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "C = n * V"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef pairwise_ratios_006928(numerators, denominators):\n    if len(numerators) != len(denominators):\n        raise ValueError('length mismatch')\n    out = []\n    for numerator, denominator in zip(numerators, denominators):\n        if denominator == 0:\n            raise ValueError('zero denominator')\n        out.append(numerator / denominator)\n    return out\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"pairwise_ratios_006928\"}", "dedupe_signature": "d88153f150f263a65b667defeda85ed4fde23ab0370544e61cd10d419c193389", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "pairwise_ratios_006928"}, "id": "code_006928_pairwise_ratios_006928", "license": "Apache-2.0", "prompt": "Write a Python function pairwise_ratios_006928(numerators, denominators) that returns a list of n/d values. Raise ValueError if lengths differ or any denominator is zero. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "pairwise_ratios_006928"}, "verifier": {"function": "pairwise_ratios_006928", "tests": ["assert pairwise_ratios_006928([2, 9], [4, 3]) == [0.5, 3.0]", "try:\n    pairwise_ratios_006928([1], [0])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass", "try:\n    pairwise_ratios_006928([1, 2], [1])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: required_fields, allowed_transformations.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"required_fields\", \"allowed_transformations\"]}", "dedupe_signature": "c17af8c251bb866ad8eb0bd04986f5a6778e3e4bea6be6c3ebe493444520c500", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["required_fields", "allowed_transformations"]}, "id": "abstain_006929_required_fields_allowed_transformations", "license": "Apache-2.0", "prompt": "Write a sanitizer for valid registry invoice records in release 776427, but the prompt does not state which fields are required or which transformations are allowed. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: required_fields, allowed_transformations.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["required_fields", "allowed_transformations"]}, "verifier": {"missing": ["required_fields", "allowed_transformations"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 9.3 kg and a = 9.25 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 86.025, \"unit\": \"N\"}", "dedupe_signature": "d2db093c22f1f3d7f725310bd25a7c751a7db4fdbce0bed438a43304d27df11d", "difficulty": "easy", "final_answer": {"answer": 86.025, "unit": "N"}, "id": "force_006930_9.3_9.25", "license": "Apache-2.0", "prompt": "A cart has mass 9.3 kg and measured acceleration 9.25 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 9.3 kg and a = 9.25 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 9.25, "mass": 9.3}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 6.75^2 and multiply by 0.5 * 13.75.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 313.2422, \"unit\": \"J\"}", "dedupe_signature": "90a8e50cd47fff963398bc52101466415ee83439e436e6336137c87e6dd63b30", "difficulty": "easy", "final_answer": {"answer": 313.2422, "unit": "J"}, "id": "ke_006931_13.75_6.75", "license": "Apache-2.0", "prompt": "A body of mass 13.75 kg moves at 6.75 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 6.75^2 and multiply by 0.5 * 13.75.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 13.75, "velocity": 6.75}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=75 degrees through the sine of 2 theta.\n3. Substitute v=82.9 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 350.2757, \"unit\": \"m\"}", "dedupe_signature": "fbe7c6dacaa878b72553b75286bfd871a68164b4467eceac0c01df06a02dc2f3", "difficulty": "medium", "final_answer": {"answer": 350.2757, "unit": "m"}, "id": "projectile_range_006932_82.9_75", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 82.9 m/s and angle 75 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=75 degrees through the sine of 2 theta.\nSubstitute v=82.9 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 75, "gravity": 9.81, "speed": 82.9}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 4.96 * 8.314 * 572 / 69.5.\nFinal: {\"answer\": 339.393, \"unit\": \"kPa\"}", "dedupe_signature": "2add2309dc8c60c9491a9a7f96f1dc779094245fe20a20988413175b80038266", "difficulty": "medium", "final_answer": {"answer": 339.393, "unit": "kPa"}, "id": "ideal_gas_006933_4.96_572_69.5", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=4.96 mol, T=572 K, and V=69.5 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 4.96 * 8.314 * 572 / 69.5.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 4.96, "temp_k": 572, "volume_l": 69.5}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1070 * 2.43 * 113.\nFinal: {\"answer\": 293811.3, \"unit\": \"J\"}", "dedupe_signature": "d5dbe13fd647842ad81701c409ced36618ae4f309d962acabe58d74ec6cd0a9d", "difficulty": "easy", "final_answer": {"answer": 293811.3, "unit": "J"}, "id": "heat_q_006934_1070_2.43_113", "license": "Apache-2.0", "prompt": "A 1070 g sample has specific heat 2.43 J/(g*K). How much heat is needed to raise its temperature by 113 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1070 * 2.43 * 113.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 113, "heat_capacity": 2.43, "mass_g": 1070}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=66.4 V and R=187.3 ohm.\nFinal: {\"answer\": 23.5396, \"unit\": \"W\"}", "dedupe_signature": "14220fbf7ff5e2485dfdac089f3284b39dc63ad0aa2d63b17e4ebf4480ec2fba", "difficulty": "easy", "final_answer": {"answer": 23.5396, "unit": "W"}, "id": "ohm_power_006935_66.4_187.3", "license": "Apache-2.0", "prompt": "A resistor has resistance 187.3 ohm and voltage 66.4 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=66.4 V and R=187.3 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 187.3, "voltage": 66.4}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=814.5 mg, t=234.5 h, and T_half=38.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 11.9494, \"unit\": \"mg\"}", "dedupe_signature": "2191b1effdaa8719ffe429d8ea74382bf23e960cd0fc2e80c662a0bf1360e691", "difficulty": "medium", "final_answer": {"answer": 11.9494, "unit": "mg"}, "id": "half_life_006936_814.5_38.5_234.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 814.5 mg. Its half-life is 38.5 hours. How many mg remain after 234.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=814.5 mg, t=234.5 h, and T_half=38.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 234.5, "half_life": 38.5, "initial_amount": 814.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 5.61 mol * 100.087 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 561.4881, \"unit\": \"g\"}", "dedupe_signature": "b6478fdaf645e888837941b888322769262318204e75152ed5b2783c4cc446b1", "difficulty": "medium", "final_answer": {"answer": 561.4881, "unit": "g"}, "id": "stoich_mass_006937_calcium_carbonate_5.61", "license": "Apache-2.0", "prompt": "A sample contains 5.61 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 5.61 mol * 100.087 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "calcium carbonate", "molar_mass": 100.087, "moles": 5.61}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 3780 mL to 3.78 L.\n3. Compute M = 1.39 / 3.78.\nFinal: {\"answer\": 0.3677, \"unit\": \"mol/L\"}", "dedupe_signature": "c99146188a1b1339c9937722d31c768f56328d9fa166b0514c72845a1ddde743", "difficulty": "medium", "final_answer": {"answer": 0.3677, "unit": "mol/L"}, "id": "molarity_006938_1.39_3780", "license": "Apache-2.0", "prompt": "A solution contains 1.39 mol of solute in 3780 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 3780 mL to 3.78 L.\nCompute M = 1.39 / 3.78.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 1.39, "volume_ml": 3780}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-1.3)=-11.76 and f(-1.1)=-10.52.\n3. The interval width is 0.2.\nFinal: {\"answer\": -2.228, \"unit\": \"area_units\"}", "dedupe_signature": "eea58c19bf6fee3541772baba567cf7321b23d28ca5be87fc24bb67ddb1183c7", "difficulty": "medium", "final_answer": {"answer": -2.228, "unit": "area_units"}, "id": "trapz_linear_006940_6.2_-3.7_-1.3_-1.1", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=6.2x+-3.7 from x=-1.3 to x=-1.1. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-1.3)=-11.76 and f(-1.1)=-10.52.\nThe interval width is 0.2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -3.7, "slope": 6.2, "x0": -1.3, "x1": -1.1}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.34 and add it to the current value.\nFinal: {\"answer\": [-0.559, 0.608, 1.106], \"unit\": \"temperature_units\"}", "dedupe_signature": "de7f09c3d8ce98bbb58b1fe381c345c8a7af156aaf1f1f428752d5acf6f199f9", "difficulty": "hard", "final_answer": {"answer": [-0.559, 0.608, 1.106], "unit": "temperature_units"}, "id": "heat_step_006941_0.34_-1.7_0.75_-0.65_1.65_2.35", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-1.7, right=2.35; current interior values are [0.75, -0.65, 1.65]. Use r=0.34. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.34 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [0.75, -0.65, 1.65], "left": -1.7, "r": 0.34, "right": 2.35}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 100 centimeters in one meter.\n2. Apply the conversion factor directly to the given value.\n3. Compute 414.0 / 100.\nFinal: {\"answer\": 4.14, \"unit\": \"m\"}", "dedupe_signature": "1bde769c758cf4c81222fcce9693acd04e1471ab67fb751f0cd89bf36f4f355c", "difficulty": "easy", "final_answer": {"answer": 4.14, "unit": "m"}, "id": "unit_convert_006942_cm_to_m_414", "license": "Apache-2.0", "prompt": "Convert 414 cm to m. Return the converted value with unit.", "reasoning_trace": "There are 100 centimeters in one meter.\nApply the conversion factor directly to the given value.\nCompute 414.0 / 100.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 414.0}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=334 degrees and keep the unit as newtons.\nFinal: {\"answer\": [390.0766, -190.2531], \"unit\": \"N\"}", "dedupe_signature": "23fcb0dec2f5e14899029daa0110a94e5321de9562aab2201fb03b13bde92594", "difficulty": "medium", "final_answer": {"answer": [390.0766, -190.2531], "unit": "N"}, "id": "vector_components_006943_434_334", "license": "Apache-2.0", "prompt": "A vector has magnitude 434 N at 334 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=334 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 334, "magnitude": 434.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [6.1, 20.5], \"unit\": \"dimensionless\"}", "dedupe_signature": "a1019e58b240f4ef4d3e9e74796ce92858dde3b7a10925101da4dcff20d9f116", "difficulty": "medium", "final_answer": {"answer": [6.1, 20.5], "unit": "dimensionless"}, "id": "line_two_point_006944_16.25_22.25_6.1_20.5", "license": "Apache-2.0", "prompt": "A line passes through points (16.25, 119.625) and (22.25, 156.225). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 16.25, "x2": 22.25, "y1": 119.625, "y2": 156.225}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. mass times acceleration has newton dimensions\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "c809fe12cb2ba53dc7fc207ef220d48cf7c6ae95152c236dc7e0c09cd183b5d8", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_006945_consistent_03f5e041_495385", "license": "Apache-2.0", "prompt": "In lab notebook case 495385, check dimensional consistency for F = m * a. The left side has dimensions kg*m/s^2 and the right side has dimensions kg*m/s^2. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nmass times acceleration has newton dimensions\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "F = m * a"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef running_total_006946(values):\n    total = 0\n    out = []\n    for value in values:\n        total += value\n        out.append(total)\n    return out\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"running_total_006946\"}", "dedupe_signature": "7775c2da4af1dbaa23844bd1d5ba00b0e7490e07af3a8d5fd0a4d5b9c3aa4677", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "running_total_006946"}, "id": "code_006946_running_total_006946", "license": "Apache-2.0", "prompt": "Write a Python function running_total_006946(values) that returns cumulative sums as a new list. It must not mutate the input list. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "running_total_006946"}, "verifier": {"function": "running_total_006946", "tests": ["assert running_total_006946([1, 2, 3]) == [1, 3, 6]", "xs = [4, -1, 2]; assert running_total_006946(xs) == [4, 3, 5] and xs == [4, -1, 2]", "assert running_total_006946([]) == []"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: target_schema, valid_examples.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"target_schema\", \"valid_examples\"]}", "dedupe_signature": "735179ba1de0a1cb1a918120529c18b3ea445eacbbafa5080aeae8c51528706a", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["target_schema", "valid_examples"]}, "id": "abstain_006947_target_schema_valid_examples", "license": "Apache-2.0", "prompt": "Write a parser that converts each field crop record from batch 322195 into the correct schema, but the prompt does not include the target schema or examples. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: target_schema, valid_examples.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["target_schema", "valid_examples"]}, "verifier": {"missing": ["target_schema", "valid_examples"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 2.75 kg and a = 2.6 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 7.15, \"unit\": \"N\"}", "dedupe_signature": "5e8b8af46c32f7ef0721446c6c8942ce112730d9360fc68cc42c8e1af48cf1c8", "difficulty": "easy", "final_answer": {"answer": 7.15, "unit": "N"}, "id": "force_006948_2.75_2.6", "license": "Apache-2.0", "prompt": "A cart has mass 2.75 kg and measured acceleration 2.6 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 2.75 kg and a = 2.6 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 2.6, "mass": 2.75}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 25.25^2 and multiply by 0.5 * 17.6.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 5610.55, \"unit\": \"J\"}", "dedupe_signature": "bb48f64a023a36a4906ac2b9503bf98a7c1c738eb7d5bf6e568dd54f6e6ddc9d", "difficulty": "easy", "final_answer": {"answer": 5610.55, "unit": "J"}, "id": "ke_006949_17.6_25.25", "license": "Apache-2.0", "prompt": "A body of mass 17.6 kg moves at 25.25 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 25.25^2 and multiply by 0.5 * 17.6.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 17.6, "velocity": 25.25}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=57 degrees through the sine of 2 theta.\n3. Substitute v=10.4 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 10.0723, \"unit\": \"m\"}", "dedupe_signature": "189480a37993f03b2a20fbeb9f1cb9b2d5ae61619bf65454a8039598e958ffc1", "difficulty": "medium", "final_answer": {"answer": 10.0723, "unit": "m"}, "id": "projectile_range_006950_10.4_57", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 10.4 m/s and angle 57 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=57 degrees through the sine of 2 theta.\nSubstitute v=10.4 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 57, "gravity": 9.81, "speed": 10.4}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 4.95 * 8.314 * 520 / 15.5.\nFinal: {\"answer\": 1380.6604, \"unit\": \"kPa\"}", "dedupe_signature": "9f47651f7e8c0c1de2b2dd510217ff16a933e0035757c257a3029989f52d560a", "difficulty": "medium", "final_answer": {"answer": 1380.6604, "unit": "kPa"}, "id": "ideal_gas_006951_4.95_520_15.5", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=4.95 mol, T=520 K, and V=15.5 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 4.95 * 8.314 * 520 / 15.5.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 4.95, "temp_k": 520, "volume_l": 15.5}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1180 * 4.57 * 24.\nFinal: {\"answer\": 129422.4, \"unit\": \"J\"}", "dedupe_signature": "78a856026233481b4c7493350d91501a42263d4698e71fd8848b581e4bc75120", "difficulty": "easy", "final_answer": {"answer": 129422.4, "unit": "J"}, "id": "heat_q_006952_1180_4.57_24", "license": "Apache-2.0", "prompt": "A 1180 g sample has specific heat 4.57 J/(g*K). How much heat is needed to raise its temperature by 24 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1180 * 4.57 * 24.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 24, "heat_capacity": 4.57, "mass_g": 1180}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=193.6 V and R=119 ohm.\nFinal: {\"answer\": 314.9661, \"unit\": \"W\"}", "dedupe_signature": "03cd67b92174f383bf8d5a2964e76a72da0d18defd8d43ccc1b01de481f17a5e", "difficulty": "easy", "final_answer": {"answer": 314.9661, "unit": "W"}, "id": "ohm_power_006953_193.6_119", "license": "Apache-2.0", "prompt": "A resistor has resistance 119 ohm and voltage 193.6 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=193.6 V and R=119 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 119.0, "voltage": 193.6}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=319.5 mg, t=81.5 h, and T_half=10 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 1.1248, \"unit\": \"mg\"}", "dedupe_signature": "b1d85af5cc792182bb8a08e7d882878e6aacc005ef272792b8147492286b65a9", "difficulty": "medium", "final_answer": {"answer": 1.1248, "unit": "mg"}, "id": "half_life_006954_319.5_10_81.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 319.5 mg. Its half-life is 10 hours. How many mg remain after 81.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=319.5 mg, t=81.5 h, and T_half=10 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 81.5, "half_life": 10.0, "initial_amount": 319.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.23 y, so each step multiplies y by 1 - h*0.23.\n3. Apply that update for 4 steps and round the final state.\nFinal: {\"answer\": 26.2567, \"unit\": \"state_units\"}", "dedupe_signature": "b8d13606784a8ed6a711acb22df631ae7734aa76433f74e2e0cc9308ea3faf8b", "difficulty": "medium", "final_answer": {"answer": 26.2567, "unit": "state_units"}, "id": "euler_decay_006957_27.5_0.23_0.05_4", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.23 y with y(0)=27.5, step size h=0.05, for 4 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.23 y, so each step multiplies y by 1 - h*0.23.\nApply that update for 4 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 27.5, "rate": 0.23, "step": 0.05, "steps": 4}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(4.8)=-0.88 and f(14.8)=3.12.\n3. The interval width is 10.\nFinal: {\"answer\": 11.2, \"unit\": \"area_units\"}", "dedupe_signature": "0c5d4435f925d56d4305023a2d953281e300fb16bac0dd918c1d58883ab8977f", "difficulty": "medium", "final_answer": {"answer": 11.2, "unit": "area_units"}, "id": "trapz_linear_006958_0.4_-2.8_4.8_14.8", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=0.4x+-2.8 from x=4.8 to x=14.8. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(4.8)=-0.88 and f(14.8)=3.12.\nThe interval width is 10.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -2.8, "slope": 0.4, "x0": 4.8, "x1": 14.8}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.22 and add it to the current value.\nFinal: {\"answer\": [0.186, -0.061, 0.5], \"unit\": \"temperature_units\"}", "dedupe_signature": "a81afff73a2a449bcb7161042732a5337ee870ebcbe0b9c0ec78ecca5ccb4b2c", "difficulty": "hard", "final_answer": {"answer": [0.186, -0.061, 0.5], "unit": "temperature_units"}, "id": "heat_step_006959_0.22_2.55_-0.65_-0.05_0.5_1.05", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=2.55, right=1.05; current interior values are [-0.65, -0.05, 0.5]. Use r=0.22. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.22 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-0.65, -0.05, 0.5], "left": 2.55, "r": 0.22, "right": 1.05}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 30940.0 / 1000.\nFinal: {\"answer\": 30.94, \"unit\": \"kg\"}", "dedupe_signature": "e7b59dbabcd5a06825edecab33f3eb111f52d0530c6aa0bce8bcd962d922bc2c", "difficulty": "easy", "final_answer": {"answer": 30.94, "unit": "kg"}, "id": "unit_convert_006960_g_to_kg_30940", "license": "Apache-2.0", "prompt": "Convert 30940 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 30940.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 30940.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=303 degrees and keep the unit as newtons.\nFinal: {\"answer\": [52.013, -80.093], \"unit\": \"N\"}", "dedupe_signature": "fdff5772596500d8335ca58f3c4c6701bee29ad04f7bcba0cd41c0dfae617f08", "difficulty": "medium", "final_answer": {"answer": [52.013, -80.093], "unit": "N"}, "id": "vector_components_006961_95.5_303", "license": "Apache-2.0", "prompt": "A vector has magnitude 95.5 N at 303 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=303 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 303, "magnitude": 95.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. m*v is momentum, not energy\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "1fa8e001acbde3e38e992f2a48450c81b01f440c53be6ca87e514700895ab49a", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_006963_inconsistent_1e14b074_950253", "license": "Apache-2.0", "prompt": "In instrument manual case 950253, check dimensional consistency for E = m * v. The left side has dimensions kg*m^2/s^2 and the right side has dimensions kg*m/s. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nm*v is momentum, not energy\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "E = m * v"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef normalize_006964(values):\n    total = sum(values)\n    if total == 0:\n        raise ValueError('cannot normalize zero-sum values')\n    return [v / total for v in values]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"normalize_006964\"}", "dedupe_signature": "da418401c3dcc344642273d514e34eeebcead75539debf06c33b82b5d2a0dde3", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "normalize_006964"}, "id": "code_006964_normalize_006964", "license": "Apache-2.0", "prompt": "Write a Python function normalize_006964(values) that returns a new list whose values sum to 1. Raise ValueError if the sum is zero. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "normalize_006964"}, "verifier": {"function": "normalize_006964", "tests": ["out = normalize_006964([2, 3, 5]); assert len(out) == 3", "assert abs(sum(normalize_006964([2, 3, 5])) - 1.0) < 1e-12", "assert normalize_006964([1, 1]) == [0.5, 0.5]", "try:\n    normalize_006964([1, -1])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: volume.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"volume\"]}", "dedupe_signature": "0bdb71be8a7d34b295434c120f608acff50e6a3dd2ea79ade86a45748cd34091", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["volume"]}, "id": "abstain_006965_volume", "license": "Apache-2.0", "prompt": "Compute pressure from the ideal gas law. The prompt gives n=3.5 mol and T=488 K, but does not give volume. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: volume.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["volume"]}, "verifier": {"missing": ["volume"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 3.65 kg and a = 1.2 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 4.38, \"unit\": \"N\"}", "dedupe_signature": "80d511cdde0a87bcac81fbbd53acc6784231c8dc3aa8dd38d337384cb6f9ea83", "difficulty": "easy", "final_answer": {"answer": 4.38, "unit": "N"}, "id": "force_006966_3.65_1.2", "license": "Apache-2.0", "prompt": "A cart has mass 3.65 kg and measured acceleration 1.2 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 3.65 kg and a = 1.2 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 1.2, "mass": 3.65}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 5.75^2 and multiply by 0.5 * 22.2.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 366.9937, \"unit\": \"J\"}", "dedupe_signature": "131aba64d2d6dbd951b939fc7ca6f020803766368da51a2ea61391c2afcc6ae9", "difficulty": "easy", "final_answer": {"answer": 366.9937, "unit": "J"}, "id": "ke_006967_22.2_5.75", "license": "Apache-2.0", "prompt": "A body of mass 22.2 kg moves at 5.75 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 5.75^2 and multiply by 0.5 * 22.2.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 22.2, "velocity": 5.75}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=76 degrees through the sine of 2 theta.\n3. Substitute v=43.8 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 91.8097, \"unit\": \"m\"}", "dedupe_signature": "4642534f445d8e31cbff0c562778dab629248548031e4bde2066fe31606370d0", "difficulty": "medium", "final_answer": {"answer": 91.8097, "unit": "m"}, "id": "projectile_range_006968_43.8_76", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 43.8 m/s and angle 76 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=76 degrees through the sine of 2 theta.\nSubstitute v=43.8 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 76, "gravity": 9.81, "speed": 43.8}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 1.67 * 8.314 * 525 / 23.4.\nFinal: {\"answer\": 311.5085, \"unit\": \"kPa\"}", "dedupe_signature": "2da042a5d72270b2d8374fd257de2d5b262e9d66619ba845b10cb4d26d8e9597", "difficulty": "medium", "final_answer": {"answer": 311.5085, "unit": "kPa"}, "id": "ideal_gas_006969_1.67_525_23.4", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=1.67 mol, T=525 K, and V=23.4 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 1.67 * 8.314 * 525 / 23.4.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 1.67, "temp_k": 525, "volume_l": 23.4}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1110 * 2.24 * 80.\nFinal: {\"answer\": 198912.0, \"unit\": \"J\"}", "dedupe_signature": "b4d6d59733253a68ad7a505a55a595846df87fe42ba8a3f4f3068a3c3e29b2e8", "difficulty": "easy", "final_answer": {"answer": 198912.0, "unit": "J"}, "id": "heat_q_006970_1110_2.24_80", "license": "Apache-2.0", "prompt": "A 1110 g sample has specific heat 2.24 J/(g*K). How much heat is needed to raise its temperature by 80 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1110 * 2.24 * 80.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 80, "heat_capacity": 2.24, "mass_g": 1110}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=13 V and R=2.5 ohm.\nFinal: {\"answer\": 67.6, \"unit\": \"W\"}", "dedupe_signature": "b362c812eda48d724b6d43fd9af6c124df32e214e9df447b8a3f66e554d33bc8", "difficulty": "easy", "final_answer": {"answer": 67.6, "unit": "W"}, "id": "ohm_power_006971_13_2.5", "license": "Apache-2.0", "prompt": "A resistor has resistance 2.5 ohm and voltage 13 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=13 V and R=2.5 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 2.5, "voltage": 13.0}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 7.63 mol * 18.015 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 137.4545, \"unit\": \"g\"}", "dedupe_signature": "fb10b4eed5fc491eca033a5e2f08c62e6a81208cfb9e212d8192bf3dd241b90d", "difficulty": "medium", "final_answer": {"answer": 137.4545, "unit": "g"}, "id": "stoich_mass_006973_water_7.63", "license": "Apache-2.0", "prompt": "A sample contains 7.63 mol of water. Using molar mass 18.015 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 7.63 mol * 18.015 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "water", "molar_mass": 18.015, "moles": 7.63}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 490 mL to 0.49 L.\n3. Compute M = 1.63 / 0.49.\nFinal: {\"answer\": 3.3265, \"unit\": \"mol/L\"}", "dedupe_signature": "b4ade6a7b4b0fb15cb133b618b361ecca7a64ccbe9d2611f3c7fe290dfa4f235", "difficulty": "medium", "final_answer": {"answer": 3.3265, "unit": "mol/L"}, "id": "molarity_006974_1.63_490", "license": "Apache-2.0", "prompt": "A solution contains 1.63 mol of solute in 490 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 490 mL to 0.49 L.\nCompute M = 1.63 / 0.49.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 1.63, "volume_ml": 490}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(4.7)=-3.15 and f(10.2)=10.6.\n3. The interval width is 5.5.\nFinal: {\"answer\": 20.4875, \"unit\": \"area_units\"}", "dedupe_signature": "48e4c8cbd8540303f1e210d3638ecb32a3dddd2407320d06a1f8c5454931c3a8", "difficulty": "medium", "final_answer": {"answer": 20.4875, "unit": "area_units"}, "id": "trapz_linear_006976_2.5_-14.9_4.7_10.2", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=2.5x+-14.9 from x=4.7 to x=10.2. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(4.7)=-3.15 and f(10.2)=10.6.\nThe interval width is 5.5.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -14.9, "slope": 2.5, "x0": 4.7, "x1": 10.2}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.24 and add it to the current value.\nFinal: {\"answer\": [-0.626, -1.082, -0.212], \"unit\": \"temperature_units\"}", "dedupe_signature": "6df42c9c5c2b6176b7d1478a13a563eb9336f56373a8b078953c7b29db0162ba", "difficulty": "hard", "final_answer": {"answer": [-0.626, -1.082, -0.212], "unit": "temperature_units"}, "id": "heat_step_006977_0.24_1.65_-1.25_-1.55_0.1_0.45", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.65, right=0.45; current interior values are [-1.25, -1.55, 0.1]. Use r=0.24. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.24 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-1.25, -1.55, 0.1], "left": 1.65, "r": 0.24, "right": 0.45}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 100 centimeters in one meter.\n2. Apply the conversion factor directly to the given value.\n3. Compute 2035.0 / 100.\nFinal: {\"answer\": 20.35, \"unit\": \"m\"}", "dedupe_signature": "41076a5cf0a0c4eadfc2f862a8f4a986308af1a7e8a7c38a44ffbeb6f23dbff7", "difficulty": "easy", "final_answer": {"answer": 20.35, "unit": "m"}, "id": "unit_convert_006978_cm_to_m_2035", "license": "Apache-2.0", "prompt": "Convert 2035 cm to m. Return the converted value with unit.", "reasoning_trace": "There are 100 centimeters in one meter.\nApply the conversion factor directly to the given value.\nCompute 2035.0 / 100.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 2035.0}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=213 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-206.7323, -134.2535], \"unit\": \"N\"}", "dedupe_signature": "e4801a46e7461ca5cf720c737f49383df183d6f0a87486c3f8319a2f6319c3ed", "difficulty": "medium", "final_answer": {"answer": [-206.7323, -134.2535], "unit": "N"}, "id": "vector_components_006979_246.5_213", "license": "Apache-2.0", "prompt": "A vector has magnitude 246.5 N at 213 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=213 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 213, "magnitude": 246.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [1.4, 27.25], \"unit\": \"dimensionless\"}", "dedupe_signature": "08e2196f20e8ce8892bf364b9a010e4e4c358d3ede42324b575b82ccf53a4782", "difficulty": "medium", "final_answer": {"answer": [1.4, 27.25], "unit": "dimensionless"}, "id": "line_two_point_006980_2_15.25_1.4_27.25", "license": "Apache-2.0", "prompt": "A line passes through points (2, 30.05) and (15.25, 48.6). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 2.0, "x2": 15.25, "y1": 30.05, "y2": 48.599999999999994}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. energy divided by length is force, not spring constant\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "c36016b2ed8fdfdf948d1e357920f5284ab9d7ecdcb13a87b5f7cbd4041a0e80", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_006981_inconsistent_56040f5d_836348", "license": "Apache-2.0", "prompt": "In model card equation case 836348, check dimensional consistency for k = E / x. The left side has dimensions N/m and the right side has dimensions J/m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nenergy divided by length is force, not spring constant\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "k = E / x"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\nimport math\n\ndef unit_vector_006982(x, y):\n    norm = math.hypot(x, y)\n    if norm == 0:\n        raise ValueError('zero vector has no direction')\n    return (x / norm, y / norm)\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"unit_vector_006982\"}", "dedupe_signature": "75035c673c3b72920b90c4a06d515f82aa47e770128ce56bb4e9758207f64e51", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "unit_vector_006982"}, "id": "code_006982_unit_vector_006982", "license": "Apache-2.0", "prompt": "Write a Python function unit_vector_006982(x, y) that returns the 2D unit vector as a tuple. Raise ValueError for the zero vector. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "unit_vector_006982"}, "verifier": {"function": "unit_vector_006982", "tests": ["ux, uy = unit_vector_006982(3, 4); assert abs(ux - 0.6) < 1e-12 and abs(uy - 0.8) < 1e-12", "assert unit_vector_006982(0, 5) == (0, 1)", "try:\n    unit_vector_006982(0, 0)\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 19.4 kg and a = 1.1 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 21.34, \"unit\": \"N\"}", "dedupe_signature": "c4e531c60274f2374c91fe638a00facf01f7fbf30462ff581720bf2947c9ff1e", "difficulty": "easy", "final_answer": {"answer": 21.34, "unit": "N"}, "id": "force_006984_19.4_1.1", "license": "Apache-2.0", "prompt": "A cart has mass 19.4 kg and measured acceleration 1.1 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 19.4 kg and a = 1.1 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 1.1, "mass": 19.4}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 25.55^2 and multiply by 0.5 * 6.8.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 2219.5285, \"unit\": \"J\"}", "dedupe_signature": "100b94d61eca921d4139201769897e5a718288fbf5ff62ba41234f54ecdfaacf", "difficulty": "easy", "final_answer": {"answer": 2219.5285, "unit": "J"}, "id": "ke_006985_6.8_25.55", "license": "Apache-2.0", "prompt": "A body of mass 6.8 kg moves at 25.55 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 25.55^2 and multiply by 0.5 * 6.8.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 6.8, "velocity": 25.55}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=81 degrees through the sine of 2 theta.\n3. Substitute v=70.2 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 155.2343, \"unit\": \"m\"}", "dedupe_signature": "b279f5455858710ec9013de6c5ab02c1a794e82307d7d297a7f2fa63dccd470d", "difficulty": "medium", "final_answer": {"answer": 155.2343, "unit": "m"}, "id": "projectile_range_006986_70.2_81", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 70.2 m/s and angle 81 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=81 degrees through the sine of 2 theta.\nSubstitute v=70.2 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 81, "gravity": 9.81, "speed": 70.2}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 3.06 * 8.314 * 599 / 60.4.\nFinal: {\"answer\": 252.3024, \"unit\": \"kPa\"}", "dedupe_signature": "618e3dfad6800e276694889c0f7137c241dc0068133005486d60c9a3c942233e", "difficulty": "medium", "final_answer": {"answer": 252.3024, "unit": "kPa"}, "id": "ideal_gas_006987_3.06_599_60.4", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=3.06 mol, T=599 K, and V=60.4 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 3.06 * 8.314 * 599 / 60.4.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 3.06, "temp_k": 599, "volume_l": 60.4}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=440 mg, t=20 h, and T_half=77 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 367.5048, \"unit\": \"mg\"}", "dedupe_signature": "0b686d4fa899ede398b4368d188bd81b3b5c665611bda6397583469e2cff3d39", "difficulty": "medium", "final_answer": {"answer": 367.5048, "unit": "mg"}, "id": "half_life_006990_440_77_20", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 440 mg. Its half-life is 77 hours. How many mg remain after 20 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=440 mg, t=20 h, and T_half=77 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 20.0, "half_life": 77.0, "initial_amount": 440.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 1.52 mol * 44.01 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 66.8952, \"unit\": \"g\"}", "dedupe_signature": "baefb158b1d064d38b2626c0bc5f9877160a7e40327c7a1100e1c0232d547851", "difficulty": "medium", "final_answer": {"answer": 66.8952, "unit": "g"}, "id": "stoich_mass_006991_carbon_dioxide_1.52", "license": "Apache-2.0", "prompt": "A sample contains 1.52 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 1.52 mol * 44.01 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "carbon dioxide", "molar_mass": 44.01, "moles": 1.52}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 3845 mL to 3.845 L.\n3. Compute M = 3.975 / 3.845.\nFinal: {\"answer\": 1.0338, \"unit\": \"mol/L\"}", "dedupe_signature": "afb585ab315f59cfa4bdba36beddf15abc56b06e04311d89c374a9759172fe0a", "difficulty": "medium", "final_answer": {"answer": 1.0338, "unit": "mol/L"}, "id": "molarity_006992_3.975_3845", "license": "Apache-2.0", "prompt": "A solution contains 3.975 mol of solute in 3845 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 3845 mL to 3.845 L.\nCompute M = 3.975 / 3.845.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 3.975, "volume_ml": 3845}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-2)=-15.4 and f(6.2)=-34.26.\n3. The interval width is 8.2.\nFinal: {\"answer\": -203.606, \"unit\": \"area_units\"}", "dedupe_signature": "aca9d04ab2b30530766fe5a526419a3b24f19458e7d1f8267aedb973cde53c39", "difficulty": "medium", "final_answer": {"answer": -203.606, "unit": "area_units"}, "id": "trapz_linear_006994_-2.3_-20_-2_6.2", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-2.3x+-20 from x=-2 to x=6.2. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-2)=-15.4 and f(6.2)=-34.26.\nThe interval width is 8.2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -20.0, "slope": -2.3, "x0": -2.0, "x1": 6.199999999999999}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.4 and add it to the current value.\nFinal: {\"answer\": [1.87, 2.25, 0.6], \"unit\": \"temperature_units\"}", "dedupe_signature": "4ce4f7838b9e3098598a70e17ad82f6700a0fdb8776b3d41168b760191600c24", "difficulty": "hard", "final_answer": {"answer": [1.87, 2.25, 0.6], "unit": "temperature_units"}, "id": "heat_step_006995_0.4_2.35_2.75_0.95_2.4_-0.65", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=2.35, right=-0.65; current interior values are [2.75, 0.95, 2.4]. Use r=0.4. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.4 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [2.75, 0.95, 2.4], "left": 2.35, "r": 0.4, "right": -0.65}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\nimport math\n\ndef unit_vector_007000(x, y):\n    norm = math.hypot(x, y)\n    if norm == 0:\n        raise ValueError('zero vector has no direction')\n    return (x / norm, y / norm)\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"unit_vector_007000\"}", "dedupe_signature": "cf46a1cddac1ea0a6a0f8967b975a0e2e03dd5c15f383cc56bd53285d6b4fc7a", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "unit_vector_007000"}, "id": "code_007000_unit_vector_007000", "license": "Apache-2.0", "prompt": "Write a Python function unit_vector_007000(x, y) that returns the 2D unit vector as a tuple. Raise ValueError for the zero vector. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "unit_vector_007000"}, "verifier": {"function": "unit_vector_007000", "tests": ["ux, uy = unit_vector_007000(3, 4); assert abs(ux - 0.6) < 1e-12 and abs(uy - 0.8) < 1e-12", "assert unit_vector_007000(0, 5) == (0, 1)", "try:\n    unit_vector_007000(0, 0)\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: left_boundary, right_boundary.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"left_boundary\", \"right_boundary\"]}", "dedupe_signature": "c6273904b414152f920853936e421de8bba67807cc7f7411698d7ad2373db265", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["left_boundary", "right_boundary"]}, "id": "abstain_007001_left_boundary_right_boundary", "license": "Apache-2.0", "prompt": "Solve the 1D heat equation after one finite-difference step. The prompt gives r=0.04 and interior values [2.75, -1.55, 1.15], but gives no boundary values. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: left_boundary, right_boundary.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["left_boundary", "right_boundary"]}, "verifier": {"missing": ["left_boundary", "right_boundary"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 14.1 kg and a = 6.2 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 87.42, \"unit\": \"N\"}", "dedupe_signature": "3588fe78fc57701f35ccd10c20f21881fa674e525f8932b9c05a55b01a59dc01", "difficulty": "easy", "final_answer": {"answer": 87.42, "unit": "N"}, "id": "force_007002_14.1_6.2", "license": "Apache-2.0", "prompt": "A cart has mass 14.1 kg and measured acceleration 6.2 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 14.1 kg and a = 6.2 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 6.2, "mass": 14.1}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 12.5^2 and multiply by 0.5 * 0.35.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 27.3438, \"unit\": \"J\"}", "dedupe_signature": "297d84e34081fcd43ac7c0597ad0c8ab0b45cac663c82dadf8eb147bbfd38f0c", "difficulty": "easy", "final_answer": {"answer": 27.3438, "unit": "J"}, "id": "ke_007003_0.35_12.5", "license": "Apache-2.0", "prompt": "A body of mass 0.35 kg moves at 12.5 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 12.5^2 and multiply by 0.5 * 0.35.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 0.35, "velocity": 12.5}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 1.51 * 8.314 * 313 / 90.0.\nFinal: {\"answer\": 43.6605, \"unit\": \"kPa\"}", "dedupe_signature": "dd604ffc36f3420bc91149e380e60d95c57046e660cb933f7c1de6e7c69ad1fc", "difficulty": "medium", "final_answer": {"answer": 43.6605, "unit": "kPa"}, "id": "ideal_gas_007005_1.51_313_90.0", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=1.51 mol, T=313 K, and V=90.0 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 1.51 * 8.314 * 313 / 90.0.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 1.51, "temp_k": 313, "volume_l": 90.0}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 985 * 1.89 * 31.\nFinal: {\"answer\": 57711.15, \"unit\": \"J\"}", "dedupe_signature": "2dccfe0b925995782f6d013b833887437ebe4550a1ff5b0af7b2b526e68f5ec9", "difficulty": "easy", "final_answer": {"answer": 57711.15, "unit": "J"}, "id": "heat_q_007006_985_1.89_31", "license": "Apache-2.0", "prompt": "A 985 g sample has specific heat 1.89 J/(g*K). How much heat is needed to raise its temperature by 31 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 985 * 1.89 * 31.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 31, "heat_capacity": 1.89, "mass_g": 985}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=84.7 V and R=140.7 ohm.\nFinal: {\"answer\": 50.9886, \"unit\": \"W\"}", "dedupe_signature": "cfeef09f6213be72b7490821a4ef8a11e46e9062712fa5ea8886a18002b54fe1", "difficulty": "easy", "final_answer": {"answer": 50.9886, "unit": "W"}, "id": "ohm_power_007007_84.7_140.7", "license": "Apache-2.0", "prompt": "A resistor has resistance 140.7 ohm and voltage 84.7 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=84.7 V and R=140.7 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 140.7, "voltage": 84.7}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 1315 mL to 1.315 L.\n3. Compute M = 3.86 / 1.315.\nFinal: {\"answer\": 2.9354, \"unit\": \"mol/L\"}", "dedupe_signature": "0093209f163717376240d2032ad9266b871f6297880adc52ce75cb27e5fe9651", "difficulty": "medium", "final_answer": {"answer": 2.9354, "unit": "mol/L"}, "id": "molarity_007010_3.86_1315", "license": "Apache-2.0", "prompt": "A solution contains 3.86 mol of solute in 1315 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 1315 mL to 1.315 L.\nCompute M = 3.86 / 1.315.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 3.86, "volume_ml": 1315}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.47 y, so each step multiplies y by 1 - h*0.47.\n3. Apply that update for 11 steps and round the final state.\nFinal: {\"answer\": 2.1237, \"unit\": \"state_units\"}", "dedupe_signature": "0aa250257aac184c36735864bf59e5442b820f4b73e782d8683874149bdfa6e1", "difficulty": "medium", "final_answer": {"answer": 2.1237, "unit": "state_units"}, "id": "euler_decay_007011_57_0.47_0.55_11", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.47 y with y(0)=57, step size h=0.55, for 11 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.47 y, so each step multiplies y by 1 - h*0.47.\nApply that update for 11 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 57.0, "rate": 0.47, "step": 0.55, "steps": 11}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-6.5)=-51.3 and f(-6.1)=-48.9.\n3. The interval width is 0.4.\nFinal: {\"answer\": -20.04, \"unit\": \"area_units\"}", "dedupe_signature": "1f109f14f92bc984e9f3591522098837ca07df337631505d502be74480e960ea", "difficulty": "medium", "final_answer": {"answer": -20.04, "unit": "area_units"}, "id": "trapz_linear_007012_6_-12.3_-6.5_-6.1", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=6x+-12.3 from x=-6.5 to x=-6.1. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-6.5)=-51.3 and f(-6.1)=-48.9.\nThe interval width is 0.4.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -12.3, "slope": 6.0, "x0": -6.5, "x1": -6.1}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.46 and add it to the current value.\nFinal: {\"answer\": [0.898, 0.186, 0.497], \"unit\": \"temperature_units\"}", "dedupe_signature": "ce5c524a46ffdcf3118a53826d107ed8ada8f40ba14d818bb12f38493b6ef364", "difficulty": "hard", "final_answer": {"answer": [0.898, 0.186, 0.497], "unit": "temperature_units"}, "id": "heat_step_007013_0.46_-0.8_-0.85_2.9_0.75_-1.95", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-0.8, right=-1.95; current interior values are [-0.85, 2.9, 0.75]. Use r=0.46. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.46 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-0.85, 2.9, 0.75], "left": -0.8, "r": 0.46, "right": -1.95}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 100 centimeters in one meter.\n2. Apply the conversion factor directly to the given value.\n3. Compute 3081.5 / 100.\nFinal: {\"answer\": 30.815, \"unit\": \"m\"}", "dedupe_signature": "dec3b79f386aa7dc9aa7992c5d6074d4cb2d33c9058f2291602a18380daa5f4d", "difficulty": "easy", "final_answer": {"answer": 30.815, "unit": "m"}, "id": "unit_convert_007014_cm_to_m_3081.5", "license": "Apache-2.0", "prompt": "Convert 3081.5 cm to m. Return the converted value with unit.", "reasoning_trace": "There are 100 centimeters in one meter.\nApply the conversion factor directly to the given value.\nCompute 3081.5 / 100.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 3081.5}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=109 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-124.367, 361.1881], \"unit\": \"N\"}", "dedupe_signature": "100f3981abd98e595119ba39d1e190359d9ea0ffd8de17175519ebea0efde8e5", "difficulty": "medium", "final_answer": {"answer": [-124.367, 361.1881], "unit": "N"}, "id": "vector_components_007015_382_109", "license": "Apache-2.0", "prompt": "A vector has magnitude 382 N at 109 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=109 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 109, "magnitude": 382.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-4.3, -6.75], \"unit\": \"dimensionless\"}", "dedupe_signature": "af12a959cebe8857c19153507663e25a875c9ede1fa0e9c646c6184458c8b340", "difficulty": "medium", "final_answer": {"answer": [-4.3, -6.75], "unit": "dimensionless"}, "id": "line_two_point_007016_4_11.75_-4.3_-6.75", "license": "Apache-2.0", "prompt": "A line passes through points (4, -23.95) and (11.75, -57.275). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 4.0, "x2": 11.75, "y1": -23.95, "y2": -57.275}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. velocity times time gives distance, not acceleration\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "6a20a08fb88aad4d2b20500e3fbec84f745f34b63fe9456028d7ad1df71ae215", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_007017_inconsistent_7481c798_386789", "license": "Apache-2.0", "prompt": "In instrument manual case 386789, check dimensional consistency for a = v * t. The left side has dimensions m/s^2 and the right side has dimensions m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nvelocity times time gives distance, not acceleration\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "a = v * t"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef clamp_007018(x, lo, hi):\n    if lo > hi:\n        raise ValueError('lo must be <= hi')\n    return min(max(x, lo), hi)\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"clamp_007018\"}", "dedupe_signature": "736c16de0a257007de3467f9b5cc354ba555ef792df7080f55cd97127315b892", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "clamp_007018"}, "id": "code_007018_clamp_007018", "license": "Apache-2.0", "prompt": "Write a Python function clamp_007018(x, lo, hi) that clips x into the inclusive interval [lo, hi]. It must raise ValueError if lo > hi. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "clamp_007018"}, "verifier": {"function": "clamp_007018", "tests": ["assert clamp_007018(5, 0, 10) == 5", "assert clamp_007018(-2, 0, 10) == 0", "assert clamp_007018(12, 0, 10) == 10", "try:\n    clamp_007018(1, 3, 2)\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 7.45 kg and a = 1.95 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 14.5275, \"unit\": \"N\"}", "dedupe_signature": "14ebd8f6fefed9353f52bee27356d20e568c1de01f248749241ad042c5791117", "difficulty": "easy", "final_answer": {"answer": 14.5275, "unit": "N"}, "id": "force_007020_7.45_1.95", "license": "Apache-2.0", "prompt": "A cart has mass 7.45 kg and measured acceleration 1.95 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 7.45 kg and a = 1.95 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 1.95, "mass": 7.45}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 16.05^2 and multiply by 0.5 * 20.75.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 2672.6259, \"unit\": \"J\"}", "dedupe_signature": "35663987a89a2c79954d181708a20065c5edfbb21e73b5573e5f7aeda04ee245", "difficulty": "easy", "final_answer": {"answer": 2672.6259, "unit": "J"}, "id": "ke_007021_20.75_16.05", "license": "Apache-2.0", "prompt": "A body of mass 20.75 kg moves at 16.05 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 16.05^2 and multiply by 0.5 * 20.75.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 20.75, "velocity": 16.05}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=70 degrees through the sine of 2 theta.\n3. Substitute v=72.4 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 343.4596, \"unit\": \"m\"}", "dedupe_signature": "8d5783a9d04481eaebafac2dd7e64f0a466f602eb5425e4bbd516d5ae6c82933", "difficulty": "medium", "final_answer": {"answer": 343.4596, "unit": "m"}, "id": "projectile_range_007022_72.4_70", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 72.4 m/s and angle 70 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=70 degrees through the sine of 2 theta.\nSubstitute v=72.4 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 70, "gravity": 9.81, "speed": 72.4}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 3.15 * 8.314 * 306 / 15.6.\nFinal: {\"answer\": 513.7093, \"unit\": \"kPa\"}", "dedupe_signature": "28f95eaeacbad9b9fd6adb5dc9344d1a851a91c431a9b36b15a8f045729c6daa", "difficulty": "medium", "final_answer": {"answer": 513.7093, "unit": "kPa"}, "id": "ideal_gas_007023_3.15_306_15.6", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=3.15 mol, T=306 K, and V=15.6 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 3.15 * 8.314 * 306 / 15.6.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 3.15, "temp_k": 306, "volume_l": 15.6}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=114.4 V and R=7.7 ohm.\nFinal: {\"answer\": 1699.6571, \"unit\": \"W\"}", "dedupe_signature": "20cb7b79a1185c96693441b19f3f4af5148f2fc0d7b9aaf0e4b8604c54cb9727", "difficulty": "easy", "final_answer": {"answer": 1699.6571, "unit": "W"}, "id": "ohm_power_007025_114.4_7.7", "license": "Apache-2.0", "prompt": "A resistor has resistance 7.7 ohm and voltage 114.4 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=114.4 V and R=7.7 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 7.7, "voltage": 114.4}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=877 mg, t=287.5 h, and T_half=46 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 11.5229, \"unit\": \"mg\"}", "dedupe_signature": "35b8558dc1d777736f6f2450b294c566bfa62d2841b12d48a98346d77e3ae548", "difficulty": "medium", "final_answer": {"answer": 11.5229, "unit": "mg"}, "id": "half_life_007026_877_46_287.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 877 mg. Its half-life is 46 hours. How many mg remain after 287.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=877 mg, t=287.5 h, and T_half=46 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 287.5, "half_life": 46.0, "initial_amount": 877.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 1.66 mol * 100.087 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 166.1444, \"unit\": \"g\"}", "dedupe_signature": "2914e359875aeea518876f9e9fe3ea82d0c144d1e52aa6755962744523565de9", "difficulty": "medium", "final_answer": {"answer": 166.1444, "unit": "g"}, "id": "stoich_mass_007027_calcium_carbonate_1.66", "license": "Apache-2.0", "prompt": "A sample contains 1.66 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 1.66 mol * 100.087 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "calcium carbonate", "molar_mass": 100.087, "moles": 1.66}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 2585 mL to 2.585 L.\n3. Compute M = 3.905 / 2.585.\nFinal: {\"answer\": 1.5106, \"unit\": \"mol/L\"}", "dedupe_signature": "4cdd1beafdc320d52cff97983abad1237ecec584d00e528b5df9b7226c3091d9", "difficulty": "medium", "final_answer": {"answer": 1.5106, "unit": "mol/L"}, "id": "molarity_007028_3.905_2585", "license": "Apache-2.0", "prompt": "A solution contains 3.905 mol of solute in 2585 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 2585 mL to 2.585 L.\nCompute M = 3.905 / 2.585.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 3.905, "volume_ml": 2585}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.75 y, so each step multiplies y by 1 - h*0.75.\n3. Apply that update for 2 steps and round the final state.\nFinal: {\"answer\": 0.0051, \"unit\": \"state_units\"}", "dedupe_signature": "c19afcd34ddfb0a71525d143c0803276fd775b2100e6f0489793c7b250519dca", "difficulty": "medium", "final_answer": {"answer": 0.0051, "unit": "state_units"}, "id": "euler_decay_007029_32.5_0.75_1.35_2", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.75 y with y(0)=32.5, step size h=1.35, for 2 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.75 y, so each step multiplies y by 1 - h*0.75.\nApply that update for 2 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 32.5, "rate": 0.75, "step": 1.35, "steps": 2}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.4 and add it to the current value.\nFinal: {\"answer\": [0.19, 1.27, 1.47], \"unit\": \"temperature_units\"}", "dedupe_signature": "163d3dfd7e573be603b994841e96696c8dd9ed686850e649b53dfced826039eb", "difficulty": "hard", "final_answer": {"answer": [0.19, 1.27, 1.47], "unit": "temperature_units"}, "id": "heat_step_007031_0.4_-1.9_1.25_1.75_1.05_1.4", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-1.9, right=1.4; current interior values are [1.25, 1.75, 1.05]. Use r=0.4. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.4 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [1.25, 1.75, 1.05], "left": -1.9, "r": 0.4, "right": 1.4}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 100 centimeters in one meter.\n2. Apply the conversion factor directly to the given value.\n3. Compute 1600.0 / 100.\nFinal: {\"answer\": 16.0, \"unit\": \"m\"}", "dedupe_signature": "22c8ec8f0416f81cf5ccebe4618467087cbf93cc089a6a35094dee0c91920386", "difficulty": "easy", "final_answer": {"answer": 16.0, "unit": "m"}, "id": "unit_convert_007032_cm_to_m_1600", "license": "Apache-2.0", "prompt": "Convert 1600 cm to m. Return the converted value with unit.", "reasoning_trace": "There are 100 centimeters in one meter.\nApply the conversion factor directly to the given value.\nCompute 1600.0 / 100.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 1600.0}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=318 degrees and keep the unit as newtons.\nFinal: {\"answer\": [75.8008, -68.2513], \"unit\": \"N\"}", "dedupe_signature": "9ec4b142d26da7f89b36eafdf4985bad53e588160cd7f39554c9ae406df7ff6a", "difficulty": "medium", "final_answer": {"answer": [75.8008, -68.2513], "unit": "N"}, "id": "vector_components_007033_102_318", "license": "Apache-2.0", "prompt": "A vector has magnitude 102 N at 318 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=318 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 318, "magnitude": 102.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. velocity times time gives distance, not acceleration\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "d16cf0dd7e3994085b942ba0f494906bbeb73b552da1aa9b7498c114e06d1987", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_007035_inconsistent_7481c798_416198", "license": "Apache-2.0", "prompt": "In sensor calibration case 416198, check dimensional consistency for a = v * t. The left side has dimensions m/s^2 and the right side has dimensions m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nvelocity times time gives distance, not acceleration\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "a = v * t"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef clamp_007036(x, lo, hi):\n    if lo > hi:\n        raise ValueError('lo must be <= hi')\n    return min(max(x, lo), hi)\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"clamp_007036\"}", "dedupe_signature": "dc3f43886d858cfb1bfedd85440c30908ef4d24e2cbd618c80171bb610d5a5ba", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "clamp_007036"}, "id": "code_007036_clamp_007036", "license": "Apache-2.0", "prompt": "Write a Python function clamp_007036(x, lo, hi) that clips x into the inclusive interval [lo, hi]. It must raise ValueError if lo > hi. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "clamp_007036"}, "verifier": {"function": "clamp_007036", "tests": ["assert clamp_007036(5, 0, 10) == 5", "assert clamp_007036(-2, 0, 10) == 0", "assert clamp_007036(12, 0, 10) == 10", "try:\n    clamp_007036(1, 3, 2)\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: launch_angle_or_vertical_velocity.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"launch_angle_or_vertical_velocity\"]}", "dedupe_signature": "8cbe6d71dbe161e09d4bd7d8c101031aac4f0d6ec39c47d95eeb2b861c743689", "difficulty": "easy", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["launch_angle_or_vertical_velocity"]}, "id": "abstain_007037_launch_angle_or_vertical_velocity", "license": "Apache-2.0", "prompt": "Compute projectile range on level ground. The prompt gives initial speed 58.4 m/s but does not give launch angle or vertical velocity. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: launch_angle_or_vertical_velocity.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["launch_angle_or_vertical_velocity"]}, "verifier": {"missing": ["launch_angle_or_vertical_velocity"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 12.1 kg and a = 12.5 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 151.25, \"unit\": \"N\"}", "dedupe_signature": "6b1b6a93bfee19f919272d97a51a890b10f97412d8fedf4b2a3ec000accb61a1", "difficulty": "easy", "final_answer": {"answer": 151.25, "unit": "N"}, "id": "force_007038_12.1_12.5", "license": "Apache-2.0", "prompt": "A cart has mass 12.1 kg and measured acceleration 12.5 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 12.1 kg and a = 12.5 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 12.5, "mass": 12.1}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 21.05^2 and multiply by 0.5 * 11.25.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 2492.4516, \"unit\": \"J\"}", "dedupe_signature": "74f56edf75b80e43e5f6b898109793acbba822b70793aaa35b70ebb4c807db7c", "difficulty": "easy", "final_answer": {"answer": 2492.4516, "unit": "J"}, "id": "ke_007039_11.25_21.05", "license": "Apache-2.0", "prompt": "A body of mass 11.25 kg moves at 21.05 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 21.05^2 and multiply by 0.5 * 11.25.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 11.25, "velocity": 21.05}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=28 degrees through the sine of 2 theta.\n3. Substitute v=9.6 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 7.7884, \"unit\": \"m\"}", "dedupe_signature": "00b2a4307b3153a97d51907e4dfe18d39792f46fa52a1308e66c9c1912f3899d", "difficulty": "medium", "final_answer": {"answer": 7.7884, "unit": "m"}, "id": "projectile_range_007040_9.6_28", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 9.6 m/s and angle 28 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=28 degrees through the sine of 2 theta.\nSubstitute v=9.6 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 28, "gravity": 9.81, "speed": 9.6}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 0.32 * 8.314 * 403 / 16.4.\nFinal: {\"answer\": 65.3764, \"unit\": \"kPa\"}", "dedupe_signature": "b9e6cfee40eab2eef0c5d721f004bd759ae0bd5f8969676a06f20ffca4f8315c", "difficulty": "medium", "final_answer": {"answer": 65.3764, "unit": "kPa"}, "id": "ideal_gas_007041_0.32_403_16.4", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=0.32 mol, T=403 K, and V=16.4 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 0.32 * 8.314 * 403 / 16.4.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 0.32, "temp_k": 403, "volume_l": 16.4}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 85 * 3.875 * 27.\nFinal: {\"answer\": 8893.125, \"unit\": \"J\"}", "dedupe_signature": "bec86a73fd0ce8d10b186e8f4eda9b089f8981aa1d6313874f69789232e0695b", "difficulty": "easy", "final_answer": {"answer": 8893.125, "unit": "J"}, "id": "heat_q_007042_85_3.875_27", "license": "Apache-2.0", "prompt": "A 85 g sample has specific heat 3.875 J/(g*K). How much heat is needed to raise its temperature by 27 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 85 * 3.875 * 27.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 27, "heat_capacity": 3.875, "mass_g": 85}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=632 mg, t=55.5 h, and T_half=33.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 200.4452, \"unit\": \"mg\"}", "dedupe_signature": "eee7e959d29175535a82997924499c015f065d4c8bb16e108cfcccb219f4c824", "difficulty": "medium", "final_answer": {"answer": 200.4452, "unit": "mg"}, "id": "half_life_007044_632_33.5_55.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 632 mg. Its half-life is 33.5 hours. How many mg remain after 55.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=632 mg, t=55.5 h, and T_half=33.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 55.5, "half_life": 33.5, "initial_amount": 632.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 2405 mL to 2.405 L.\n3. Compute M = 0.17 / 2.405.\nFinal: {\"answer\": 0.0707, \"unit\": \"mol/L\"}", "dedupe_signature": "fbbcdf9d0914703e296577cb604c44966e11b8503d10d823d8e4a44bfa95513a", "difficulty": "medium", "final_answer": {"answer": 0.0707, "unit": "mol/L"}, "id": "molarity_007046_0.17_2405", "license": "Apache-2.0", "prompt": "A solution contains 0.17 mol of solute in 2405 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 2405 mL to 2.405 L.\nCompute M = 0.17 / 2.405.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 0.17, "volume_ml": 2405}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.96 y, so each step multiplies y by 1 - h*0.96.\n3. Apply that update for 6 steps and round the final state.\nFinal: {\"answer\": 0.0, \"unit\": \"state_units\"}", "dedupe_signature": "3e8886f35a1f0b789e23cb96aac93094aaca13991fcb1d461edec4799d6a2619", "difficulty": "medium", "final_answer": {"answer": 0.0, "unit": "state_units"}, "id": "euler_decay_007047_3.5_0.96_0.95_6", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.96 y with y(0)=3.5, step size h=0.95, for 6 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.96 y, so each step multiplies y by 1 - h*0.96.\nApply that update for 6 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 3.5, "rate": 0.96, "step": 0.95, "steps": 6}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(2.9)=-25.36 and f(8.6)=-67.54.\n3. The interval width is 5.7.\nFinal: {\"answer\": -264.765, \"unit\": \"area_units\"}", "dedupe_signature": "9231f83d72737b89877ca7a78555b0e1a7122bf3e1af1f82de20d494e2511f3b", "difficulty": "medium", "final_answer": {"answer": -264.765, "unit": "area_units"}, "id": "trapz_linear_007048_-7.4_-3.9_2.9_8.6", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-7.4x+-3.9 from x=2.9 to x=8.6. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(2.9)=-25.36 and f(8.6)=-67.54.\nThe interval width is 5.7.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -3.9, "slope": -7.4, "x0": 2.9, "x1": 8.6}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.24 and add it to the current value.\nFinal: {\"answer\": [-0.062, 0.102, 0.254], \"unit\": \"temperature_units\"}", "dedupe_signature": "23922d6ad20b3f3a42375dc56463d03b7f945e9b7e95a1ec84018ba0b3c21084", "difficulty": "hard", "final_answer": {"answer": [-0.062, 0.102, 0.254], "unit": "temperature_units"}, "id": "heat_step_007049_0.24_1.05_-0.95_0.75_-0.25_0.85", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.05, right=0.85; current interior values are [-0.95, 0.75, -0.25]. Use r=0.24. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.24 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-0.95, 0.75, -0.25], "left": 1.05, "r": 0.24, "right": 0.85}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 9469.0 / 1000.\nFinal: {\"answer\": 9.469, \"unit\": \"kg\"}", "dedupe_signature": "b2edf5c20528b3b5b44a7c3fe31b1f2f2d6268bfe1e8cd875352bd4f20c526c6", "difficulty": "easy", "final_answer": {"answer": 9.469, "unit": "kg"}, "id": "unit_convert_007050_g_to_kg_9469", "license": "Apache-2.0", "prompt": "Convert 9469 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 9469.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 9469.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=82 degrees and keep the unit as newtons.\nFinal: {\"answer\": [43.5612, 309.9539], \"unit\": \"N\"}", "dedupe_signature": "5a7495c465ca0dd72e692ed01a229485d222fe063623636924aaeb14830cb895", "difficulty": "medium", "final_answer": {"answer": [43.5612, 309.9539], "unit": "N"}, "id": "vector_components_007051_313_82", "license": "Apache-2.0", "prompt": "A vector has magnitude 313 N at 82 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=82 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 82, "magnitude": 313.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-4.0, 23.0], \"unit\": \"dimensionless\"}", "dedupe_signature": "aba5f0960d683ab9ae41891f6a55f3fc238a1a2163a927290017f24b35487475", "difficulty": "medium", "final_answer": {"answer": [-4.0, 23.0], "unit": "dimensionless"}, "id": "line_two_point_007052_-6.5_4.5_-4_23", "license": "Apache-2.0", "prompt": "A line passes through points (-6.5, 49) and (4.5, 5). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -6.5, "x2": 4.5, "y1": 49.0, "y2": 5.0}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. mass times acceleration has newton dimensions\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "6794d698fe6ba469636d9200ad454c98336950dfd431357e3ca7023650938771", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_007053_consistent_03f5e041_37207", "license": "Apache-2.0", "prompt": "In instrument manual case 37207, check dimensional consistency for F = m * a. The left side has dimensions kg*m/s^2 and the right side has dimensions kg*m/s^2. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nmass times acceleration has newton dimensions\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "F = m * a"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\nimport math\n\ndef unit_vector_007054(x, y):\n    norm = math.hypot(x, y)\n    if norm == 0:\n        raise ValueError('zero vector has no direction')\n    return (x / norm, y / norm)\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"unit_vector_007054\"}", "dedupe_signature": "6da5f6dc81ae9ffd49ec9ce8dd2e29709855c43c48cb5e970898c585d0252937", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "unit_vector_007054"}, "id": "code_007054_unit_vector_007054", "license": "Apache-2.0", "prompt": "Write a Python function unit_vector_007054(x, y) that returns the 2D unit vector as a tuple. Raise ValueError for the zero vector. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "unit_vector_007054"}, "verifier": {"function": "unit_vector_007054", "tests": ["ux, uy = unit_vector_007054(3, 4); assert abs(ux - 0.6) < 1e-12 and abs(uy - 0.8) < 1e-12", "assert unit_vector_007054(0, 5) == (0, 1)", "try:\n    unit_vector_007054(0, 0)\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: recurrence, objective, tie_breaking_rule.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"recurrence\", \"objective\", \"tie_breaking_rule\"]}", "dedupe_signature": "4202c2817b04691304d9d5eeeedfcb458d8e6de9f0226f1fddac0a29e56b0324", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["recurrence", "objective", "tie_breaking_rule"]}, "id": "abstain_007055_recurrence_objective_tie_breaking_rule", "license": "Apache-2.0", "prompt": "Write a dynamic-programming solver for a scheduler scoring problem with 4822 items and budget 69820, but the recurrence, objective, and tie-breaking rule are all absent. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: recurrence, objective, tie_breaking_rule.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["recurrence", "objective", "tie_breaking_rule"]}, "verifier": {"missing": ["recurrence", "objective", "tie_breaking_rule"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=64 degrees through the sine of 2 theta.\n3. Substitute v=56.8 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 259.1551, \"unit\": \"m\"}", "dedupe_signature": "4d5dd6ffe6d62fb146ffb380b445f45b9da7d607a9f99b2972a2d1b34c330803", "difficulty": "medium", "final_answer": {"answer": 259.1551, "unit": "m"}, "id": "projectile_range_007058_56.8_64", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 56.8 m/s and angle 64 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=64 degrees through the sine of 2 theta.\nSubstitute v=56.8 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 64, "gravity": 9.81, "speed": 56.8}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 3.87 * 8.314 * 519 / 70.8.\nFinal: {\"answer\": 235.8604, \"unit\": \"kPa\"}", "dedupe_signature": "d85ad52f25ae77cf6a2f9002ce371162977d91262a59b20520b23feed54d7a15", "difficulty": "medium", "final_answer": {"answer": 235.8604, "unit": "kPa"}, "id": "ideal_gas_007059_3.87_519_70.8", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=3.87 mol, T=519 K, and V=70.8 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 3.87 * 8.314 * 519 / 70.8.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 3.87, "temp_k": 519, "volume_l": 70.8}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1640 * 4.32 * 120.\nFinal: {\"answer\": 850176.0, \"unit\": \"J\"}", "dedupe_signature": "e69299ef0cc3c99eb05e86a9a3c3e44d316ce19feba3d15eae6bad053f4ec894", "difficulty": "easy", "final_answer": {"answer": 850176.0, "unit": "J"}, "id": "heat_q_007060_1640_4.32_120", "license": "Apache-2.0", "prompt": "A 1640 g sample has specific heat 4.32 J/(g*K). How much heat is needed to raise its temperature by 120 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1640 * 4.32 * 120.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 120, "heat_capacity": 4.32, "mass_g": 1640}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=234 V and R=35.1 ohm.\nFinal: {\"answer\": 1560.0, \"unit\": \"W\"}", "dedupe_signature": "9abc6edb2dcea6b7aecd927d8e26b2a4571d8f65ea591f14dec9a546aabc559d", "difficulty": "easy", "final_answer": {"answer": 1560.0, "unit": "W"}, "id": "ohm_power_007061_234_35.1", "license": "Apache-2.0", "prompt": "A resistor has resistance 35.1 ohm and voltage 234 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=234 V and R=35.1 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 35.1, "voltage": 234.0}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=844.5 mg, t=139 h, and T_half=92 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 296.3348, \"unit\": \"mg\"}", "dedupe_signature": "e21b3e18274a4a672da8f081fb7c97281a0d4f50a82d1e22dfecbb9a865dfe03", "difficulty": "medium", "final_answer": {"answer": 296.3348, "unit": "mg"}, "id": "half_life_007062_844.5_92_139", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 844.5 mg. Its half-life is 92 hours. How many mg remain after 139 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=844.5 mg, t=139 h, and T_half=92 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 139.0, "half_life": 92.0, "initial_amount": 844.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 4.19 mol * 100.087 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 419.3645, \"unit\": \"g\"}", "dedupe_signature": "aaecb2d49a722c24ddd7cd8fbb58876876ca25289c87daa051512ef8998d0574", "difficulty": "medium", "final_answer": {"answer": 419.3645, "unit": "g"}, "id": "stoich_mass_007063_calcium_carbonate_4.19", "license": "Apache-2.0", "prompt": "A sample contains 4.19 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 4.19 mol * 100.087 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "calcium carbonate", "molar_mass": 100.087, "moles": 4.19}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 2035 mL to 2.035 L.\n3. Compute M = 2.435 / 2.035.\nFinal: {\"answer\": 1.1966, \"unit\": \"mol/L\"}", "dedupe_signature": "da0951a140f5fce6835f2763b77ba62a2c29f0010928301793e22cfd8088494f", "difficulty": "medium", "final_answer": {"answer": 1.1966, "unit": "mol/L"}, "id": "molarity_007064_2.435_2035", "license": "Apache-2.0", "prompt": "A solution contains 2.435 mol of solute in 2035 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 2035 mL to 2.035 L.\nCompute M = 2.435 / 2.035.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 2.435, "volume_ml": 2035}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.85 y, so each step multiplies y by 1 - h*0.85.\n3. Apply that update for 7 steps and round the final state.\nFinal: {\"answer\": 2.7386, \"unit\": \"state_units\"}", "dedupe_signature": "e25aef4c30bbff9d6ce7cc710560ba88d84ee8edf4b80c8357af218dcdbc9f93", "difficulty": "medium", "final_answer": {"answer": 2.7386, "unit": "state_units"}, "id": "euler_decay_007065_21.5_0.85_0.3_7", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.85 y with y(0)=21.5, step size h=0.3, for 7 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.85 y, so each step multiplies y by 1 - h*0.85.\nApply that update for 7 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 21.5, "rate": 0.85, "step": 0.3, "steps": 7}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-1.7)=1.53 and f(3.4)=-33.66.\n3. The interval width is 5.1.\nFinal: {\"answer\": -81.9315, \"unit\": \"area_units\"}", "dedupe_signature": "0831a0abd1568292ddd551d411fda7766d43eba606e33e8dae74bacfc1596dde", "difficulty": "medium", "final_answer": {"answer": -81.9315, "unit": "area_units"}, "id": "trapz_linear_007066_-6.9_-10.2_-1.7_3.4", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-6.9x+-10.2 from x=-1.7 to x=3.4. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-1.7)=1.53 and f(3.4)=-33.66.\nThe interval width is 5.1.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -10.2, "slope": -6.9, "x0": -1.7, "x1": 3.3999999999999995}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.08 and add it to the current value.\nFinal: {\"answer\": [0.634, 1.284, 2.532], \"unit\": \"temperature_units\"}", "dedupe_signature": "e925cf515229118c8e18df92418305b01138d437a9c37c8b6b5f5621a2c95155", "difficulty": "hard", "final_answer": {"answer": [0.634, 1.284, 2.532], "unit": "temperature_units"}, "id": "heat_step_007067_0.08_-0.1_0.65_1.2_2.8_1.05", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-0.1, right=1.05; current interior values are [0.65, 1.2, 2.8]. Use r=0.08. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.08 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [0.65, 1.2, 2.8], "left": -0.1, "r": 0.08, "right": 1.05}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 7326.0 / 1000.\nFinal: {\"answer\": 7.326, \"unit\": \"kg\"}", "dedupe_signature": "7b083e23199584fad748cc0565729be237b050d6ca5d8270625e46353938208c", "difficulty": "easy", "final_answer": {"answer": 7.326, "unit": "kg"}, "id": "unit_convert_007068_g_to_kg_7326", "license": "Apache-2.0", "prompt": "Convert 7326 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 7326.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 7326.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-8.8, 29.75], \"unit\": \"dimensionless\"}", "dedupe_signature": "8635ab35b538a4848bebc6730fd99128783149518729ec90f08d59128eb9d3d6", "difficulty": "medium", "final_answer": {"answer": [-8.8, 29.75], "unit": "dimensionless"}, "id": "line_two_point_007070_19_19.5_-8.8_29.75", "license": "Apache-2.0", "prompt": "A line passes through points (19, -137.45) and (19.5, -141.85). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 19.0, "x2": 19.5, "y1": -137.45000000000002, "y2": -141.85000000000002}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef normalize_007072(values):\n    total = sum(values)\n    if total == 0:\n        raise ValueError('cannot normalize zero-sum values')\n    return [v / total for v in values]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"normalize_007072\"}", "dedupe_signature": "882fa99135eb5dbd84a7e4a8e807bf4a060b946de84fdffec49cfe6ab81e64ec", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "normalize_007072"}, "id": "code_007072_normalize_007072", "license": "Apache-2.0", "prompt": "Write a Python function normalize_007072(values) that returns a new list whose values sum to 1. Raise ValueError if the sum is zero. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "normalize_007072"}, "verifier": {"function": "normalize_007072", "tests": ["out = normalize_007072([2, 3, 5]); assert len(out) == 3", "assert abs(sum(normalize_007072([2, 3, 5])) - 1.0) < 1e-12", "assert normalize_007072([1, 1]) == [0.5, 0.5]", "try:\n    normalize_007072([1, -1])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: launch_angle_or_vertical_velocity.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"launch_angle_or_vertical_velocity\"]}", "dedupe_signature": "d65109e6c6d64be48311d697759ca02308a5f6cd36e1398278f4df14a86e0bdf", "difficulty": "easy", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["launch_angle_or_vertical_velocity"]}, "id": "abstain_007073_launch_angle_or_vertical_velocity", "license": "Apache-2.0", "prompt": "Compute projectile range on level ground. The prompt gives initial speed 62.2 m/s but does not give launch angle or vertical velocity. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: launch_angle_or_vertical_velocity.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["launch_angle_or_vertical_velocity"]}, "verifier": {"missing": ["launch_angle_or_vertical_velocity"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 15.7 kg and a = 4.85 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 76.145, \"unit\": \"N\"}", "dedupe_signature": "a0838d56576f1c097ec45581ab63f8121434bfe220f100bacc56df3c85a5aef4", "difficulty": "easy", "final_answer": {"answer": 76.145, "unit": "N"}, "id": "force_007074_15.7_4.85", "license": "Apache-2.0", "prompt": "A cart has mass 15.7 kg and measured acceleration 4.85 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 15.7 kg and a = 4.85 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 4.85, "mass": 15.7}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 44.45^2 and multiply by 0.5 * 14.2.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 14028.1978, \"unit\": \"J\"}", "dedupe_signature": "c7393744846c54bc6131556bb486d2fc971b07513c9b75e47c4b9d67b04b88a2", "difficulty": "easy", "final_answer": {"answer": 14028.1978, "unit": "J"}, "id": "ke_007075_14.2_44.45", "license": "Apache-2.0", "prompt": "A body of mass 14.2 kg moves at 44.45 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 44.45^2 and multiply by 0.5 * 14.2.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 14.2, "velocity": 44.45}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=74 degrees through the sine of 2 theta.\n3. Substitute v=34.8 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 65.4183, \"unit\": \"m\"}", "dedupe_signature": "6a2f57a57edfc6e1f58a3848190a56a1ea360f74e59e1cc9be07ce21746f055f", "difficulty": "medium", "final_answer": {"answer": 65.4183, "unit": "m"}, "id": "projectile_range_007076_34.8_74", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 34.8 m/s and angle 74 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=74 degrees through the sine of 2 theta.\nSubstitute v=34.8 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 74, "gravity": 9.81, "speed": 34.8}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=83.5 V and R=13.3 ohm.\nFinal: {\"answer\": 524.2293, \"unit\": \"W\"}", "dedupe_signature": "7d3e0bebc33f438ce19145f9aa8f18884c231fc639f6defd8162c3aa00f2ce08", "difficulty": "easy", "final_answer": {"answer": 524.2293, "unit": "W"}, "id": "ohm_power_007079_83.5_13.3", "license": "Apache-2.0", "prompt": "A resistor has resistance 13.3 ohm and voltage 83.5 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=83.5 V and R=13.3 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 13.3, "voltage": 83.5}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=33.5 mg, t=150.5 h, and T_half=106 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 12.521, \"unit\": \"mg\"}", "dedupe_signature": "20b56059d03ab4d827628e7d32b0ab8e556b0b740c2d2c38a422cd51b002f9b4", "difficulty": "medium", "final_answer": {"answer": 12.521, "unit": "mg"}, "id": "half_life_007080_33.5_106_150.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 33.5 mg. Its half-life is 106 hours. How many mg remain after 150.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=33.5 mg, t=150.5 h, and T_half=106 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 150.5, "half_life": 106.0, "initial_amount": 33.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 3.78 mol * 180.156 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 680.9897, \"unit\": \"g\"}", "dedupe_signature": "61cc8fa81450fe2231b5d04ba4d9401fe9fd344bb3aff9335eda5a0777f2b516", "difficulty": "medium", "final_answer": {"answer": 680.9897, "unit": "g"}, "id": "stoich_mass_007081_glucose_3.78", "license": "Apache-2.0", "prompt": "A sample contains 3.78 mol of glucose. Using molar mass 180.156 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 3.78 mol * 180.156 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "glucose", "molar_mass": 180.156, "moles": 3.78}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 2680 mL to 2.68 L.\n3. Compute M = 0.29 / 2.68.\nFinal: {\"answer\": 0.1082, \"unit\": \"mol/L\"}", "dedupe_signature": "10304bd803c3307916b3ebf581cb2d05745037da2a9cc1aaf43d7b7cca49ee3e", "difficulty": "medium", "final_answer": {"answer": 0.1082, "unit": "mol/L"}, "id": "molarity_007082_0.29_2680", "license": "Apache-2.0", "prompt": "A solution contains 0.29 mol of solute in 2680 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 2680 mL to 2.68 L.\nCompute M = 0.29 / 2.68.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 0.29, "volume_ml": 2680}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.99 y, so each step multiplies y by 1 - h*0.99.\n3. Apply that update for 12 steps and round the final state.\nFinal: {\"answer\": 0.0002, \"unit\": \"state_units\"}", "dedupe_signature": "42e2de1fd5038105a06d2690e52d9c9bd63e45f11c94dea106cdda394597db42", "difficulty": "medium", "final_answer": {"answer": 0.0002, "unit": "state_units"}, "id": "euler_decay_007083_58_0.99_0.65_12", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.99 y with y(0)=58, step size h=0.65, for 12 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.99 y, so each step multiplies y by 1 - h*0.99.\nApply that update for 12 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 58.0, "rate": 0.99, "step": 0.65, "steps": 12}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-4.9)=-14.85 and f(1.8)=15.3.\n3. The interval width is 6.7.\nFinal: {\"answer\": 1.5075, \"unit\": \"area_units\"}", "dedupe_signature": "6d6255ac6c925e536e41ac2e36b0d4a7d74e97ed917b229e07340476870b9fda", "difficulty": "medium", "final_answer": {"answer": 1.5075, "unit": "area_units"}, "id": "trapz_linear_007084_4.5_7.2_-4.9_1.8", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=4.5x+7.2 from x=-4.9 to x=1.8. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-4.9)=-14.85 and f(1.8)=15.3.\nThe interval width is 6.7.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 7.2, "slope": 4.5, "x0": -4.9, "x1": 1.7999999999999998}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.16 and add it to the current value.\nFinal: {\"answer\": [-0.452, -0.084, -0.734], \"unit\": \"temperature_units\"}", "dedupe_signature": "a81c02f775ecb69dd18ef68d1cdedd563d1b1824cf5bebf42486be1ef63a7245", "difficulty": "hard", "final_answer": {"answer": [-0.452, -0.084, -0.734], "unit": "temperature_units"}, "id": "heat_step_007085_0.16_1.35_-1.1_0.5_-1.55_1.5", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.35, right=1.5; current interior values are [-1.1, 0.5, -1.55]. Use r=0.16. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.16 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-1.1, 0.5, -1.55], "left": 1.35, "r": 0.16, "right": 1.5}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 100 centimeters in one meter.\n2. Apply the conversion factor directly to the given value.\n3. Compute 3493.0 / 100.\nFinal: {\"answer\": 34.93, \"unit\": \"m\"}", "dedupe_signature": "84459e2c9e5109cdf9108159a7a50170755feb0a1098edd2901408a57db133b4", "difficulty": "easy", "final_answer": {"answer": 34.93, "unit": "m"}, "id": "unit_convert_007086_cm_to_m_3493", "license": "Apache-2.0", "prompt": "Convert 3493 cm to m. Return the converted value with unit.", "reasoning_trace": "There are 100 centimeters in one meter.\nApply the conversion factor directly to the given value.\nCompute 3493.0 / 100.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 3493.0}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=303 degrees and keep the unit as newtons.\nFinal: {\"answer\": [162.0301, -249.5045], \"unit\": \"N\"}", "dedupe_signature": "e3cc693d53e6f46adc468ce717369e6d12fab07d8fd6c672ea214d5075950ee0", "difficulty": "medium", "final_answer": {"answer": [162.0301, -249.5045], "unit": "N"}, "id": "vector_components_007087_297.5_303", "license": "Apache-2.0", "prompt": "A vector has magnitude 297.5 N at 303 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=303 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 303, "magnitude": 297.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef safe_mean_007090(values):\n    if not values:\n        raise ValueError('safe_mean requires at least one value')\n    return sum(values) / len(values)\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"safe_mean_007090\"}", "dedupe_signature": "b4ca8b8a85ebe01816bcadef2656a1a67887caa320687c88cd3f315375d63e3c", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "safe_mean_007090"}, "id": "code_007090_safe_mean_007090", "license": "Apache-2.0", "prompt": "Write a Python function safe_mean_007090(values) that returns the arithmetic mean. It must raise ValueError for an empty input and must not mutate the input list. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "safe_mean_007090"}, "verifier": {"function": "safe_mean_007090", "tests": ["assert safe_mean_007090([2, 4, 6]) == 4", "xs = [1, 2, 3]; assert safe_mean_007090(xs) == 2 and xs == [1, 2, 3]", "try:\n    safe_mean_007090([])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: recurrence, objective, tie_breaking_rule.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"recurrence\", \"objective\", \"tie_breaking_rule\"]}", "dedupe_signature": "bcc97422fc3301445f51e8af2c86cf7dcb6500a4d11a9afc1baefce4a95ba74c", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["recurrence", "objective", "tie_breaking_rule"]}, "id": "abstain_007091_recurrence_objective_tie_breaking_rule", "license": "Apache-2.0", "prompt": "Write a dynamic-programming solver for a alignment scoring problem with 2938 items and budget 5965, but the recurrence, objective, and tie-breaking rule are all absent. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: recurrence, objective, tie_breaking_rule.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["recurrence", "objective", "tie_breaking_rule"]}, "verifier": {"missing": ["recurrence", "objective", "tie_breaking_rule"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 23.65 kg and a = 6.2 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 146.63, \"unit\": \"N\"}", "dedupe_signature": "9cdcb0cd49bc7cab7fdaee5fe27b87ea7213f8560b3678d7320961816e017e2a", "difficulty": "easy", "final_answer": {"answer": 146.63, "unit": "N"}, "id": "force_007092_23.65_6.2", "license": "Apache-2.0", "prompt": "A cart has mass 23.65 kg and measured acceleration 6.2 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 23.65 kg and a = 6.2 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 6.2, "mass": 23.65}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 9.45^2 and multiply by 0.5 * 20.95.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 935.4437, \"unit\": \"J\"}", "dedupe_signature": "dd35b2ddf26bc4f3cb2064a093b2e8522fb9462ea4fa1004268d90bb42e0e053", "difficulty": "easy", "final_answer": {"answer": 935.4437, "unit": "J"}, "id": "ke_007093_20.95_9.45", "license": "Apache-2.0", "prompt": "A body of mass 20.95 kg moves at 9.45 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 9.45^2 and multiply by 0.5 * 20.95.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 20.95, "velocity": 9.45}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=71 degrees through the sine of 2 theta.\n3. Substitute v=62.7 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 246.7221, \"unit\": \"m\"}", "dedupe_signature": "3ae3074bbe3788833796489e14f76da96e445dfff87425c381252068660465a8", "difficulty": "medium", "final_answer": {"answer": 246.7221, "unit": "m"}, "id": "projectile_range_007094_62.7_71", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 62.7 m/s and angle 71 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=71 degrees through the sine of 2 theta.\nSubstitute v=62.7 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 71, "gravity": 9.81, "speed": 62.7}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 830 * 1.525 * 19.\nFinal: {\"answer\": 24049.25, \"unit\": \"J\"}", "dedupe_signature": "ebd8895ff9d236160e1ea4e24b5bbeca91de0b264d937e99562016b3f474851b", "difficulty": "easy", "final_answer": {"answer": 24049.25, "unit": "J"}, "id": "heat_q_007096_830_1.525_19", "license": "Apache-2.0", "prompt": "A 830 g sample has specific heat 1.525 J/(g*K). How much heat is needed to raise its temperature by 19 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 830 * 1.525 * 19.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 19, "heat_capacity": 1.525, "mass_g": 830}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=50 V and R=155.1 ohm.\nFinal: {\"answer\": 16.1186, \"unit\": \"W\"}", "dedupe_signature": "67c1c572b88cae82b90d1ac7679b7b32ff467742b20833d3e8cf8cd7ee8569c6", "difficulty": "easy", "final_answer": {"answer": 16.1186, "unit": "W"}, "id": "ohm_power_007097_50_155.1", "license": "Apache-2.0", "prompt": "A resistor has resistance 155.1 ohm and voltage 50 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=50 V and R=155.1 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 155.1, "voltage": 50.0}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=894.5 mg, t=351 h, and T_half=54 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 9.8829, \"unit\": \"mg\"}", "dedupe_signature": "41d842c36d616f56af87e18f1d20bcea3ebdfcc802b14ac7fb8b25e8189794db", "difficulty": "medium", "final_answer": {"answer": 9.8829, "unit": "mg"}, "id": "half_life_007098_894.5_54_351", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 894.5 mg. Its half-life is 54 hours. How many mg remain after 351 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=894.5 mg, t=351 h, and T_half=54 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 351.0, "half_life": 54.0, "initial_amount": 894.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 6.54 mol * 100.087 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 654.569, \"unit\": \"g\"}", "dedupe_signature": "9fbbb3fc8748df8ee0787879f99e37bac22303e8b11010558e687430432ec2c3", "difficulty": "medium", "final_answer": {"answer": 654.569, "unit": "g"}, "id": "stoich_mass_007099_calcium_carbonate_6.54", "license": "Apache-2.0", "prompt": "A sample contains 6.54 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 6.54 mol * 100.087 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "calcium carbonate", "molar_mass": 100.087, "moles": 6.54}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 2440 mL to 2.44 L.\n3. Compute M = 3.75 / 2.44.\nFinal: {\"answer\": 1.5369, \"unit\": \"mol/L\"}", "dedupe_signature": "c0bc04868ec18b5408aa112d01a7c126d3c7d16b79ee05760cc2758a55bdd923", "difficulty": "medium", "final_answer": {"answer": 1.5369, "unit": "mol/L"}, "id": "molarity_007100_3.75_2440", "license": "Apache-2.0", "prompt": "A solution contains 3.75 mol of solute in 2440 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 2440 mL to 2.44 L.\nCompute M = 3.75 / 2.44.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 3.75, "volume_ml": 2440}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(9.4)=-68.72 and f(11.8)=-87.44.\n3. The interval width is 2.4.\nFinal: {\"answer\": -187.392, \"unit\": \"area_units\"}", "dedupe_signature": "e0e141e183640755c84e803e556efb4e07e7644998c79ffbae9c3fc3fd1f529f", "difficulty": "medium", "final_answer": {"answer": -187.392, "unit": "area_units"}, "id": "trapz_linear_007102_-7.8_4.6_9.4_11.8", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-7.8x+4.6 from x=9.4 to x=11.8. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(9.4)=-68.72 and f(11.8)=-87.44.\nThe interval width is 2.4.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 4.6, "slope": -7.8, "x0": 9.4, "x1": 11.8}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.4 and add it to the current value.\nFinal: {\"answer\": [-0.07, -0.77, 0.02], \"unit\": \"temperature_units\"}", "dedupe_signature": "7271309b08a59cddee2516f88ff6a6e00bb4b7040c99aa1fd7e9fffcecd2c06e", "difficulty": "hard", "final_answer": {"answer": [-0.07, -0.77, 0.02], "unit": "temperature_units"}, "id": "heat_step_007103_0.4_1.65_-1.35_-1.15_0.0_1.2", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.65, right=1.2; current interior values are [-1.35, -1.15, 0.0]. Use r=0.4. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.4 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-1.35, -1.15, 0.0], "left": 1.65, "r": 0.4, "right": 1.2}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 29101.0 / 1000.\nFinal: {\"answer\": 29.101, \"unit\": \"kg\"}", "dedupe_signature": "1678ddc076efe296fd5c37cbd64394f57a644612659c76f81bde55cb088e7ff8", "difficulty": "easy", "final_answer": {"answer": 29.101, "unit": "kg"}, "id": "unit_convert_007104_g_to_kg_29101", "license": "Apache-2.0", "prompt": "Convert 29101 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 29101.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 29101.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=34 degrees and keep the unit as newtons.\nFinal: {\"answer\": [257.0016, 173.3498], \"unit\": \"N\"}", "dedupe_signature": "a4ef48d0d82e08e0edda1c4013aa24160ae852db93465390e348bd6a8239f7d4", "difficulty": "medium", "final_answer": {"answer": [257.0016, 173.3498], "unit": "N"}, "id": "vector_components_007105_310_34", "license": "Apache-2.0", "prompt": "A vector has magnitude 310 N at 34 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=34 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 34, "magnitude": 310.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-8.4, 21.25], \"unit\": \"dimensionless\"}", "dedupe_signature": "3271ec6bb99fbeca3500c2adb1d3994792d7799e19e5e6aa5538b8c225b9c145", "difficulty": "medium", "final_answer": {"answer": [-8.4, 21.25], "unit": "dimensionless"}, "id": "line_two_point_007106_-12.25_-9.25_-8.4_21.25", "license": "Apache-2.0", "prompt": "A line passes through points (-12.25, 124.15) and (-9.25, 98.95). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -12.25, "x2": -9.25, "y1": 124.15, "y2": 98.95}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. velocity times time gives distance, not acceleration\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "9d6c52933a1ebbe3ebc05225e0c1283177c4eacb3fb0938dbd41f94b571b7307", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_007107_inconsistent_7481c798_299588", "license": "Apache-2.0", "prompt": "In lab notebook case 299588, check dimensional consistency for a = v * t. The left side has dimensions m/s^2 and the right side has dimensions m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nvelocity times time gives distance, not acceleration\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "a = v * t"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: required_fields, allowed_transformations.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"required_fields\", \"allowed_transformations\"]}", "dedupe_signature": "97247503fbc36c6464c7d5b372837ed08815c1453a3968596d8656d5457a2e6c", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["required_fields", "allowed_transformations"]}, "id": "abstain_007109_required_fields_allowed_transformations", "license": "Apache-2.0", "prompt": "Write a sanitizer for valid field clinical records in release 64048, but the prompt does not state which fields are required or which transformations are allowed. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: required_fields, allowed_transformations.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["required_fields", "allowed_transformations"]}, "verifier": {"missing": ["required_fields", "allowed_transformations"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 24.5 kg and a = 11.6 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 284.2, \"unit\": \"N\"}", "dedupe_signature": "47d49e27982483898547e07ab31af892b1e6791fa90123f681e749491e0f8aae", "difficulty": "easy", "final_answer": {"answer": 284.2, "unit": "N"}, "id": "force_007110_24.5_11.6", "license": "Apache-2.0", "prompt": "A cart has mass 24.5 kg and measured acceleration 11.6 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 24.5 kg and a = 11.6 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 11.6, "mass": 24.5}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 35.2^2 and multiply by 0.5 * 21.95.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 13598.464, \"unit\": \"J\"}", "dedupe_signature": "c351318269420376a3547ca2fdfc0974bb220740c0f230b0399fb8b5e500307c", "difficulty": "easy", "final_answer": {"answer": 13598.464, "unit": "J"}, "id": "ke_007111_21.95_35.2", "license": "Apache-2.0", "prompt": "A body of mass 21.95 kg moves at 35.2 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 35.2^2 and multiply by 0.5 * 21.95.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 21.95, "velocity": 35.2}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 3.32 * 8.314 * 369 / 5.8.\nFinal: {\"answer\": 1756.0888, \"unit\": \"kPa\"}", "dedupe_signature": "704946cfe6015a07d2dd190d9931cc84d1c3a01470615e84b10b5839d8243058", "difficulty": "medium", "final_answer": {"answer": 1756.0888, "unit": "kPa"}, "id": "ideal_gas_007113_3.32_369_5.8", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=3.32 mol, T=369 K, and V=5.8 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 3.32 * 8.314 * 369 / 5.8.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 3.32, "temp_k": 369, "volume_l": 5.8}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 1.38 mol * 18.015 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 24.8607, \"unit\": \"g\"}", "dedupe_signature": "324b12ef600854dfb298fa276b15504090524b630965b19c213be20d107b96ff", "difficulty": "medium", "final_answer": {"answer": 24.8607, "unit": "g"}, "id": "stoich_mass_007117_water_1.38", "license": "Apache-2.0", "prompt": "A sample contains 1.38 mol of water. Using molar mass 18.015 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 1.38 mol * 18.015 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "water", "molar_mass": 18.015, "moles": 1.38}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 835 mL to 0.835 L.\n3. Compute M = 0.12 / 0.835.\nFinal: {\"answer\": 0.1437, \"unit\": \"mol/L\"}", "dedupe_signature": "a0180061d8eeb064e361b8623b90631b6cf2444d6ee24b24a14ee45eced2f002", "difficulty": "medium", "final_answer": {"answer": 0.1437, "unit": "mol/L"}, "id": "molarity_007118_0.12_835", "license": "Apache-2.0", "prompt": "A solution contains 0.12 mol of solute in 835 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 835 mL to 0.835 L.\nCompute M = 0.12 / 0.835.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 0.12, "volume_ml": 835}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.03 y, so each step multiplies y by 1 - h*0.03.\n3. Apply that update for 2 steps and round the final state.\nFinal: {\"answer\": 61.6289, \"unit\": \"state_units\"}", "dedupe_signature": "446a360ae91f4d341114f855c405bf43a7a7ed65de1304969750f14355dfb0cd", "difficulty": "medium", "final_answer": {"answer": 61.6289, "unit": "state_units"}, "id": "euler_decay_007119_65.5_0.03_1_2", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.03 y with y(0)=65.5, step size h=1, for 2 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.03 y, so each step multiplies y by 1 - h*0.03.\nApply that update for 2 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 65.5, "rate": 0.03, "step": 1.0, "steps": 2}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-4.3)=12.48 and f(-0.5)=14.\n3. The interval width is 3.8.\nFinal: {\"answer\": 50.312, \"unit\": \"area_units\"}", "dedupe_signature": "d0b1f52935a7bbfc94a2c34cd5d1a5bf03ce881d71cfc293bd56704c20eaa362", "difficulty": "medium", "final_answer": {"answer": 50.312, "unit": "area_units"}, "id": "trapz_linear_007120_0.4_14.2_-4.3_-0.5", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=0.4x+14.2 from x=-4.3 to x=-0.5. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-4.3)=12.48 and f(-0.5)=14.\nThe interval width is 3.8.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 14.2, "slope": 0.4, "x0": -4.3, "x1": -0.5}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.28 and add it to the current value.\nFinal: {\"answer\": [0.36, 0.65, 0.768], \"unit\": \"temperature_units\"}", "dedupe_signature": "115b45c449f253e302e66247390591c6fe4f46fe76372bcd595a9cbc8a735df0", "difficulty": "hard", "final_answer": {"answer": [0.36, 0.65, 0.768], "unit": "temperature_units"}, "id": "heat_step_007121_0.28_-0.8_2.25_-1.45_2.35_0.5", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-0.8, right=0.5; current interior values are [2.25, -1.45, 2.35]. Use r=0.28. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.28 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [2.25, -1.45, 2.35], "left": -0.8, "r": 0.28, "right": 0.5}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kelvin equals Celsius plus 273.15.\n2. Apply the conversion factor directly to the given value.\n3. Compute 247.5 + 273.15.\nFinal: {\"answer\": 520.65, \"unit\": \"K\"}", "dedupe_signature": "c15d4b22bbe6aada9eb2e8154b5f35825291d3c060a51d3c1a42db8331f5e091", "difficulty": "easy", "final_answer": {"answer": 520.65, "unit": "K"}, "id": "unit_convert_007122_c_to_k_247.5", "license": "Apache-2.0", "prompt": "Convert 247.5 degC to K. Return the converted value with unit.", "reasoning_trace": "Kelvin equals Celsius plus 273.15.\nApply the conversion factor directly to the given value.\nCompute 247.5 + 273.15.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 247.5}, "verifier": {"formula": "value + 273.15", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=307 degrees and keep the unit as newtons.\nFinal: {\"answer\": [96.8922, -128.5803], \"unit\": \"N\"}", "dedupe_signature": "19f69f1a69045e53bab3635401f525d7af78829ae336e82dbcd5e6719a776b21", "difficulty": "medium", "final_answer": {"answer": [96.8922, -128.5803], "unit": "N"}, "id": "vector_components_007123_161_307", "license": "Apache-2.0", "prompt": "A vector has magnitude 161 N at 307 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=307 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 307, "magnitude": 161.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [5.9, 17.25], \"unit\": \"dimensionless\"}", "dedupe_signature": "544dedbc947fe2b004a0fa90eafa76c26abf0d2b416523cbfa742aad37485572", "difficulty": "medium", "final_answer": {"answer": [5.9, 17.25], "unit": "dimensionless"}, "id": "line_two_point_007124_-12.5_-2.25_5.9_17.25", "license": "Apache-2.0", "prompt": "A line passes through points (-12.5, -56.5) and (-2.25, 3.975). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -12.5, "x2": -2.25, "y1": -56.5, "y2": 3.9749999999999996}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. grams cancel with J/(g*K), and kelvin cancels, leaving joules\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "6091851d70c316f584a646dc80cd2db426645a7aa70a017bcdd07de5d3c266ec", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_007125_consistent_4153435f_262402", "license": "Apache-2.0", "prompt": "In sensor calibration case 262402, check dimensional consistency for Q = m * c * DeltaT. The left side has dimensions J and the right side has dimensions J. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\ngrams cancel with J/(g*K), and kelvin cancels, leaving joules\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "Q = m * c * DeltaT"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef center_values_007126(values):\n    if not values:\n        raise ValueError('center_values requires at least one value')\n    mean = sum(values) / len(values)\n    return [value - mean for value in values]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"center_values_007126\"}", "dedupe_signature": "70acaf7951ee861763e71e6bd56b58f2b2398e3088985f51aa1d9a8cc3a7c97f", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "center_values_007126"}, "id": "code_007126_center_values_007126", "license": "Apache-2.0", "prompt": "Write a Python function center_values_007126(values) that subtracts the arithmetic mean from each value and returns a new list. Raise ValueError for an empty input. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "center_values_007126"}, "verifier": {"function": "center_values_007126", "tests": ["out = center_values_007126([1, 2, 3]); assert out == [-1, 0, 1]", "assert center_values_007126([5]) == [0]", "try:\n    center_values_007126([])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: target_schema, valid_examples.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"target_schema\", \"valid_examples\"]}", "dedupe_signature": "c5b0a134230c369d830cd4e0ecac3d66325a9f9f7079d537266a50e4a4dfafb6", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["target_schema", "valid_examples"]}, "id": "abstain_007127_target_schema_valid_examples", "license": "Apache-2.0", "prompt": "Write a parser that converts each mobile ledger record from batch 109517 into the correct schema, but the prompt does not include the target schema or examples. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: target_schema, valid_examples.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["target_schema", "valid_examples"]}, "verifier": {"missing": ["target_schema", "valid_examples"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 7.95 kg and a = 1.45 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 11.5275, \"unit\": \"N\"}", "dedupe_signature": "960b03bb19c39eb501e00ec516c4e38a6550412af7a16d9cd628ca57ca802d13", "difficulty": "easy", "final_answer": {"answer": 11.5275, "unit": "N"}, "id": "force_007128_7.95_1.45", "license": "Apache-2.0", "prompt": "A cart has mass 7.95 kg and measured acceleration 1.45 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 7.95 kg and a = 1.45 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 1.45, "mass": 7.95}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 7.1^2 and multiply by 0.5 * 1.85.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 46.6292, \"unit\": \"J\"}", "dedupe_signature": "091a216f37f22a4ff50eb3ca7e87af4751c69982ba696f7ef245a2fcfe0da30d", "difficulty": "easy", "final_answer": {"answer": 46.6292, "unit": "J"}, "id": "ke_007129_1.85_7.1", "license": "Apache-2.0", "prompt": "A body of mass 1.85 kg moves at 7.1 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 7.1^2 and multiply by 0.5 * 1.85.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 1.85, "velocity": 7.1}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=76 degrees through the sine of 2 theta.\n3. Substitute v=56.6 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 153.3109, \"unit\": \"m\"}", "dedupe_signature": "7cdc97695967690025b0fa32d001b2e78c528ead6c6c18f1a52e939a4ba02a4f", "difficulty": "medium", "final_answer": {"answer": 153.3109, "unit": "m"}, "id": "projectile_range_007130_56.6_76", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 56.6 m/s and angle 76 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=76 degrees through the sine of 2 theta.\nSubstitute v=56.6 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 76, "gravity": 9.81, "speed": 56.6}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 1.29 * 8.314 * 324 / 8.4.\nFinal: {\"answer\": 413.6809, \"unit\": \"kPa\"}", "dedupe_signature": "a482f3a25677c51b7cde9fb3a65a9185a7554f9b1ff3e1667fc1bf00a7b4248e", "difficulty": "medium", "final_answer": {"answer": 413.6809, "unit": "kPa"}, "id": "ideal_gas_007131_1.29_324_8.4", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=1.29 mol, T=324 K, and V=8.4 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 1.29 * 8.314 * 324 / 8.4.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 1.29, "temp_k": 324, "volume_l": 8.4}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=77.9 V and R=1.5 ohm.\nFinal: {\"answer\": 4045.6067, \"unit\": \"W\"}", "dedupe_signature": "8f6d955753f7b2fdb558230d6dacf7af2bc7c0279a21eaf2414ba10f7ebbb767", "difficulty": "easy", "final_answer": {"answer": 4045.6067, "unit": "W"}, "id": "ohm_power_007133_77.9_1.5", "license": "Apache-2.0", "prompt": "A resistor has resistance 1.5 ohm and voltage 77.9 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=77.9 V and R=1.5 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 1.5, "voltage": 77.9}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 1550 mL to 1.55 L.\n3. Compute M = 2.365 / 1.55.\nFinal: {\"answer\": 1.5258, \"unit\": \"mol/L\"}", "dedupe_signature": "339394bf41be7fbe08835155fdee0849663d89c3429a7b7e983a9ffced3629fc", "difficulty": "medium", "final_answer": {"answer": 1.5258, "unit": "mol/L"}, "id": "molarity_007136_2.365_1550", "license": "Apache-2.0", "prompt": "A solution contains 2.365 mol of solute in 1550 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 1550 mL to 1.55 L.\nCompute M = 2.365 / 1.55.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 2.365, "volume_ml": 1550}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.05 y, so each step multiplies y by 1 - h*0.05.\n3. Apply that update for 3 steps and round the final state.\nFinal: {\"answer\": 1.4948, \"unit\": \"state_units\"}", "dedupe_signature": "e0623e30643c77f2ce7f22366cf22294b011bafc5353915fda22b8b5690939bd", "difficulty": "medium", "final_answer": {"answer": 1.4948, "unit": "state_units"}, "id": "euler_decay_007137_2_0.05_1.85_3", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.05 y with y(0)=2, step size h=1.85, for 3 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.05 y, so each step multiplies y by 1 - h*0.05.\nApply that update for 3 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 2.0, "rate": 0.05, "step": 1.85, "steps": 3}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-9.9)=36.11 and f(-1.7)=-4.07.\n3. The interval width is 8.2.\nFinal: {\"answer\": 131.364, \"unit\": \"area_units\"}", "dedupe_signature": "5bb138b1bc3c1374b9958727e99645e38ba9a3d4fdebcb60f8d35b0aca1d6d4f", "difficulty": "medium", "final_answer": {"answer": 131.364, "unit": "area_units"}, "id": "trapz_linear_007138_-4.9_-12.4_-9.9_-1.7", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-4.9x+-12.4 from x=-9.9 to x=-1.7. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-9.9)=36.11 and f(-1.7)=-4.07.\nThe interval width is 8.2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -12.4, "slope": -4.9, "x0": -9.9, "x1": -1.700000000000001}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.12 and add it to the current value.\nFinal: {\"answer\": [-0.364, -1.614, -0.994], \"unit\": \"temperature_units\"}", "dedupe_signature": "29a86d02ca78f45fded3aae598719c9ed1a1943c4dd91b49bc8f640934233fb9", "difficulty": "hard", "final_answer": {"answer": [-0.364, -1.614, -0.994], "unit": "temperature_units"}, "id": "heat_step_007139_0.12_-1.4_0.05_-1.95_-1.15_0.95", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-1.4, right=0.95; current interior values are [0.05, -1.95, -1.15]. Use r=0.12. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.12 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [0.05, -1.95, -1.15], "left": -1.4, "r": 0.12, "right": 0.95}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kelvin equals Celsius plus 273.15.\n2. Apply the conversion factor directly to the given value.\n3. Compute 196.5 + 273.15.\nFinal: {\"answer\": 469.65, \"unit\": \"K\"}", "dedupe_signature": "6e52c3bc7855fa203822948991c151eba753c5e38d43266238c556c2f8373813", "difficulty": "easy", "final_answer": {"answer": 469.65, "unit": "K"}, "id": "unit_convert_007140_c_to_k_196.5", "license": "Apache-2.0", "prompt": "Convert 196.5 degC to K. Return the converted value with unit.", "reasoning_trace": "Kelvin equals Celsius plus 273.15.\nApply the conversion factor directly to the given value.\nCompute 196.5 + 273.15.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 196.5}, "verifier": {"formula": "value + 273.15", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=349 degrees and keep the unit as newtons.\nFinal: {\"answer\": [475.1076, -92.3516], \"unit\": \"N\"}", "dedupe_signature": "2db88ddc5c2f706889b15e2c9eaf0e9e7c52ed3a924e157818aa2f26dbb4bf68", "difficulty": "medium", "final_answer": {"answer": [475.1076, -92.3516], "unit": "N"}, "id": "vector_components_007141_484_349", "license": "Apache-2.0", "prompt": "A vector has magnitude 484 N at 349 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=349 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 349, "magnitude": 484.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [6.5, 2.0], \"unit\": \"dimensionless\"}", "dedupe_signature": "5c220beb610f6364c6faa2aecd65f20c5607a9164da8672e96846e6c41961582", "difficulty": "medium", "final_answer": {"answer": [6.5, 2.0], "unit": "dimensionless"}, "id": "line_two_point_007142_0.5_8.5_6.5_2", "license": "Apache-2.0", "prompt": "A line passes through points (0.5, 5.25) and (8.5, 57.25). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 0.5, "x2": 8.5, "y1": 5.25, "y2": 57.25}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. amount times volume is not concentration\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "9ff90d108b8afb2a1b1841fb7f21e6a6f607f50b5d90bd0029a7423e1a95f183", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_007143_inconsistent_74ac0b02_806532", "license": "Apache-2.0", "prompt": "In quality-control check case 806532, check dimensional consistency for C = n * V. The left side has dimensions mol/L and the right side has dimensions mol*L. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\namount times volume is not concentration\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "C = n * V"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef center_values_007144(values):\n    if not values:\n        raise ValueError('center_values requires at least one value')\n    mean = sum(values) / len(values)\n    return [value - mean for value in values]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"center_values_007144\"}", "dedupe_signature": "d9a13587934ce5ab2749bd9828bfd31bc9411d363d6b55b1fad35aeddccf946d", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "center_values_007144"}, "id": "code_007144_center_values_007144", "license": "Apache-2.0", "prompt": "Write a Python function center_values_007144(values) that subtracts the arithmetic mean from each value and returns a new list. Raise ValueError for an empty input. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "center_values_007144"}, "verifier": {"function": "center_values_007144", "tests": ["out = center_values_007144([1, 2, 3]); assert out == [-1, 0, 1]", "assert center_values_007144([5]) == [0]", "try:\n    center_values_007144([])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: required_fields, allowed_transformations.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"required_fields\", \"allowed_transformations\"]}", "dedupe_signature": "40bb9cc4e9a9040ed12f5e3c6455910e7fa8c1b5ac308203e129ce7f221d1c66", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["required_fields", "allowed_transformations"]}, "id": "abstain_007145_required_fields_allowed_transformations", "license": "Apache-2.0", "prompt": "Write a sanitizer for valid billing invoice records in release 155638, but the prompt does not state which fields are required or which transformations are allowed. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: required_fields, allowed_transformations.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["required_fields", "allowed_transformations"]}, "verifier": {"missing": ["required_fields", "allowed_transformations"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 4.5 kg and a = 14.9 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 67.05, \"unit\": \"N\"}", "dedupe_signature": "ae754fa90873104f9e4594afebe73ce5bc3532129ef8fdef12189c1751458145", "difficulty": "easy", "final_answer": {"answer": 67.05, "unit": "N"}, "id": "force_007146_4.5_14.9", "license": "Apache-2.0", "prompt": "A cart has mass 4.5 kg and measured acceleration 14.9 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 4.5 kg and a = 14.9 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 14.9, "mass": 4.5}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 32.25^2 and multiply by 0.5 * 25.75.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 13390.8047, \"unit\": \"J\"}", "dedupe_signature": "07067ebc14d1f2639304fe985c8aacb57c89803578655b6e994649864745afb6", "difficulty": "easy", "final_answer": {"answer": 13390.8047, "unit": "J"}, "id": "ke_007147_25.75_32.25", "license": "Apache-2.0", "prompt": "A body of mass 25.75 kg moves at 32.25 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 32.25^2 and multiply by 0.5 * 25.75.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 25.75, "velocity": 32.25}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 4.99 * 8.314 * 314 / 49.6.\nFinal: {\"answer\": 262.6386, \"unit\": \"kPa\"}", "dedupe_signature": "bdcaef46bc228baea57059c57f56749c94a61e8600e71d68ca9d87cc48afcaaa", "difficulty": "medium", "final_answer": {"answer": 262.6386, "unit": "kPa"}, "id": "ideal_gas_007149_4.99_314_49.6", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=4.99 mol, T=314 K, and V=49.6 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 4.99 * 8.314 * 314 / 49.6.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 4.99, "temp_k": 314, "volume_l": 49.6}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1480 * 3.545 * 12.\nFinal: {\"answer\": 62959.2, \"unit\": \"J\"}", "dedupe_signature": "4672445f5e166fee4e1e0287d988cca0fa49948cb95979a5ab9e514c8412492a", "difficulty": "easy", "final_answer": {"answer": 62959.2, "unit": "J"}, "id": "heat_q_007150_1480_3.545_12", "license": "Apache-2.0", "prompt": "A 1480 g sample has specific heat 3.545 J/(g*K). How much heat is needed to raise its temperature by 12 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1480 * 3.545 * 12.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 12, "heat_capacity": 3.545, "mass_g": 1480}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=141.1 V and R=135.8 ohm.\nFinal: {\"answer\": 146.6068, \"unit\": \"W\"}", "dedupe_signature": "817ab3b8e86104b0b1034f18cf163782502db3d59cb87a73698087fa8bd83d8d", "difficulty": "easy", "final_answer": {"answer": 146.6068, "unit": "W"}, "id": "ohm_power_007151_141.1_135.8", "license": "Apache-2.0", "prompt": "A resistor has resistance 135.8 ohm and voltage 141.1 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=141.1 V and R=135.8 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 135.8, "voltage": 141.1}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=978.5 mg, t=83.5 h, and T_half=2 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 0.0, \"unit\": \"mg\"}", "dedupe_signature": "d61d1186bc329f49d36931c33a21cb90adc4f3995e94750648a495db89e51464", "difficulty": "medium", "final_answer": {"answer": 0.0, "unit": "mg"}, "id": "half_life_007152_978.5_2_83.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 978.5 mg. Its half-life is 2 hours. How many mg remain after 83.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=978.5 mg, t=83.5 h, and T_half=2 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 83.5, "half_life": 2.0, "initial_amount": 978.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 65 mL to 0.065 L.\n3. Compute M = 0.13 / 0.065.\nFinal: {\"answer\": 2.0, \"unit\": \"mol/L\"}", "dedupe_signature": "1d36ebc0e2ad74c36d5cf84a42d2a108087389b6f2e7bbcf99b86f5d9f48c3a6", "difficulty": "medium", "final_answer": {"answer": 2.0, "unit": "mol/L"}, "id": "molarity_007154_0.13_65", "license": "Apache-2.0", "prompt": "A solution contains 0.13 mol of solute in 65 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 65 mL to 0.065 L.\nCompute M = 0.13 / 0.065.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 0.13, "volume_ml": 65}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-6.6)=54.94 and f(-2.5)=22.55.\n3. The interval width is 4.1.\nFinal: {\"answer\": 158.8545, \"unit\": \"area_units\"}", "dedupe_signature": "59e65dd507385a88cea7b16ca08df48948a419f5286ddef161f07dcca9fbeb74", "difficulty": "medium", "final_answer": {"answer": 158.8545, "unit": "area_units"}, "id": "trapz_linear_007156_-7.9_2.8_-6.6_-2.5", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-7.9x+2.8 from x=-6.6 to x=-2.5. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-6.6)=54.94 and f(-2.5)=22.55.\nThe interval width is 4.1.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 2.8, "slope": -7.9, "x0": -6.6, "x1": -2.5}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 46822.0 / 1000.\nFinal: {\"answer\": 46.822, \"unit\": \"kg\"}", "dedupe_signature": "888f678c1d2425bc034b53cd6766dd0d24cb9f3f23c3551491cb115fe0a328d9", "difficulty": "easy", "final_answer": {"answer": 46.822, "unit": "kg"}, "id": "unit_convert_007158_g_to_kg_46822", "license": "Apache-2.0", "prompt": "Convert 46822 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 46822.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 46822.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=89 degrees and keep the unit as newtons.\nFinal: {\"answer\": [6.6232, 379.4422], \"unit\": \"N\"}", "dedupe_signature": "08237c1a480feddf40384674cbcdf6266cc6898551e1d188ae6230680ce7af95", "difficulty": "medium", "final_answer": {"answer": [6.6232, 379.4422], "unit": "N"}, "id": "vector_components_007159_379.5_89", "license": "Apache-2.0", "prompt": "A vector has magnitude 379.5 N at 89 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=89 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 89, "magnitude": 379.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [2.15, 4.75], \"unit\": \"dimensionless\"}", "dedupe_signature": "1439337006a396c4e6e0d92c3dfe338f17ff017a0ded9baf3480d568b014cbde", "difficulty": "medium", "final_answer": {"answer": [2.15, 4.75], "unit": "dimensionless"}, "id": "line_two_point_007160_2_3.75_2.15_4.75", "license": "Apache-2.0", "prompt": "A line passes through points (2, 9.05) and (3.75, 12.8125). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 2.0, "x2": 3.75, "y1": 9.05, "y2": 12.8125}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef threshold_flags_007162(values, threshold):\n    return [value >= threshold for value in values]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"threshold_flags_007162\"}", "dedupe_signature": "8fa23a6650ba317febcbf9caf9dde88e7c8b73c9204cf2081cc6144b82c96482", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "threshold_flags_007162"}, "id": "code_007162_threshold_flags_007162", "license": "Apache-2.0", "prompt": "Write a Python function threshold_flags_007162(values, threshold) that returns a list of booleans showing whether each value is greater than or equal to threshold. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "threshold_flags_007162"}, "verifier": {"function": "threshold_flags_007162", "tests": ["assert threshold_flags_007162([1, 2, 3], 2) == [False, True, True]", "assert threshold_flags_007162([], 5) == []", "assert threshold_flags_007162([-1, 0], 0) == [False, True]"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: rate_constant, number_of_steps.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"rate_constant\", \"number_of_steps\"]}", "dedupe_signature": "abe52ff859e6de2c6f8a2bf2870a45492fa68518905cee65a56332d16d6f3938", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["rate_constant", "number_of_steps"]}, "id": "abstain_007163_rate_constant_number_of_steps", "license": "Apache-2.0", "prompt": "Use explicit Euler for dy/dt = -k y. The prompt gives y(0)=71 and h=1.4, but omits both k and the number of steps. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: rate_constant, number_of_steps.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["rate_constant", "number_of_steps"]}, "verifier": {"missing": ["rate_constant", "number_of_steps"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 19.7 kg and a = 3.25 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 64.025, \"unit\": \"N\"}", "dedupe_signature": "49a0f41fb4519b4260980380a806cb260748259377679b37eb61a9159e7de864", "difficulty": "easy", "final_answer": {"answer": 64.025, "unit": "N"}, "id": "force_007164_19.7_3.25", "license": "Apache-2.0", "prompt": "A cart has mass 19.7 kg and measured acceleration 3.25 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 19.7 kg and a = 3.25 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 3.25, "mass": 19.7}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 11.85^2 and multiply by 0.5 * 17.3.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 1214.6546, \"unit\": \"J\"}", "dedupe_signature": "e5d02691bb9bc7040339a694206546139bed41efa9e91191272e4ad38c8ed3af", "difficulty": "easy", "final_answer": {"answer": 1214.6546, "unit": "J"}, "id": "ke_007165_17.3_11.85", "license": "Apache-2.0", "prompt": "A body of mass 17.3 kg moves at 11.85 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 11.85^2 and multiply by 0.5 * 17.3.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 17.3, "velocity": 11.85}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=80 degrees through the sine of 2 theta.\n3. Substitute v=51.7 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 93.1888, \"unit\": \"m\"}", "dedupe_signature": "ba27bf5fbb5f89a8657d31f3152fb2c2586babfc42562d821a86ce1ea12497a1", "difficulty": "medium", "final_answer": {"answer": 93.1888, "unit": "m"}, "id": "projectile_range_007166_51.7_80", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 51.7 m/s and angle 80 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=80 degrees through the sine of 2 theta.\nSubstitute v=51.7 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 80, "gravity": 9.81, "speed": 51.7}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 5.72 * 8.314 * 419 / 65.0.\nFinal: {\"answer\": 306.5538, \"unit\": \"kPa\"}", "dedupe_signature": "66135fb6caa8c473a2705890929ff0d6cc3e738545d5f0e857738b7332ffb21f", "difficulty": "medium", "final_answer": {"answer": 306.5538, "unit": "kPa"}, "id": "ideal_gas_007167_5.72_419_65.0", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=5.72 mol, T=419 K, and V=65.0 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 5.72 * 8.314 * 419 / 65.0.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 5.72, "temp_k": 419, "volume_l": 65.0}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 510 * 1.47 * 110.\nFinal: {\"answer\": 82467.0, \"unit\": \"J\"}", "dedupe_signature": "9af6169173086c74e172850608ad37c70e9b5f9c5be2ee3ab1f72f2a9e170410", "difficulty": "easy", "final_answer": {"answer": 82467.0, "unit": "J"}, "id": "heat_q_007168_510_1.47_110", "license": "Apache-2.0", "prompt": "A 510 g sample has specific heat 1.47 J/(g*K). How much heat is needed to raise its temperature by 110 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 510 * 1.47 * 110.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 110, "heat_capacity": 1.47, "mass_g": 510}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=74 V and R=66.8 ohm.\nFinal: {\"answer\": 81.976, \"unit\": \"W\"}", "dedupe_signature": "f1284367eb5269afbe077ec636aa187e3db595034c1ad56a57e96f701ba34200", "difficulty": "easy", "final_answer": {"answer": 81.976, "unit": "W"}, "id": "ohm_power_007169_74_66.8", "license": "Apache-2.0", "prompt": "A resistor has resistance 66.8 ohm and voltage 74 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=74 V and R=66.8 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 66.8, "voltage": 74.0}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=767 mg, t=309 h, and T_half=11 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 0.0, \"unit\": \"mg\"}", "dedupe_signature": "debd6da949df16c3e2b062cf0f240ef90219b5a5fe7add5ce781774f3604ea9f", "difficulty": "medium", "final_answer": {"answer": 0.0, "unit": "mg"}, "id": "half_life_007170_767_11_309", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 767 mg. Its half-life is 11 hours. How many mg remain after 309 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=767 mg, t=309 h, and T_half=11 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 309.0, "half_life": 11.0, "initial_amount": 767.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 200 mL to 0.2 L.\n3. Compute M = 1.455 / 0.2.\nFinal: {\"answer\": 7.275, \"unit\": \"mol/L\"}", "dedupe_signature": "e5e16a6c35d64f586fb183c626a8a647214951092aa83e30faec99f55dd17994", "difficulty": "medium", "final_answer": {"answer": 7.275, "unit": "mol/L"}, "id": "molarity_007172_1.455_200", "license": "Apache-2.0", "prompt": "A solution contains 1.455 mol of solute in 200 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 200 mL to 0.2 L.\nCompute M = 1.455 / 0.2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 1.455, "volume_ml": 200}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.04 y, so each step multiplies y by 1 - h*0.04.\n3. Apply that update for 7 steps and round the final state.\nFinal: {\"answer\": 61.4462, \"unit\": \"state_units\"}", "dedupe_signature": "71b4e2e9f5b247fb5bc53bdba9ce3b9c3f5077f5b4c556a8442dbe0b53fa6955", "difficulty": "medium", "final_answer": {"answer": 61.4462, "unit": "state_units"}, "id": "euler_decay_007173_65_0.04_0.2_7", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.04 y with y(0)=65, step size h=0.2, for 7 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.04 y, so each step multiplies y by 1 - h*0.04.\nApply that update for 7 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 65.0, "rate": 0.04, "step": 0.2, "steps": 7}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(0)=-17.3 and f(7.1)=-3.81.\n3. The interval width is 7.1.\nFinal: {\"answer\": -74.9405, \"unit\": \"area_units\"}", "dedupe_signature": "2bf0a95418c0916c1bd777502ff1edc09578ea2c1c851a98a99425a264ab0683", "difficulty": "medium", "final_answer": {"answer": -74.9405, "unit": "area_units"}, "id": "trapz_linear_007174_1.9_-17.3_0_7.1", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=1.9x+-17.3 from x=0 to x=7.1. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(0)=-17.3 and f(7.1)=-3.81.\nThe interval width is 7.1.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -17.3, "slope": 1.9, "x0": 0.0, "x1": 7.1}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=94 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-9.8705, 141.1553], \"unit\": \"N\"}", "dedupe_signature": "4fe35a93df87a39f2717e8bc8d5a286090984e0c364f59334064b5bdf147f884", "difficulty": "medium", "final_answer": {"answer": [-9.8705, 141.1553], "unit": "N"}, "id": "vector_components_007177_141.5_94", "license": "Apache-2.0", "prompt": "A vector has magnitude 141.5 N at 94 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=94 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 94, "magnitude": 141.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-7.0, 9.5], \"unit\": \"dimensionless\"}", "dedupe_signature": "b63de206db6ebe7146aafcfc60c40509ea3988990bf46a6a41b145be1321f15b", "difficulty": "medium", "final_answer": {"answer": [-7.0, 9.5], "unit": "dimensionless"}, "id": "line_two_point_007178_10.5_18_-7_9.5", "license": "Apache-2.0", "prompt": "A line passes through points (10.5, -64) and (18, -116.5). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 10.5, "x2": 18.0, "y1": -64.0, "y2": -116.5}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. grams cancel with J/(g*K), and kelvin cancels, leaving joules\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "a4d01e8bdf4e748144ada58062b7c0fd3e59262ee7ca622798de8f6a73355964", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_007179_consistent_4153435f_114550", "license": "Apache-2.0", "prompt": "In quality-control check case 114550, check dimensional consistency for Q = m * c * DeltaT. The left side has dimensions J and the right side has dimensions J. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\ngrams cancel with J/(g*K), and kelvin cancels, leaving joules\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "Q = m * c * DeltaT"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef running_total_007180(values):\n    total = 0\n    out = []\n    for value in values:\n        total += value\n        out.append(total)\n    return out\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"running_total_007180\"}", "dedupe_signature": "1c96494d8540bf68f967d962d287530cc6a708f713e2b00acecca4fa6b62c034", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "running_total_007180"}, "id": "code_007180_running_total_007180", "license": "Apache-2.0", "prompt": "Write a Python function running_total_007180(values) that returns cumulative sums as a new list. It must not mutate the input list. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "running_total_007180"}, "verifier": {"function": "running_total_007180", "tests": ["assert running_total_007180([1, 2, 3]) == [1, 3, 6]", "xs = [4, -1, 2]; assert running_total_007180(xs) == [4, 3, 5] and xs == [4, -1, 2]", "assert running_total_007180([]) == []"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: rate_constant, number_of_steps.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"rate_constant\", \"number_of_steps\"]}", "dedupe_signature": "22dba007ffd9cfbb4c32ac15a554acb9f051d73c8f400b0a890ce60fd5b710ca", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["rate_constant", "number_of_steps"]}, "id": "abstain_007181_rate_constant_number_of_steps", "license": "Apache-2.0", "prompt": "Use explicit Euler for dy/dt = -k y. The prompt gives y(0)=73.5 and h=1.2, but omits both k and the number of steps. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: rate_constant, number_of_steps.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["rate_constant", "number_of_steps"]}, "verifier": {"missing": ["rate_constant", "number_of_steps"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 15.3 kg and a = 14.75 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 225.675, \"unit\": \"N\"}", "dedupe_signature": "18535b94590fcbdf3542e059295d2f9921967b5e05063c177bcd5d00ae110faa", "difficulty": "easy", "final_answer": {"answer": 225.675, "unit": "N"}, "id": "force_007182_15.3_14.75", "license": "Apache-2.0", "prompt": "A cart has mass 15.3 kg and measured acceleration 14.75 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 15.3 kg and a = 14.75 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 14.75, "mass": 15.3}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 24^2 and multiply by 0.5 * 23.55.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 6782.4, \"unit\": \"J\"}", "dedupe_signature": "22a31e0e21d9111690c6d53ecf8183bf4edd6ccc3869048cdf4dce5a8951add5", "difficulty": "easy", "final_answer": {"answer": 6782.4, "unit": "J"}, "id": "ke_007183_23.55_24", "license": "Apache-2.0", "prompt": "A body of mass 23.55 kg moves at 24 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 24^2 and multiply by 0.5 * 23.55.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 23.55, "velocity": 24.0}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=24 degrees through the sine of 2 theta.\n3. Substitute v=32.9 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 81.9967, \"unit\": \"m\"}", "dedupe_signature": "00e582bb75b2b3780adb982208b008540f991d4760eb047232c02c4632304388", "difficulty": "medium", "final_answer": {"answer": 81.9967, "unit": "m"}, "id": "projectile_range_007184_32.9_24", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 32.9 m/s and angle 24 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=24 degrees through the sine of 2 theta.\nSubstitute v=32.9 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 24, "gravity": 9.81, "speed": 32.9}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1115 * 4.065 * 24.\nFinal: {\"answer\": 108779.4, \"unit\": \"J\"}", "dedupe_signature": "22b03aa2879d50d2e0c4df2dd8835da3215ab919d2e77e5b5f1ca311fe56e540", "difficulty": "easy", "final_answer": {"answer": 108779.4, "unit": "J"}, "id": "heat_q_007186_1115_4.065_24", "license": "Apache-2.0", "prompt": "A 1115 g sample has specific heat 4.065 J/(g*K). How much heat is needed to raise its temperature by 24 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1115 * 4.065 * 24.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 24, "heat_capacity": 4.065, "mass_g": 1115}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=191.6 V and R=15.8 ohm.\nFinal: {\"answer\": 2323.4532, \"unit\": \"W\"}", "dedupe_signature": "e75c0cf9fa1c06b1f78e95886a552fd2f909336383710185917855598e0b22c1", "difficulty": "easy", "final_answer": {"answer": 2323.4532, "unit": "W"}, "id": "ohm_power_007187_191.6_15.8", "license": "Apache-2.0", "prompt": "A resistor has resistance 15.8 ohm and voltage 191.6 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=191.6 V and R=15.8 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 15.8, "voltage": 191.6}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 665 mL to 0.665 L.\n3. Compute M = 4.435 / 0.665.\nFinal: {\"answer\": 6.6692, \"unit\": \"mol/L\"}", "dedupe_signature": "6eb66fbe4321057946aae8490223acf1eca5a7af6b2a8a0b6c60665d2a95824b", "difficulty": "medium", "final_answer": {"answer": 6.6692, "unit": "mol/L"}, "id": "molarity_007190_4.435_665", "license": "Apache-2.0", "prompt": "A solution contains 4.435 mol of solute in 665 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 665 mL to 0.665 L.\nCompute M = 4.435 / 0.665.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 4.435, "volume_ml": 665}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.21 y, so each step multiplies y by 1 - h*0.21.\n3. Apply that update for 7 steps and round the final state.\nFinal: {\"answer\": 0.7406, \"unit\": \"state_units\"}", "dedupe_signature": "acf103d3244ea8caeb500c74090129cd9aab486faf4d08b3611e0d8101c9dcb2", "difficulty": "medium", "final_answer": {"answer": 0.7406, "unit": "state_units"}, "id": "euler_decay_007191_1_0.21_0.2_7", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.21 y with y(0)=1, step size h=0.2, for 7 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.21 y, so each step multiplies y by 1 - h*0.21.\nApply that update for 7 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 1.0, "rate": 0.21, "step": 0.2, "steps": 7}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-5.5)=-3.35 and f(-3.6)=1.78.\n3. The interval width is 1.9.\nFinal: {\"answer\": -1.4915, \"unit\": \"area_units\"}", "dedupe_signature": "7dd7ecc940d0bb804b6289ca12ecd1ae9e2ad6d683c5c4586155618e3fa8a0f1", "difficulty": "medium", "final_answer": {"answer": -1.4915, "unit": "area_units"}, "id": "trapz_linear_007192_2.7_11.5_-5.5_-3.6", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=2.7x+11.5 from x=-5.5 to x=-3.6. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-5.5)=-3.35 and f(-3.6)=1.78.\nThe interval width is 1.9.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 11.5, "slope": 2.7, "x0": -5.5, "x1": -3.6}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.06 and add it to the current value.\nFinal: {\"answer\": [0.789, -1.269, 1.787], \"unit\": \"temperature_units\"}", "dedupe_signature": "d81f9a4958201b93ac3ac03022fd34b254b09d1446be740fa7d93564e66d1f13", "difficulty": "hard", "final_answer": {"answer": [0.789, -1.269, 1.787], "unit": "temperature_units"}, "id": "heat_step_007193_0.06_-0.6_1.05_-1.65_2.0_2.1", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-0.6, right=2.1; current interior values are [1.05, -1.65, 2.0]. Use r=0.06. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.06 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [1.05, -1.65, 2.0], "left": -0.6, "r": 0.06, "right": 2.1}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 100 centimeters in one meter.\n2. Apply the conversion factor directly to the given value.\n3. Compute 469.5 / 100.\nFinal: {\"answer\": 4.695, \"unit\": \"m\"}", "dedupe_signature": "d908f5355e3788fff921616836c2eb786bf858fb782c1ff8c921ea8a7866cb24", "difficulty": "easy", "final_answer": {"answer": 4.695, "unit": "m"}, "id": "unit_convert_007194_cm_to_m_469.5", "license": "Apache-2.0", "prompt": "Convert 469.5 cm to m. Return the converted value with unit.", "reasoning_trace": "There are 100 centimeters in one meter.\nApply the conversion factor directly to the given value.\nCompute 469.5 / 100.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 469.5}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. density times acceleration times height gives kg/(m*s^2), or pascal\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "e5111bcb95166efbb15af103af03728a052feda8c03661806f84e6db9c16da43", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_007197_consistent_b7d3eed1_500729", "license": "Apache-2.0", "prompt": "In student derivation case 500729, check dimensional consistency for p = rho * g * h. The left side has dimensions Pa and the right side has dimensions Pa. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\ndensity times acceleration times height gives kg/(m*s^2), or pascal\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "p = rho * g * h"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef threshold_flags_007198(values, threshold):\n    return [value >= threshold for value in values]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"threshold_flags_007198\"}", "dedupe_signature": "9c164c18798562da99614fa1c4aa617e3c804d6a0ade888a8e05ae5c5178e0b6", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "threshold_flags_007198"}, "id": "code_007198_threshold_flags_007198", "license": "Apache-2.0", "prompt": "Write a Python function threshold_flags_007198(values, threshold) that returns a list of booleans showing whether each value is greater than or equal to threshold. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "threshold_flags_007198"}, "verifier": {"function": "threshold_flags_007198", "tests": ["assert threshold_flags_007198([1, 2, 3], 2) == [False, True, True]", "assert threshold_flags_007198([], 5) == []", "assert threshold_flags_007198([-1, 0], 0) == [False, True]"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: recurrence, objective, tie_breaking_rule.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"recurrence\", \"objective\", \"tie_breaking_rule\"]}", "dedupe_signature": "14c60d38977d23369e707e6096ffaa2889f6cb36cce0c0de57cd2cc001500fc7", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["recurrence", "objective", "tie_breaking_rule"]}, "id": "abstain_007199_recurrence_objective_tie_breaking_rule", "license": "Apache-2.0", "prompt": "Write a dynamic-programming solver for a allocation scoring problem with 2831 items and budget 31520, but the recurrence, objective, and tie-breaking rule are all absent. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: recurrence, objective, tie_breaking_rule.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["recurrence", "objective", "tie_breaking_rule"]}, "verifier": {"missing": ["recurrence", "objective", "tie_breaking_rule"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 13.95 kg and a = 5.15 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 71.8425, \"unit\": \"N\"}", "dedupe_signature": "1a39881aa96a0b067d3e7bb9154697de64ad639e43257043df264e909a8b3824", "difficulty": "easy", "final_answer": {"answer": 71.8425, "unit": "N"}, "id": "force_007200_13.95_5.15", "license": "Apache-2.0", "prompt": "A cart has mass 13.95 kg and measured acceleration 5.15 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 13.95 kg and a = 5.15 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 5.15, "mass": 13.95}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 28.85^2 and multiply by 0.5 * 22.15.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 9217.9717, \"unit\": \"J\"}", "dedupe_signature": "1b993b11112374ede1b8240a81463bd396f4f83c59d735ac406478d989c55623", "difficulty": "easy", "final_answer": {"answer": 9217.9717, "unit": "J"}, "id": "ke_007201_22.15_28.85", "license": "Apache-2.0", "prompt": "A body of mass 22.15 kg moves at 28.85 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 28.85^2 and multiply by 0.5 * 22.15.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 22.15, "velocity": 28.85}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=84 degrees through the sine of 2 theta.\n3. Substitute v=77 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 125.6584, \"unit\": \"m\"}", "dedupe_signature": "1910b0e4b9f5b4340fe5f9197038e4c628439aa6ad2aff71ee2388972308e0e7", "difficulty": "medium", "final_answer": {"answer": 125.6584, "unit": "m"}, "id": "projectile_range_007202_77_84", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 77 m/s and angle 84 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=84 degrees through the sine of 2 theta.\nSubstitute v=77 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 84, "gravity": 9.81, "speed": 77.0}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 3.98 * 8.314 * 381 / 35.9.\nFinal: {\"answer\": 351.175, \"unit\": \"kPa\"}", "dedupe_signature": "205b6bfef10b830e88d1be5d1577a7a3823b0510fdbb9db9c79a01aae6feb883", "difficulty": "medium", "final_answer": {"answer": 351.175, "unit": "kPa"}, "id": "ideal_gas_007203_3.98_381_35.9", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=3.98 mol, T=381 K, and V=35.9 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 3.98 * 8.314 * 381 / 35.9.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 3.98, "temp_k": 381, "volume_l": 35.9}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 725 * 4.1 * 38.\nFinal: {\"answer\": 112955.0, \"unit\": \"J\"}", "dedupe_signature": "0461f04faeb43336f2d54d0cc5ed65ffc5e1db0483ca80b32e1ea2e7cb40deaf", "difficulty": "easy", "final_answer": {"answer": 112955.0, "unit": "J"}, "id": "heat_q_007204_725_4.1_38", "license": "Apache-2.0", "prompt": "A 725 g sample has specific heat 4.1 J/(g*K). How much heat is needed to raise its temperature by 38 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 725 * 4.1 * 38.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 38, "heat_capacity": 4.1, "mass_g": 725}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=1.5 V and R=97.4 ohm.\nFinal: {\"answer\": 0.0231, \"unit\": \"W\"}", "dedupe_signature": "5376553fcf4d7c01b52f8d3a0c5863c4891fedaa99b9f0829df80181f34b8121", "difficulty": "easy", "final_answer": {"answer": 0.0231, "unit": "W"}, "id": "ohm_power_007205_1.5_97.4", "license": "Apache-2.0", "prompt": "A resistor has resistance 97.4 ohm and voltage 1.5 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=1.5 V and R=97.4 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 97.4, "voltage": 1.5}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=792.5 mg, t=235 h, and T_half=79.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 102.1321, \"unit\": \"mg\"}", "dedupe_signature": "03c2f36d04a1996cec7bf6ed96b4200c4d481788519f1910079b2539f9ac7060", "difficulty": "medium", "final_answer": {"answer": 102.1321, "unit": "mg"}, "id": "half_life_007206_792.5_79.5_235", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 792.5 mg. Its half-life is 79.5 hours. How many mg remain after 235 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=792.5 mg, t=235 h, and T_half=79.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 235.0, "half_life": 79.5, "initial_amount": 792.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 5.89 mol * 44.01 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 259.2189, \"unit\": \"g\"}", "dedupe_signature": "1d5300648b7f7c98b9041e254e6577d7abccc2c9f92b723ff3b32f6a9403846e", "difficulty": "medium", "final_answer": {"answer": 259.2189, "unit": "g"}, "id": "stoich_mass_007207_carbon_dioxide_5.89", "license": "Apache-2.0", "prompt": "A sample contains 5.89 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 5.89 mol * 44.01 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "carbon dioxide", "molar_mass": 44.01, "moles": 5.89}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 3090 mL to 3.09 L.\n3. Compute M = 2.39 / 3.09.\nFinal: {\"answer\": 0.7735, \"unit\": \"mol/L\"}", "dedupe_signature": "77f1be4ec8cb866979e70b247a262ab45afbc2fde5a4170f472ee10e96374792", "difficulty": "medium", "final_answer": {"answer": 0.7735, "unit": "mol/L"}, "id": "molarity_007208_2.39_3090", "license": "Apache-2.0", "prompt": "A solution contains 2.39 mol of solute in 3090 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 3090 mL to 3.09 L.\nCompute M = 2.39 / 3.09.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 2.39, "volume_ml": 3090}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.72 y, so each step multiplies y by 1 - h*0.72.\n3. Apply that update for 4 steps and round the final state.\nFinal: {\"answer\": 0.1396, \"unit\": \"state_units\"}", "dedupe_signature": "2d9e78adc9d330ab8e6ca366a14d8552bdcb5a3ce9ecc4b6e30fadb795246027", "difficulty": "medium", "final_answer": {"answer": 0.1396, "unit": "state_units"}, "id": "euler_decay_007209_14_0.72_0.95_4", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.72 y with y(0)=14, step size h=0.95, for 4 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.72 y, so each step multiplies y by 1 - h*0.72.\nApply that update for 4 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 14.0, "rate": 0.72, "step": 0.95, "steps": 4}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(3.3)=18.81 and f(7.9)=40.43.\n3. The interval width is 4.6.\nFinal: {\"answer\": 136.252, \"unit\": \"area_units\"}", "dedupe_signature": "deacc5cdecdb4ac09bb09047757845e239500c15ee1f3953c5a279275e6f4b19", "difficulty": "medium", "final_answer": {"answer": 136.252, "unit": "area_units"}, "id": "trapz_linear_007210_4.7_3.3_3.3_7.9", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=4.7x+3.3 from x=3.3 to x=7.9. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(3.3)=18.81 and f(7.9)=40.43.\nThe interval width is 4.6.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 3.3, "slope": 4.7, "x0": 3.3, "x1": 7.8999999999999995}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.48 and add it to the current value.\nFinal: {\"answer\": [1.286, -1.024, 0.066], \"unit\": \"temperature_units\"}", "dedupe_signature": "7bfd37c3f24a453a2b50766cfa9e9c12a377abbcdfcf33e97718344c6aa89198", "difficulty": "hard", "final_answer": {"answer": [1.286, -1.024, 0.066], "unit": "temperature_units"}, "id": "heat_step_007211_0.48_2.0_-1.45_0.8_-0.75_-0.6", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=2, right=-0.6; current interior values are [-1.45, 0.8, -0.75]. Use r=0.48. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.48 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-1.45, 0.8, -0.75], "left": 2.0, "r": 0.48, "right": -0.6}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kelvin equals Celsius plus 273.15.\n2. Apply the conversion factor directly to the given value.\n3. Compute 68.5 + 273.15.\nFinal: {\"answer\": 341.65, \"unit\": \"K\"}", "dedupe_signature": "3d2d85017a26cfa5536bc669b8476342d1a327ad9925a112250fcc2dc066d735", "difficulty": "easy", "final_answer": {"answer": 341.65, "unit": "K"}, "id": "unit_convert_007212_c_to_k_68.5", "license": "Apache-2.0", "prompt": "Convert 68.5 degC to K. Return the converted value with unit.", "reasoning_trace": "Kelvin equals Celsius plus 273.15.\nApply the conversion factor directly to the given value.\nCompute 68.5 + 273.15.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 68.5}, "verifier": {"formula": "value + 273.15", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=299 degrees and keep the unit as newtons.\nFinal: {\"answer\": [107.3853, -193.7283], \"unit\": \"N\"}", "dedupe_signature": "377c4000fb925a8c358342960be764ad34dd57a6f86dea6d1c9a35b8bbd11aef", "difficulty": "medium", "final_answer": {"answer": [107.3853, -193.7283], "unit": "N"}, "id": "vector_components_007213_221.5_299", "license": "Apache-2.0", "prompt": "A vector has magnitude 221.5 N at 299 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=299 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 299, "magnitude": 221.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-1.5, -23.25], \"unit\": \"dimensionless\"}", "dedupe_signature": "7f5437d0280b45202d760bd8b10e37637b82aaf043b76915b331922b8271b008", "difficulty": "medium", "final_answer": {"answer": [-1.5, -23.25], "unit": "dimensionless"}, "id": "line_two_point_007214_18.5_23.5_-1.5_-23.25", "license": "Apache-2.0", "prompt": "A line passes through points (18.5, -51) and (23.5, -58.5). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 18.5, "x2": 23.5, "y1": -51.0, "y2": -58.5}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. velocity divided by time is acceleration\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "4b638812d28b18c9f4310b7133fd55c40a08e63d9dbcac9fdf7c76a434760096", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_007215_inconsistent_c1271127_693670", "license": "Apache-2.0", "prompt": "In student derivation case 693670, check dimensional consistency for x = v / t. The left side has dimensions m and the right side has dimensions m/s^2. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nvelocity divided by time is acceleration\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "x = v / t"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: required_fields, allowed_transformations.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"required_fields\", \"allowed_transformations\"]}", "dedupe_signature": "ca8b9cf87fc008918d58cdfcd62a2693c60bd3e7d8a05205cf184401f34ae2b5", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["required_fields", "allowed_transformations"]}, "id": "abstain_007217_required_fields_allowed_transformations", "license": "Apache-2.0", "prompt": "Write a sanitizer for valid warehouse clinical records in release 232161, but the prompt does not state which fields are required or which transformations are allowed. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: required_fields, allowed_transformations.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["required_fields", "allowed_transformations"]}, "verifier": {"missing": ["required_fields", "allowed_transformations"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 16 kg and a = 8.1 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 129.6, \"unit\": \"N\"}", "dedupe_signature": "b98ca896fa5ec10e841bb7ea3c00f47642c446b420e30b20432760256a3cca7d", "difficulty": "easy", "final_answer": {"answer": 129.6, "unit": "N"}, "id": "force_007218_16_8.1", "license": "Apache-2.0", "prompt": "A cart has mass 16 kg and measured acceleration 8.1 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 16 kg and a = 8.1 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 8.1, "mass": 16.0}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 2.55^2 and multiply by 0.5 * 26.15.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 85.0202, \"unit\": \"J\"}", "dedupe_signature": "cd3546298995c2d2d13a91f9ebcf00cfb6e81bdbcd95f01bfb6563189107ee7a", "difficulty": "easy", "final_answer": {"answer": 85.0202, "unit": "J"}, "id": "ke_007219_26.15_2.55", "license": "Apache-2.0", "prompt": "A body of mass 26.15 kg moves at 2.55 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 2.55^2 and multiply by 0.5 * 26.15.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 26.15, "velocity": 2.55}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=34 degrees through the sine of 2 theta.\n3. Substitute v=71.7 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 485.8869, \"unit\": \"m\"}", "dedupe_signature": "eed214c6fb7c9fcc06034020b4b17e0f41079f049585128b27eef0d8c9ee617b", "difficulty": "medium", "final_answer": {"answer": 485.8869, "unit": "m"}, "id": "projectile_range_007220_71.7_34", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 71.7 m/s and angle 34 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=34 degrees through the sine of 2 theta.\nSubstitute v=71.7 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 34, "gravity": 9.81, "speed": 71.7}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 4.48 * 8.314 * 393 / 59.8.\nFinal: {\"answer\": 244.782, \"unit\": \"kPa\"}", "dedupe_signature": "b62972e6093c93bb265312579af3e70898a05ac6b291340db19c52f5b2c15704", "difficulty": "medium", "final_answer": {"answer": 244.782, "unit": "kPa"}, "id": "ideal_gas_007221_4.48_393_59.8", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=4.48 mol, T=393 K, and V=59.8 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 4.48 * 8.314 * 393 / 59.8.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 4.48, "temp_k": 393, "volume_l": 59.8}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 910 * 1.925 * 58.\nFinal: {\"answer\": 101601.5, \"unit\": \"J\"}", "dedupe_signature": "6592264f3a48f54cef2f796cb0f37fcfec11925687053823a882addc2bb1947c", "difficulty": "easy", "final_answer": {"answer": 101601.5, "unit": "J"}, "id": "heat_q_007222_910_1.925_58", "license": "Apache-2.0", "prompt": "A 910 g sample has specific heat 1.925 J/(g*K). How much heat is needed to raise its temperature by 58 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 910 * 1.925 * 58.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 58, "heat_capacity": 1.925, "mass_g": 910}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=966.5 mg, t=51.5 h, and T_half=107.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 693.4058, \"unit\": \"mg\"}", "dedupe_signature": "2f8884b7228b0bfacab2fa34795d7032fda3fadc5bdbac047a7aeb75fe3cc01a", "difficulty": "medium", "final_answer": {"answer": 693.4058, "unit": "mg"}, "id": "half_life_007224_966.5_107.5_51.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 966.5 mg. Its half-life is 107.5 hours. How many mg remain after 51.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=966.5 mg, t=51.5 h, and T_half=107.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 51.5, "half_life": 107.5, "initial_amount": 966.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 0.68 mol * 18.015 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 12.2502, \"unit\": \"g\"}", "dedupe_signature": "144b50d0a18948bf1f2d108516f084c4ba6425236ee62788c05133c426ec375a", "difficulty": "medium", "final_answer": {"answer": 12.2502, "unit": "g"}, "id": "stoich_mass_007225_water_0.68", "license": "Apache-2.0", "prompt": "A sample contains 0.68 mol of water. Using molar mass 18.015 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 0.68 mol * 18.015 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "water", "molar_mass": 18.015, "moles": 0.68}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 550 mL to 0.55 L.\n3. Compute M = 1.645 / 0.55.\nFinal: {\"answer\": 2.9909, \"unit\": \"mol/L\"}", "dedupe_signature": "2ad87bdccfb887381ab59bda212e39a614034ae23820288e2d812d749c876f47", "difficulty": "medium", "final_answer": {"answer": 2.9909, "unit": "mol/L"}, "id": "molarity_007226_1.645_550", "license": "Apache-2.0", "prompt": "A solution contains 1.645 mol of solute in 550 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 550 mL to 0.55 L.\nCompute M = 1.645 / 0.55.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 1.645, "volume_ml": 550}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.9 y, so each step multiplies y by 1 - h*0.9.\n3. Apply that update for 9 steps and round the final state.\nFinal: {\"answer\": 0.0, \"unit\": \"state_units\"}", "dedupe_signature": "e4bcf77105862f886a84bdfa097498876cc8be713f05fa950795c96ea166de0a", "difficulty": "medium", "final_answer": {"answer": 0.0, "unit": "state_units"}, "id": "euler_decay_007227_40_0.9_1.25_9", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.9 y with y(0)=40, step size h=1.25, for 9 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.9 y, so each step multiplies y by 1 - h*0.9.\nApply that update for 9 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 40.0, "rate": 0.9, "step": 1.25, "steps": 9}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(9.1)=72.84 and f(9.6)=76.54.\n3. The interval width is 0.5.\nFinal: {\"answer\": 37.345, \"unit\": \"area_units\"}", "dedupe_signature": "79822d4b54df18d5fd4acd0e4fa4bfd6d0d2b5a50855f28de6c5130faaaa490c", "difficulty": "medium", "final_answer": {"answer": 37.345, "unit": "area_units"}, "id": "trapz_linear_007228_7.4_5.5_9.1_9.6", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=7.4x+5.5 from x=9.1 to x=9.6. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(9.1)=72.84 and f(9.6)=76.54.\nThe interval width is 0.5.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 5.5, "slope": 7.4, "x0": 9.1, "x1": 9.6}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.42 and add it to the current value.\nFinal: {\"answer\": [-0.99, 1.046, 0.099], \"unit\": \"temperature_units\"}", "dedupe_signature": "124869f1aeccc5e393bc920d15c7bd48948a7e156fff37fda31870d2278cc7a1", "difficulty": "hard", "final_answer": {"answer": [-0.99, 1.046, 0.099], "unit": "temperature_units"}, "id": "heat_step_007229_0.42_-1.75_-0.15_-0.55_2.85_-0.3", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-1.75, right=-0.3; current interior values are [-0.15, -0.55, 2.85]. Use r=0.42. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.42 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-0.15, -0.55, 2.85], "left": -1.75, "r": 0.42, "right": -0.3}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=68 degrees and keep the unit as newtons.\nFinal: {\"answer\": [112.1947, 277.6916], \"unit\": \"N\"}", "dedupe_signature": "7ba99de4d921c6b2cebac4b4526f7690d1cb017c203cf9ec2cdb179095dce850", "difficulty": "medium", "final_answer": {"answer": [112.1947, 277.6916], "unit": "N"}, "id": "vector_components_007231_299.5_68", "license": "Apache-2.0", "prompt": "A vector has magnitude 299.5 N at 68 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=68 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 68, "magnitude": 299.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-8.1, -16.0], \"unit\": \"dimensionless\"}", "dedupe_signature": "78fdec7cb896d6fd3c862521d71b089a1c13fdd265bc4587fbb0b231bcdec07f", "difficulty": "medium", "final_answer": {"answer": [-8.1, -16.0], "unit": "dimensionless"}, "id": "line_two_point_007232_-1.75_12_-8.1_-16", "license": "Apache-2.0", "prompt": "A line passes through points (-1.75, -1.825) and (12, -113.2). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -1.75, "x2": 12.0, "y1": -1.825000000000001, "y2": -113.19999999999999}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef weighted_sum_007234(values, weights):\n    if len(values) != len(weights):\n        raise ValueError('length mismatch')\n    return sum(value * weight for value, weight in zip(values, weights))\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"weighted_sum_007234\"}", "dedupe_signature": "9efdc0027ec48d43f8da64845645c0505489ee849ebdc4a5fc7bd1037712fcd7", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "weighted_sum_007234"}, "id": "code_007234_weighted_sum_007234", "license": "Apache-2.0", "prompt": "Write a Python function weighted_sum_007234(values, weights) that returns sum(value*weight). Raise ValueError when the two inputs have different lengths. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "weighted_sum_007234"}, "verifier": {"function": "weighted_sum_007234", "tests": ["assert weighted_sum_007234([2, 3], [4, 5]) == 23", "assert weighted_sum_007234([], []) == 0", "try:\n    weighted_sum_007234([1], [1, 2])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: recurrence, objective, tie_breaking_rule.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"recurrence\", \"objective\", \"tie_breaking_rule\"]}", "dedupe_signature": "b241c3af24e5a131a3e086afaa691ec3ea31204bc2e291041239568e1ba571ed", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["recurrence", "objective", "tie_breaking_rule"]}, "id": "abstain_007235_recurrence_objective_tie_breaking_rule", "license": "Apache-2.0", "prompt": "Write a dynamic-programming solver for a knapsack scoring problem with 3957 items and budget 82785, but the recurrence, objective, and tie-breaking rule are all absent. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: recurrence, objective, tie_breaking_rule.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["recurrence", "objective", "tie_breaking_rule"]}, "verifier": {"missing": ["recurrence", "objective", "tie_breaking_rule"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 1.95 kg and a = 15.4 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 30.03, \"unit\": \"N\"}", "dedupe_signature": "ab1a8acc725661f358d6393859bc550bd6231ec41ed57646138efb46119c3a6b", "difficulty": "easy", "final_answer": {"answer": 30.03, "unit": "N"}, "id": "force_007236_1.95_15.4", "license": "Apache-2.0", "prompt": "A cart has mass 1.95 kg and measured acceleration 15.4 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 1.95 kg and a = 15.4 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 15.4, "mass": 1.95}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 34.2^2 and multiply by 0.5 * 11.35.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 6637.707, \"unit\": \"J\"}", "dedupe_signature": "710edb0e2dce73bd37e63195c5c48608e402d4c862c21d1c152caf70610bf220", "difficulty": "easy", "final_answer": {"answer": 6637.707, "unit": "J"}, "id": "ke_007237_11.35_34.2", "license": "Apache-2.0", "prompt": "A body of mass 11.35 kg moves at 34.2 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 34.2^2 and multiply by 0.5 * 11.35.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 11.35, "velocity": 34.2}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=210 mg, t=79.5 h, and T_half=35.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 44.4715, \"unit\": \"mg\"}", "dedupe_signature": "6cf1c6294a8fe2565bf8dafdc4c77dd85ca231cd11ae9a8217c540d3b558cd37", "difficulty": "medium", "final_answer": {"answer": 44.4715, "unit": "mg"}, "id": "half_life_007242_210_35.5_79.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 210 mg. Its half-life is 35.5 hours. How many mg remain after 79.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=210 mg, t=79.5 h, and T_half=35.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 79.5, "half_life": 35.5, "initial_amount": 210.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 5.79 mol * 180.156 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 1043.1032, \"unit\": \"g\"}", "dedupe_signature": "bfa4407c97458f1d1b98faf3f1bc875b83650a6902dd80dbc80d1951144d2733", "difficulty": "medium", "final_answer": {"answer": 1043.1032, "unit": "g"}, "id": "stoich_mass_007243_glucose_5.79", "license": "Apache-2.0", "prompt": "A sample contains 5.79 mol of glucose. Using molar mass 180.156 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 5.79 mol * 180.156 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "glucose", "molar_mass": 180.156, "moles": 5.79}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 1695 mL to 1.695 L.\n3. Compute M = 1.16 / 1.695.\nFinal: {\"answer\": 0.6844, \"unit\": \"mol/L\"}", "dedupe_signature": "a0bc0323c3fa38a293439a79bb84d486872d9f56fef886fe3a7de30847ac9881", "difficulty": "medium", "final_answer": {"answer": 0.6844, "unit": "mol/L"}, "id": "molarity_007244_1.16_1695", "license": "Apache-2.0", "prompt": "A solution contains 1.16 mol of solute in 1695 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 1695 mL to 1.695 L.\nCompute M = 1.16 / 1.695.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 1.16, "volume_ml": 1695}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.47 y, so each step multiplies y by 1 - h*0.47.\n3. Apply that update for 5 steps and round the final state.\nFinal: {\"answer\": 0.0008, \"unit\": \"state_units\"}", "dedupe_signature": "06f40a6c4d293b0b35cd8c1794f024f23a28e06dc15f6b8c9b3f31f558081715", "difficulty": "medium", "final_answer": {"answer": 0.0008, "unit": "state_units"}, "id": "euler_decay_007245_60.5_0.47_1.9_5", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.47 y with y(0)=60.5, step size h=1.9, for 5 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.47 y, so each step multiplies y by 1 - h*0.47.\nApply that update for 5 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 60.5, "rate": 0.47, "step": 1.9, "steps": 5}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-5.4)=-3.14 and f(0.7)=21.87.\n3. The interval width is 6.1.\nFinal: {\"answer\": 57.1265, \"unit\": \"area_units\"}", "dedupe_signature": "de3b43bf5b85a2749d314393b67ab43f22ec780779a4c3357633f33a0c1f062a", "difficulty": "medium", "final_answer": {"answer": 57.1265, "unit": "area_units"}, "id": "trapz_linear_007246_4.1_19_-5.4_0.7", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=4.1x+19 from x=-5.4 to x=0.7. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-5.4)=-3.14 and f(0.7)=21.87.\nThe interval width is 6.1.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 19.0, "slope": 4.1, "x0": -5.4, "x1": 0.6999999999999993}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.36 and add it to the current value.\nFinal: {\"answer\": [-0.526, 0.328, -0.472], \"unit\": \"temperature_units\"}", "dedupe_signature": "7bba97e6010a4f7c2dc5db6c75cf54b756e6887d4308d7969d4dc13c17459df6", "difficulty": "hard", "final_answer": {"answer": [-0.526, 0.328, -0.472], "unit": "temperature_units"}, "id": "heat_step_007247_0.36_-1.4_2.3_-1.85_0.05_0.5", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-1.4, right=0.5; current interior values are [2.3, -1.85, 0.05]. Use r=0.36. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.36 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [2.3, -1.85, 0.05], "left": -1.4, "r": 0.36, "right": 0.5}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 100 centimeters in one meter.\n2. Apply the conversion factor directly to the given value.\n3. Compute 4531.5 / 100.\nFinal: {\"answer\": 45.315, \"unit\": \"m\"}", "dedupe_signature": "a386dac411a84982829df4b6c152e71a997035d5b793b72d27bab3b973f70faf", "difficulty": "easy", "final_answer": {"answer": 45.315, "unit": "m"}, "id": "unit_convert_007248_cm_to_m_4531.5", "license": "Apache-2.0", "prompt": "Convert 4531.5 cm to m. Return the converted value with unit.", "reasoning_trace": "There are 100 centimeters in one meter.\nApply the conversion factor directly to the given value.\nCompute 4531.5 / 100.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 4531.5}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=53 degrees and keep the unit as newtons.\nFinal: {\"answer\": [124.2748, 164.9182], \"unit\": \"N\"}", "dedupe_signature": "ef327a3b0871f8bcb026cd695e732b9ad6fedc1bf97a0dcff62a277a9300da0f", "difficulty": "medium", "final_answer": {"answer": [124.2748, 164.9182], "unit": "N"}, "id": "vector_components_007249_206.5_53", "license": "Apache-2.0", "prompt": "A vector has magnitude 206.5 N at 53 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=53 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 53, "magnitude": 206.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. grams cancel with J/(g*K), and kelvin cancels, leaving joules\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "69b4e2bb9df119998976d6d02d41918b62172e2304e7e8fdc122f529e2e651fe", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_007251_consistent_4153435f_870696", "license": "Apache-2.0", "prompt": "In quality-control check case 870696, check dimensional consistency for Q = m * c * DeltaT. The left side has dimensions J and the right side has dimensions J. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\ngrams cancel with J/(g*K), and kelvin cancels, leaving joules\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "Q = m * c * DeltaT"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef finite_differences_007252(values):\n    return [values[i + 1] - values[i] for i in range(len(values) - 1)]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"finite_differences_007252\"}", "dedupe_signature": "5b6901c61644f5599eabd91a21febe81e7ef4e5b5c127b276c42c409e016390d", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "finite_differences_007252"}, "id": "code_007252_finite_differences_007252", "license": "Apache-2.0", "prompt": "Write a Python function finite_differences_007252(values) that returns the list of successive differences values[i+1] - values[i]. It must return [] for fewer than two values. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "finite_differences_007252"}, "verifier": {"function": "finite_differences_007252", "tests": ["assert finite_differences_007252([1, 4, 9, 16]) == [3, 5, 7]", "assert finite_differences_007252([5]) == []", "assert finite_differences_007252([]) == []"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=52 degrees through the sine of 2 theta.\n3. Substitute v=24.5 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 59.37, \"unit\": \"m\"}", "dedupe_signature": "654eb803c65262b2e79b440b9664fbb261dfb99a23734a31348f14a6b6c93586", "difficulty": "medium", "final_answer": {"answer": 59.37, "unit": "m"}, "id": "projectile_range_007256_24.5_52", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 24.5 m/s and angle 52 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=52 degrees through the sine of 2 theta.\nSubstitute v=24.5 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 52, "gravity": 9.81, "speed": 24.5}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 2.36 * 8.314 * 298 / 114.0.\nFinal: {\"answer\": 51.2901, \"unit\": \"kPa\"}", "dedupe_signature": "c3cf3970f33df4f7830e4b841b630266e43ae8dac79d29af3385df2ee804a8ff", "difficulty": "medium", "final_answer": {"answer": 51.2901, "unit": "kPa"}, "id": "ideal_gas_007257_2.36_298_114.0", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=2.36 mol, T=298 K, and V=114.0 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 2.36 * 8.314 * 298 / 114.0.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 2.36, "temp_k": 298, "volume_l": 114.0}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1750 * 4.115 * 6.\nFinal: {\"answer\": 43207.5, \"unit\": \"J\"}", "dedupe_signature": "1426f89fcd82b5dd7f606e58ac27d8852efd1de24f9c89621ccb18796d7885d3", "difficulty": "easy", "final_answer": {"answer": 43207.5, "unit": "J"}, "id": "heat_q_007258_1750_4.115_6", "license": "Apache-2.0", "prompt": "A 1750 g sample has specific heat 4.115 J/(g*K). How much heat is needed to raise its temperature by 6 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1750 * 4.115 * 6.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 6, "heat_capacity": 4.115, "mass_g": 1750}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=194.5 V and R=145.3 ohm.\nFinal: {\"answer\": 260.3596, \"unit\": \"W\"}", "dedupe_signature": "f159c89474a3b05224e6b11f2f4db3b5482bb520b6a1088a79fe1ae5d9695428", "difficulty": "easy", "final_answer": {"answer": 260.3596, "unit": "W"}, "id": "ohm_power_007259_194.5_145.3", "license": "Apache-2.0", "prompt": "A resistor has resistance 145.3 ohm and voltage 194.5 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=194.5 V and R=145.3 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 145.3, "voltage": 194.5}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=364.5 mg, t=216.5 h, and T_half=88.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 66.8774, \"unit\": \"mg\"}", "dedupe_signature": "895f9904057da32977f34e2e42ae4f96af3828427f4a0dc5832d231d86f48d8e", "difficulty": "medium", "final_answer": {"answer": 66.8774, "unit": "mg"}, "id": "half_life_007260_364.5_88.5_216.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 364.5 mg. Its half-life is 88.5 hours. How many mg remain after 216.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=364.5 mg, t=216.5 h, and T_half=88.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 216.5, "half_life": 88.5, "initial_amount": 364.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.71 y, so each step multiplies y by 1 - h*0.71.\n3. Apply that update for 11 steps and round the final state.\nFinal: {\"answer\": 0.0817, \"unit\": \"state_units\"}", "dedupe_signature": "c071d0583541fcc7909d5b6b5a41ecedab4beb48785f404b4a8a3fd5cea8c9ba", "difficulty": "medium", "final_answer": {"answer": 0.0817, "unit": "state_units"}, "id": "euler_decay_007263_74_0.71_0.65_11", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.71 y with y(0)=74, step size h=0.65, for 11 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.71 y, so each step multiplies y by 1 - h*0.71.\nApply that update for 11 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 74.0, "rate": 0.71, "step": 0.65, "steps": 11}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.2 and add it to the current value.\nFinal: {\"answer\": [1.22, 1.77, 0.05], \"unit\": \"temperature_units\"}", "dedupe_signature": "1b5b3c8494a05da4dc77f15e1c9569a58e820bd6dfd2a241fed6c7b408c7a0bc", "difficulty": "hard", "final_answer": {"answer": [1.22, 1.77, 0.05], "unit": "temperature_units"}, "id": "heat_step_007265_0.2_-1.2_1.55_2.65_-0.65_-0.45", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-1.2, right=-0.45; current interior values are [1.55, 2.65, -0.65]. Use r=0.2. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.2 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [1.55, 2.65, -0.65], "left": -1.2, "r": 0.2, "right": -0.45}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=106 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-77.5919, 270.5952], \"unit\": \"N\"}", "dedupe_signature": "95787e01d5891a6179d4dcaead65aed8112c91a5f0bf4d72144379eaa104456e", "difficulty": "medium", "final_answer": {"answer": [-77.5919, 270.5952], "unit": "N"}, "id": "vector_components_007267_281.5_106", "license": "Apache-2.0", "prompt": "A vector has magnitude 281.5 N at 106 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=106 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 106, "magnitude": 281.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [7.45, 28.0], \"unit\": \"dimensionless\"}", "dedupe_signature": "9f6d8855828fdf78e494e3619bc941fe1e8212970d73fc065c92be8938b10b8d", "difficulty": "medium", "final_answer": {"answer": [7.45, 28.0], "unit": "dimensionless"}, "id": "line_two_point_007268_10.5_22_7.45_28", "license": "Apache-2.0", "prompt": "A line passes through points (10.5, 106.225) and (22, 191.9). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 10.5, "x2": 22.0, "y1": 106.22500000000001, "y2": 191.9}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. velocity divided by time is acceleration\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "e40c36d07313c77cd93a081f9cd18e45699384233250ad2d109589534a34f904", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_007269_inconsistent_c1271127_909932", "license": "Apache-2.0", "prompt": "In simulation spec case 909932, check dimensional consistency for x = v / t. The left side has dimensions m and the right side has dimensions m/s^2. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nvelocity divided by time is acceleration\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "x = v / t"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef running_total_007270(values):\n    total = 0\n    out = []\n    for value in values:\n        total += value\n        out.append(total)\n    return out\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"running_total_007270\"}", "dedupe_signature": "9e9e950ba946815227cb0eaebcd43a1346fbb6889b6e168b990256bd3a25f4d0", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "running_total_007270"}, "id": "code_007270_running_total_007270", "license": "Apache-2.0", "prompt": "Write a Python function running_total_007270(values) that returns cumulative sums as a new list. It must not mutate the input list. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "running_total_007270"}, "verifier": {"function": "running_total_007270", "tests": ["assert running_total_007270([1, 2, 3]) == [1, 3, 6]", "xs = [4, -1, 2]; assert running_total_007270(xs) == [4, 3, 5] and xs == [4, -1, 2]", "assert running_total_007270([]) == []"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: volume.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"volume\"]}", "dedupe_signature": "b9b2fbd98e2c2bfc1dc5c8deb669b1a70e20d2efd4049885a4a827e62cda5859", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["volume"]}, "id": "abstain_007271_volume", "license": "Apache-2.0", "prompt": "Compute pressure from the ideal gas law. The prompt gives n=0.47 mol and T=456 K, but does not give volume. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: volume.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["volume"]}, "verifier": {"missing": ["volume"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 5.1 kg and a = 5.6 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 28.56, \"unit\": \"N\"}", "dedupe_signature": "f6163761b956c7a2e9f3541f90ecc9e748ff96d2118f643f57b7c5be4418d46f", "difficulty": "easy", "final_answer": {"answer": 28.56, "unit": "N"}, "id": "force_007272_5.1_5.6", "license": "Apache-2.0", "prompt": "A cart has mass 5.1 kg and measured acceleration 5.6 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 5.1 kg and a = 5.6 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 5.6, "mass": 5.1}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 22^2 and multiply by 0.5 * 13.75.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 3327.5, \"unit\": \"J\"}", "dedupe_signature": "e7a12f6f5c04c9f1536cb48475e3655bd8b651810ac2c1e891cbc5874fe92e13", "difficulty": "easy", "final_answer": {"answer": 3327.5, "unit": "J"}, "id": "ke_007273_13.75_22", "license": "Apache-2.0", "prompt": "A body of mass 13.75 kg moves at 22 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 22^2 and multiply by 0.5 * 13.75.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 13.75, "velocity": 22.0}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=66 degrees through the sine of 2 theta.\n3. Substitute v=73.8 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 412.5886, \"unit\": \"m\"}", "dedupe_signature": "dec2bea39cc411d31cbc58743f863fdc8304da4395edc0d18bfa1d9cf30f68c9", "difficulty": "medium", "final_answer": {"answer": 412.5886, "unit": "m"}, "id": "projectile_range_007274_73.8_66", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 73.8 m/s and angle 66 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=66 degrees through the sine of 2 theta.\nSubstitute v=73.8 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 66, "gravity": 9.81, "speed": 73.8}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 3.27 * 8.314 * 270 / 5.3.\nFinal: {\"answer\": 1384.9869, \"unit\": \"kPa\"}", "dedupe_signature": "bfc1813941d1dd13f151bd1601d0c46c90085859d63f95a5165240369e2e766d", "difficulty": "medium", "final_answer": {"answer": 1384.9869, "unit": "kPa"}, "id": "ideal_gas_007275_3.27_270_5.3", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=3.27 mol, T=270 K, and V=5.3 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 3.27 * 8.314 * 270 / 5.3.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 3.27, "temp_k": 270, "volume_l": 5.3}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 560 * 0.545 * 14.\nFinal: {\"answer\": 4272.8, \"unit\": \"J\"}", "dedupe_signature": "c2f40519f9fb812ee0b908df57882b57dd03cd8d5bcc045dd8c9cd8a2bb25c5a", "difficulty": "easy", "final_answer": {"answer": 4272.8, "unit": "J"}, "id": "heat_q_007276_560_0.545_14", "license": "Apache-2.0", "prompt": "A 560 g sample has specific heat 0.545 J/(g*K). How much heat is needed to raise its temperature by 14 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 560 * 0.545 * 14.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 14, "heat_capacity": 0.545, "mass_g": 560}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=125.3 V and R=165.8 ohm.\nFinal: {\"answer\": 94.6929, \"unit\": \"W\"}", "dedupe_signature": "cdf38cdf245bdee4489bfdbc251379381744802d83371a1d76abd5a1c5c8f817", "difficulty": "easy", "final_answer": {"answer": 94.6929, "unit": "W"}, "id": "ohm_power_007277_125.3_165.8", "license": "Apache-2.0", "prompt": "A resistor has resistance 165.8 ohm and voltage 125.3 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=125.3 V and R=165.8 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 165.8, "voltage": 125.3}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 0.06 mol * 18.015 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 1.0809, \"unit\": \"g\"}", "dedupe_signature": "12e80fbb0142958cc7847caa7427ece5ec50b54a3b452ba61be9247e587d4472", "difficulty": "medium", "final_answer": {"answer": 1.0809, "unit": "g"}, "id": "stoich_mass_007279_water_0.06", "license": "Apache-2.0", "prompt": "A sample contains 0.06 mol of water. Using molar mass 18.015 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 0.06 mol * 18.015 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "water", "molar_mass": 18.015, "moles": 0.06}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 4020 mL to 4.02 L.\n3. Compute M = 1.75 / 4.02.\nFinal: {\"answer\": 0.4353, \"unit\": \"mol/L\"}", "dedupe_signature": "408afa7b2a6b0627eb1ae0fd9945d099ba6c7305afc26aff952d8705bcf49645", "difficulty": "medium", "final_answer": {"answer": 0.4353, "unit": "mol/L"}, "id": "molarity_007280_1.75_4020", "license": "Apache-2.0", "prompt": "A solution contains 1.75 mol of solute in 4020 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 4020 mL to 4.02 L.\nCompute M = 1.75 / 4.02.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 1.75, "volume_ml": 4020}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.35 y, so each step multiplies y by 1 - h*0.35.\n3. Apply that update for 12 steps and round the final state.\nFinal: {\"answer\": 0.0078, \"unit\": \"state_units\"}", "dedupe_signature": "2350132ce5490d57523f83ce627d229b77cc87ab4c798405e7fe84347136ee78", "difficulty": "medium", "final_answer": {"answer": 0.0078, "unit": "state_units"}, "id": "euler_decay_007281_59.5_0.35_1.5_12", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.35 y with y(0)=59.5, step size h=1.5, for 12 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.35 y, so each step multiplies y by 1 - h*0.35.\nApply that update for 12 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 59.5, "rate": 0.35, "step": 1.5, "steps": 12}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-8.7)=36.94 and f(-7.6)=34.52.\n3. The interval width is 1.1.\nFinal: {\"answer\": 39.303, \"unit\": \"area_units\"}", "dedupe_signature": "ccbc6ab6ef35c3faea5a34da3ee93eeda3dd942f59734a274b765a8b83f0b984", "difficulty": "medium", "final_answer": {"answer": 39.303, "unit": "area_units"}, "id": "trapz_linear_007282_-2.2_17.8_-8.7_-7.6", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-2.2x+17.8 from x=-8.7 to x=-7.6. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-8.7)=36.94 and f(-7.6)=34.52.\nThe interval width is 1.1.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 17.8, "slope": -2.2, "x0": -8.7, "x1": -7.6}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.26 and add it to the current value.\nFinal: {\"answer\": [1.547, 1.407, 1.644], \"unit\": \"temperature_units\"}", "dedupe_signature": "7653056344aa79edf111272e3a775a48f78d84f13a0692a5902919895ed876b7", "difficulty": "hard", "final_answer": {"answer": [1.547, 1.407, 1.644], "unit": "temperature_units"}, "id": "heat_step_007283_0.26_2.65_1.3_0.9_2.45_0.9", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=2.65, right=0.9; current interior values are [1.3, 0.9, 2.45]. Use r=0.26. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.26 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [1.3, 0.9, 2.45], "left": 2.65, "r": 0.26, "right": 0.9}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 100 centimeters in one meter.\n2. Apply the conversion factor directly to the given value.\n3. Compute 3891.5 / 100.\nFinal: {\"answer\": 38.915, \"unit\": \"m\"}", "dedupe_signature": "40dc5a5d652bd23f56f80cf637d324a8f7e19c409e694b145b0f33f96653e17f", "difficulty": "easy", "final_answer": {"answer": 38.915, "unit": "m"}, "id": "unit_convert_007284_cm_to_m_3891.5", "license": "Apache-2.0", "prompt": "Convert 3891.5 cm to m. Return the converted value with unit.", "reasoning_trace": "There are 100 centimeters in one meter.\nApply the conversion factor directly to the given value.\nCompute 3891.5 / 100.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 3891.5}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-9.75, -16.0], \"unit\": \"dimensionless\"}", "dedupe_signature": "1e652dbdc67dc10502794a8a40f2773b25ad57bafa118382d4e928ca2b5e4678", "difficulty": "medium", "final_answer": {"answer": [-9.75, -16.0], "unit": "dimensionless"}, "id": "line_two_point_007286_-4.25_-0.75_-9.75_-16", "license": "Apache-2.0", "prompt": "A line passes through points (-4.25, 25.4375) and (-0.75, -8.6875). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -4.25, "x2": -0.75, "y1": 25.4375, "y2": -8.6875}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. grams cancel with J/(g*K), and kelvin cancels, leaving joules\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "83433c5b37441fff5dde7a1d9acc20d93cd5f44ff1546e6f0ef6348d2aeeac98", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_007287_consistent_4153435f_892858", "license": "Apache-2.0", "prompt": "In student derivation case 892858, check dimensional consistency for Q = m * c * DeltaT. The left side has dimensions J and the right side has dimensions J. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\ngrams cancel with J/(g*K), and kelvin cancels, leaving joules\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "Q = m * c * DeltaT"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 10.5 kg and a = 5.7 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 59.85, \"unit\": \"N\"}", "dedupe_signature": "bcc9e62eb0d47a8d920f8e894ba2207222f589f3d98bc10e3c0b9aab353695fd", "difficulty": "easy", "final_answer": {"answer": 59.85, "unit": "N"}, "id": "force_007290_10.5_5.7", "license": "Apache-2.0", "prompt": "A cart has mass 10.5 kg and measured acceleration 5.7 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 10.5 kg and a = 5.7 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 5.7, "mass": 10.5}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 18.7^2 and multiply by 0.5 * 8.55.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 1494.9248, \"unit\": \"J\"}", "dedupe_signature": "4c00624a8834dbabc0fa19fa7948c1fbbbc8663427e5a8247fec95864c403200", "difficulty": "easy", "final_answer": {"answer": 1494.9248, "unit": "J"}, "id": "ke_007291_8.55_18.7", "license": "Apache-2.0", "prompt": "A body of mass 8.55 kg moves at 18.7 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 18.7^2 and multiply by 0.5 * 8.55.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 8.55, "velocity": 18.7}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=19 degrees through the sine of 2 theta.\n3. Substitute v=36.7 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 84.5289, \"unit\": \"m\"}", "dedupe_signature": "8bda8f41a3048ed06ca9afddd01f762bea03e051b5e8737b7b38347e3eb38586", "difficulty": "medium", "final_answer": {"answer": 84.5289, "unit": "m"}, "id": "projectile_range_007292_36.7_19", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 36.7 m/s and angle 19 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=19 degrees through the sine of 2 theta.\nSubstitute v=36.7 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 19, "gravity": 9.81, "speed": 36.7}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 5.48 * 8.314 * 352 / 8.8.\nFinal: {\"answer\": 1822.4288, \"unit\": \"kPa\"}", "dedupe_signature": "5d1d27d4ffd0fd7350b99cfc44fbf3fa36e55a9f1dd62fbb5f1d17aed5ed57da", "difficulty": "medium", "final_answer": {"answer": 1822.4288, "unit": "kPa"}, "id": "ideal_gas_007293_5.48_352_8.8", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=5.48 mol, T=352 K, and V=8.8 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 5.48 * 8.314 * 352 / 8.8.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 5.48, "temp_k": 352, "volume_l": 8.8}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1945 * 4.775 * 92.\nFinal: {\"answer\": 854438.5, \"unit\": \"J\"}", "dedupe_signature": "636f75f7e0fe295d818437c47b2a97d2e4037864070e4725ec81e9f1a0ec45ed", "difficulty": "easy", "final_answer": {"answer": 854438.5, "unit": "J"}, "id": "heat_q_007294_1945_4.775_92", "license": "Apache-2.0", "prompt": "A 1945 g sample has specific heat 4.775 J/(g*K). How much heat is needed to raise its temperature by 92 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1945 * 4.775 * 92.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 92, "heat_capacity": 4.775, "mass_g": 1945}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=780 mg, t=95 h, and T_half=118 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 446.4162, \"unit\": \"mg\"}", "dedupe_signature": "21b04f93190fcfdad502f71e790c418c8ef79f3d85675c1919a0a8def41895ac", "difficulty": "medium", "final_answer": {"answer": 446.4162, "unit": "mg"}, "id": "half_life_007296_780_118_95", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 780 mg. Its half-life is 118 hours. How many mg remain after 95 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=780 mg, t=95 h, and T_half=118 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 95.0, "half_life": 118.0, "initial_amount": 780.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 4.31 mol * 18.015 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 77.6446, \"unit\": \"g\"}", "dedupe_signature": "d49f992d868f075f6ebd22213ce22a842ce329f0799da06e616648c34b4806d5", "difficulty": "medium", "final_answer": {"answer": 77.6446, "unit": "g"}, "id": "stoich_mass_007297_water_4.31", "license": "Apache-2.0", "prompt": "A sample contains 4.31 mol of water. Using molar mass 18.015 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 4.31 mol * 18.015 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "water", "molar_mass": 18.015, "moles": 4.31}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 4485 mL to 4.485 L.\n3. Compute M = 0.675 / 4.485.\nFinal: {\"answer\": 0.1505, \"unit\": \"mol/L\"}", "dedupe_signature": "c357b4f46909330a3a20e364371bb9180d6f20a450d869b37f78f2b592e77b5e", "difficulty": "medium", "final_answer": {"answer": 0.1505, "unit": "mol/L"}, "id": "molarity_007298_0.675_4485", "license": "Apache-2.0", "prompt": "A solution contains 0.675 mol of solute in 4485 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 4485 mL to 4.485 L.\nCompute M = 0.675 / 4.485.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 0.675, "volume_ml": 4485}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(6.5)=-7.95 and f(8.3)=-10.65.\n3. The interval width is 1.8.\nFinal: {\"answer\": -16.74, \"unit\": \"area_units\"}", "dedupe_signature": "e56e84d4a1a5ca8bb473e24a3eccb5791e669fe9abc100fbf9c715e80d348c61", "difficulty": "medium", "final_answer": {"answer": -16.74, "unit": "area_units"}, "id": "trapz_linear_007300_-1.5_1.8_6.5_8.3", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-1.5x+1.8 from x=6.5 to x=8.3. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(6.5)=-7.95 and f(8.3)=-10.65.\nThe interval width is 1.8.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 1.8, "slope": -1.5, "x0": 6.5, "x1": 8.3}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.18 and add it to the current value.\nFinal: {\"answer\": [0.192, 1.255, 2.329], \"unit\": \"temperature_units\"}", "dedupe_signature": "7a6982462015f461c6b33fb7749d09873ac899a6a22b1377557c060f116f79ff", "difficulty": "hard", "final_answer": {"answer": [0.192, 1.255, 2.329], "unit": "temperature_units"}, "id": "heat_step_007301_0.18_0.3_-0.15_1.3_2.5_2.75", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=0.3, right=2.75; current interior values are [-0.15, 1.3, 2.5]. Use r=0.18. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.18 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-0.15, 1.3, 2.5], "left": 0.3, "r": 0.18, "right": 2.75}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 36205.0 / 1000.\nFinal: {\"answer\": 36.205, \"unit\": \"kg\"}", "dedupe_signature": "73fbcc29fed87b661d4271ab70c595acf0ebac90d78acfa7767dea37ebbc0750", "difficulty": "easy", "final_answer": {"answer": 36.205, "unit": "kg"}, "id": "unit_convert_007302_g_to_kg_36205", "license": "Apache-2.0", "prompt": "Convert 36205 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 36205.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 36205.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. coulomb per second is ampere\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "77af7d5e088452f076da519ea7f4d5137509bebe33d703b2c213ba514a043a40", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_007305_consistent_8b38953d_896461", "license": "Apache-2.0", "prompt": "In model card equation case 896461, check dimensional consistency for I = Q / t. The left side has dimensions A and the right side has dimensions A. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\ncoulomb per second is ampere\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "I = Q / t"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef normalize_007306(values):\n    total = sum(values)\n    if total == 0:\n        raise ValueError('cannot normalize zero-sum values')\n    return [v / total for v in values]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"normalize_007306\"}", "dedupe_signature": "61b18d920a816eae9f1b5130406a5982f1d85474970e9221d81fb00ac0d56ff9", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "normalize_007306"}, "id": "code_007306_normalize_007306", "license": "Apache-2.0", "prompt": "Write a Python function normalize_007306(values) that returns a new list whose values sum to 1. Raise ValueError if the sum is zero. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "normalize_007306"}, "verifier": {"function": "normalize_007306", "tests": ["out = normalize_007306([2, 3, 5]); assert len(out) == 3", "assert abs(sum(normalize_007306([2, 3, 5])) - 1.0) < 1e-12", "assert normalize_007306([1, 1]) == [0.5, 0.5]", "try:\n    normalize_007306([1, -1])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: required_fields, allowed_transformations.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"required_fields\", \"allowed_transformations\"]}", "dedupe_signature": "fc40e94d2c16a2427c9738b3a63b5b2ec3f1951595aa9e28e3deaac3707adbe3", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["required_fields", "allowed_transformations"]}, "id": "abstain_007307_required_fields_allowed_transformations", "license": "Apache-2.0", "prompt": "Write a sanitizer for valid registry sensor records in release 199333, but the prompt does not state which fields are required or which transformations are allowed. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: required_fields, allowed_transformations.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["required_fields", "allowed_transformations"]}, "verifier": {"missing": ["required_fields", "allowed_transformations"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 10.3 kg and a = 7.55 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 77.765, \"unit\": \"N\"}", "dedupe_signature": "cf824ce68860e5fd8ef4a2846416c2b67fa0eec5ff35f3972e45a27c8d1c13b3", "difficulty": "easy", "final_answer": {"answer": 77.765, "unit": "N"}, "id": "force_007308_10.3_7.55", "license": "Apache-2.0", "prompt": "A cart has mass 10.3 kg and measured acceleration 7.55 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 10.3 kg and a = 7.55 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 7.55, "mass": 10.3}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 31.9^2 and multiply by 0.5 * 23.2.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 11804.276, \"unit\": \"J\"}", "dedupe_signature": "e27990a9750c4af1a7ce66717be6d0de21214d517a9f63a4bed7ea49be293574", "difficulty": "easy", "final_answer": {"answer": 11804.276, "unit": "J"}, "id": "ke_007309_23.2_31.9", "license": "Apache-2.0", "prompt": "A body of mass 23.2 kg moves at 31.9 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 31.9^2 and multiply by 0.5 * 23.2.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 23.2, "velocity": 31.9}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=83 degrees through the sine of 2 theta.\n3. Substitute v=50.8 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 63.6405, \"unit\": \"m\"}", "dedupe_signature": "3e2a8ad5163cfdaedbebc7ab4360a8575fe41808a9b66ce2cd9a2d7a59a24858", "difficulty": "medium", "final_answer": {"answer": 63.6405, "unit": "m"}, "id": "projectile_range_007310_50.8_83", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 50.8 m/s and angle 83 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=83 degrees through the sine of 2 theta.\nSubstitute v=50.8 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 83, "gravity": 9.81, "speed": 50.8}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1455 * 1.95 * 103.\nFinal: {\"answer\": 292236.75, \"unit\": \"J\"}", "dedupe_signature": "d70490da0a0c82abcec91e4c19d2a04961f82941663a767225708e2ce4e704c8", "difficulty": "easy", "final_answer": {"answer": 292236.75, "unit": "J"}, "id": "heat_q_007312_1455_1.95_103", "license": "Apache-2.0", "prompt": "A 1455 g sample has specific heat 1.95 J/(g*K). How much heat is needed to raise its temperature by 103 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1455 * 1.95 * 103.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 103, "heat_capacity": 1.95, "mass_g": 1455}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=948.5 mg, t=167 h, and T_half=110.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 332.7262, \"unit\": \"mg\"}", "dedupe_signature": "afa7f3f4464b3af3149b7c8c9a676f2619ee5d1df1931ad201d2ec24e23e845e", "difficulty": "medium", "final_answer": {"answer": 332.7262, "unit": "mg"}, "id": "half_life_007314_948.5_110.5_167", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 948.5 mg. Its half-life is 110.5 hours. How many mg remain after 167 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=948.5 mg, t=167 h, and T_half=110.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 167.0, "half_life": 110.5, "initial_amount": 948.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 3.23 mol * 180.156 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 581.9039, \"unit\": \"g\"}", "dedupe_signature": "302f03a82317f43564c1e2742753101fc5486dcb4b114fdda47ec2ea2a4c7088", "difficulty": "medium", "final_answer": {"answer": 581.9039, "unit": "g"}, "id": "stoich_mass_007315_glucose_3.23", "license": "Apache-2.0", "prompt": "A sample contains 3.23 mol of glucose. Using molar mass 180.156 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 3.23 mol * 180.156 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "glucose", "molar_mass": 180.156, "moles": 3.23}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 420 mL to 0.42 L.\n3. Compute M = 4.84 / 0.42.\nFinal: {\"answer\": 11.5238, \"unit\": \"mol/L\"}", "dedupe_signature": "e7d9ea657a4efa8b40c801cd7347a7b5a32aaf0ce74c590aba449a05c71a4d1c", "difficulty": "medium", "final_answer": {"answer": 11.5238, "unit": "mol/L"}, "id": "molarity_007316_4.84_420", "license": "Apache-2.0", "prompt": "A solution contains 4.84 mol of solute in 420 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 420 mL to 0.42 L.\nCompute M = 4.84 / 0.42.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 4.84, "volume_ml": 420}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.09 y, so each step multiplies y by 1 - h*0.09.\n3. Apply that update for 11 steps and round the final state.\nFinal: {\"answer\": 3.6746, \"unit\": \"state_units\"}", "dedupe_signature": "6554d0a4340df73903238b102375def0ef0fae120ddc8f6ac7424d0d798ef6ed", "difficulty": "medium", "final_answer": {"answer": 3.6746, "unit": "state_units"}, "id": "euler_decay_007317_5.5_0.09_0.4_11", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.09 y with y(0)=5.5, step size h=0.4, for 11 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.09 y, so each step multiplies y by 1 - h*0.09.\nApply that update for 11 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 5.5, "rate": 0.09, "step": 0.4, "steps": 11}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(4.2)=-18.36 and f(8.7)=-21.96.\n3. The interval width is 4.5.\nFinal: {\"answer\": -90.72, \"unit\": \"area_units\"}", "dedupe_signature": "623ce1e69aa2b074a4fb37d1e6fbf9765c9dc823ef959e48260556bef7a534b4", "difficulty": "medium", "final_answer": {"answer": -90.72, "unit": "area_units"}, "id": "trapz_linear_007318_-0.8_-15_4.2_8.7", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-0.8x+-15 from x=4.2 to x=8.7. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(4.2)=-18.36 and f(8.7)=-21.96.\nThe interval width is 4.5.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -15.0, "slope": -0.8, "x0": 4.2, "x1": 8.7}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.38 and add it to the current value.\nFinal: {\"answer\": [-0.037, 0.949, 1.419], \"unit\": \"temperature_units\"}", "dedupe_signature": "ede020a4e3b5171f0d23810ec6168ae69ea543f4f08d04e1c1173c34004b89b1", "difficulty": "hard", "final_answer": {"answer": [-0.037, 0.949, 1.419], "unit": "temperature_units"}, "id": "heat_step_007319_0.38_0.05_0.4_-0.4_2.35_2.65", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=0.05, right=2.65; current interior values are [0.4, -0.4, 2.35]. Use r=0.38. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.38 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [0.4, -0.4, 2.35], "left": 0.05, "r": 0.38, "right": 2.65}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=65 degrees and keep the unit as newtons.\nFinal: {\"answer\": [106.9224, 229.2959], \"unit\": \"N\"}", "dedupe_signature": "bb353718bc6ea76e1cb8a1290732aed705a6f31c319f60f7b0af32be7193d98f", "difficulty": "medium", "final_answer": {"answer": [106.9224, 229.2959], "unit": "N"}, "id": "vector_components_007321_253_65", "license": "Apache-2.0", "prompt": "A vector has magnitude 253 N at 65 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=65 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 65, "magnitude": 253.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [2.1, -17.25], \"unit\": \"dimensionless\"}", "dedupe_signature": "324610459dc5ed9bd036743c4dc8d9227798454d61987444f04627c7eb489c18", "difficulty": "medium", "final_answer": {"answer": [2.1, -17.25], "unit": "dimensionless"}, "id": "line_two_point_007322_-1.75_-0.25_2.1_-17.25", "license": "Apache-2.0", "prompt": "A line passes through points (-1.75, -20.925) and (-0.25, -17.775). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -1.75, "x2": -0.25, "y1": -20.925, "y2": -17.775}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. speed squared over acceleration has units of meters\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "5f8b7ee37145c6d376398652f134d398b989236f7bc7d4409de8a71f9e09b592", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_007323_consistent_741d4e34_75135", "license": "Apache-2.0", "prompt": "In field worksheet case 75135, check dimensional consistency for R = v^2 * sin(theta) / g. The left side has dimensions m and the right side has dimensions m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nspeed squared over acceleration has units of meters\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "R = v^2 * sin(theta) / g"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 10.1 kg and a = 11.25 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 113.625, \"unit\": \"N\"}", "dedupe_signature": "a07b3419429e4a9f19765a3625d3244537c91edf34e809f84147d899facfda85", "difficulty": "easy", "final_answer": {"answer": 113.625, "unit": "N"}, "id": "force_007326_10.1_11.25", "license": "Apache-2.0", "prompt": "A cart has mass 10.1 kg and measured acceleration 11.25 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 10.1 kg and a = 11.25 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 11.25, "mass": 10.1}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 35^2 and multiply by 0.5 * 28.9.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 17701.25, \"unit\": \"J\"}", "dedupe_signature": "21ec5df30845ab74824c213eee2c58fa34505c58b44039641b4a9ddf3e35aa9c", "difficulty": "easy", "final_answer": {"answer": 17701.25, "unit": "J"}, "id": "ke_007327_28.9_35", "license": "Apache-2.0", "prompt": "A body of mass 28.9 kg moves at 35 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 35^2 and multiply by 0.5 * 28.9.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 28.9, "velocity": 35.0}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=64 degrees through the sine of 2 theta.\n3. Substitute v=17.7 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 25.1657, \"unit\": \"m\"}", "dedupe_signature": "1a3741a0c89569c274686b91730c2bbf180970dd1873ba14344a37401e8e7d6e", "difficulty": "medium", "final_answer": {"answer": 25.1657, "unit": "m"}, "id": "projectile_range_007328_17.7_64", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 17.7 m/s and angle 64 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=64 degrees through the sine of 2 theta.\nSubstitute v=17.7 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 64, "gravity": 9.81, "speed": 17.7}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 4.49 * 8.314 * 448 / 44.4.\nFinal: {\"answer\": 376.6617, \"unit\": \"kPa\"}", "dedupe_signature": "2f140e61f9ab405ce49143a7a65a8fabdcd98f335b2fc25cecdb0d16d82ad62c", "difficulty": "medium", "final_answer": {"answer": 376.6617, "unit": "kPa"}, "id": "ideal_gas_007329_4.49_448_44.4", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=4.49 mol, T=448 K, and V=44.4 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 4.49 * 8.314 * 448 / 44.4.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 4.49, "temp_k": 448, "volume_l": 44.4}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1985 * 1.12 * 1.\nFinal: {\"answer\": 2223.2, \"unit\": \"J\"}", "dedupe_signature": "b08b106757e874476713dd6ee91c5b5daf8ede52245e0d21ec8472dd64a90c91", "difficulty": "easy", "final_answer": {"answer": 2223.2, "unit": "J"}, "id": "heat_q_007330_1985_1.12_1", "license": "Apache-2.0", "prompt": "A 1985 g sample has specific heat 1.12 J/(g*K). How much heat is needed to raise its temperature by 1 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1985 * 1.12 * 1.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 1, "heat_capacity": 1.12, "mass_g": 1985}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=129.8 V and R=100.3 ohm.\nFinal: {\"answer\": 167.9765, \"unit\": \"W\"}", "dedupe_signature": "1bf629ff0c2eb8361212d9737d9131b73835154f57d084f9acb628f6d6e5a931", "difficulty": "easy", "final_answer": {"answer": 167.9765, "unit": "W"}, "id": "ohm_power_007331_129.8_100.3", "license": "Apache-2.0", "prompt": "A resistor has resistance 100.3 ohm and voltage 129.8 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=129.8 V and R=100.3 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 100.3, "voltage": 129.8}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=888 mg, t=74.5 h, and T_half=17.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 46.4393, \"unit\": \"mg\"}", "dedupe_signature": "809f63a1d7fe4838d07b9eb730144f2cfe3cd8f93c7b21aa22bc91c114d4d283", "difficulty": "medium", "final_answer": {"answer": 46.4393, "unit": "mg"}, "id": "half_life_007332_888_17.5_74.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 888 mg. Its half-life is 17.5 hours. How many mg remain after 74.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=888 mg, t=74.5 h, and T_half=17.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 74.5, "half_life": 17.5, "initial_amount": 888.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 2535 mL to 2.535 L.\n3. Compute M = 2.905 / 2.535.\nFinal: {\"answer\": 1.146, \"unit\": \"mol/L\"}", "dedupe_signature": "8bcf8d78050cdaab01c8332680fedf48d027999b95b6eadf72a99e40198446c3", "difficulty": "medium", "final_answer": {"answer": 1.146, "unit": "mol/L"}, "id": "molarity_007334_2.905_2535", "license": "Apache-2.0", "prompt": "A solution contains 2.905 mol of solute in 2535 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 2535 mL to 2.535 L.\nCompute M = 2.905 / 2.535.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 2.905, "volume_ml": 2535}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.63 y, so each step multiplies y by 1 - h*0.63.\n3. Apply that update for 8 steps and round the final state.\nFinal: {\"answer\": 0.0005, \"unit\": \"state_units\"}", "dedupe_signature": "1625f226f3b443483477ceaf670119ac6e8ec1d0ea1d7498beebf202faace66c", "difficulty": "medium", "final_answer": {"answer": 0.0005, "unit": "state_units"}, "id": "euler_decay_007335_6.5_0.63_1.1_8", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.63 y with y(0)=6.5, step size h=1.1, for 8 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.63 y, so each step multiplies y by 1 - h*0.63.\nApply that update for 8 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 6.5, "rate": 0.63, "step": 1.1, "steps": 8}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-5.7)=-34.59 and f(0.1)=-7.33.\n3. The interval width is 5.8.\nFinal: {\"answer\": -121.568, \"unit\": \"area_units\"}", "dedupe_signature": "3f969803701d7a3283ed0bf199cbc4efda1f0609767d164796d9953907ed78f4", "difficulty": "medium", "final_answer": {"answer": -121.568, "unit": "area_units"}, "id": "trapz_linear_007336_4.7_-7.8_-5.7_0.1", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=4.7x+-7.8 from x=-5.7 to x=0.1. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-5.7)=-34.59 and f(0.1)=-7.33.\nThe interval width is 5.8.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -7.8, "slope": 4.7, "x0": -5.7, "x1": 0.09999999999999964}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.3 and add it to the current value.\nFinal: {\"answer\": [0.925, 0.12, -0.455], \"unit\": \"temperature_units\"}", "dedupe_signature": "c075ef65d1c291c4245caf36b59966fe8e2b85969f5f6dfb0de7df957abb674c", "difficulty": "hard", "final_answer": {"answer": [0.925, 0.12, -0.455], "unit": "temperature_units"}, "id": "heat_step_007337_0.3_2.0_-0.65_1.95_-1.55_-1.4", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=2, right=-1.4; current interior values are [-0.65, 1.95, -1.55]. Use r=0.3. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.3 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-0.65, 1.95, -1.55], "left": 2.0, "r": 0.3, "right": -1.4}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 43115.0 / 1000.\nFinal: {\"answer\": 43.115, \"unit\": \"kg\"}", "dedupe_signature": "cb8a44102fb88e3bbd9f551ec403a9265c425dbc7424ca5d7be669bb1caad28d", "difficulty": "easy", "final_answer": {"answer": 43.115, "unit": "kg"}, "id": "unit_convert_007338_g_to_kg_43115", "license": "Apache-2.0", "prompt": "Convert 43115 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 43115.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 43115.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. velocity divided by time is acceleration\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "b78f137f1cfb8e3cfa23c74ee6dc270e45f179fe310e443fff1579214c41381b", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_007341_inconsistent_c1271127_741195", "license": "Apache-2.0", "prompt": "In field worksheet case 741195, check dimensional consistency for x = v / t. The left side has dimensions m and the right side has dimensions m/s^2. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nvelocity divided by time is acceleration\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "x = v / t"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef center_values_007342(values):\n    if not values:\n        raise ValueError('center_values requires at least one value')\n    mean = sum(values) / len(values)\n    return [value - mean for value in values]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"center_values_007342\"}", "dedupe_signature": "d8a0b99147e681d4689c8e49896369e6040edd9da7f028bc9df848eb02c8cc0c", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "center_values_007342"}, "id": "code_007342_center_values_007342", "license": "Apache-2.0", "prompt": "Write a Python function center_values_007342(values) that subtracts the arithmetic mean from each value and returns a new list. Raise ValueError for an empty input. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "center_values_007342"}, "verifier": {"function": "center_values_007342", "tests": ["out = center_values_007342([1, 2, 3]); assert out == [-1, 0, 1]", "assert center_values_007342([5]) == [0]", "try:\n    center_values_007342([])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: required_fields, allowed_transformations.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"required_fields\", \"allowed_transformations\"]}", "dedupe_signature": "2360d295de70ca9aff09f1933e66341dc1b6ee9206454aac16c75c520158837a", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["required_fields", "allowed_transformations"]}, "id": "abstain_007343_required_fields_allowed_transformations", "license": "Apache-2.0", "prompt": "Write a sanitizer for valid billing crop records in release 990617, but the prompt does not state which fields are required or which transformations are allowed. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: required_fields, allowed_transformations.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["required_fields", "allowed_transformations"]}, "verifier": {"missing": ["required_fields", "allowed_transformations"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 16.45 kg and a = 5.15 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 84.7175, \"unit\": \"N\"}", "dedupe_signature": "c6ec8caadd49c8b1b441c2bd0b832e5dfb2f012cb025fce15991e2471c2bfd2f", "difficulty": "easy", "final_answer": {"answer": 84.7175, "unit": "N"}, "id": "force_007344_16.45_5.15", "license": "Apache-2.0", "prompt": "A cart has mass 16.45 kg and measured acceleration 5.15 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 16.45 kg and a = 5.15 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 5.15, "mass": 16.45}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 20.25^2 and multiply by 0.5 * 25.5.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 5228.2969, \"unit\": \"J\"}", "dedupe_signature": "789f6129e17a3b9adce8f520436bd1afb2617095bf548f5af32f587256a0cfcc", "difficulty": "easy", "final_answer": {"answer": 5228.2969, "unit": "J"}, "id": "ke_007345_25.5_20.25", "license": "Apache-2.0", "prompt": "A body of mass 25.5 kg moves at 20.25 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 20.25^2 and multiply by 0.5 * 25.5.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 25.5, "velocity": 20.25}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=48 degrees through the sine of 2 theta.\n3. Substitute v=28.7 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 83.5044, \"unit\": \"m\"}", "dedupe_signature": "d0debff41dd6a5853f0b9ca69f6911945e1ca13526f6aac956f0b716ec699f9c", "difficulty": "medium", "final_answer": {"answer": 83.5044, "unit": "m"}, "id": "projectile_range_007346_28.7_48", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 28.7 m/s and angle 48 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=48 degrees through the sine of 2 theta.\nSubstitute v=28.7 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 48, "gravity": 9.81, "speed": 28.7}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 2.49 * 8.314 * 538 / 19.7.\nFinal: {\"answer\": 565.3604, \"unit\": \"kPa\"}", "dedupe_signature": "e766646fc36216136029f5a7b052598d396a39f0ad8b1cd9de8171280be75ada", "difficulty": "medium", "final_answer": {"answer": 565.3604, "unit": "kPa"}, "id": "ideal_gas_007347_2.49_538_19.7", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=2.49 mol, T=538 K, and V=19.7 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 2.49 * 8.314 * 538 / 19.7.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 2.49, "temp_k": 538, "volume_l": 19.7}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 605 * 4.3 * 60.\nFinal: {\"answer\": 156090.0, \"unit\": \"J\"}", "dedupe_signature": "95efee8225799abcd0166571ec225d40b71b8e969ca435c648ab826471abb5c8", "difficulty": "easy", "final_answer": {"answer": 156090.0, "unit": "J"}, "id": "heat_q_007348_605_4.3_60", "license": "Apache-2.0", "prompt": "A 605 g sample has specific heat 4.3 J/(g*K). How much heat is needed to raise its temperature by 60 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 605 * 4.3 * 60.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 60, "heat_capacity": 4.3, "mass_g": 605}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=105.9 V and R=101.1 ohm.\nFinal: {\"answer\": 110.9279, \"unit\": \"W\"}", "dedupe_signature": "508c2c0f8b269cf6495f52b9ce1342d2dbfdcc4bbd92a8dc39a1bc582e43b5ee", "difficulty": "easy", "final_answer": {"answer": 110.9279, "unit": "W"}, "id": "ohm_power_007349_105.9_101.1", "license": "Apache-2.0", "prompt": "A resistor has resistance 101.1 ohm and voltage 105.9 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=105.9 V and R=101.1 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 101.1, "voltage": 105.9}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 0.47 mol * 44.01 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 20.6847, \"unit\": \"g\"}", "dedupe_signature": "2df98a91d81bb89c76b8f47de46059633d5a34e82b6b249d9331200b48d63f09", "difficulty": "medium", "final_answer": {"answer": 20.6847, "unit": "g"}, "id": "stoich_mass_007351_carbon_dioxide_0.47", "license": "Apache-2.0", "prompt": "A sample contains 0.47 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 0.47 mol * 44.01 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "carbon dioxide", "molar_mass": 44.01, "moles": 0.47}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 1055 mL to 1.055 L.\n3. Compute M = 1.795 / 1.055.\nFinal: {\"answer\": 1.7014, \"unit\": \"mol/L\"}", "dedupe_signature": "e2fe51eb743816a8ecd28e7fae970cde6142d0276b5d24a4abd42b7d5366498b", "difficulty": "medium", "final_answer": {"answer": 1.7014, "unit": "mol/L"}, "id": "molarity_007352_1.795_1055", "license": "Apache-2.0", "prompt": "A solution contains 1.795 mol of solute in 1055 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 1055 mL to 1.055 L.\nCompute M = 1.795 / 1.055.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 1.795, "volume_ml": 1055}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.08 y, so each step multiplies y by 1 - h*0.08.\n3. Apply that update for 2 steps and round the final state.\nFinal: {\"answer\": 62.5165, \"unit\": \"state_units\"}", "dedupe_signature": "d1e53596e1f9522cf756eb8f25fd2aeb096f276f0abc517c0d50b0977835f21b", "difficulty": "medium", "final_answer": {"answer": 62.5165, "unit": "state_units"}, "id": "euler_decay_007353_80_0.08_1.45_2", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.08 y with y(0)=80, step size h=1.45, for 2 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.08 y, so each step multiplies y by 1 - h*0.08.\nApply that update for 2 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 80.0, "rate": 0.08, "step": 1.45, "steps": 2}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-1.5)=5.45 and f(-0.6)=9.14.\n3. The interval width is 0.9.\nFinal: {\"answer\": 6.5655, \"unit\": \"area_units\"}", "dedupe_signature": "06ba9f4560dd966d4713589708fa6546d020d092f341d56b3b6fdc5b63d2db92", "difficulty": "medium", "final_answer": {"answer": 6.5655, "unit": "area_units"}, "id": "trapz_linear_007354_4.1_11.6_-1.5_-0.6", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=4.1x+11.6 from x=-1.5 to x=-0.6. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-1.5)=5.45 and f(-0.6)=9.14.\nThe interval width is 0.9.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 11.6, "slope": 4.1, "x0": -1.5, "x1": -0.6}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.04 and add it to the current value.\nFinal: {\"answer\": [0.34, -1.198, 0.73], \"unit\": \"temperature_units\"}", "dedupe_signature": "d027824bc0544298276220f1f9b1f7dbfe80d64a18cc035523e5b53609887b9d", "difficulty": "hard", "final_answer": {"answer": [0.34, -1.198, 0.73], "unit": "temperature_units"}, "id": "heat_step_007355_0.04_1.8_0.35_-1.35_0.75_2.35", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.8, right=2.35; current interior values are [0.35, -1.35, 0.75]. Use r=0.04. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.04 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [0.35, -1.35, 0.75], "left": 1.8, "r": 0.04, "right": 2.35}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=311 degrees and keep the unit as newtons.\nFinal: {\"answer\": [196.8177, -226.4129], \"unit\": \"N\"}", "dedupe_signature": "0ebff4d931138211d19665c4720a1d3c5e613f5e72a53718b15ace45c30dd7c1", "difficulty": "medium", "final_answer": {"answer": [196.8177, -226.4129], "unit": "N"}, "id": "vector_components_007357_300_311", "license": "Apache-2.0", "prompt": "A vector has magnitude 300 N at 311 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=311 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 311, "magnitude": 300.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [4.85, 28.75], \"unit\": \"dimensionless\"}", "dedupe_signature": "684dc6c9bde60473ef3c7a0a87ed2d29bb3b6929ef835524de0bb2a640b72fd5", "difficulty": "medium", "final_answer": {"answer": [4.85, 28.75], "unit": "dimensionless"}, "id": "line_two_point_007358_-7.75_5.25_4.85_28.75", "license": "Apache-2.0", "prompt": "A line passes through points (-7.75, -8.8375) and (5.25, 54.2125). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -7.75, "x2": 5.25, "y1": -8.837499999999999, "y2": 54.2125}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. lever arm times force has torque dimensions\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "bd5e4febab957c02b3a0b0f62399e94d54650bd296ec1ae30f62152df6a9ae50", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_007359_consistent_5ca82cb9_797101", "license": "Apache-2.0", "prompt": "In instrument manual case 797101, check dimensional consistency for tau = r * F. The left side has dimensions N*m and the right side has dimensions N*m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nlever arm times force has torque dimensions\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "tau = r * F"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef safe_mean_007360(values):\n    if not values:\n        raise ValueError('safe_mean requires at least one value')\n    return sum(values) / len(values)\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"safe_mean_007360\"}", "dedupe_signature": "bec653d27b2de76150386c9919b7df0529e5b4a3c8d821d9acc12298f00003aa", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "safe_mean_007360"}, "id": "code_007360_safe_mean_007360", "license": "Apache-2.0", "prompt": "Write a Python function safe_mean_007360(values) that returns the arithmetic mean. It must raise ValueError for an empty input and must not mutate the input list. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "safe_mean_007360"}, "verifier": {"function": "safe_mean_007360", "tests": ["assert safe_mean_007360([2, 4, 6]) == 4", "xs = [1, 2, 3]; assert safe_mean_007360(xs) == 2 and xs == [1, 2, 3]", "try:\n    safe_mean_007360([])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: required_fields, allowed_transformations.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"required_fields\", \"allowed_transformations\"]}", "dedupe_signature": "84a656486be9ec97c9c4e15d7fcef19ae52af79d7d7cad93bef38e8b58901561", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["required_fields", "allowed_transformations"]}, "id": "abstain_007361_required_fields_allowed_transformations", "license": "Apache-2.0", "prompt": "Write a sanitizer for valid field experiment records in release 469632, but the prompt does not state which fields are required or which transformations are allowed. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: required_fields, allowed_transformations.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["required_fields", "allowed_transformations"]}, "verifier": {"missing": ["required_fields", "allowed_transformations"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 1.75^2 and multiply by 0.5 * 25.3.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 38.7406, \"unit\": \"J\"}", "dedupe_signature": "367cb700801d4d9ed73dd365976fc6843e6363350b103b0acccf9ae11308de9c", "difficulty": "easy", "final_answer": {"answer": 38.7406, "unit": "J"}, "id": "ke_007363_25.3_1.75", "license": "Apache-2.0", "prompt": "A body of mass 25.3 kg moves at 1.75 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 1.75^2 and multiply by 0.5 * 25.3.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 25.3, "velocity": 1.75}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=32 degrees through the sine of 2 theta.\n3. Substitute v=25 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 57.2626, \"unit\": \"m\"}", "dedupe_signature": "97b12eba935daadaa88fd832abbb2bd6c95ada6eaa9dfc96f213fcf321ca81c7", "difficulty": "medium", "final_answer": {"answer": 57.2626, "unit": "m"}, "id": "projectile_range_007364_25_32", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 25 m/s and angle 32 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=32 degrees through the sine of 2 theta.\nSubstitute v=25 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 32, "gravity": 9.81, "speed": 25.0}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 2.13 * 8.314 * 439 / 71.8.\nFinal: {\"answer\": 108.2754, \"unit\": \"kPa\"}", "dedupe_signature": "66c080acaf566d9e5f76d0c84fa419f11949ce1be4de965d681cb7e389e45de2", "difficulty": "medium", "final_answer": {"answer": 108.2754, "unit": "kPa"}, "id": "ideal_gas_007365_2.13_439_71.8", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=2.13 mol, T=439 K, and V=71.8 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 2.13 * 8.314 * 439 / 71.8.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 2.13, "temp_k": 439, "volume_l": 71.8}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1695 * 4.235 * 114.\nFinal: {\"answer\": 818329.05, \"unit\": \"J\"}", "dedupe_signature": "ef7ea4be1812215ae18aaeb0fa67f2738bf352d4bdcef65f86241c3a409791cd", "difficulty": "easy", "final_answer": {"answer": 818329.05, "unit": "J"}, "id": "heat_q_007366_1695_4.235_114", "license": "Apache-2.0", "prompt": "A 1695 g sample has specific heat 4.235 J/(g*K). How much heat is needed to raise its temperature by 114 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1695 * 4.235 * 114.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 114, "heat_capacity": 4.235, "mass_g": 1695}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 4140 mL to 4.14 L.\n3. Compute M = 2.035 / 4.14.\nFinal: {\"answer\": 0.4915, \"unit\": \"mol/L\"}", "dedupe_signature": "81ee91fc87b794c7a6e704270f727094fdc77ef9cb419663bf8c6988efccae6b", "difficulty": "medium", "final_answer": {"answer": 0.4915, "unit": "mol/L"}, "id": "molarity_007370_2.035_4140", "license": "Apache-2.0", "prompt": "A solution contains 2.035 mol of solute in 4140 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 4140 mL to 4.14 L.\nCompute M = 2.035 / 4.14.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 2.035, "volume_ml": 4140}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.28 y, so each step multiplies y by 1 - h*0.28.\n3. Apply that update for 12 steps and round the final state.\nFinal: {\"answer\": 0.1569, \"unit\": \"state_units\"}", "dedupe_signature": "3feb1cccf094c8ec01a0cef9fc9dcfed00dc6f47e501c0a67c671a8f2c57e03e", "difficulty": "medium", "final_answer": {"answer": 0.1569, "unit": "state_units"}, "id": "euler_decay_007371_61.5_0.28_1.4_12", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.28 y with y(0)=61.5, step size h=1.4, for 12 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.28 y, so each step multiplies y by 1 - h*0.28.\nApply that update for 12 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 61.5, "rate": 0.28, "step": 1.4, "steps": 12}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-1.6)=-4.12 and f(3.4)=4.38.\n3. The interval width is 5.\nFinal: {\"answer\": 0.65, \"unit\": \"area_units\"}", "dedupe_signature": "f2b181dfe8bd445b3bd6ff010727ab0f522d5d899c95df276c552a0862428a98", "difficulty": "medium", "final_answer": {"answer": 0.65, "unit": "area_units"}, "id": "trapz_linear_007372_1.7_-1.4_-1.6_3.4", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=1.7x+-1.4 from x=-1.6 to x=3.4. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-1.6)=-4.12 and f(3.4)=4.38.\nThe interval width is 5.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -1.4, "slope": 1.7, "x0": -1.6, "x1": 3.4}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 15944.0 / 1000.\nFinal: {\"answer\": 15.944, \"unit\": \"kg\"}", "dedupe_signature": "068341afb676e113348e00e722ce41c730f94ee0caf1c42b6efa7bc789dd00eb", "difficulty": "easy", "final_answer": {"answer": 15.944, "unit": "kg"}, "id": "unit_convert_007374_g_to_kg_15944", "license": "Apache-2.0", "prompt": "Convert 15944 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 15944.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 15944.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=174 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-475.3815, 49.9646], \"unit\": \"N\"}", "dedupe_signature": "2bcf7c12560e943247b1d90c0d38d91663b68bdc8cfc4785451a394a6e400cb1", "difficulty": "medium", "final_answer": {"answer": [-475.3815, 49.9646], "unit": "N"}, "id": "vector_components_007375_478_174", "license": "Apache-2.0", "prompt": "A vector has magnitude 478 N at 174 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=174 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 174, "magnitude": 478.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-6.25, 8.5], \"unit\": \"dimensionless\"}", "dedupe_signature": "eb48d926f67f19c1eee0295088f3d3b9b2d41335241b2471958794083af15714", "difficulty": "medium", "final_answer": {"answer": [-6.25, 8.5], "unit": "dimensionless"}, "id": "line_two_point_007376_-4.75_3.75_-6.25_8.5", "license": "Apache-2.0", "prompt": "A line passes through points (-4.75, 38.1875) and (3.75, -14.9375). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -4.75, "x2": 3.75, "y1": 38.1875, "y2": -14.9375}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. amount times volume is not concentration\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "f8d93740ce459fb3f812032981f33bda53581ddcfacf2390e6e82285c6a983e8", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_007377_inconsistent_74ac0b02_675143", "license": "Apache-2.0", "prompt": "In student derivation case 675143, check dimensional consistency for C = n * V. The left side has dimensions mol/L and the right side has dimensions mol*L. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\namount times volume is not concentration\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "C = n * V"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef running_total_007378(values):\n    total = 0\n    out = []\n    for value in values:\n        total += value\n        out.append(total)\n    return out\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"running_total_007378\"}", "dedupe_signature": "91580f0c27c360495735c6ced6d1fb7cbdb0fc8a177cd36bb93d235397ec0a59", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "running_total_007378"}, "id": "code_007378_running_total_007378", "license": "Apache-2.0", "prompt": "Write a Python function running_total_007378(values) that returns cumulative sums as a new list. It must not mutate the input list. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "running_total_007378"}, "verifier": {"function": "running_total_007378", "tests": ["assert running_total_007378([1, 2, 3]) == [1, 3, 6]", "xs = [4, -1, 2]; assert running_total_007378(xs) == [4, 3, 5] and xs == [4, -1, 2]", "assert running_total_007378([]) == []"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: launch_angle_or_vertical_velocity.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"launch_angle_or_vertical_velocity\"]}", "dedupe_signature": "69b3459e4b9b966fd53884874adc26fc44c5e5a448db8619212730e3577c27eb", "difficulty": "easy", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["launch_angle_or_vertical_velocity"]}, "id": "abstain_007379_launch_angle_or_vertical_velocity", "license": "Apache-2.0", "prompt": "Compute projectile range on level ground. The prompt gives initial speed 17.3 m/s but does not give launch angle or vertical velocity. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: launch_angle_or_vertical_velocity.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["launch_angle_or_vertical_velocity"]}, "verifier": {"missing": ["launch_angle_or_vertical_velocity"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 13.2 kg and a = 0.8 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 10.56, \"unit\": \"N\"}", "dedupe_signature": "2fd121baf33580b2175d8aa8acc9e554b609993bd880be6df1d127ff8cf14666", "difficulty": "easy", "final_answer": {"answer": 10.56, "unit": "N"}, "id": "force_007380_13.2_0.8", "license": "Apache-2.0", "prompt": "A cart has mass 13.2 kg and measured acceleration 0.8 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 13.2 kg and a = 0.8 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 0.8, "mass": 13.2}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 15.85^2 and multiply by 0.5 * 11.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 1381.7237, \"unit\": \"J\"}", "dedupe_signature": "9442e7915f7c84ea287b5e3792aae4781d481506cd5bd1240e9c68cd59b65882", "difficulty": "easy", "final_answer": {"answer": 1381.7237, "unit": "J"}, "id": "ke_007381_11_15.85", "license": "Apache-2.0", "prompt": "A body of mass 11 kg moves at 15.85 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 15.85^2 and multiply by 0.5 * 11.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 11.0, "velocity": 15.85}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=29 degrees through the sine of 2 theta.\n3. Substitute v=21.6 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 40.3329, \"unit\": \"m\"}", "dedupe_signature": "e50500d6069c1589913ab37125388036144e0527d57babd6753b6f97df41b115", "difficulty": "medium", "final_answer": {"answer": 40.3329, "unit": "m"}, "id": "projectile_range_007382_21.6_29", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 21.6 m/s and angle 29 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=29 degrees through the sine of 2 theta.\nSubstitute v=21.6 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 29, "gravity": 9.81, "speed": 21.6}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 5.68 * 8.314 * 416 / 107.0.\nFinal: {\"answer\": 183.598, \"unit\": \"kPa\"}", "dedupe_signature": "718d76586de46402cac5ecb03b87a3380dd34cea7a3e014498be39af8d62c0de", "difficulty": "medium", "final_answer": {"answer": 183.598, "unit": "kPa"}, "id": "ideal_gas_007383_5.68_416_107.0", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=5.68 mol, T=416 K, and V=107.0 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 5.68 * 8.314 * 416 / 107.0.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 5.68, "temp_k": 416, "volume_l": 107.0}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 825 * 3.93 * 82.\nFinal: {\"answer\": 265864.5, \"unit\": \"J\"}", "dedupe_signature": "d2f6cf4300eb642e5bc3a418e87885d9d34b8331d658ed5f2ab8d54363372e5e", "difficulty": "easy", "final_answer": {"answer": 265864.5, "unit": "J"}, "id": "heat_q_007384_825_3.93_82", "license": "Apache-2.0", "prompt": "A 825 g sample has specific heat 3.93 J/(g*K). How much heat is needed to raise its temperature by 82 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 825 * 3.93 * 82.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 82, "heat_capacity": 3.93, "mass_g": 825}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=122.4 V and R=138.3 ohm.\nFinal: {\"answer\": 108.328, \"unit\": \"W\"}", "dedupe_signature": "22f0f1d60b0275654831459ff6113a0d0e8d2489a0341c6657e5f20104a25c56", "difficulty": "easy", "final_answer": {"answer": 108.328, "unit": "W"}, "id": "ohm_power_007385_122.4_138.3", "license": "Apache-2.0", "prompt": "A resistor has resistance 138.3 ohm and voltage 122.4 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=122.4 V and R=138.3 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 138.3, "voltage": 122.4}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=613 mg, t=56 h, and T_half=39.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 229.4477, \"unit\": \"mg\"}", "dedupe_signature": "1d419753f1535acdcca95b5f690434e5ab898dc4cdbb0b266588f076d98e68e3", "difficulty": "medium", "final_answer": {"answer": 229.4477, "unit": "mg"}, "id": "half_life_007386_613_39.5_56", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 613 mg. Its half-life is 39.5 hours. How many mg remain after 56 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=613 mg, t=56 h, and T_half=39.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 56.0, "half_life": 39.5, "initial_amount": 613.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 0.06 mol * 58.44 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 3.5064, \"unit\": \"g\"}", "dedupe_signature": "6225f92dd383430cc382eb7c1b33749708267ac3e19363a1463755f87ecd2333", "difficulty": "medium", "final_answer": {"answer": 3.5064, "unit": "g"}, "id": "stoich_mass_007387_sodium_chloride_0.06", "license": "Apache-2.0", "prompt": "A sample contains 0.06 mol of sodium chloride. Using molar mass 58.44 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 0.06 mol * 58.44 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "sodium chloride", "molar_mass": 58.44, "moles": 0.06}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(1.7)=11.23 and f(3.4)=14.46.\n3. The interval width is 1.7.\nFinal: {\"answer\": 21.8365, \"unit\": \"area_units\"}", "dedupe_signature": "605af40b82ded27867b67c1fda13f1f526976dddfb409442eece57ec0184adda", "difficulty": "medium", "final_answer": {"answer": 21.8365, "unit": "area_units"}, "id": "trapz_linear_007390_1.9_8_1.7_3.4", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=1.9x+8 from x=1.7 to x=3.4. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(1.7)=11.23 and f(3.4)=14.46.\nThe interval width is 1.7.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 8.0, "slope": 1.9, "x0": 1.7, "x1": 3.4}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.12 and add it to the current value.\nFinal: {\"answer\": [1.208, 0.888, -0.398], \"unit\": \"temperature_units\"}", "dedupe_signature": "6c1502d4770e13310d491a94c16172a5e5a2c62874005579192f6366f0797b9f", "difficulty": "hard", "final_answer": {"answer": [1.208, 0.888, -0.398], "unit": "temperature_units"}, "id": "heat_step_007391_0.12_0.15_1.4_1.05_-0.65_-0.25", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=0.15, right=-0.25; current interior values are [1.4, 1.05, -0.65]. Use r=0.12. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.12 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [1.4, 1.05, -0.65], "left": 0.15, "r": 0.12, "right": -0.25}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 100 centimeters in one meter.\n2. Apply the conversion factor directly to the given value.\n3. Compute 780.5 / 100.\nFinal: {\"answer\": 7.805, \"unit\": \"m\"}", "dedupe_signature": "9d624bce1046ef497b0d8721e756f80094b652b798a1cd9ba4244c6d2ae2bee9", "difficulty": "easy", "final_answer": {"answer": 7.805, "unit": "m"}, "id": "unit_convert_007392_cm_to_m_780.5", "license": "Apache-2.0", "prompt": "Convert 780.5 cm to m. Return the converted value with unit.", "reasoning_trace": "There are 100 centimeters in one meter.\nApply the conversion factor directly to the given value.\nCompute 780.5 / 100.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 780.5}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=166 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-448.2766, 111.7679], \"unit\": \"N\"}", "dedupe_signature": "93814a25e3375d2a89dff3d7bd8ec509910f4e85f6b1c55f20f1390753dc02eb", "difficulty": "medium", "final_answer": {"answer": [-448.2766, 111.7679], "unit": "N"}, "id": "vector_components_007393_462_166", "license": "Apache-2.0", "prompt": "A vector has magnitude 462 N at 166 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=166 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 166, "magnitude": 462.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. lever arm times force has torque dimensions\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "904e7cece28825fea60c8da1da7e51b81666d4b735fea7b10c33b3117ae426de", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_007395_consistent_5ca82cb9_112415", "license": "Apache-2.0", "prompt": "In field worksheet case 112415, check dimensional consistency for tau = r * F. The left side has dimensions N*m and the right side has dimensions N*m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nlever arm times force has torque dimensions\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "tau = r * F"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: target_schema, valid_examples.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"target_schema\", \"valid_examples\"]}", "dedupe_signature": "85e56a022b72c22f55d1606e4261f379fd7c5c911ba48ea6562ed97958b9e8de", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["target_schema", "valid_examples"]}, "id": "abstain_007397_target_schema_valid_examples", "license": "Apache-2.0", "prompt": "Write a parser that converts each laboratory clinical record from batch 404925 into the correct schema, but the prompt does not include the target schema or examples. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: target_schema, valid_examples.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["target_schema", "valid_examples"]}, "verifier": {"missing": ["target_schema", "valid_examples"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 22 kg and a = 0.85 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 18.7, \"unit\": \"N\"}", "dedupe_signature": "d2ac45a8203ae372ef9c016dd5600c41871b9e2e1abb50b7ccda2263137fe204", "difficulty": "easy", "final_answer": {"answer": 18.7, "unit": "N"}, "id": "force_007398_22_0.85", "license": "Apache-2.0", "prompt": "A cart has mass 22 kg and measured acceleration 0.85 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 22 kg and a = 0.85 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 0.85, "mass": 22.0}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 39.8^2 and multiply by 0.5 * 5.15.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 4078.903, \"unit\": \"J\"}", "dedupe_signature": "47d23d29d6df1875cfe17529ede25ed0f4bf53e03a1d466c322fbe648ad07bc3", "difficulty": "easy", "final_answer": {"answer": 4078.903, "unit": "J"}, "id": "ke_007399_5.15_39.8", "license": "Apache-2.0", "prompt": "A body of mass 5.15 kg moves at 39.8 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 39.8^2 and multiply by 0.5 * 5.15.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 5.15, "velocity": 39.8}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=49 degrees through the sine of 2 theta.\n3. Substitute v=29.3 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 86.6601, \"unit\": \"m\"}", "dedupe_signature": "70293fd971ca7b02af282fe19809fa3654d9deb7e19c80ae5dd16f2223217d31", "difficulty": "medium", "final_answer": {"answer": 86.6601, "unit": "m"}, "id": "projectile_range_007400_29.3_49", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 29.3 m/s and angle 49 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=49 degrees through the sine of 2 theta.\nSubstitute v=29.3 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 49, "gravity": 9.81, "speed": 29.3}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=48.9 V and R=66 ohm.\nFinal: {\"answer\": 36.2305, \"unit\": \"W\"}", "dedupe_signature": "9e714eb75f985968c1bcab647eed0f2859ee655cacbc0a32732112f388c93d0c", "difficulty": "easy", "final_answer": {"answer": 36.2305, "unit": "W"}, "id": "ohm_power_007403_48.9_66", "license": "Apache-2.0", "prompt": "A resistor has resistance 66 ohm and voltage 48.9 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=48.9 V and R=66 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 66.0, "voltage": 48.9}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=558.5 mg, t=301.5 h, and T_half=69.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 27.6132, \"unit\": \"mg\"}", "dedupe_signature": "e454171bc7763b045ec9dd15ce401c678c0dc6fb9aac248a272e6f3d61c3b76a", "difficulty": "medium", "final_answer": {"answer": 27.6132, "unit": "mg"}, "id": "half_life_007404_558.5_69.5_301.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 558.5 mg. Its half-life is 69.5 hours. How many mg remain after 301.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=558.5 mg, t=301.5 h, and T_half=69.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 301.5, "half_life": 69.5, "initial_amount": 558.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 5.08 mol * 180.156 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 915.1925, \"unit\": \"g\"}", "dedupe_signature": "b21838067c7f7a29f00b1d1705d85d53a9d1b9aeaedf5a5af5d6a9ae60527fed", "difficulty": "medium", "final_answer": {"answer": 915.1925, "unit": "g"}, "id": "stoich_mass_007405_glucose_5.08", "license": "Apache-2.0", "prompt": "A sample contains 5.08 mol of glucose. Using molar mass 180.156 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 5.08 mol * 180.156 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "glucose", "molar_mass": 180.156, "moles": 5.08}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 2940 mL to 2.94 L.\n3. Compute M = 4.13 / 2.94.\nFinal: {\"answer\": 1.4048, \"unit\": \"mol/L\"}", "dedupe_signature": "d3984a5dc0090075e09770f98dcb8156f0d5e51150870aa60f99a23cc831014b", "difficulty": "medium", "final_answer": {"answer": 1.4048, "unit": "mol/L"}, "id": "molarity_007406_4.13_2940", "license": "Apache-2.0", "prompt": "A solution contains 4.13 mol of solute in 2940 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 2940 mL to 2.94 L.\nCompute M = 4.13 / 2.94.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 4.13, "volume_ml": 2940}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.42 y, so each step multiplies y by 1 - h*0.42.\n3. Apply that update for 8 steps and round the final state.\nFinal: {\"answer\": 0.0772, \"unit\": \"state_units\"}", "dedupe_signature": "ecd857355b2b6fc8f325d3c7e394a2da411634b93fdbfa899ad202641a8bbcb4", "difficulty": "medium", "final_answer": {"answer": 0.0772, "unit": "state_units"}, "id": "euler_decay_007407_11_0.42_1.1_8", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.42 y with y(0)=11, step size h=1.1, for 8 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.42 y, so each step multiplies y by 1 - h*0.42.\nApply that update for 8 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 11.0, "rate": 0.42, "step": 1.1, "steps": 8}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(7.8)=42.3 and f(10.4)=61.8.\n3. The interval width is 2.6.\nFinal: {\"answer\": 135.33, \"unit\": \"area_units\"}", "dedupe_signature": "aa2ff5e1cf54b65a3d6a02a1e106e1d8cd1331fdd246ddde8f85a4c8c35eb9c6", "difficulty": "medium", "final_answer": {"answer": 135.33, "unit": "area_units"}, "id": "trapz_linear_007408_7.5_-16.2_7.8_10.4", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=7.5x+-16.2 from x=7.8 to x=10.4. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(7.8)=42.3 and f(10.4)=61.8.\nThe interval width is 2.6.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -16.2, "slope": 7.5, "x0": 7.8, "x1": 10.4}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.32 and add it to the current value.\nFinal: {\"answer\": [-0.286, -0.196, -0.672], \"unit\": \"temperature_units\"}", "dedupe_signature": "a50ee9d504cc50c5afd2ae3b5f169fe4769f0cb0a938f16d30a6ee4a444fe30d", "difficulty": "hard", "final_answer": {"answer": [-0.286, -0.196, -0.672], "unit": "temperature_units"}, "id": "heat_step_007409_0.32_-0.1_0.45_-1.3_0.4_-1.25", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-0.1, right=-1.25; current interior values are [0.45, -1.3, 0.4]. Use r=0.32. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.32 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [0.45, -1.3, 0.4], "left": -0.1, "r": 0.32, "right": -1.25}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 100 centimeters in one meter.\n2. Apply the conversion factor directly to the given value.\n3. Compute 551.5 / 100.\nFinal: {\"answer\": 5.515, \"unit\": \"m\"}", "dedupe_signature": "928e6c84c722affeab257c1b07905aa1058f012624195ad3623c8127bdc543f1", "difficulty": "easy", "final_answer": {"answer": 5.515, "unit": "m"}, "id": "unit_convert_007410_cm_to_m_551.5", "license": "Apache-2.0", "prompt": "Convert 551.5 cm to m. Return the converted value with unit.", "reasoning_trace": "There are 100 centimeters in one meter.\nApply the conversion factor directly to the given value.\nCompute 551.5 / 100.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 551.5}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=102 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-96.0552, 451.9042], \"unit\": \"N\"}", "dedupe_signature": "f1548d638936f3aa961c95583fbdeede36c539a534c4d74550906a304a301a37", "difficulty": "medium", "final_answer": {"answer": [-96.0552, 451.9042], "unit": "N"}, "id": "vector_components_007411_462_102", "license": "Apache-2.0", "prompt": "A vector has magnitude 462 N at 102 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=102 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 102, "magnitude": 462.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [2.35, -5.25], \"unit\": \"dimensionless\"}", "dedupe_signature": "d91aed6c334f0803dfed960bbe58550daf7991ab503c93932b7039cbbfbc77e1", "difficulty": "medium", "final_answer": {"answer": [2.35, -5.25], "unit": "dimensionless"}, "id": "line_two_point_007412_-20_-11.5_2.35_-5.25", "license": "Apache-2.0", "prompt": "A line passes through points (-20, -52.25) and (-11.5, -32.275). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -20.0, "x2": -11.5, "y1": -52.25, "y2": -32.275000000000006}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. m*v is momentum, not energy\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "8794e515a5647c912bc9862ea7d837edfcde1d44afa97a35af869313ce073ea1", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_007413_inconsistent_1e14b074_563403", "license": "Apache-2.0", "prompt": "In sensor calibration case 563403, check dimensional consistency for E = m * v. The left side has dimensions kg*m^2/s^2 and the right side has dimensions kg*m/s. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nm*v is momentum, not energy\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "E = m * v"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: launch_angle_or_vertical_velocity.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"launch_angle_or_vertical_velocity\"]}", "dedupe_signature": "1d3a665a89a45ffaea960424a7f196ddb900a77775b44d4f65a8176cdfa5115f", "difficulty": "easy", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["launch_angle_or_vertical_velocity"]}, "id": "abstain_007415_launch_angle_or_vertical_velocity", "license": "Apache-2.0", "prompt": "Compute projectile range on level ground. The prompt gives initial speed 38.6 m/s but does not give launch angle or vertical velocity. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: launch_angle_or_vertical_velocity.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["launch_angle_or_vertical_velocity"]}, "verifier": {"missing": ["launch_angle_or_vertical_velocity"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 0.55 kg and a = 1.8 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 0.99, \"unit\": \"N\"}", "dedupe_signature": "bf5c6457c65768067bdc565c2a5db630304fad8b5ed66537f917176afd101515", "difficulty": "easy", "final_answer": {"answer": 0.99, "unit": "N"}, "id": "force_007416_0.55_1.8", "license": "Apache-2.0", "prompt": "A cart has mass 0.55 kg and measured acceleration 1.8 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 0.55 kg and a = 1.8 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 1.8, "mass": 0.55}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 10.7^2 and multiply by 0.5 * 7.35.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 420.7507, \"unit\": \"J\"}", "dedupe_signature": "e4253b4781cff946360f478cf233c55427b2707e6020f32df6e22acc693e7dba", "difficulty": "easy", "final_answer": {"answer": 420.7507, "unit": "J"}, "id": "ke_007417_7.35_10.7", "license": "Apache-2.0", "prompt": "A body of mass 7.35 kg moves at 10.7 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 10.7^2 and multiply by 0.5 * 7.35.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 7.35, "velocity": 10.7}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=75 degrees through the sine of 2 theta.\n3. Substitute v=31.3 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 49.9332, \"unit\": \"m\"}", "dedupe_signature": "a86ec3321723f8958bd6ddb78f1b68bf4ba529ab1ee683614047e3cb72ac6b4f", "difficulty": "medium", "final_answer": {"answer": 49.9332, "unit": "m"}, "id": "projectile_range_007418_31.3_75", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 31.3 m/s and angle 75 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=75 degrees through the sine of 2 theta.\nSubstitute v=31.3 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 75, "gravity": 9.81, "speed": 31.3}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 560 * 0.515 * 95.\nFinal: {\"answer\": 27398.0, \"unit\": \"J\"}", "dedupe_signature": "50c8b88e564370ea5b54fbe32df35e9c8559a0494a0919df90bd11d22f433e47", "difficulty": "easy", "final_answer": {"answer": 27398.0, "unit": "J"}, "id": "heat_q_007420_560_0.515_95", "license": "Apache-2.0", "prompt": "A 560 g sample has specific heat 0.515 J/(g*K). How much heat is needed to raise its temperature by 95 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 560 * 0.515 * 95.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 95, "heat_capacity": 0.515, "mass_g": 560}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=109.3 V and R=178.6 ohm.\nFinal: {\"answer\": 66.8896, \"unit\": \"W\"}", "dedupe_signature": "74e5cc220e87394c063f13c794dfae014344ae3fb235197c99309112ee61e870", "difficulty": "easy", "final_answer": {"answer": 66.8896, "unit": "W"}, "id": "ohm_power_007421_109.3_178.6", "license": "Apache-2.0", "prompt": "A resistor has resistance 178.6 ohm and voltage 109.3 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=109.3 V and R=178.6 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 178.6, "voltage": 109.3}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 4 mol * 100.087 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 400.348, \"unit\": \"g\"}", "dedupe_signature": "724d7036b2566ff116fbf885c47aeb138088156f40c987463c0c35f85ff07fd0", "difficulty": "medium", "final_answer": {"answer": 400.348, "unit": "g"}, "id": "stoich_mass_007423_calcium_carbonate_4", "license": "Apache-2.0", "prompt": "A sample contains 4 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 4 mol * 100.087 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "calcium carbonate", "molar_mass": 100.087, "moles": 4.0}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.68 y, so each step multiplies y by 1 - h*0.68.\n3. Apply that update for 7 steps and round the final state.\nFinal: {\"answer\": -0.0096, \"unit\": \"state_units\"}", "dedupe_signature": "d83f1e5e078f6d43446cb7dd07eb1ed54921361d5597c2f494a23712772566bc", "difficulty": "medium", "final_answer": {"answer": -0.0096, "unit": "state_units"}, "id": "euler_decay_007425_53_0.68_1.9_7", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.68 y with y(0)=53, step size h=1.9, for 7 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.68 y, so each step multiplies y by 1 - h*0.68.\nApply that update for 7 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 53.0, "rate": 0.68, "step": 1.9, "steps": 7}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-3.2)=3.92 and f(6)=-38.4.\n3. The interval width is 9.2.\nFinal: {\"answer\": -158.608, \"unit\": \"area_units\"}", "dedupe_signature": "5ed090f50045c57127aefbeea25510ac4dead115fb0fc8c6f35c9c06fb066377", "difficulty": "medium", "final_answer": {"answer": -158.608, "unit": "area_units"}, "id": "trapz_linear_007426_-4.6_-10.8_-3.2_6", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-4.6x+-10.8 from x=-3.2 to x=6. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-3.2)=3.92 and f(6)=-38.4.\nThe interval width is 9.2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -10.8, "slope": -4.6, "x0": -3.2, "x1": 5.999999999999999}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.42 and add it to the current value.\nFinal: {\"answer\": [-0.389, -0.684, -0.17], \"unit\": \"temperature_units\"}", "dedupe_signature": "78b1241316df96242bd8028f2009bd4f1252352705e989fe6f1af5af2e144fcb", "difficulty": "hard", "final_answer": {"answer": [-0.389, -0.684, -0.17], "unit": "temperature_units"}, "id": "heat_step_007427_0.42_0.4_0.85_-1.65_-1.85_1.95", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=0.4, right=1.95; current interior values are [0.85, -1.65, -1.85]. Use r=0.42. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.42 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [0.85, -1.65, -1.85], "left": 0.4, "r": 0.42, "right": 1.95}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kelvin equals Celsius plus 273.15.\n2. Apply the conversion factor directly to the given value.\n3. Compute 55.0 + 273.15.\nFinal: {\"answer\": 328.15, \"unit\": \"K\"}", "dedupe_signature": "3fe0d04f040876e08e0c057ec68c2914c6b590cc65be017e40e8e0170448b667", "difficulty": "easy", "final_answer": {"answer": 328.15, "unit": "K"}, "id": "unit_convert_007428_c_to_k_55", "license": "Apache-2.0", "prompt": "Convert 55 degC to K. Return the converted value with unit.", "reasoning_trace": "Kelvin equals Celsius plus 273.15.\nApply the conversion factor directly to the given value.\nCompute 55.0 + 273.15.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 55.0}, "verifier": {"formula": "value + 273.15", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=64 degrees and keep the unit as newtons.\nFinal: {\"answer\": [117.9218, 241.7756], \"unit\": \"N\"}", "dedupe_signature": "c2b1568a5607b36c30c88c07a2391a11991c6ae23b477338e08fa81c1333ef78", "difficulty": "medium", "final_answer": {"answer": [117.9218, 241.7756], "unit": "N"}, "id": "vector_components_007429_269_64", "license": "Apache-2.0", "prompt": "A vector has magnitude 269 N at 64 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=64 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 64, "magnitude": 269.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-10.0, -17.0], \"unit\": \"dimensionless\"}", "dedupe_signature": "b99de1b264376a669fa9f3f599c5a2d56c24fba9c8323bb093751dc24d57d5f5", "difficulty": "medium", "final_answer": {"answer": [-10.0, -17.0], "unit": "dimensionless"}, "id": "line_two_point_007430_1.5_4.25_-10_-17", "license": "Apache-2.0", "prompt": "A line passes through points (1.5, -32) and (4.25, -59.5). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 1.5, "x2": 4.25, "y1": -32.0, "y2": -59.5}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. speed squared over acceleration has units of meters\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "35b125761637e1368ff75734b55260459c5b66db5f775059fbefcbd3a2d666c3", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_007431_consistent_741d4e34_538333", "license": "Apache-2.0", "prompt": "In instrument manual case 538333, check dimensional consistency for R = v^2 * sin(theta) / g. The left side has dimensions m and the right side has dimensions m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nspeed squared over acceleration has units of meters\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "R = v^2 * sin(theta) / g"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef weighted_sum_007432(values, weights):\n    if len(values) != len(weights):\n        raise ValueError('length mismatch')\n    return sum(value * weight for value, weight in zip(values, weights))\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"weighted_sum_007432\"}", "dedupe_signature": "b8614a6341d645522d643de55d0c4180664c25bb11e112ae293bcc68c41bb4a1", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "weighted_sum_007432"}, "id": "code_007432_weighted_sum_007432", "license": "Apache-2.0", "prompt": "Write a Python function weighted_sum_007432(values, weights) that returns sum(value*weight). Raise ValueError when the two inputs have different lengths. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "weighted_sum_007432"}, "verifier": {"function": "weighted_sum_007432", "tests": ["assert weighted_sum_007432([2, 3], [4, 5]) == 23", "assert weighted_sum_007432([], []) == 0", "try:\n    weighted_sum_007432([1], [1, 2])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: volume.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"volume\"]}", "dedupe_signature": "31b700a68743883fee3e613b0d4edcf41e30d0e9b627ab645e23b41fdc48311e", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["volume"]}, "id": "abstain_007433_volume", "license": "Apache-2.0", "prompt": "Compute pressure from the ideal gas law. The prompt gives n=4.62 mol and T=607 K, but does not give volume. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: volume.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["volume"]}, "verifier": {"missing": ["volume"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 3.75 kg and a = 8.95 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 33.5625, \"unit\": \"N\"}", "dedupe_signature": "a7a60203d86703318e358feb97ccbc3b3428455563b1a4e50ec09b0f363b4a78", "difficulty": "easy", "final_answer": {"answer": 33.5625, "unit": "N"}, "id": "force_007434_3.75_8.95", "license": "Apache-2.0", "prompt": "A cart has mass 3.75 kg and measured acceleration 8.95 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 3.75 kg and a = 8.95 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 8.95, "mass": 3.75}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=11 degrees through the sine of 2 theta.\n3. Substitute v=39 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 58.0812, \"unit\": \"m\"}", "dedupe_signature": "dae9843f02a7057d8cf90f523f38f3f94299e23945456d239d9bce647c03bc04", "difficulty": "medium", "final_answer": {"answer": 58.0812, "unit": "m"}, "id": "projectile_range_007436_39_11", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 39 m/s and angle 11 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=11 degrees through the sine of 2 theta.\nSubstitute v=39 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 11, "gravity": 9.81, "speed": 39.0}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 3.4 * 8.314 * 584 / 79.9.\nFinal: {\"answer\": 206.6117, \"unit\": \"kPa\"}", "dedupe_signature": "994c025b4d6e97d40735063c4087c28d03c3f37d69c19ae34ec14288d4135d6e", "difficulty": "medium", "final_answer": {"answer": 206.6117, "unit": "kPa"}, "id": "ideal_gas_007437_3.4_584_79.9", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=3.4 mol, T=584 K, and V=79.9 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 3.4 * 8.314 * 584 / 79.9.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 3.4, "temp_k": 584, "volume_l": 79.9}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 165 * 1.82 * 43.\nFinal: {\"answer\": 12912.9, \"unit\": \"J\"}", "dedupe_signature": "bd64c960862bd0aa31f6bc99cf8c28d1fcb1778c0a9c0a3cbd118e80de2165fb", "difficulty": "easy", "final_answer": {"answer": 12912.9, "unit": "J"}, "id": "heat_q_007438_165_1.82_43", "license": "Apache-2.0", "prompt": "A 165 g sample has specific heat 1.82 J/(g*K). How much heat is needed to raise its temperature by 43 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 165 * 1.82 * 43.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 43, "heat_capacity": 1.82, "mass_g": 165}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=171.3 V and R=71.8 ohm.\nFinal: {\"answer\": 408.6865, \"unit\": \"W\"}", "dedupe_signature": "b638e4a2f955238fd022f959ea316b92c1e2a03f27e29f9e910025c5877e60a9", "difficulty": "easy", "final_answer": {"answer": 408.6865, "unit": "W"}, "id": "ohm_power_007439_171.3_71.8", "license": "Apache-2.0", "prompt": "A resistor has resistance 71.8 ohm and voltage 171.3 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=171.3 V and R=71.8 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 71.8, "voltage": 171.3}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=467.5 mg, t=294 h, and T_half=46 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 5.5694, \"unit\": \"mg\"}", "dedupe_signature": "7b10a773b63ebf61474544911eb802dd280595ba5bf048eeb50cf2e41582cf71", "difficulty": "medium", "final_answer": {"answer": 5.5694, "unit": "mg"}, "id": "half_life_007440_467.5_46_294", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 467.5 mg. Its half-life is 46 hours. How many mg remain after 294 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=467.5 mg, t=294 h, and T_half=46 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 294.0, "half_life": 46.0, "initial_amount": 467.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.74 y, so each step multiplies y by 1 - h*0.74.\n3. Apply that update for 9 steps and round the final state.\nFinal: {\"answer\": 1.2116, \"unit\": \"state_units\"}", "dedupe_signature": "5fcc807e540db7b73d46e8c5649b9c66b7f38ce1e6569c2cb93b65e8908a4ee1", "difficulty": "medium", "final_answer": {"answer": 1.2116, "unit": "state_units"}, "id": "euler_decay_007443_77.5_0.74_0.5_9", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.74 y with y(0)=77.5, step size h=0.5, for 9 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.74 y, so each step multiplies y by 1 - h*0.74.\nApply that update for 9 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 77.5, "rate": 0.74, "step": 0.5, "steps": 9}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(0.5)=6.9 and f(5.6)=-0.24.\n3. The interval width is 5.1.\nFinal: {\"answer\": 16.983, \"unit\": \"area_units\"}", "dedupe_signature": "b89ee7f6c8e39f68efead5382de89c23ca04c988940d75fb98eba85b74c6673a", "difficulty": "medium", "final_answer": {"answer": 16.983, "unit": "area_units"}, "id": "trapz_linear_007444_-1.4_7.6_0.5_5.6", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-1.4x+7.6 from x=0.5 to x=5.6. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(0.5)=6.9 and f(5.6)=-0.24.\nThe interval width is 5.1.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 7.6, "slope": -1.4, "x0": 0.5, "x1": 5.6}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.38 and add it to the current value.\nFinal: {\"answer\": [0.515, 0.712, 1.105], \"unit\": \"temperature_units\"}", "dedupe_signature": "d5355e31123ae22fa6442cc4e71e796ed5ffe73d250c7d9899a5544918efeea9", "difficulty": "hard", "final_answer": {"answer": [0.515, 0.712, 1.105], "unit": "temperature_units"}, "id": "heat_step_007445_0.38_1.05_0.8_-0.2_1.2_2.35", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.05, right=2.35; current interior values are [0.8, -0.2, 1.2]. Use r=0.38. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.38 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [0.8, -0.2, 1.2], "left": 1.05, "r": 0.38, "right": 2.35}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 100 centimeters in one meter.\n2. Apply the conversion factor directly to the given value.\n3. Compute 4159.0 / 100.\nFinal: {\"answer\": 41.59, \"unit\": \"m\"}", "dedupe_signature": "f4c5c60c0b8b65ec535f69109bd31109b638130c7adacdb57f39be75a7266706", "difficulty": "easy", "final_answer": {"answer": 41.59, "unit": "m"}, "id": "unit_convert_007446_cm_to_m_4159", "license": "Apache-2.0", "prompt": "Convert 4159 cm to m. Return the converted value with unit.", "reasoning_trace": "There are 100 centimeters in one meter.\nApply the conversion factor directly to the given value.\nCompute 4159.0 / 100.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 4159.0}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=352 degrees and keep the unit as newtons.\nFinal: {\"answer\": [162.404, -22.8244], \"unit\": \"N\"}", "dedupe_signature": "3cae798364f76e6b18cbf1e1be819a9dfadd223f915b5a544bf8b32ab340cedf", "difficulty": "medium", "final_answer": {"answer": [162.404, -22.8244], "unit": "N"}, "id": "vector_components_007447_164_352", "license": "Apache-2.0", "prompt": "A vector has magnitude 164 N at 352 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=352 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 352, "magnitude": 164.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. lever arm times force has torque dimensions\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "46c2769a0cd0aed853b0edeec2a7d1e391e6d12b66745d2220cc184b67faa972", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_007449_consistent_5ca82cb9_466970", "license": "Apache-2.0", "prompt": "In sensor calibration case 466970, check dimensional consistency for tau = r * F. The left side has dimensions N*m and the right side has dimensions N*m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nlever arm times force has torque dimensions\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "tau = r * F"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef finite_differences_007450(values):\n    return [values[i + 1] - values[i] for i in range(len(values) - 1)]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"finite_differences_007450\"}", "dedupe_signature": "02b60428d9116cb763c7a087e817999e96b8e546d10a6be053cdbb9683d6d440", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "finite_differences_007450"}, "id": "code_007450_finite_differences_007450", "license": "Apache-2.0", "prompt": "Write a Python function finite_differences_007450(values) that returns the list of successive differences values[i+1] - values[i]. It must return [] for fewer than two values. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "finite_differences_007450"}, "verifier": {"function": "finite_differences_007450", "tests": ["assert finite_differences_007450([1, 4, 9, 16]) == [3, 5, 7]", "assert finite_differences_007450([5]) == []", "assert finite_differences_007450([]) == []"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: volume.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"volume\"]}", "dedupe_signature": "7383f4d5bfdd72cff3865a65f429ed490945e169843ea897a6f7b49c0158b4ed", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["volume"]}, "id": "abstain_007451_volume", "license": "Apache-2.0", "prompt": "Compute pressure from the ideal gas law. The prompt gives n=5.5 mol and T=397 K, but does not give volume. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: volume.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["volume"]}, "verifier": {"missing": ["volume"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 32.3^2 and multiply by 0.5 * 20.55.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 10719.8047, \"unit\": \"J\"}", "dedupe_signature": "9005f174ecce3a25376bf47afa3c265ee0fa60975cd70b586ac9bebf5d582270", "difficulty": "easy", "final_answer": {"answer": 10719.8047, "unit": "J"}, "id": "ke_007453_20.55_32.3", "license": "Apache-2.0", "prompt": "A body of mass 20.55 kg moves at 32.3 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 32.3^2 and multiply by 0.5 * 20.55.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 20.55, "velocity": 32.3}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=49 degrees through the sine of 2 theta.\n3. Substitute v=40.6 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 166.3933, \"unit\": \"m\"}", "dedupe_signature": "553a3a4bac2f37f787928690149ddee80d59fa2bed2b4c9b3a836eecdac30efb", "difficulty": "medium", "final_answer": {"answer": 166.3933, "unit": "m"}, "id": "projectile_range_007454_40.6_49", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 40.6 m/s and angle 49 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=49 degrees through the sine of 2 theta.\nSubstitute v=40.6 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 49, "gravity": 9.81, "speed": 40.6}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 1.05 * 8.314 * 488 / 9.9.\nFinal: {\"answer\": 430.3125, \"unit\": \"kPa\"}", "dedupe_signature": "2b76d0ac0540836046370cbac51a82a5a5255e905cc0c976ab7bfa304b022874", "difficulty": "medium", "final_answer": {"answer": 430.3125, "unit": "kPa"}, "id": "ideal_gas_007455_1.05_488_9.9", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=1.05 mol, T=488 K, and V=9.9 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 1.05 * 8.314 * 488 / 9.9.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 1.05, "temp_k": 488, "volume_l": 9.9}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1685 * 4.685 * 88.\nFinal: {\"answer\": 694691.8, \"unit\": \"J\"}", "dedupe_signature": "c0a0eae0f48df0e7561cba863a51baf721aecdb8d119dcea655bdab377f8347d", "difficulty": "easy", "final_answer": {"answer": 694691.8, "unit": "J"}, "id": "heat_q_007456_1685_4.685_88", "license": "Apache-2.0", "prompt": "A 1685 g sample has specific heat 4.685 J/(g*K). How much heat is needed to raise its temperature by 88 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1685 * 4.685 * 88.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 88, "heat_capacity": 4.685, "mass_g": 1685}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=691 mg, t=283 h, and T_half=46.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 10.1719, \"unit\": \"mg\"}", "dedupe_signature": "b396b4aa9ae3dbc21ca83810a945d869ddaf4f6f5ed9b670f20da8e575ec1ed2", "difficulty": "medium", "final_answer": {"answer": 10.1719, "unit": "mg"}, "id": "half_life_007458_691_46.5_283", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 691 mg. Its half-life is 46.5 hours. How many mg remain after 283 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=691 mg, t=283 h, and T_half=46.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 283.0, "half_life": 46.5, "initial_amount": 691.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 0.22 mol * 44.01 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 9.6822, \"unit\": \"g\"}", "dedupe_signature": "9b90b5ab1ebf742e16629e399d0b0970122cbd297d4261f966bc304bbf8373a2", "difficulty": "medium", "final_answer": {"answer": 9.6822, "unit": "g"}, "id": "stoich_mass_007459_carbon_dioxide_0.22", "license": "Apache-2.0", "prompt": "A sample contains 0.22 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 0.22 mol * 44.01 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "carbon dioxide", "molar_mass": 44.01, "moles": 0.22}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 4105 mL to 4.105 L.\n3. Compute M = 0.49 / 4.105.\nFinal: {\"answer\": 0.1194, \"unit\": \"mol/L\"}", "dedupe_signature": "698815d31c0bdde55c96747ae2f26bc38080b48875012b072c86df6b93e80b0d", "difficulty": "medium", "final_answer": {"answer": 0.1194, "unit": "mol/L"}, "id": "molarity_007460_0.49_4105", "license": "Apache-2.0", "prompt": "A solution contains 0.49 mol of solute in 4105 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 4105 mL to 4.105 L.\nCompute M = 0.49 / 4.105.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 0.49, "volume_ml": 4105}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -1 y, so each step multiplies y by 1 - h*1.\n3. Apply that update for 4 steps and round the final state.\nFinal: {\"answer\": 45.5, \"unit\": \"state_units\"}", "dedupe_signature": "2898925300049e3bec74bdabfcfa1f33a5262fabd4dd1e76ab0bfbc8142af218", "difficulty": "medium", "final_answer": {"answer": 45.5, "unit": "state_units"}, "id": "euler_decay_007461_45.5_1_2_4", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -1 y with y(0)=45.5, step size h=2, for 4 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -1 y, so each step multiplies y by 1 - h*1.\nApply that update for 4 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 45.5, "rate": 1.0, "step": 2.0, "steps": 4}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(6.6)=13.16 and f(8.1)=19.31.\n3. The interval width is 1.5.\nFinal: {\"answer\": 24.3525, \"unit\": \"area_units\"}", "dedupe_signature": "7c601f76fcb56f0b493f87e4f95361e375bb130db6c41c46b4413f296e53908d", "difficulty": "medium", "final_answer": {"answer": 24.3525, "unit": "area_units"}, "id": "trapz_linear_007462_4.1_-13.9_6.6_8.1", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=4.1x+-13.9 from x=6.6 to x=8.1. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(6.6)=13.16 and f(8.1)=19.31.\nThe interval width is 1.5.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -13.9, "slope": 4.1, "x0": 6.6, "x1": 8.1}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.18 and add it to the current value.\nFinal: {\"answer\": [0.602, -0.508, -0.753], \"unit\": \"temperature_units\"}", "dedupe_signature": "079009c77197687205586c4ec4dcb5d410d2db358a3c1c4a363379ec5bb7b3bd", "difficulty": "hard", "final_answer": {"answer": [0.602, -0.508, -0.753], "unit": "temperature_units"}, "id": "heat_step_007463_0.18_-1.85_1.7_-0.85_-1.5_2.0", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-1.85, right=2; current interior values are [1.7, -0.85, -1.5]. Use r=0.18. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.18 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [1.7, -0.85, -1.5], "left": -1.85, "r": 0.18, "right": 2.0}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. velocity times time gives distance, not acceleration\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "a6a6bda1a7f4b9828bfef97f8cbb84dcfc4db2743c72c0ac1d5085b7b96f2f79", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_007467_inconsistent_7481c798_733095", "license": "Apache-2.0", "prompt": "In field worksheet case 733095, check dimensional consistency for a = v * t. The left side has dimensions m/s^2 and the right side has dimensions m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nvelocity times time gives distance, not acceleration\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "a = v * t"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef pairwise_ratios_007468(numerators, denominators):\n    if len(numerators) != len(denominators):\n        raise ValueError('length mismatch')\n    out = []\n    for numerator, denominator in zip(numerators, denominators):\n        if denominator == 0:\n            raise ValueError('zero denominator')\n        out.append(numerator / denominator)\n    return out\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"pairwise_ratios_007468\"}", "dedupe_signature": "5a62e3254173b7f053b2493540730bf775e3c9e949c8972e4631f136206b0cbe", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "pairwise_ratios_007468"}, "id": "code_007468_pairwise_ratios_007468", "license": "Apache-2.0", "prompt": "Write a Python function pairwise_ratios_007468(numerators, denominators) that returns a list of n/d values. Raise ValueError if lengths differ or any denominator is zero. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "pairwise_ratios_007468"}, "verifier": {"function": "pairwise_ratios_007468", "tests": ["assert pairwise_ratios_007468([2, 9], [4, 3]) == [0.5, 3.0]", "try:\n    pairwise_ratios_007468([1], [0])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass", "try:\n    pairwise_ratios_007468([1, 2], [1])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: left_boundary, right_boundary.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"left_boundary\", \"right_boundary\"]}", "dedupe_signature": "b36364850952188fbbc898893996057ff6c4a079c583e4bd5f80eef3fd3b11d2", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["left_boundary", "right_boundary"]}, "id": "abstain_007469_left_boundary_right_boundary", "license": "Apache-2.0", "prompt": "Solve the 1D heat equation after one finite-difference step. The prompt gives r=0.48 and interior values [2.0, 0.5, -1.4], but gives no boundary values. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: left_boundary, right_boundary.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["left_boundary", "right_boundary"]}, "verifier": {"missing": ["left_boundary", "right_boundary"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 26.9^2 and multiply by 0.5 * 24.7.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 8936.5835, \"unit\": \"J\"}", "dedupe_signature": "981d8c7ec3375b6e1cda8de725c7474409b46c8e626fce146ba243ee5579887e", "difficulty": "easy", "final_answer": {"answer": 8936.5835, "unit": "J"}, "id": "ke_007471_24.7_26.9", "license": "Apache-2.0", "prompt": "A body of mass 24.7 kg moves at 26.9 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 26.9^2 and multiply by 0.5 * 24.7.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 24.7, "velocity": 26.9}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 2.45 * 8.314 * 611 / 52.2.\nFinal: {\"answer\": 238.4223, \"unit\": \"kPa\"}", "dedupe_signature": "e82ed2e650b6615431b75460f51763a24bb79812dcb8112857eeb74d509d81f6", "difficulty": "medium", "final_answer": {"answer": 238.4223, "unit": "kPa"}, "id": "ideal_gas_007473_2.45_611_52.2", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=2.45 mol, T=611 K, and V=52.2 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 2.45 * 8.314 * 611 / 52.2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 2.45, "temp_k": 611, "volume_l": 52.2}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1255 * 4.52 * 115.\nFinal: {\"answer\": 652349.0, \"unit\": \"J\"}", "dedupe_signature": "2c549d99d0a5e5fa0759485cd2d35a964c4455f45ab00e96aeb3b20cf9e86378", "difficulty": "easy", "final_answer": {"answer": 652349.0, "unit": "J"}, "id": "heat_q_007474_1255_4.52_115", "license": "Apache-2.0", "prompt": "A 1255 g sample has specific heat 4.52 J/(g*K). How much heat is needed to raise its temperature by 115 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1255 * 4.52 * 115.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 115, "heat_capacity": 4.52, "mass_g": 1255}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=218.6 V and R=8.3 ohm.\nFinal: {\"answer\": 5757.3446, \"unit\": \"W\"}", "dedupe_signature": "92943cda7c5b55099495cb8b1459615742a248d915e50061510df3c2d24c0ed4", "difficulty": "easy", "final_answer": {"answer": 5757.3446, "unit": "W"}, "id": "ohm_power_007475_218.6_8.3", "license": "Apache-2.0", "prompt": "A resistor has resistance 8.3 ohm and voltage 218.6 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=218.6 V and R=8.3 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 8.3, "voltage": 218.6}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=179.5 mg, t=21.5 h, and T_half=116 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 157.8593, \"unit\": \"mg\"}", "dedupe_signature": "32b481698af4d33b6f77a32c32123bbdb9a5b69f3a836de34f0d43738b9bbbd7", "difficulty": "medium", "final_answer": {"answer": 157.8593, "unit": "mg"}, "id": "half_life_007476_179.5_116_21.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 179.5 mg. Its half-life is 116 hours. How many mg remain after 21.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=179.5 mg, t=21.5 h, and T_half=116 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 21.5, "half_life": 116.0, "initial_amount": 179.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 1.79 mol * 100.087 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 179.1557, \"unit\": \"g\"}", "dedupe_signature": "f441c0627509b5d3ac3fcb326a14c7d80c44ff81c8c9a15943b1c35b35a3e5b4", "difficulty": "medium", "final_answer": {"answer": 179.1557, "unit": "g"}, "id": "stoich_mass_007477_calcium_carbonate_1.79", "license": "Apache-2.0", "prompt": "A sample contains 1.79 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 1.79 mol * 100.087 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "calcium carbonate", "molar_mass": 100.087, "moles": 1.79}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 2995 mL to 2.995 L.\n3. Compute M = 2.66 / 2.995.\nFinal: {\"answer\": 0.8881, \"unit\": \"mol/L\"}", "dedupe_signature": "4f261a5f1320f512983dc8b7c84167989f8bab931502e0b38f72e4daa5840e50", "difficulty": "medium", "final_answer": {"answer": 0.8881, "unit": "mol/L"}, "id": "molarity_007478_2.66_2995", "license": "Apache-2.0", "prompt": "A solution contains 2.66 mol of solute in 2995 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 2995 mL to 2.995 L.\nCompute M = 2.66 / 2.995.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 2.66, "volume_ml": 2995}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.28 y, so each step multiplies y by 1 - h*0.28.\n3. Apply that update for 7 steps and round the final state.\nFinal: {\"answer\": 0.1003, \"unit\": \"state_units\"}", "dedupe_signature": "0274dcd558bbe481e947af22b54510f63d698a1804303101d5158d4c18611df1", "difficulty": "medium", "final_answer": {"answer": 0.1003, "unit": "state_units"}, "id": "euler_decay_007479_1_0.28_1_7", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.28 y with y(0)=1, step size h=1, for 7 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.28 y, so each step multiplies y by 1 - h*0.28.\nApply that update for 7 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 1.0, "rate": 0.28, "step": 1.0, "steps": 7}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(0.7)=-20.64 and f(10.2)=-60.54.\n3. The interval width is 9.5.\nFinal: {\"answer\": -385.605, \"unit\": \"area_units\"}", "dedupe_signature": "bbacaba2f52d302adde72b00fdb1246da9dc811df6908a30ac6737c7f3448381", "difficulty": "medium", "final_answer": {"answer": -385.605, "unit": "area_units"}, "id": "trapz_linear_007480_-4.2_-17.7_0.7_10.2", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-4.2x+-17.7 from x=0.7 to x=10.2. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(0.7)=-20.64 and f(10.2)=-60.54.\nThe interval width is 9.5.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -17.7, "slope": -4.2, "x0": 0.7, "x1": 10.2}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.18 and add it to the current value.\nFinal: {\"answer\": [1.662, 0.87, 1.45], \"unit\": \"temperature_units\"}", "dedupe_signature": "2cc1caccbd776d014294c9f287971a7e033ad9aeef198e84ce5a3fb5486147bb", "difficulty": "hard", "final_answer": {"answer": [1.662, 0.87, 1.45], "unit": "temperature_units"}, "id": "heat_step_007481_0.18_2.15_1.95_0.15_2.35_-0.45", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=2.15, right=-0.45; current interior values are [1.95, 0.15, 2.35]. Use r=0.18. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.18 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [1.95, 0.15, 2.35], "left": 2.15, "r": 0.18, "right": -0.45}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 14172.0 / 1000.\nFinal: {\"answer\": 14.172, \"unit\": \"kg\"}", "dedupe_signature": "4adfed7efa3e5d2167cdecaebd296f101bcf5554a9ae2a09de02c26d59fa1143", "difficulty": "easy", "final_answer": {"answer": 14.172, "unit": "kg"}, "id": "unit_convert_007482_g_to_kg_14172", "license": "Apache-2.0", "prompt": "Convert 14172 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 14172.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 14172.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-6.45, 10.5], \"unit\": \"dimensionless\"}", "dedupe_signature": "16157343cc0829c3827afdaa792f8312abea81d50e75d2550efd002efdbb5977", "difficulty": "medium", "final_answer": {"answer": [-6.45, 10.5], "unit": "dimensionless"}, "id": "line_two_point_007484_10.75_13.5_-6.45_10.5", "license": "Apache-2.0", "prompt": "A line passes through points (10.75, -58.8375) and (13.5, -76.575). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 10.75, "x2": 13.5, "y1": -58.837500000000006, "y2": -76.575}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. energy divided by length is force, not spring constant\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "b82d7e9e544bd68e88a3d987a17d094af42831d95d95e78fbd7da4748e7595e5", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_007485_inconsistent_56040f5d_432359", "license": "Apache-2.0", "prompt": "In instrument manual case 432359, check dimensional consistency for k = E / x. The left side has dimensions N/m and the right side has dimensions J/m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nenergy divided by length is force, not spring constant\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "k = E / x"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef threshold_flags_007486(values, threshold):\n    return [value >= threshold for value in values]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"threshold_flags_007486\"}", "dedupe_signature": "71dfd1be4ba5b1bbea6f40d65f3ecd4ed17edc233bc3ad2797f1acaefef4fac3", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "threshold_flags_007486"}, "id": "code_007486_threshold_flags_007486", "license": "Apache-2.0", "prompt": "Write a Python function threshold_flags_007486(values, threshold) that returns a list of booleans showing whether each value is greater than or equal to threshold. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "threshold_flags_007486"}, "verifier": {"function": "threshold_flags_007486", "tests": ["assert threshold_flags_007486([1, 2, 3], 2) == [False, True, True]", "assert threshold_flags_007486([], 5) == []", "assert threshold_flags_007486([-1, 0], 0) == [False, True]"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: recurrence, objective, tie_breaking_rule.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"recurrence\", \"objective\", \"tie_breaking_rule\"]}", "dedupe_signature": "041dc28bc2ccf64da65593cf61b7be72a2bb0eab6717e50e78f9118d7c838a1c", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["recurrence", "objective", "tie_breaking_rule"]}, "id": "abstain_007487_recurrence_objective_tie_breaking_rule", "license": "Apache-2.0", "prompt": "Write a dynamic-programming solver for a alignment scoring problem with 1588 items and budget 74040, but the recurrence, objective, and tie-breaking rule are all absent. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: recurrence, objective, tie_breaking_rule.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["recurrence", "objective", "tie_breaking_rule"]}, "verifier": {"missing": ["recurrence", "objective", "tie_breaking_rule"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 14.15^2 and multiply by 0.5 * 18.7.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 1872.0804, \"unit\": \"J\"}", "dedupe_signature": "6fca11cf4c876fe0dc97485bb4d5711c3c8b4e933ea09e4ba2b3a3be0a7245cc", "difficulty": "easy", "final_answer": {"answer": 1872.0804, "unit": "J"}, "id": "ke_007489_18.7_14.15", "license": "Apache-2.0", "prompt": "A body of mass 18.7 kg moves at 14.15 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 14.15^2 and multiply by 0.5 * 18.7.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 18.7, "velocity": 14.15}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=8 degrees through the sine of 2 theta.\n3. Substitute v=7.9 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 1.7536, \"unit\": \"m\"}", "dedupe_signature": "5b711d405c431294dd0ad466c144b83f6336032af05bb94e4b2ace3185bb1e5b", "difficulty": "medium", "final_answer": {"answer": 1.7536, "unit": "m"}, "id": "projectile_range_007490_7.9_8", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 7.9 m/s and angle 8 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=8 degrees through the sine of 2 theta.\nSubstitute v=7.9 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 8, "gravity": 9.81, "speed": 7.9}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 5.96 * 8.314 * 485 / 35.0.\nFinal: {\"answer\": 686.6414, \"unit\": \"kPa\"}", "dedupe_signature": "9492751243c17e0d4c605091e8e4368429c412d8d7b83bf9287a9bb1bab64310", "difficulty": "medium", "final_answer": {"answer": 686.6414, "unit": "kPa"}, "id": "ideal_gas_007491_5.96_485_35.0", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=5.96 mol, T=485 K, and V=35.0 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 5.96 * 8.314 * 485 / 35.0.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 5.96, "temp_k": 485, "volume_l": 35.0}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 220 * 4.32 * 5.\nFinal: {\"answer\": 4752.0, \"unit\": \"J\"}", "dedupe_signature": "fb01e3f8f6057806bb75218353dc60a0316c2b21b57da70800774da07a3d1382", "difficulty": "easy", "final_answer": {"answer": 4752.0, "unit": "J"}, "id": "heat_q_007492_220_4.32_5", "license": "Apache-2.0", "prompt": "A 220 g sample has specific heat 4.32 J/(g*K). How much heat is needed to raise its temperature by 5 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 220 * 4.32 * 5.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 5, "heat_capacity": 4.32, "mass_g": 220}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=65.8 V and R=117 ohm.\nFinal: {\"answer\": 37.0055, \"unit\": \"W\"}", "dedupe_signature": "4a1791d02aca3d62fa54228650cc6757cee4a04d50a1b05f516ee47b1f8a8862", "difficulty": "easy", "final_answer": {"answer": 37.0055, "unit": "W"}, "id": "ohm_power_007493_65.8_117", "license": "Apache-2.0", "prompt": "A resistor has resistance 117 ohm and voltage 65.8 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=65.8 V and R=117 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 117.0, "voltage": 65.8}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 400 mL to 0.4 L.\n3. Compute M = 2.745 / 0.4.\nFinal: {\"answer\": 6.8625, \"unit\": \"mol/L\"}", "dedupe_signature": "d8ee64bebaa263fc690d85644b905b5ee8b16c2d9d393870371d1ebddded0fc0", "difficulty": "medium", "final_answer": {"answer": 6.8625, "unit": "mol/L"}, "id": "molarity_007496_2.745_400", "license": "Apache-2.0", "prompt": "A solution contains 2.745 mol of solute in 400 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 400 mL to 0.4 L.\nCompute M = 2.745 / 0.4.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 2.745, "volume_ml": 400}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.74 y, so each step multiplies y by 1 - h*0.74.\n3. Apply that update for 4 steps and round the final state.\nFinal: {\"answer\": 25.0295, \"unit\": \"state_units\"}", "dedupe_signature": "c2dd3ac23f48387e0c53c98cf25c161411ad7abac157ac08692d39e7512ffecf", "difficulty": "medium", "final_answer": {"answer": 25.0295, "unit": "state_units"}, "id": "euler_decay_007497_47.5_0.74_0.2_4", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.74 y with y(0)=47.5, step size h=0.2, for 4 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.74 y, so each step multiplies y by 1 - h*0.74.\nApply that update for 4 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 47.5, "rate": 0.74, "step": 0.2, "steps": 4}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(2.7)=40.25 and f(8.2)=81.5.\n3. The interval width is 5.5.\nFinal: {\"answer\": 334.8125, \"unit\": \"area_units\"}", "dedupe_signature": "677f9dadc88aeb19e14e027bb003da751e364979dfb14430d83fe8990f9f209b", "difficulty": "medium", "final_answer": {"answer": 334.8125, "unit": "area_units"}, "id": "trapz_linear_007498_7.5_20_2.7_8.2", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=7.5x+20 from x=2.7 to x=8.2. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(2.7)=40.25 and f(8.2)=81.5.\nThe interval width is 5.5.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 20.0, "slope": 7.5, "x0": 2.7, "x1": 8.2}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 8865.0 / 1000.\nFinal: {\"answer\": 8.865, \"unit\": \"kg\"}", "dedupe_signature": "7a768c2f6ff67f823ed3d340fbaa989a594853bd010686c35352f4a2b2061e74", "difficulty": "easy", "final_answer": {"answer": 8.865, "unit": "kg"}, "id": "unit_convert_007500_g_to_kg_8865", "license": "Apache-2.0", "prompt": "Convert 8865 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 8865.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 8865.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=65 degrees and keep the unit as newtons.\nFinal: {\"answer\": [201.5889, 432.3088], \"unit\": \"N\"}", "dedupe_signature": "952d5a6cdb1097a56116d448fc56447eae22a86b5c32c93b1a594e39df93c729", "difficulty": "medium", "final_answer": {"answer": [201.5889, 432.3088], "unit": "N"}, "id": "vector_components_007501_477_65", "license": "Apache-2.0", "prompt": "A vector has magnitude 477 N at 65 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=65 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 65, "magnitude": 477.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. speed squared over acceleration has units of meters\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "0ce011a31513840ca4e4019d46cd8a82fa111986dfc6b5c18217df88f5bfef08", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_007503_consistent_741d4e34_945398", "license": "Apache-2.0", "prompt": "In lab notebook case 945398, check dimensional consistency for R = v^2 * sin(theta) / g. The left side has dimensions m and the right side has dimensions m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nspeed squared over acceleration has units of meters\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "R = v^2 * sin(theta) / g"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef safe_mean_007504(values):\n    if not values:\n        raise ValueError('safe_mean requires at least one value')\n    return sum(values) / len(values)\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"safe_mean_007504\"}", "dedupe_signature": "e0562e1a0270757ca470709f7eb3b20a0908543554d17f1d828421f57ed4c5fd", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "safe_mean_007504"}, "id": "code_007504_safe_mean_007504", "license": "Apache-2.0", "prompt": "Write a Python function safe_mean_007504(values) that returns the arithmetic mean. It must raise ValueError for an empty input and must not mutate the input list. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "safe_mean_007504"}, "verifier": {"function": "safe_mean_007504", "tests": ["assert safe_mean_007504([2, 4, 6]) == 4", "xs = [1, 2, 3]; assert safe_mean_007504(xs) == 2 and xs == [1, 2, 3]", "try:\n    safe_mean_007504([])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 3.35 kg and a = 14.25 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 47.7375, \"unit\": \"N\"}", "dedupe_signature": "ca698f4f4caed90206e52e3312cf41d81a37ad2a5c349e0da9427619810b1e66", "difficulty": "easy", "final_answer": {"answer": 47.7375, "unit": "N"}, "id": "force_007506_3.35_14.25", "license": "Apache-2.0", "prompt": "A cart has mass 3.35 kg and measured acceleration 14.25 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 3.35 kg and a = 14.25 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 14.25, "mass": 3.35}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 13.45^2 and multiply by 0.5 * 23.2.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 2098.469, \"unit\": \"J\"}", "dedupe_signature": "2c871abf3944529cd679c73b86faae6cbd048d461694244ab56e51dccf930e4f", "difficulty": "easy", "final_answer": {"answer": 2098.469, "unit": "J"}, "id": "ke_007507_23.2_13.45", "license": "Apache-2.0", "prompt": "A body of mass 23.2 kg moves at 13.45 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 13.45^2 and multiply by 0.5 * 23.2.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 23.2, "velocity": 13.45}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 1.36 * 8.314 * 474 / 118.2.\nFinal: {\"answer\": 45.343, \"unit\": \"kPa\"}", "dedupe_signature": "b47b74b9edc9785cc3a467d6cc56ff071b30554692c9ad3e1f36f323bd695fd3", "difficulty": "medium", "final_answer": {"answer": 45.343, "unit": "kPa"}, "id": "ideal_gas_007509_1.36_474_118.2", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=1.36 mol, T=474 K, and V=118.2 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 1.36 * 8.314 * 474 / 118.2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 1.36, "temp_k": 474, "volume_l": 118.2}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1045 * 2.065 * 38.\nFinal: {\"answer\": 82001.15, \"unit\": \"J\"}", "dedupe_signature": "8b3e2434d739b82b0519206c29cd332d50a153f12629e6587e8242e575100250", "difficulty": "easy", "final_answer": {"answer": 82001.15, "unit": "J"}, "id": "heat_q_007510_1045_2.065_38", "license": "Apache-2.0", "prompt": "A 1045 g sample has specific heat 2.065 J/(g*K). How much heat is needed to raise its temperature by 38 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1045 * 2.065 * 38.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 38, "heat_capacity": 2.065, "mass_g": 1045}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=139.4 V and R=134.8 ohm.\nFinal: {\"answer\": 144.157, \"unit\": \"W\"}", "dedupe_signature": "5b05ee5b14bbbc4158b697cf6d7e15e56ae3f57be2415eb37a8a31887becaea7", "difficulty": "easy", "final_answer": {"answer": 144.157, "unit": "W"}, "id": "ohm_power_007511_139.4_134.8", "license": "Apache-2.0", "prompt": "A resistor has resistance 134.8 ohm and voltage 139.4 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=139.4 V and R=134.8 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 134.8, "voltage": 139.4}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.64 y, so each step multiplies y by 1 - h*0.64.\n3. Apply that update for 3 steps and round the final state.\nFinal: {\"answer\": 9.1185, \"unit\": \"state_units\"}", "dedupe_signature": "b31e68c8866123184f0aa3b13df07548641faa250974f4e17e87588705fe58f2", "difficulty": "medium", "final_answer": {"answer": 9.1185, "unit": "state_units"}, "id": "euler_decay_007515_29_0.64_0.5_3", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.64 y with y(0)=29, step size h=0.5, for 3 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.64 y, so each step multiplies y by 1 - h*0.64.\nApply that update for 3 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 29.0, "rate": 0.64, "step": 0.5, "steps": 3}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(8.7)=43.72 and f(10.2)=53.62.\n3. The interval width is 1.5.\nFinal: {\"answer\": 73.005, \"unit\": \"area_units\"}", "dedupe_signature": "22ebb9a6927a0709be6ef9e3ee1cffff9c62ca7d220c813949de6c1328395c0d", "difficulty": "medium", "final_answer": {"answer": 73.005, "unit": "area_units"}, "id": "trapz_linear_007516_6.6_-13.7_8.7_10.2", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=6.6x+-13.7 from x=8.7 to x=10.2. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(8.7)=43.72 and f(10.2)=53.62.\nThe interval width is 1.5.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -13.7, "slope": 6.6, "x0": 8.7, "x1": 10.2}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.24 and add it to the current value.\nFinal: {\"answer\": [-0.336, -0.774, -0.026], \"unit\": \"temperature_units\"}", "dedupe_signature": "8d46e2cac50f0aadb1b6146582e8aad08a0ac52a495d123eca299c5b1d177efb", "difficulty": "hard", "final_answer": {"answer": [-0.336, -0.774, -0.026], "unit": "temperature_units"}, "id": "heat_step_007517_0.24_-0.35_0.0_-1.05_-0.95_3.0", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-0.35, right=3; current interior values are [0.0, -1.05, -0.95]. Use r=0.24. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.24 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [0.0, -1.05, -0.95], "left": -0.35, "r": 0.24, "right": 3.0}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=280 degrees and keep the unit as newtons.\nFinal: {\"answer\": [14.7601, -83.7087], \"unit\": \"N\"}", "dedupe_signature": "5ed0938167c7bdb544a46433463e4f68e55795bb10c0549683d3def7119fe3bf", "difficulty": "medium", "final_answer": {"answer": [14.7601, -83.7087], "unit": "N"}, "id": "vector_components_007519_85_280", "license": "Apache-2.0", "prompt": "A vector has magnitude 85 N at 280 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=280 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 280, "magnitude": 85.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-1.65, -24.25], \"unit\": \"dimensionless\"}", "dedupe_signature": "4b1c094d109808afbc0603ee6d76ead2b7182032814d9ba5664059447fd71fd6", "difficulty": "medium", "final_answer": {"answer": [-1.65, -24.25], "unit": "dimensionless"}, "id": "line_two_point_007520_17.25_30.5_-1.65_-24.25", "license": "Apache-2.0", "prompt": "A line passes through points (17.25, -52.7125) and (30.5, -74.575). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 17.25, "x2": 30.5, "y1": -52.7125, "y2": -74.57499999999999}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. m*v is momentum, not energy\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "a5bb220e51a9447eef0359163716e9679b14f3e0e293bf04fdf10e8feaa54a34", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_007521_inconsistent_1e14b074_417964", "license": "Apache-2.0", "prompt": "In simulation spec case 417964, check dimensional consistency for E = m * v. The left side has dimensions kg*m^2/s^2 and the right side has dimensions kg*m/s. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nm*v is momentum, not energy\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "E = m * v"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef running_total_007522(values):\n    total = 0\n    out = []\n    for value in values:\n        total += value\n        out.append(total)\n    return out\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"running_total_007522\"}", "dedupe_signature": "a1d18cd97c74195ca9d2f92eede27cd017b0e2ac2df54bda9c63c9bfd6ecca06", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "running_total_007522"}, "id": "code_007522_running_total_007522", "license": "Apache-2.0", "prompt": "Write a Python function running_total_007522(values) that returns cumulative sums as a new list. It must not mutate the input list. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "running_total_007522"}, "verifier": {"function": "running_total_007522", "tests": ["assert running_total_007522([1, 2, 3]) == [1, 3, 6]", "xs = [4, -1, 2]; assert running_total_007522(xs) == [4, 3, 5] and xs == [4, -1, 2]", "assert running_total_007522([]) == []"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: required_fields, allowed_transformations.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"required_fields\", \"allowed_transformations\"]}", "dedupe_signature": "f5d2c1ab894d2691c8c37485c611cc8e8af85cb4ecbc04c45823df7935355caf", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["required_fields", "allowed_transformations"]}, "id": "abstain_007523_required_fields_allowed_transformations", "license": "Apache-2.0", "prompt": "Write a sanitizer for valid warehouse survey records in release 218991, but the prompt does not state which fields are required or which transformations are allowed. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: required_fields, allowed_transformations.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["required_fields", "allowed_transformations"]}, "verifier": {"missing": ["required_fields", "allowed_transformations"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 5.9 kg and a = 7 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 41.3, \"unit\": \"N\"}", "dedupe_signature": "b3aeb24af05212c0a422bc4e4826be11a8b8ce8781c27bd32dfb8f4f9abbb0ac", "difficulty": "easy", "final_answer": {"answer": 41.3, "unit": "N"}, "id": "force_007524_5.9_7", "license": "Apache-2.0", "prompt": "A cart has mass 5.9 kg and measured acceleration 7 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 5.9 kg and a = 7 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 7.0, "mass": 5.9}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 8.7^2 and multiply by 0.5 * 12.5.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 473.0625, \"unit\": \"J\"}", "dedupe_signature": "923839c54179feb56cbbb6e58b1c25fac624baea2abd377777beb0b18e2c1a89", "difficulty": "easy", "final_answer": {"answer": 473.0625, "unit": "J"}, "id": "ke_007525_12.5_8.7", "license": "Apache-2.0", "prompt": "A body of mass 12.5 kg moves at 8.7 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 8.7^2 and multiply by 0.5 * 12.5.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 12.5, "velocity": 8.7}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=23 degrees through the sine of 2 theta.\n3. Substitute v=56.4 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 233.2509, \"unit\": \"m\"}", "dedupe_signature": "12495a2983c25c2ee1dd2e3a8a3cfb53d91603f9cc1f6859820eb075e5c7e31c", "difficulty": "medium", "final_answer": {"answer": 233.2509, "unit": "m"}, "id": "projectile_range_007526_56.4_23", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 56.4 m/s and angle 23 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=23 degrees through the sine of 2 theta.\nSubstitute v=56.4 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 23, "gravity": 9.81, "speed": 56.4}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 2.26 * 8.314 * 419 / 64.4.\nFinal: {\"answer\": 122.2494, \"unit\": \"kPa\"}", "dedupe_signature": "decacf417fe21dc23d67539142098178ab1edf3adfe59c9b92c4bf838dad9a58", "difficulty": "medium", "final_answer": {"answer": 122.2494, "unit": "kPa"}, "id": "ideal_gas_007527_2.26_419_64.4", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=2.26 mol, T=419 K, and V=64.4 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 2.26 * 8.314 * 419 / 64.4.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 2.26, "temp_k": 419, "volume_l": 64.4}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 965 * 1.075 * 28.\nFinal: {\"answer\": 29046.5, \"unit\": \"J\"}", "dedupe_signature": "ce632811adbaa1acb50fd69de912c0307089a81be86091a1f13b0867202afefb", "difficulty": "easy", "final_answer": {"answer": 29046.5, "unit": "J"}, "id": "heat_q_007528_965_1.075_28", "license": "Apache-2.0", "prompt": "A 965 g sample has specific heat 1.075 J/(g*K). How much heat is needed to raise its temperature by 28 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 965 * 1.075 * 28.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 28, "heat_capacity": 1.075, "mass_g": 965}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=191.4 V and R=132 ohm.\nFinal: {\"answer\": 277.53, \"unit\": \"W\"}", "dedupe_signature": "20b7817694f80f44ae6b2464ab4a4d734f71ab41e04c84106502ab14361c0dc0", "difficulty": "easy", "final_answer": {"answer": 277.53, "unit": "W"}, "id": "ohm_power_007529_191.4_132", "license": "Apache-2.0", "prompt": "A resistor has resistance 132 ohm and voltage 191.4 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=191.4 V and R=132 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 132.0, "voltage": 191.4}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=369 mg, t=277 h, and T_half=53.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 10.1958, \"unit\": \"mg\"}", "dedupe_signature": "687e7381c730398195dc85b22be1386ebc8159b861edf4dd6f70b6ec8dded505", "difficulty": "medium", "final_answer": {"answer": 10.1958, "unit": "mg"}, "id": "half_life_007530_369_53.5_277", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 369 mg. Its half-life is 53.5 hours. How many mg remain after 277 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=369 mg, t=277 h, and T_half=53.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 277.0, "half_life": 53.5, "initial_amount": 369.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.08 y, so each step multiplies y by 1 - h*0.08.\n3. Apply that update for 2 steps and round the final state.\nFinal: {\"answer\": 64.8007, \"unit\": \"state_units\"}", "dedupe_signature": "e90618a1bd759a49e7b0a97f70acc64ba8c41cd81adfff6433903f81bf55b08b", "difficulty": "medium", "final_answer": {"answer": 64.8007, "unit": "state_units"}, "id": "euler_decay_007533_71.5_0.08_0.6_2", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.08 y with y(0)=71.5, step size h=0.6, for 2 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.08 y, so each step multiplies y by 1 - h*0.08.\nApply that update for 2 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 71.5, "rate": 0.08, "step": 0.6, "steps": 2}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(9.5)=-3.25 and f(10.8)=-5.72.\n3. The interval width is 1.3.\nFinal: {\"answer\": -5.8305, \"unit\": \"area_units\"}", "dedupe_signature": "da4f856fa2654248fbb61d269f2c2e5946af0f3e42450f0c99b0067f8b2afba9", "difficulty": "medium", "final_answer": {"answer": -5.8305, "unit": "area_units"}, "id": "trapz_linear_007534_-1.9_14.8_9.5_10.8", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-1.9x+14.8 from x=9.5 to x=10.8. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(9.5)=-3.25 and f(10.8)=-5.72.\nThe interval width is 1.3.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 14.8, "slope": -1.9, "x0": 9.5, "x1": 10.8}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.12 and add it to the current value.\nFinal: {\"answer\": [0.138, 0.482, 2.156], \"unit\": \"temperature_units\"}", "dedupe_signature": "de9ed1238516044255656c561f2a1e9e9043ec85566284a4893e87d4e23b2d6f", "difficulty": "hard", "final_answer": {"answer": [0.138, 0.482, 2.156], "unit": "temperature_units"}, "id": "heat_step_007535_0.12_0.0_0.15_0.2_2.6_1.3", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=0, right=1.3; current interior values are [0.15, 0.2, 2.6]. Use r=0.12. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.12 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [0.15, 0.2, 2.6], "left": 0.0, "r": 0.12, "right": 1.3}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kelvin equals Celsius plus 273.15.\n2. Apply the conversion factor directly to the given value.\n3. Compute 49.0 + 273.15.\nFinal: {\"answer\": 322.15, \"unit\": \"K\"}", "dedupe_signature": "25de2dd2ccd9d25fde7cee78a605004c4b070bfa2e2fb2ebbf05e4475f3dcc49", "difficulty": "easy", "final_answer": {"answer": 322.15, "unit": "K"}, "id": "unit_convert_007536_c_to_k_49", "license": "Apache-2.0", "prompt": "Convert 49 degC to K. Return the converted value with unit.", "reasoning_trace": "Kelvin equals Celsius plus 273.15.\nApply the conversion factor directly to the given value.\nCompute 49.0 + 273.15.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 49.0}, "verifier": {"formula": "value + 273.15", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=340 degrees and keep the unit as newtons.\nFinal: {\"answer\": [107.5948, -39.1613], \"unit\": \"N\"}", "dedupe_signature": "7b0cc16eb710fa9399a522b10c08b0cd4f489d3b9d730a0577f605cbd660c4c4", "difficulty": "medium", "final_answer": {"answer": [107.5948, -39.1613], "unit": "N"}, "id": "vector_components_007537_114.5_340", "license": "Apache-2.0", "prompt": "A vector has magnitude 114.5 N at 340 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=340 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 340, "magnitude": 114.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [5.7, 15.75], \"unit\": \"dimensionless\"}", "dedupe_signature": "97f0e66b657fcdf86bcf242a4757f5577ceffa3bc0574c624c32257851f9634b", "difficulty": "medium", "final_answer": {"answer": [5.7, 15.75], "unit": "dimensionless"}, "id": "line_two_point_007538_4.75_10_5.7_15.75", "license": "Apache-2.0", "prompt": "A line passes through points (4.75, 42.825) and (10, 72.75). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 4.75, "x2": 10.0, "y1": 42.825, "y2": 72.75}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. speed squared over acceleration has units of meters\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "5174da22c86abaf914df3ccc568ba0b61d5801d045cdd1a8e799803af80248f3", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_007539_consistent_741d4e34_859385", "license": "Apache-2.0", "prompt": "In student derivation case 859385, check dimensional consistency for R = v^2 * sin(theta) / g. The left side has dimensions m and the right side has dimensions m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nspeed squared over acceleration has units of meters\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "R = v^2 * sin(theta) / g"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef normalize_007540(values):\n    total = sum(values)\n    if total == 0:\n        raise ValueError('cannot normalize zero-sum values')\n    return [v / total for v in values]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"normalize_007540\"}", "dedupe_signature": "ac28b9dc2e1b2e7a8ce8943ed3995e27c2d28bcfdfa9a159262e1fc276e2087d", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "normalize_007540"}, "id": "code_007540_normalize_007540", "license": "Apache-2.0", "prompt": "Write a Python function normalize_007540(values) that returns a new list whose values sum to 1. Raise ValueError if the sum is zero. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "normalize_007540"}, "verifier": {"function": "normalize_007540", "tests": ["out = normalize_007540([2, 3, 5]); assert len(out) == 3", "assert abs(sum(normalize_007540([2, 3, 5])) - 1.0) < 1e-12", "assert normalize_007540([1, 1]) == [0.5, 0.5]", "try:\n    normalize_007540([1, -1])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: rate_constant, number_of_steps.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"rate_constant\", \"number_of_steps\"]}", "dedupe_signature": "4c31cc817aefd1661a7a3c30b1afc79023763ff64dd4303c4c1aa8301fffa51c", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["rate_constant", "number_of_steps"]}, "id": "abstain_007541_rate_constant_number_of_steps", "license": "Apache-2.0", "prompt": "Use explicit Euler for dy/dt = -k y. The prompt gives y(0)=56.5 and h=0.55, but omits both k and the number of steps. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: rate_constant, number_of_steps.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["rate_constant", "number_of_steps"]}, "verifier": {"missing": ["rate_constant", "number_of_steps"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 18 kg and a = 13 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 234.0, \"unit\": \"N\"}", "dedupe_signature": "59d9392cdef49acfbe9c28421eb4aa2ca29c4b97222b809438b1d84c91c7a9ec", "difficulty": "easy", "final_answer": {"answer": 234.0, "unit": "N"}, "id": "force_007542_18_13", "license": "Apache-2.0", "prompt": "A cart has mass 18 kg and measured acceleration 13 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 18 kg and a = 13 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 13.0, "mass": 18.0}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 34.3^2 and multiply by 0.5 * 10.9.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 6411.8705, \"unit\": \"J\"}", "dedupe_signature": "93c9d99d547291a92cf0bc1fa83b7eb2d7299ab085d4c552b85c7e3137c926a5", "difficulty": "easy", "final_answer": {"answer": 6411.8705, "unit": "J"}, "id": "ke_007543_10.9_34.3", "license": "Apache-2.0", "prompt": "A body of mass 10.9 kg moves at 34.3 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 34.3^2 and multiply by 0.5 * 10.9.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 10.9, "velocity": 34.3}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=30 degrees through the sine of 2 theta.\n3. Substitute v=18.6 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 30.5413, \"unit\": \"m\"}", "dedupe_signature": "ece19a1a205ccc6f346d473a1dd8cd364471075c2ba6c1d04cda7f1f35d24e23", "difficulty": "medium", "final_answer": {"answer": 30.5413, "unit": "m"}, "id": "projectile_range_007544_18.6_30", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 18.6 m/s and angle 30 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=30 degrees through the sine of 2 theta.\nSubstitute v=18.6 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 30, "gravity": 9.81, "speed": 18.6}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 4.77 * 8.314 * 329 / 48.5.\nFinal: {\"answer\": 269.0188, \"unit\": \"kPa\"}", "dedupe_signature": "d3cba5022943499226cc2f197b1033ddf843ff424a21fd23209ede5c7c087527", "difficulty": "medium", "final_answer": {"answer": 269.0188, "unit": "kPa"}, "id": "ideal_gas_007545_4.77_329_48.5", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=4.77 mol, T=329 K, and V=48.5 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 4.77 * 8.314 * 329 / 48.5.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 4.77, "temp_k": 329, "volume_l": 48.5}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1085 * 0.53 * 31.\nFinal: {\"answer\": 17826.55, \"unit\": \"J\"}", "dedupe_signature": "137dea787759c5defc29124cfc58945d465821370dbe7f7dc22989fdd5f13615", "difficulty": "easy", "final_answer": {"answer": 17826.55, "unit": "J"}, "id": "heat_q_007546_1085_0.53_31", "license": "Apache-2.0", "prompt": "A 1085 g sample has specific heat 0.53 J/(g*K). How much heat is needed to raise its temperature by 31 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1085 * 0.53 * 31.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 31, "heat_capacity": 0.53, "mass_g": 1085}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=236.7 V and R=73.3 ohm.\nFinal: {\"answer\": 764.3505, \"unit\": \"W\"}", "dedupe_signature": "23952cb2488d42f37a90ee3c2db93869bcd09067c2364b9befca72f049c1e7c0", "difficulty": "easy", "final_answer": {"answer": 764.3505, "unit": "W"}, "id": "ohm_power_007547_236.7_73.3", "license": "Apache-2.0", "prompt": "A resistor has resistance 73.3 ohm and voltage 236.7 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=236.7 V and R=73.3 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 73.3, "voltage": 236.7}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=946.5 mg, t=17.5 h, and T_half=33 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 655.3654, \"unit\": \"mg\"}", "dedupe_signature": "cacc28f320303bf8107acb3d24f763087670387d3acdf3a36dfb106d27bb62ea", "difficulty": "medium", "final_answer": {"answer": 655.3654, "unit": "mg"}, "id": "half_life_007548_946.5_33_17.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 946.5 mg. Its half-life is 33 hours. How many mg remain after 17.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=946.5 mg, t=17.5 h, and T_half=33 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 17.5, "half_life": 33.0, "initial_amount": 946.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.14 y, so each step multiplies y by 1 - h*0.14.\n3. Apply that update for 2 steps and round the final state.\nFinal: {\"answer\": 2.4244, \"unit\": \"state_units\"}", "dedupe_signature": "b62f87c4058fb49e37ee3cf3ed7796d61607c4025a0951630ec10ba342db9d4b", "difficulty": "medium", "final_answer": {"answer": 2.4244, "unit": "state_units"}, "id": "euler_decay_007551_4.5_0.14_1.9_2", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.14 y with y(0)=4.5, step size h=1.9, for 2 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.14 y, so each step multiplies y by 1 - h*0.14.\nApply that update for 2 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 4.5, "rate": 0.14, "step": 1.9, "steps": 2}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-5.8)=48.54 and f(2.4)=5.08.\n3. The interval width is 8.2.\nFinal: {\"answer\": 219.842, \"unit\": \"area_units\"}", "dedupe_signature": "c3c15461486a321d505147434d30722891eec06d742498c03c675d58ffeb22e3", "difficulty": "medium", "final_answer": {"answer": 219.842, "unit": "area_units"}, "id": "trapz_linear_007552_-5.3_17.8_-5.8_2.4", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-5.3x+17.8 from x=-5.8 to x=2.4. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-5.8)=48.54 and f(2.4)=5.08.\nThe interval width is 8.2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 17.8, "slope": -5.3, "x0": -5.8, "x1": 2.3999999999999995}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.16 and add it to the current value.\nFinal: {\"answer\": [-1.402, -0.396, -0.866], \"unit\": \"temperature_units\"}", "dedupe_signature": "5ab02ce3788b9539020f8dd86c25fae367b78b353b296f42430f84fe7285551e", "difficulty": "hard", "final_answer": {"answer": [-1.402, -0.396, -0.866], "unit": "temperature_units"}, "id": "heat_step_007553_0.16_-1.85_-1.65_0.1_-1.25_-0.2", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-1.85, right=-0.2; current interior values are [-1.65, 0.1, -1.25]. Use r=0.16. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.16 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-1.65, 0.1, -1.25], "left": -1.85, "r": 0.16, "right": -0.2}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kelvin equals Celsius plus 273.15.\n2. Apply the conversion factor directly to the given value.\n3. Compute 109.5 + 273.15.\nFinal: {\"answer\": 382.65, \"unit\": \"K\"}", "dedupe_signature": "d339530ea531bed6caefdd22d1ffdc3256cec1f8386163f3e7f103531279dd75", "difficulty": "easy", "final_answer": {"answer": 382.65, "unit": "K"}, "id": "unit_convert_007554_c_to_k_109.5", "license": "Apache-2.0", "prompt": "Convert 109.5 degC to K. Return the converted value with unit.", "reasoning_trace": "Kelvin equals Celsius plus 273.15.\nApply the conversion factor directly to the given value.\nCompute 109.5 + 273.15.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 109.5}, "verifier": {"formula": "value + 273.15", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=257 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-68.9475, -298.6444], \"unit\": \"N\"}", "dedupe_signature": "cc915028b323f1a38a715f4480dcd0bc75b6294e39b65e1fb0c16c7e4b6880e2", "difficulty": "medium", "final_answer": {"answer": [-68.9475, -298.6444], "unit": "N"}, "id": "vector_components_007555_306.5_257", "license": "Apache-2.0", "prompt": "A vector has magnitude 306.5 N at 257 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=257 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 257, "magnitude": 306.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [7.1, 23.25], \"unit\": \"dimensionless\"}", "dedupe_signature": "584fd5a43c72e622385f9d12e78a2f2952374dc79036d9538b5c0e4f2d103a8b", "difficulty": "medium", "final_answer": {"answer": [7.1, 23.25], "unit": "dimensionless"}, "id": "line_two_point_007556_-6.75_7.5_7.1_23.25", "license": "Apache-2.0", "prompt": "A line passes through points (-6.75, -24.675) and (7.5, 76.5). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -6.75, "x2": 7.5, "y1": -24.674999999999997, "y2": 76.5}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. velocity divided by time is acceleration\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "309ebc62362e7d15977bf3b1a21aac5235747b65cbb6138a6d49f80fe88f86f4", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_007557_inconsistent_c1271127_545439", "license": "Apache-2.0", "prompt": "In simulation spec case 545439, check dimensional consistency for x = v / t. The left side has dimensions m and the right side has dimensions m/s^2. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nvelocity divided by time is acceleration\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "x = v / t"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef threshold_flags_007558(values, threshold):\n    return [value >= threshold for value in values]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"threshold_flags_007558\"}", "dedupe_signature": "d180ac86c5bac4ee85bc735f05ac22e74bc12c1544c8ca6d9893ad28e9a4c81d", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "threshold_flags_007558"}, "id": "code_007558_threshold_flags_007558", "license": "Apache-2.0", "prompt": "Write a Python function threshold_flags_007558(values, threshold) that returns a list of booleans showing whether each value is greater than or equal to threshold. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "threshold_flags_007558"}, "verifier": {"function": "threshold_flags_007558", "tests": ["assert threshold_flags_007558([1, 2, 3], 2) == [False, True, True]", "assert threshold_flags_007558([], 5) == []", "assert threshold_flags_007558([-1, 0], 0) == [False, True]"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 37.55^2 and multiply by 0.5 * 2.75.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 1938.7534, \"unit\": \"J\"}", "dedupe_signature": "452f88fe5300096314cf93a94c292e291c6b7676a1af41dac6ac1059488cad9a", "difficulty": "easy", "final_answer": {"answer": 1938.7534, "unit": "J"}, "id": "ke_007561_2.75_37.55", "license": "Apache-2.0", "prompt": "A body of mass 2.75 kg moves at 37.55 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 37.55^2 and multiply by 0.5 * 2.75.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 2.75, "velocity": 37.55}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 3.53 * 8.314 * 389 / 115.3.\nFinal: {\"answer\": 99.0159, \"unit\": \"kPa\"}", "dedupe_signature": "247dd0d4cb800b0f4b8088c33dfdefa099d00b74a8c51b5c2189db3eb4c80eda", "difficulty": "medium", "final_answer": {"answer": 99.0159, "unit": "kPa"}, "id": "ideal_gas_007563_3.53_389_115.3", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=3.53 mol, T=389 K, and V=115.3 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 3.53 * 8.314 * 389 / 115.3.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 3.53, "temp_k": 389, "volume_l": 115.3}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 640 * 4.24 * 43.\nFinal: {\"answer\": 116684.8, \"unit\": \"J\"}", "dedupe_signature": "44d17ac876307cefe33c7650e2030db7c4123395b3103ff537fb22bca4fe10d8", "difficulty": "easy", "final_answer": {"answer": 116684.8, "unit": "J"}, "id": "heat_q_007564_640_4.24_43", "license": "Apache-2.0", "prompt": "A 640 g sample has specific heat 4.24 J/(g*K). How much heat is needed to raise its temperature by 43 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 640 * 4.24 * 43.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 43, "heat_capacity": 4.24, "mass_g": 640}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=235.1 V and R=102.5 ohm.\nFinal: {\"answer\": 539.2391, \"unit\": \"W\"}", "dedupe_signature": "83f603e47e2dffa3014066272591b708ca414c401b85b7163b1522da0bf4ef4b", "difficulty": "easy", "final_answer": {"answer": 539.2391, "unit": "W"}, "id": "ohm_power_007565_235.1_102.5", "license": "Apache-2.0", "prompt": "A resistor has resistance 102.5 ohm and voltage 235.1 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=235.1 V and R=102.5 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 102.5, "voltage": 235.1}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=806 mg, t=243.5 h, and T_half=101.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 152.8128, \"unit\": \"mg\"}", "dedupe_signature": "890888f7a641d583200e1d48959d542d4656d098c40efda85a8bbd74fb9c44e5", "difficulty": "medium", "final_answer": {"answer": 152.8128, "unit": "mg"}, "id": "half_life_007566_806_101.5_243.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 806 mg. Its half-life is 101.5 hours. How many mg remain after 243.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=806 mg, t=243.5 h, and T_half=101.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 243.5, "half_life": 101.5, "initial_amount": 806.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 1040 mL to 1.04 L.\n3. Compute M = 2.25 / 1.04.\nFinal: {\"answer\": 2.1635, \"unit\": \"mol/L\"}", "dedupe_signature": "3d4873b940ebd43c05b1358c322d82450a98ecdbde5a32dc59b56d08aaaafdbe", "difficulty": "medium", "final_answer": {"answer": 2.1635, "unit": "mol/L"}, "id": "molarity_007568_2.25_1040", "license": "Apache-2.0", "prompt": "A solution contains 2.25 mol of solute in 1040 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 1040 mL to 1.04 L.\nCompute M = 2.25 / 1.04.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 2.25, "volume_ml": 1040}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.59 y, so each step multiplies y by 1 - h*0.59.\n3. Apply that update for 3 steps and round the final state.\nFinal: {\"answer\": -0.0107, \"unit\": \"state_units\"}", "dedupe_signature": "d737e01cb649c03d0495b52fd379c5dc0b17ae06f59bbf76df4ccbace23dc25e", "difficulty": "medium", "final_answer": {"answer": -0.0107, "unit": "state_units"}, "id": "euler_decay_007569_45_0.59_1.8_3", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.59 y with y(0)=45, step size h=1.8, for 3 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.59 y, so each step multiplies y by 1 - h*0.59.\nApply that update for 3 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 45.0, "rate": 0.59, "step": 1.8, "steps": 3}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(3)=12.7 and f(5.9)=20.82.\n3. The interval width is 2.9.\nFinal: {\"answer\": 48.604, \"unit\": \"area_units\"}", "dedupe_signature": "926baa810e38ea9eee99d6882a3d43efd5dd9bc5a3257f82cb1bcbd2037fe312", "difficulty": "medium", "final_answer": {"answer": 48.604, "unit": "area_units"}, "id": "trapz_linear_007570_2.8_4.3_3_5.9", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=2.8x+4.3 from x=3 to x=5.9. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(3)=12.7 and f(5.9)=20.82.\nThe interval width is 2.9.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 4.3, "slope": 2.8, "x0": 3.0, "x1": 5.9}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 100 centimeters in one meter.\n2. Apply the conversion factor directly to the given value.\n3. Compute 4021.0 / 100.\nFinal: {\"answer\": 40.21, \"unit\": \"m\"}", "dedupe_signature": "8aeb2e9e653a3c01b4e9464182168bbe5c29003aa5c10fec0d83642dd9cb8494", "difficulty": "easy", "final_answer": {"answer": 40.21, "unit": "m"}, "id": "unit_convert_007572_cm_to_m_4021", "license": "Apache-2.0", "prompt": "Convert 4021 cm to m. Return the converted value with unit.", "reasoning_trace": "There are 100 centimeters in one meter.\nApply the conversion factor directly to the given value.\nCompute 4021.0 / 100.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 4021.0}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=94 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-10.2891, 147.1407], \"unit\": \"N\"}", "dedupe_signature": "316506b9d6cbfd5378f460f12d7367a5f6a0ea0efeff79af5461806b9141c1ce", "difficulty": "medium", "final_answer": {"answer": [-10.2891, 147.1407], "unit": "N"}, "id": "vector_components_007573_147.5_94", "license": "Apache-2.0", "prompt": "A vector has magnitude 147.5 N at 94 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=94 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 94, "magnitude": 147.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [9.45, -4.25], \"unit\": \"dimensionless\"}", "dedupe_signature": "1e24bb09bf427f69a601928c4884b7dc9bce7d6ebb98085edc82850e5b135316", "difficulty": "medium", "final_answer": {"answer": [9.45, -4.25], "unit": "dimensionless"}, "id": "line_two_point_007574_-8.25_-0.75_9.45_-4.25", "license": "Apache-2.0", "prompt": "A line passes through points (-8.25, -82.2125) and (-0.75, -11.3375). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -8.25, "x2": -0.75, "y1": -82.21249999999999, "y2": -11.337499999999999}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. velocity divided by time is acceleration\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "6022528af0e5239f4b56cafec09481ab1e991f4565d60aa2cebbfadfe397ea57", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_007575_inconsistent_c1271127_753975", "license": "Apache-2.0", "prompt": "In sensor calibration case 753975, check dimensional consistency for x = v / t. The left side has dimensions m and the right side has dimensions m/s^2. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nvelocity divided by time is acceleration\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "x = v / t"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef normalize_007576(values):\n    total = sum(values)\n    if total == 0:\n        raise ValueError('cannot normalize zero-sum values')\n    return [v / total for v in values]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"normalize_007576\"}", "dedupe_signature": "fbc3f9a66a19a204d9e2b60b0130dc4ece9d2ae5d89086eba842adfbe727fb7f", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "normalize_007576"}, "id": "code_007576_normalize_007576", "license": "Apache-2.0", "prompt": "Write a Python function normalize_007576(values) that returns a new list whose values sum to 1. Raise ValueError if the sum is zero. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "normalize_007576"}, "verifier": {"function": "normalize_007576", "tests": ["out = normalize_007576([2, 3, 5]); assert len(out) == 3", "assert abs(sum(normalize_007576([2, 3, 5])) - 1.0) < 1e-12", "assert normalize_007576([1, 1]) == [0.5, 0.5]", "try:\n    normalize_007576([1, -1])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: launch_angle_or_vertical_velocity.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"launch_angle_or_vertical_velocity\"]}", "dedupe_signature": "79930a2fc906416a74b125298f0ff3cddade3da46af0c8dea827c7bc897da8eb", "difficulty": "easy", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["launch_angle_or_vertical_velocity"]}, "id": "abstain_007577_launch_angle_or_vertical_velocity", "license": "Apache-2.0", "prompt": "Compute projectile range on level ground. The prompt gives initial speed 33.1 m/s but does not give launch angle or vertical velocity. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: launch_angle_or_vertical_velocity.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["launch_angle_or_vertical_velocity"]}, "verifier": {"missing": ["launch_angle_or_vertical_velocity"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 1.25 kg and a = 5.7 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 7.125, \"unit\": \"N\"}", "dedupe_signature": "6ded9bb89b71bd729d7390e1cd953c304dea991e98a5581dbed02e84cda76f1c", "difficulty": "easy", "final_answer": {"answer": 7.125, "unit": "N"}, "id": "force_007578_1.25_5.7", "license": "Apache-2.0", "prompt": "A cart has mass 1.25 kg and measured acceleration 5.7 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 1.25 kg and a = 5.7 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 5.7, "mass": 1.25}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 21.85^2 and multiply by 0.5 * 11.05.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 2637.7593, \"unit\": \"J\"}", "dedupe_signature": "b277e0049a5b7b9a0ad8703e27e4c1ddfa95292783d5829b2c80016ab87a3c71", "difficulty": "easy", "final_answer": {"answer": 2637.7593, "unit": "J"}, "id": "ke_007579_11.05_21.85", "license": "Apache-2.0", "prompt": "A body of mass 11.05 kg moves at 21.85 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 21.85^2 and multiply by 0.5 * 11.05.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 11.05, "velocity": 21.85}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=58 degrees through the sine of 2 theta.\n3. Substitute v=12.8 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 15.0111, \"unit\": \"m\"}", "dedupe_signature": "eb5ab6acc3198cc8e80cc617b5771dd6afa81d17ba788af828fcde2bcc4fca93", "difficulty": "medium", "final_answer": {"answer": 15.0111, "unit": "m"}, "id": "projectile_range_007580_12.8_58", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 12.8 m/s and angle 58 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=58 degrees through the sine of 2 theta.\nSubstitute v=12.8 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 58, "gravity": 9.81, "speed": 12.8}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 5.34 * 8.314 * 498 / 38.7.\nFinal: {\"answer\": 571.3071, \"unit\": \"kPa\"}", "dedupe_signature": "ce864db8a4925843ba80fe323191c77f1258c0e5ef3919b10d1b9d2127f45e01", "difficulty": "medium", "final_answer": {"answer": 571.3071, "unit": "kPa"}, "id": "ideal_gas_007581_5.34_498_38.7", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=5.34 mol, T=498 K, and V=38.7 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 5.34 * 8.314 * 498 / 38.7.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 5.34, "temp_k": 498, "volume_l": 38.7}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1695 * 1 * 73.\nFinal: {\"answer\": 123735.0, \"unit\": \"J\"}", "dedupe_signature": "4bdd61314462a388e7bf72c91f575748a957d6c7a2ee9cb0dec608682c287892", "difficulty": "easy", "final_answer": {"answer": 123735.0, "unit": "J"}, "id": "heat_q_007582_1695_1_73", "license": "Apache-2.0", "prompt": "A 1695 g sample has specific heat 1 J/(g*K). How much heat is needed to raise its temperature by 73 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1695 * 1 * 73.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 73, "heat_capacity": 1.0, "mass_g": 1695}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=34.2 V and R=137.2 ohm.\nFinal: {\"answer\": 8.5251, \"unit\": \"W\"}", "dedupe_signature": "d22eb72683f49373542ec31d87dd14eb31312bf26614a0873f9309bd5108ddac", "difficulty": "easy", "final_answer": {"answer": 8.5251, "unit": "W"}, "id": "ohm_power_007583_34.2_137.2", "license": "Apache-2.0", "prompt": "A resistor has resistance 137.2 ohm and voltage 34.2 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=34.2 V and R=137.2 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 137.2, "voltage": 34.2}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 2.65 mol * 100.087 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 265.2305, \"unit\": \"g\"}", "dedupe_signature": "652170dee03d2fcbe6e71024b6836494b25d30780deddbf83cea0dca95abfedf", "difficulty": "medium", "final_answer": {"answer": 265.2305, "unit": "g"}, "id": "stoich_mass_007585_calcium_carbonate_2.65", "license": "Apache-2.0", "prompt": "A sample contains 2.65 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 2.65 mol * 100.087 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "calcium carbonate", "molar_mass": 100.087, "moles": 2.65}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 2005 mL to 2.005 L.\n3. Compute M = 0.62 / 2.005.\nFinal: {\"answer\": 0.3092, \"unit\": \"mol/L\"}", "dedupe_signature": "6547db87b92a3058fc9e78e9438252ef631ed85acfba6d5b54fc53ecea83dc3f", "difficulty": "medium", "final_answer": {"answer": 0.3092, "unit": "mol/L"}, "id": "molarity_007586_0.62_2005", "license": "Apache-2.0", "prompt": "A solution contains 0.62 mol of solute in 2005 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 2005 mL to 2.005 L.\nCompute M = 0.62 / 2.005.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 0.62, "volume_ml": 2005}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.43 y, so each step multiplies y by 1 - h*0.43.\n3. Apply that update for 5 steps and round the final state.\nFinal: {\"answer\": 6.483, \"unit\": \"state_units\"}", "dedupe_signature": "ec3fb8462a50f130f3ca1641c96d307f64efd0cfcd5da51bd30944c61292ec15", "difficulty": "medium", "final_answer": {"answer": 6.483, "unit": "state_units"}, "id": "euler_decay_007587_19_0.43_0.45_5", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.43 y with y(0)=19, step size h=0.45, for 5 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.43 y, so each step multiplies y by 1 - h*0.43.\nApply that update for 5 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 19.0, "rate": 0.43, "step": 0.45, "steps": 5}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(4.7)=10.33 and f(5.5)=12.65.\n3. The interval width is 0.8.\nFinal: {\"answer\": 9.192, \"unit\": \"area_units\"}", "dedupe_signature": "aecf397846d26575556568d3c424b2965380137018164392efeed977a671d195", "difficulty": "medium", "final_answer": {"answer": 9.192, "unit": "area_units"}, "id": "trapz_linear_007588_2.9_-3.3_4.7_5.5", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=2.9x+-3.3 from x=4.7 to x=5.5. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(4.7)=10.33 and f(5.5)=12.65.\nThe interval width is 0.8.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -3.3, "slope": 2.9, "x0": 4.7, "x1": 5.5}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.44 and add it to the current value.\nFinal: {\"answer\": [-0.754, 1.468, 0.598], \"unit\": \"temperature_units\"}", "dedupe_signature": "65c4591ab8fae1396df77c1fd47f49b3e1f1eae7bc615fee2bb3f4a47485816f", "difficulty": "hard", "final_answer": {"answer": [-0.754, 1.468, 0.598], "unit": "temperature_units"}, "id": "heat_step_007589_0.44_-1.0_1.6_-1.15_2.05_1.95", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-1, right=1.95; current interior values are [1.6, -1.15, 2.05]. Use r=0.44. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.44 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [1.6, -1.15, 2.05], "left": -1.0, "r": 0.44, "right": 1.95}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=355 degrees and keep the unit as newtons.\nFinal: {\"answer\": [112.0719, -9.805], \"unit\": \"N\"}", "dedupe_signature": "beb2e3815e9efa31328ec67f2127aa3dfe97a4d87556154b6cf8e1cacca13b62", "difficulty": "medium", "final_answer": {"answer": [112.0719, -9.805], "unit": "N"}, "id": "vector_components_007591_112.5_355", "license": "Apache-2.0", "prompt": "A vector has magnitude 112.5 N at 355 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=355 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 355, "magnitude": 112.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-6.15, 24.75], \"unit\": \"dimensionless\"}", "dedupe_signature": "29e038c07e31cb02881e9f8d73fdc763db8455761c7ba9d36605a84e1644e933", "difficulty": "medium", "final_answer": {"answer": [-6.15, 24.75], "unit": "dimensionless"}, "id": "line_two_point_007592_-3.75_4_-6.15_24.75", "license": "Apache-2.0", "prompt": "A line passes through points (-3.75, 47.8125) and (4, 0.15). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -3.75, "x2": 4.0, "y1": 47.8125, "y2": 0.14999999999999858}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef center_values_007594(values):\n    if not values:\n        raise ValueError('center_values requires at least one value')\n    mean = sum(values) / len(values)\n    return [value - mean for value in values]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"center_values_007594\"}", "dedupe_signature": "fdeb9dc86821a6f26f7c9b618236610bc3f034550625dfc2777cebf602d60214", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "center_values_007594"}, "id": "code_007594_center_values_007594", "license": "Apache-2.0", "prompt": "Write a Python function center_values_007594(values) that subtracts the arithmetic mean from each value and returns a new list. Raise ValueError for an empty input. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "center_values_007594"}, "verifier": {"function": "center_values_007594", "tests": ["out = center_values_007594([1, 2, 3]); assert out == [-1, 0, 1]", "assert center_values_007594([5]) == [0]", "try:\n    center_values_007594([])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 22.05 kg and a = 5.6 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 123.48, \"unit\": \"N\"}", "dedupe_signature": "5694ccdf297cc2f6d2f0484e57cce34fd63f2be03360ac90df3779228bbd970e", "difficulty": "easy", "final_answer": {"answer": 123.48, "unit": "N"}, "id": "force_007596_22.05_5.6", "license": "Apache-2.0", "prompt": "A cart has mass 22.05 kg and measured acceleration 5.6 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 22.05 kg and a = 5.6 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 5.6, "mass": 22.05}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 36.5^2 and multiply by 0.5 * 26.85.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 17885.4562, \"unit\": \"J\"}", "dedupe_signature": "0158c4b64c9ec152ffc6c09ab671e5857b78ef30e97f9e82d781d686fdf8f756", "difficulty": "easy", "final_answer": {"answer": 17885.4562, "unit": "J"}, "id": "ke_007597_26.85_36.5", "license": "Apache-2.0", "prompt": "A body of mass 26.85 kg moves at 36.5 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 36.5^2 and multiply by 0.5 * 26.85.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 26.85, "velocity": 36.5}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 2.57 * 8.314 * 615 / 96.0.\nFinal: {\"answer\": 136.8822, \"unit\": \"kPa\"}", "dedupe_signature": "1ba63258923611d6a1e8c32231264331125326b69e81a56d846049706e29d4a9", "difficulty": "medium", "final_answer": {"answer": 136.8822, "unit": "kPa"}, "id": "ideal_gas_007599_2.57_615_96.0", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=2.57 mol, T=615 K, and V=96.0 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 2.57 * 8.314 * 615 / 96.0.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 2.57, "temp_k": 615, "volume_l": 96.0}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 845 * 4.195 * 79.\nFinal: {\"answer\": 280037.225, \"unit\": \"J\"}", "dedupe_signature": "56bc887658b7dcafd515b289e976072593b1ae3d72563f06141710929f4bc328", "difficulty": "easy", "final_answer": {"answer": 280037.225, "unit": "J"}, "id": "heat_q_007600_845_4.195_79", "license": "Apache-2.0", "prompt": "A 845 g sample has specific heat 4.195 J/(g*K). How much heat is needed to raise its temperature by 79 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 845 * 4.195 * 79.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 79, "heat_capacity": 4.195, "mass_g": 845}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=8.3 V and R=1.9 ohm.\nFinal: {\"answer\": 36.2579, \"unit\": \"W\"}", "dedupe_signature": "00d7bf227cae53f89610abfe5b3659451b8336cc41e7836c19e1dedce611771e", "difficulty": "easy", "final_answer": {"answer": 36.2579, "unit": "W"}, "id": "ohm_power_007601_8.3_1.9", "license": "Apache-2.0", "prompt": "A resistor has resistance 1.9 ohm and voltage 8.3 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=8.3 V and R=1.9 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 1.9, "voltage": 8.3}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=423 mg, t=19 h, and T_half=35.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 291.8944, \"unit\": \"mg\"}", "dedupe_signature": "ad96633a9df0e247bee6b2a473c40e28d76d57251b5a9ac01d6e99493b30ea49", "difficulty": "medium", "final_answer": {"answer": 291.8944, "unit": "mg"}, "id": "half_life_007602_423_35.5_19", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 423 mg. Its half-life is 35.5 hours. How many mg remain after 19 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=423 mg, t=19 h, and T_half=35.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 19.0, "half_life": 35.5, "initial_amount": 423.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 1.23 mol * 44.01 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 54.1323, \"unit\": \"g\"}", "dedupe_signature": "1a84e441d53332ca61ea297fb3d45bdb056242a4b99a32c675d65d3996e62214", "difficulty": "medium", "final_answer": {"answer": 54.1323, "unit": "g"}, "id": "stoich_mass_007603_carbon_dioxide_1.23", "license": "Apache-2.0", "prompt": "A sample contains 1.23 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 1.23 mol * 44.01 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "carbon dioxide", "molar_mass": 44.01, "moles": 1.23}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 1525 mL to 1.525 L.\n3. Compute M = 0.99 / 1.525.\nFinal: {\"answer\": 0.6492, \"unit\": \"mol/L\"}", "dedupe_signature": "d552f743da63e31b9f6105cff03be98a26fb83694b84ba0c54a6f73bcd9c14e5", "difficulty": "medium", "final_answer": {"answer": 0.6492, "unit": "mol/L"}, "id": "molarity_007604_0.99_1525", "license": "Apache-2.0", "prompt": "A solution contains 0.99 mol of solute in 1525 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 1525 mL to 1.525 L.\nCompute M = 0.99 / 1.525.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 0.99, "volume_ml": 1525}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.64 y, so each step multiplies y by 1 - h*0.64.\n3. Apply that update for 4 steps and round the final state.\nFinal: {\"answer\": 0.0034, \"unit\": \"state_units\"}", "dedupe_signature": "df684c609e860019a738de4d51051c12ada7ce541461a25062d4659f2662075c", "difficulty": "medium", "final_answer": {"answer": 0.0034, "unit": "state_units"}, "id": "euler_decay_007605_16.5_0.64_1.75_4", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.64 y with y(0)=16.5, step size h=1.75, for 4 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.64 y, so each step multiplies y by 1 - h*0.64.\nApply that update for 4 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 16.5, "rate": 0.64, "step": 1.75, "steps": 4}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-6.8)=58 and f(-3.9)=39.15.\n3. The interval width is 2.9.\nFinal: {\"answer\": 140.8675, \"unit\": \"area_units\"}", "dedupe_signature": "dc5a418a6b56c80cad7be1a6be9f3f3bb9397d6ad00f362878524ce03bfa24cd", "difficulty": "medium", "final_answer": {"answer": 140.8675, "unit": "area_units"}, "id": "trapz_linear_007606_-6.5_13.8_-6.8_-3.9", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-6.5x+13.8 from x=-6.8 to x=-3.9. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-6.8)=58 and f(-3.9)=39.15.\nThe interval width is 2.9.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 13.8, "slope": -6.5, "x0": -6.8, "x1": -3.9}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.2 and add it to the current value.\nFinal: {\"answer\": [1.66, 1.92, 2.0], \"unit\": \"temperature_units\"}", "dedupe_signature": "7ff88a405c306405d2b1d6a234710044409501e199a9d10daca67ad392d294b8", "difficulty": "hard", "final_answer": {"answer": [1.66, 1.92, 2.0], "unit": "temperature_units"}, "id": "heat_step_007607_0.2_-0.8_2.55_1.45_2.7_0.45", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-0.8, right=0.45; current interior values are [2.55, 1.45, 2.7]. Use r=0.2. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.2 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [2.55, 1.45, 2.7], "left": -0.8, "r": 0.2, "right": 0.45}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=320 degrees and keep the unit as newtons.\nFinal: {\"answer\": [291.0969, -244.2593], \"unit\": \"N\"}", "dedupe_signature": "d8899a9a745ef0bf3221f35414afcf8e616ea716ffe81699112db50d0ccd94b9", "difficulty": "medium", "final_answer": {"answer": [291.0969, -244.2593], "unit": "N"}, "id": "vector_components_007609_380_320", "license": "Apache-2.0", "prompt": "A vector has magnitude 380 N at 320 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=320 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 320, "magnitude": 380.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [1.95, 0.25], \"unit\": \"dimensionless\"}", "dedupe_signature": "7e69d35ee3d6402e83bd51e4662a8bbf39cd6697e1d448e8cd3c9a675de3e9b0", "difficulty": "medium", "final_answer": {"answer": [1.95, 0.25], "unit": "dimensionless"}, "id": "line_two_point_007610_-19.75_-5.75_1.95_0.25", "license": "Apache-2.0", "prompt": "A line passes through points (-19.75, -38.2625) and (-5.75, -10.9625). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -19.75, "x2": -5.75, "y1": -38.262499999999996, "y2": -10.9625}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. amount times volume is not concentration\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "b41e3a4e1d11158803910e900a89ddf2265730d329abf99b0e34e1f471dd96d3", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_007611_inconsistent_74ac0b02_368017", "license": "Apache-2.0", "prompt": "In instrument manual case 368017, check dimensional consistency for C = n * V. The left side has dimensions mol/L and the right side has dimensions mol*L. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\namount times volume is not concentration\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "C = n * V"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\nimport math\n\ndef unit_vector_007612(x, y):\n    norm = math.hypot(x, y)\n    if norm == 0:\n        raise ValueError('zero vector has no direction')\n    return (x / norm, y / norm)\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"unit_vector_007612\"}", "dedupe_signature": "fa0f80bad42e544c8ee4cd8dee4ad369e8028b7e1347d344467708d0e11d5b90", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "unit_vector_007612"}, "id": "code_007612_unit_vector_007612", "license": "Apache-2.0", "prompt": "Write a Python function unit_vector_007612(x, y) that returns the 2D unit vector as a tuple. Raise ValueError for the zero vector. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "unit_vector_007612"}, "verifier": {"function": "unit_vector_007612", "tests": ["ux, uy = unit_vector_007612(3, 4); assert abs(ux - 0.6) < 1e-12 and abs(uy - 0.8) < 1e-12", "assert unit_vector_007612(0, 5) == (0, 1)", "try:\n    unit_vector_007612(0, 0)\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: required_fields, allowed_transformations.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"required_fields\", \"allowed_transformations\"]}", "dedupe_signature": "d68ebbd95636cbd67dcaaaea8578828e3dc45670ce8a1d049175867acf60192a", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["required_fields", "allowed_transformations"]}, "id": "abstain_007613_required_fields_allowed_transformations", "license": "Apache-2.0", "prompt": "Write a sanitizer for valid registry invoice records in release 933485, but the prompt does not state which fields are required or which transformations are allowed. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: required_fields, allowed_transformations.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["required_fields", "allowed_transformations"]}, "verifier": {"missing": ["required_fields", "allowed_transformations"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 19.8^2 and multiply by 0.5 * 16.75.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 3283.335, \"unit\": \"J\"}", "dedupe_signature": "776c211c27aa506c89638310f28d638b7a00b5bea199461b6b552c92436a97f9", "difficulty": "easy", "final_answer": {"answer": 3283.335, "unit": "J"}, "id": "ke_007615_16.75_19.8", "license": "Apache-2.0", "prompt": "A body of mass 16.75 kg moves at 19.8 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 19.8^2 and multiply by 0.5 * 16.75.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 16.75, "velocity": 19.8}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=25 degrees through the sine of 2 theta.\n3. Substitute v=49.9 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 194.4402, \"unit\": \"m\"}", "dedupe_signature": "c11f154cf5e5c3d8064b9676d3f266201992ea45c092c8166cbe1ccfc204c5d7", "difficulty": "medium", "final_answer": {"answer": 194.4402, "unit": "m"}, "id": "projectile_range_007616_49.9_25", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 49.9 m/s and angle 25 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=25 degrees through the sine of 2 theta.\nSubstitute v=49.9 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 25, "gravity": 9.81, "speed": 49.9}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 2.17 * 8.314 * 615 / 53.0.\nFinal: {\"answer\": 209.3481, \"unit\": \"kPa\"}", "dedupe_signature": "2e865c27db7b48c39f1eadb73d40cab7ba01cdb0fc3a711b1c1dcf06996af7f2", "difficulty": "medium", "final_answer": {"answer": 209.3481, "unit": "kPa"}, "id": "ideal_gas_007617_2.17_615_53.0", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=2.17 mol, T=615 K, and V=53.0 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 2.17 * 8.314 * 615 / 53.0.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 2.17, "temp_k": 615, "volume_l": 53.0}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1275 * 4.03 * 16.\nFinal: {\"answer\": 82212.0, \"unit\": \"J\"}", "dedupe_signature": "a078e72d8722243582ab0843b4f1a20f58de2c6c815d4476a600e877ba686d76", "difficulty": "easy", "final_answer": {"answer": 82212.0, "unit": "J"}, "id": "heat_q_007618_1275_4.03_16", "license": "Apache-2.0", "prompt": "A 1275 g sample has specific heat 4.03 J/(g*K). How much heat is needed to raise its temperature by 16 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1275 * 4.03 * 16.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 16, "heat_capacity": 4.03, "mass_g": 1275}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=108.8 V and R=156.4 ohm.\nFinal: {\"answer\": 75.687, \"unit\": \"W\"}", "dedupe_signature": "56199fb9ca5de6da5cb7c79073b57406a4a9ab57f4849e9f21b5a30d322f60bd", "difficulty": "easy", "final_answer": {"answer": 75.687, "unit": "W"}, "id": "ohm_power_007619_108.8_156.4", "license": "Apache-2.0", "prompt": "A resistor has resistance 156.4 ohm and voltage 108.8 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=108.8 V and R=156.4 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 156.4, "voltage": 108.8}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 3.14 mol * 44.01 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 138.1914, \"unit\": \"g\"}", "dedupe_signature": "b581977caf42c19adafe3aedb2bc953fb72cc36c9c8feac932270599bfa9956c", "difficulty": "medium", "final_answer": {"answer": 138.1914, "unit": "g"}, "id": "stoich_mass_007621_carbon_dioxide_3.14", "license": "Apache-2.0", "prompt": "A sample contains 3.14 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 3.14 mol * 44.01 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "carbon dioxide", "molar_mass": 44.01, "moles": 3.14}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 3030 mL to 3.03 L.\n3. Compute M = 0.15 / 3.03.\nFinal: {\"answer\": 0.0495, \"unit\": \"mol/L\"}", "dedupe_signature": "ebbcce1a57f83dfa56f6811ecf798b1307cfed960fd451ac070cdfe3d70c4f7b", "difficulty": "medium", "final_answer": {"answer": 0.0495, "unit": "mol/L"}, "id": "molarity_007622_0.15_3030", "license": "Apache-2.0", "prompt": "A solution contains 0.15 mol of solute in 3030 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 3030 mL to 3.03 L.\nCompute M = 0.15 / 3.03.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 0.15, "volume_ml": 3030}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.1 y, so each step multiplies y by 1 - h*0.1.\n3. Apply that update for 5 steps and round the final state.\nFinal: {\"answer\": 27.4054, \"unit\": \"state_units\"}", "dedupe_signature": "b0a5713e6acd6b049b8d48f1f5129a3690963e38a1b23d1d2742d59e13a3410d", "difficulty": "medium", "final_answer": {"answer": 27.4054, "unit": "state_units"}, "id": "euler_decay_007623_34.5_0.1_0.45_5", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.1 y with y(0)=34.5, step size h=0.45, for 5 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.1 y, so each step multiplies y by 1 - h*0.1.\nApply that update for 5 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 34.5, "rate": 0.1, "step": 0.45, "steps": 5}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-5.7)=-22.13 and f(2.6)=18.54.\n3. The interval width is 8.3.\nFinal: {\"answer\": -14.8985, \"unit\": \"area_units\"}", "dedupe_signature": "2ffcfac51078febc4d642388b26259b35828acf5ed10e093590ae64591baab9d", "difficulty": "medium", "final_answer": {"answer": -14.8985, "unit": "area_units"}, "id": "trapz_linear_007624_4.9_5.8_-5.7_2.6", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=4.9x+5.8 from x=-5.7 to x=2.6. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-5.7)=-22.13 and f(2.6)=18.54.\nThe interval width is 8.3.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 5.8, "slope": 4.9, "x0": -5.7, "x1": 2.6000000000000005}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.26 and add it to the current value.\nFinal: {\"answer\": [1.358, 0.724, 1.155], \"unit\": \"temperature_units\"}", "dedupe_signature": "584b3d1b4585262d36089ac18683192c9dd6d57adf97ca335be3f6b15b1b5b62", "difficulty": "hard", "final_answer": {"answer": [1.358, 0.724, 1.155], "unit": "temperature_units"}, "id": "heat_step_007625_0.26_1.25_2.45_-0.55_1.35_2.5", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.25, right=2.5; current interior values are [2.45, -0.55, 1.35]. Use r=0.26. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.26 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [2.45, -0.55, 1.35], "left": 1.25, "r": 0.26, "right": 2.5}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 29647.0 / 1000.\nFinal: {\"answer\": 29.647, \"unit\": \"kg\"}", "dedupe_signature": "5d62a2fb2cc391df22b3572710ee9474872b08ed50ef461c9b3de26d34b05d41", "difficulty": "easy", "final_answer": {"answer": 29.647, "unit": "kg"}, "id": "unit_convert_007626_g_to_kg_29647", "license": "Apache-2.0", "prompt": "Convert 29647 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 29647.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 29647.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=277 degrees and keep the unit as newtons.\nFinal: {\"answer\": [21.3881, -174.1918], \"unit\": \"N\"}", "dedupe_signature": "27fdb5683ac462ad141bd6bc1cbc8872c247249cc2bed1e00f0c87bfe9080d77", "difficulty": "medium", "final_answer": {"answer": [21.3881, -174.1918], "unit": "N"}, "id": "vector_components_007627_175.5_277", "license": "Apache-2.0", "prompt": "A vector has magnitude 175.5 N at 277 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=277 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 277, "magnitude": 175.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-1.2, 11.0], \"unit\": \"dimensionless\"}", "dedupe_signature": "077fa9e3337699d5f32809c2c477365489e25dfd7150f7db914a5adce43182ab", "difficulty": "medium", "final_answer": {"answer": [-1.2, 11.0], "unit": "dimensionless"}, "id": "line_two_point_007628_18.75_25.25_-1.2_11", "license": "Apache-2.0", "prompt": "A line passes through points (18.75, -11.5) and (25.25, -19.3). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 18.75, "x2": 25.25, "y1": -11.5, "y2": -19.299999999999997}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef threshold_flags_007630(values, threshold):\n    return [value >= threshold for value in values]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"threshold_flags_007630\"}", "dedupe_signature": "9ab920e15810f7a2e3993a5e5b5a08bf03986272342a9971ded5c52ae3cf2962", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "threshold_flags_007630"}, "id": "code_007630_threshold_flags_007630", "license": "Apache-2.0", "prompt": "Write a Python function threshold_flags_007630(values, threshold) that returns a list of booleans showing whether each value is greater than or equal to threshold. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "threshold_flags_007630"}, "verifier": {"function": "threshold_flags_007630", "tests": ["assert threshold_flags_007630([1, 2, 3], 2) == [False, True, True]", "assert threshold_flags_007630([], 5) == []", "assert threshold_flags_007630([-1, 0], 0) == [False, True]"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: required_fields, allowed_transformations.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"required_fields\", \"allowed_transformations\"]}", "dedupe_signature": "212efc98b806816f9e7ece284f94df5bbac778ed736ab535b27f83a3d25fb2e4", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["required_fields", "allowed_transformations"]}, "id": "abstain_007631_required_fields_allowed_transformations", "license": "Apache-2.0", "prompt": "Write a sanitizer for valid field clinical records in release 614339, but the prompt does not state which fields are required or which transformations are allowed. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: required_fields, allowed_transformations.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["required_fields", "allowed_transformations"]}, "verifier": {"missing": ["required_fields", "allowed_transformations"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 16.9 kg and a = 2.5 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 42.25, \"unit\": \"N\"}", "dedupe_signature": "5387e5d7ca4d91283c8ef281ded414e837c8d008759cd2a1f626daa6a2d82da5", "difficulty": "easy", "final_answer": {"answer": 42.25, "unit": "N"}, "id": "force_007632_16.9_2.5", "license": "Apache-2.0", "prompt": "A cart has mass 16.9 kg and measured acceleration 2.5 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 16.9 kg and a = 2.5 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 2.5, "mass": 16.9}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 24.6^2 and multiply by 0.5 * 7.5.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 2269.35, \"unit\": \"J\"}", "dedupe_signature": "dc69bf376fe8771620ced32537654e9276ca57e18cea1d654493fef09e571c2e", "difficulty": "easy", "final_answer": {"answer": 2269.35, "unit": "J"}, "id": "ke_007633_7.5_24.6", "license": "Apache-2.0", "prompt": "A body of mass 7.5 kg moves at 24.6 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 24.6^2 and multiply by 0.5 * 7.5.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 7.5, "velocity": 24.6}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 1.9 * 8.314 * 310 / 107.2.\nFinal: {\"answer\": 45.6805, \"unit\": \"kPa\"}", "dedupe_signature": "3edb9c744445a98eb2d6f8e187fff6edfbc2ddd22ddc74d8eb8143535dbea1a0", "difficulty": "medium", "final_answer": {"answer": 45.6805, "unit": "kPa"}, "id": "ideal_gas_007635_1.9_310_107.2", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=1.9 mol, T=310 K, and V=107.2 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 1.9 * 8.314 * 310 / 107.2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 1.9, "temp_k": 310, "volume_l": 107.2}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 555 * 3.79 * 75.\nFinal: {\"answer\": 157758.75, \"unit\": \"J\"}", "dedupe_signature": "a1b5f992b82b2be36e0989076d33386131478bf22344881a62c0ffba01d707a3", "difficulty": "easy", "final_answer": {"answer": 157758.75, "unit": "J"}, "id": "heat_q_007636_555_3.79_75", "license": "Apache-2.0", "prompt": "A 555 g sample has specific heat 3.79 J/(g*K). How much heat is needed to raise its temperature by 75 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 555 * 3.79 * 75.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 75, "heat_capacity": 3.79, "mass_g": 555}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=18.2 V and R=153.4 ohm.\nFinal: {\"answer\": 2.1593, \"unit\": \"W\"}", "dedupe_signature": "b12e4ae4be269da178d03e71820d1c123e9990d175e5afe7b25075e3524badb3", "difficulty": "easy", "final_answer": {"answer": 2.1593, "unit": "W"}, "id": "ohm_power_007637_18.2_153.4", "license": "Apache-2.0", "prompt": "A resistor has resistance 153.4 ohm and voltage 18.2 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=18.2 V and R=153.4 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 153.4, "voltage": 18.2}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=34.5 mg, t=283.5 h, and T_half=33 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 0.0895, \"unit\": \"mg\"}", "dedupe_signature": "c58e7fb90d4a0654da45685002e946e34233a22e17f7c8ec79fc6a5a68e0cd60", "difficulty": "medium", "final_answer": {"answer": 0.0895, "unit": "mg"}, "id": "half_life_007638_34.5_33_283.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 34.5 mg. Its half-life is 33 hours. How many mg remain after 283.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=34.5 mg, t=283.5 h, and T_half=33 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 283.5, "half_life": 33.0, "initial_amount": 34.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 7.38 mol * 180.156 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 1329.5513, \"unit\": \"g\"}", "dedupe_signature": "1f9c9ec1d8792647d1fded6b0149c3f5e5cb1ba40f17393123656af92b2c436f", "difficulty": "medium", "final_answer": {"answer": 1329.5513, "unit": "g"}, "id": "stoich_mass_007639_glucose_7.38", "license": "Apache-2.0", "prompt": "A sample contains 7.38 mol of glucose. Using molar mass 180.156 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 7.38 mol * 180.156 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "glucose", "molar_mass": 180.156, "moles": 7.38}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 3055 mL to 3.055 L.\n3. Compute M = 3.545 / 3.055.\nFinal: {\"answer\": 1.1604, \"unit\": \"mol/L\"}", "dedupe_signature": "9227fda2a43f840cff3ae734d1b77b7abaab038f6ca25c9f45266a707ada2ff9", "difficulty": "medium", "final_answer": {"answer": 1.1604, "unit": "mol/L"}, "id": "molarity_007640_3.545_3055", "license": "Apache-2.0", "prompt": "A solution contains 3.545 mol of solute in 3055 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 3055 mL to 3.055 L.\nCompute M = 3.545 / 3.055.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 3.545, "volume_ml": 3055}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.6 y, so each step multiplies y by 1 - h*0.6.\n3. Apply that update for 12 steps and round the final state.\nFinal: {\"answer\": 0.0013, \"unit\": \"state_units\"}", "dedupe_signature": "42d61e8b8f2ffefdf3e70494c19c042b62be0abcc05fd86cb268c3e6d979883a", "difficulty": "medium", "final_answer": {"answer": 0.0013, "unit": "state_units"}, "id": "euler_decay_007641_79.5_0.6_1_12", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.6 y with y(0)=79.5, step size h=1, for 12 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.6 y, so each step multiplies y by 1 - h*0.6.\nApply that update for 12 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 79.5, "rate": 0.6, "step": 1.0, "steps": 12}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(6.1)=-57.35 and f(7.4)=-67.1.\n3. The interval width is 1.3.\nFinal: {\"answer\": -80.8925, \"unit\": \"area_units\"}", "dedupe_signature": "1080379e0929ffb0a72d2c71056dc9e189bacfc7418a78ec14234d8c9a1e01d9", "difficulty": "medium", "final_answer": {"answer": -80.8925, "unit": "area_units"}, "id": "trapz_linear_007642_-7.5_-11.6_6.1_7.4", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-7.5x+-11.6 from x=6.1 to x=7.4. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(6.1)=-57.35 and f(7.4)=-67.1.\nThe interval width is 1.3.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -11.6, "slope": -7.5, "x0": 6.1, "x1": 7.3999999999999995}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.18 and add it to the current value.\nFinal: {\"answer\": [-0.102, 2.118, 1.886], \"unit\": \"temperature_units\"}", "dedupe_signature": "a48098b5bdb8b47e5a44ce81f2390e592feccd49244c9f5e77ed760823584488", "difficulty": "hard", "final_answer": {"answer": [-0.102, 2.118, 1.886], "unit": "temperature_units"}, "id": "heat_step_007643_0.18_-0.9_-0.75_3.0_1.85_0.9", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-0.9, right=0.9; current interior values are [-0.75, 3.0, 1.85]. Use r=0.18. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.18 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-0.75, 3.0, 1.85], "left": -0.9, "r": 0.18, "right": 0.9}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 100 centimeters in one meter.\n2. Apply the conversion factor directly to the given value.\n3. Compute 1407.0 / 100.\nFinal: {\"answer\": 14.07, \"unit\": \"m\"}", "dedupe_signature": "0a562fd1945c37a4da1fd370556b99f82a0f40e7038da22581cb807d0c8990bc", "difficulty": "easy", "final_answer": {"answer": 14.07, "unit": "m"}, "id": "unit_convert_007644_cm_to_m_1407", "license": "Apache-2.0", "prompt": "Convert 1407 cm to m. Return the converted value with unit.", "reasoning_trace": "There are 100 centimeters in one meter.\nApply the conversion factor directly to the given value.\nCompute 1407.0 / 100.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 1407.0}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=88 degrees and keep the unit as newtons.\nFinal: {\"answer\": [4.694, 134.4181], \"unit\": \"N\"}", "dedupe_signature": "8a023d4cc346111567f8f9bd0d2326e50dccb04796341df2abf2f99823f25e35", "difficulty": "medium", "final_answer": {"answer": [4.694, 134.4181], "unit": "N"}, "id": "vector_components_007645_134.5_88", "license": "Apache-2.0", "prompt": "A vector has magnitude 134.5 N at 88 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=88 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 88, "magnitude": 134.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. speed squared over acceleration has units of meters\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "79904c14b4390012269053bd54d824ea12b82003e7d0878e7479c0894546bc7d", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_007647_consistent_741d4e34_976397", "license": "Apache-2.0", "prompt": "In simulation spec case 976397, check dimensional consistency for R = v^2 * sin(theta) / g. The left side has dimensions m and the right side has dimensions m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nspeed squared over acceleration has units of meters\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "R = v^2 * sin(theta) / g"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef running_total_007648(values):\n    total = 0\n    out = []\n    for value in values:\n        total += value\n        out.append(total)\n    return out\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"running_total_007648\"}", "dedupe_signature": "0280d80759da742c30167224fade4d9adf42c86a28152354219901485b0cc83a", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "running_total_007648"}, "id": "code_007648_running_total_007648", "license": "Apache-2.0", "prompt": "Write a Python function running_total_007648(values) that returns cumulative sums as a new list. It must not mutate the input list. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "running_total_007648"}, "verifier": {"function": "running_total_007648", "tests": ["assert running_total_007648([1, 2, 3]) == [1, 3, 6]", "xs = [4, -1, 2]; assert running_total_007648(xs) == [4, 3, 5] and xs == [4, -1, 2]", "assert running_total_007648([]) == []"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: launch_angle_or_vertical_velocity.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"launch_angle_or_vertical_velocity\"]}", "dedupe_signature": "5f81f2879021bc4439eb2631cd76d880486c3991162e3dbda77382d6476b014c", "difficulty": "easy", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["launch_angle_or_vertical_velocity"]}, "id": "abstain_007649_launch_angle_or_vertical_velocity", "license": "Apache-2.0", "prompt": "Compute projectile range on level ground. The prompt gives initial speed 13.7 m/s but does not give launch angle or vertical velocity. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: launch_angle_or_vertical_velocity.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["launch_angle_or_vertical_velocity"]}, "verifier": {"missing": ["launch_angle_or_vertical_velocity"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 3.35 kg and a = 14.1 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 47.235, \"unit\": \"N\"}", "dedupe_signature": "89c122e48283dad3ba78dafbf1d40cb788b7bed8920102776c4772f573a1631c", "difficulty": "easy", "final_answer": {"answer": 47.235, "unit": "N"}, "id": "force_007650_3.35_14.1", "license": "Apache-2.0", "prompt": "A cart has mass 3.35 kg and measured acceleration 14.1 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 3.35 kg and a = 14.1 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 14.1, "mass": 3.35}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=55 degrees through the sine of 2 theta.\n3. Substitute v=11.5 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 12.6681, \"unit\": \"m\"}", "dedupe_signature": "f6d95ad8de808dc29058608cfc845d639d6ffae79e9f10cd6335531f78c0a855", "difficulty": "medium", "final_answer": {"answer": 12.6681, "unit": "m"}, "id": "projectile_range_007652_11.5_55", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 11.5 m/s and angle 55 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=55 degrees through the sine of 2 theta.\nSubstitute v=11.5 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 55, "gravity": 9.81, "speed": 11.5}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 2.51 * 8.314 * 537 / 97.6.\nFinal: {\"answer\": 114.8175, \"unit\": \"kPa\"}", "dedupe_signature": "48c6b7b19d118ea4116b00a6255db439ea00a344220dc45f94cab6fc4834d76f", "difficulty": "medium", "final_answer": {"answer": 114.8175, "unit": "kPa"}, "id": "ideal_gas_007653_2.51_537_97.6", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=2.51 mol, T=537 K, and V=97.6 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 2.51 * 8.314 * 537 / 97.6.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 2.51, "temp_k": 537, "volume_l": 97.6}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1845 * 2.115 * 81.\nFinal: {\"answer\": 316076.175, \"unit\": \"J\"}", "dedupe_signature": "424fb2f84dd5ec9be8786b3c78b41d2f04ed35e68727176fdcc43e5a75d81a5d", "difficulty": "easy", "final_answer": {"answer": 316076.175, "unit": "J"}, "id": "heat_q_007654_1845_2.115_81", "license": "Apache-2.0", "prompt": "A 1845 g sample has specific heat 2.115 J/(g*K). How much heat is needed to raise its temperature by 81 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1845 * 2.115 * 81.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 81, "heat_capacity": 2.115, "mass_g": 1845}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=179.1 V and R=83.6 ohm.\nFinal: {\"answer\": 383.6939, \"unit\": \"W\"}", "dedupe_signature": "330606167f008bc545426436a078fd8463bc0d6dc6feb4d199732f29669ad11e", "difficulty": "easy", "final_answer": {"answer": 383.6939, "unit": "W"}, "id": "ohm_power_007655_179.1_83.6", "license": "Apache-2.0", "prompt": "A resistor has resistance 83.6 ohm and voltage 179.1 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=179.1 V and R=83.6 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 83.6, "voltage": 179.1}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=25.5 mg, t=49 h, and T_half=74.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 16.1639, \"unit\": \"mg\"}", "dedupe_signature": "9b9244ded60c79116a0635cba95bf36bd6c1b3a91b1406cf5de7345cdfd2b547", "difficulty": "medium", "final_answer": {"answer": 16.1639, "unit": "mg"}, "id": "half_life_007656_25.5_74.5_49", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 25.5 mg. Its half-life is 74.5 hours. How many mg remain after 49 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=25.5 mg, t=49 h, and T_half=74.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 49.0, "half_life": 74.5, "initial_amount": 25.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 1.76 mol * 58.44 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 102.8544, \"unit\": \"g\"}", "dedupe_signature": "22923f892ad6819d4b8efc7fbf5e76cc847e0d4ca1df185bc78729688050c83b", "difficulty": "medium", "final_answer": {"answer": 102.8544, "unit": "g"}, "id": "stoich_mass_007657_sodium_chloride_1.76", "license": "Apache-2.0", "prompt": "A sample contains 1.76 mol of sodium chloride. Using molar mass 58.44 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 1.76 mol * 58.44 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "sodium chloride", "molar_mass": 58.44, "moles": 1.76}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 4090 mL to 4.09 L.\n3. Compute M = 0.925 / 4.09.\nFinal: {\"answer\": 0.2262, \"unit\": \"mol/L\"}", "dedupe_signature": "a0c2ac0b858af1958043e50c3f4666b4741fbd190c68dcf656babc41eff27159", "difficulty": "medium", "final_answer": {"answer": 0.2262, "unit": "mol/L"}, "id": "molarity_007658_0.925_4090", "license": "Apache-2.0", "prompt": "A solution contains 0.925 mol of solute in 4090 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 4090 mL to 4.09 L.\nCompute M = 0.925 / 4.09.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 0.925, "volume_ml": 4090}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.36 y, so each step multiplies y by 1 - h*0.36.\n3. Apply that update for 9 steps and round the final state.\nFinal: {\"answer\": 10.141, \"unit\": \"state_units\"}", "dedupe_signature": "d7de89b29fffc86715779e1d60aa53b64bb25e91befc36336a22e72e0e14d2be", "difficulty": "medium", "final_answer": {"answer": 10.141, "unit": "state_units"}, "id": "euler_decay_007659_60.5_0.36_0.5_9", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.36 y with y(0)=60.5, step size h=0.5, for 9 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.36 y, so each step multiplies y by 1 - h*0.36.\nApply that update for 9 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 60.5, "rate": 0.36, "step": 0.5, "steps": 9}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(1.6)=-5.26 and f(5.1)=20.64.\n3. The interval width is 3.5.\nFinal: {\"answer\": 26.915, \"unit\": \"area_units\"}", "dedupe_signature": "760f8ffb601adbd8a0bfb153b44a9db9f05c68ceb25c04b4bde93ffcb62754c5", "difficulty": "medium", "final_answer": {"answer": 26.915, "unit": "area_units"}, "id": "trapz_linear_007660_7.4_-17.1_1.6_5.1", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=7.4x+-17.1 from x=1.6 to x=5.1. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(1.6)=-5.26 and f(5.1)=20.64.\nThe interval width is 3.5.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -17.1, "slope": 7.4, "x0": 1.6, "x1": 5.1}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.22 and add it to the current value.\nFinal: {\"answer\": [-0.547, -0.646, -0.163], \"unit\": \"temperature_units\"}", "dedupe_signature": "131d080bdd6956359e435fb7faf5860e7f2b0ff4fca77c4e136de02a701f0776", "difficulty": "hard", "final_answer": {"answer": [-0.547, -0.646, -0.163], "unit": "temperature_units"}, "id": "heat_step_007661_0.22_-1.9_0.3_-1.35_0.2_0.1", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-1.9, right=0.1; current interior values are [0.3, -1.35, 0.2]. Use r=0.22. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.22 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [0.3, -1.35, 0.2], "left": -1.9, "r": 0.22, "right": 0.1}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kelvin equals Celsius plus 273.15.\n2. Apply the conversion factor directly to the given value.\n3. Compute -44.0 + 273.15.\nFinal: {\"answer\": 229.15, \"unit\": \"K\"}", "dedupe_signature": "ce6fdbad8af559925e81265f21c2a3c102f6248ed07c86418fa593a605d3b249", "difficulty": "easy", "final_answer": {"answer": 229.15, "unit": "K"}, "id": "unit_convert_007662_c_to_k_-44", "license": "Apache-2.0", "prompt": "Convert -44 degC to K. Return the converted value with unit.", "reasoning_trace": "Kelvin equals Celsius plus 273.15.\nApply the conversion factor directly to the given value.\nCompute -44.0 + 273.15.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": -44.0}, "verifier": {"formula": "value + 273.15", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-9.95, 6.0], \"unit\": \"dimensionless\"}", "dedupe_signature": "bd372cebd554895f51bc4dd9fec6b378910b31f8ff2c62ece46e8206e981f702", "difficulty": "medium", "final_answer": {"answer": [-9.95, 6.0], "unit": "dimensionless"}, "id": "line_two_point_007664_-2_1.25_-9.95_6", "license": "Apache-2.0", "prompt": "A line passes through points (-2, 25.9) and (1.25, -6.4375). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -2.0, "x2": 1.25, "y1": 25.9, "y2": -6.4375}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. amount times volume is not concentration\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "ff02302c6703ceb5593d426cfb8d74df7014c5c688b63a1604d4716d2a393b9d", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_007665_inconsistent_74ac0b02_796349", "license": "Apache-2.0", "prompt": "In student derivation case 796349, check dimensional consistency for C = n * V. The left side has dimensions mol/L and the right side has dimensions mol*L. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\namount times volume is not concentration\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "C = n * V"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 4.85 kg and a = 15.95 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 77.3575, \"unit\": \"N\"}", "dedupe_signature": "5302c8caa24e95cc6837316463d0ef7737b07bfb7c98ed003b838da80ae7671c", "difficulty": "easy", "final_answer": {"answer": 77.3575, "unit": "N"}, "id": "force_007668_4.85_15.95", "license": "Apache-2.0", "prompt": "A cart has mass 4.85 kg and measured acceleration 15.95 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 4.85 kg and a = 15.95 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 15.95, "mass": 4.85}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 15.95^2 and multiply by 0.5 * 8.85.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 1125.7311, \"unit\": \"J\"}", "dedupe_signature": "32fdaa62db980afaccb2da9a9e54f6fb4bc087929d6dd7eeba104bd02c9402c3", "difficulty": "easy", "final_answer": {"answer": 1125.7311, "unit": "J"}, "id": "ke_007669_8.85_15.95", "license": "Apache-2.0", "prompt": "A body of mass 8.85 kg moves at 15.95 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 15.95^2 and multiply by 0.5 * 8.85.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 8.85, "velocity": 15.95}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=34 degrees through the sine of 2 theta.\n3. Substitute v=62.8 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 372.7487, \"unit\": \"m\"}", "dedupe_signature": "3ba55306955450c4162ba193acf1bd2f9394055d0f4e7c3fc7e488eb85bd81cf", "difficulty": "medium", "final_answer": {"answer": 372.7487, "unit": "m"}, "id": "projectile_range_007670_62.8_34", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 62.8 m/s and angle 34 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=34 degrees through the sine of 2 theta.\nSubstitute v=62.8 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 34, "gravity": 9.81, "speed": 62.8}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 2.53 * 8.314 * 260 / 105.5.\nFinal: {\"answer\": 51.8384, \"unit\": \"kPa\"}", "dedupe_signature": "75f0425d4eeb612772606e95b487f2b173379bff937ea13248d6b8243a8877bd", "difficulty": "medium", "final_answer": {"answer": 51.8384, "unit": "kPa"}, "id": "ideal_gas_007671_2.53_260_105.5", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=2.53 mol, T=260 K, and V=105.5 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 2.53 * 8.314 * 260 / 105.5.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 2.53, "temp_k": 260, "volume_l": 105.5}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1200 * 1.42 * 60.\nFinal: {\"answer\": 102240.0, \"unit\": \"J\"}", "dedupe_signature": "487789fd4289cbda98909c243b993259ff2c93a604adf9f7aac0df02258a7413", "difficulty": "easy", "final_answer": {"answer": 102240.0, "unit": "J"}, "id": "heat_q_007672_1200_1.42_60", "license": "Apache-2.0", "prompt": "A 1200 g sample has specific heat 1.42 J/(g*K). How much heat is needed to raise its temperature by 60 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1200 * 1.42 * 60.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 60, "heat_capacity": 1.42, "mass_g": 1200}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=64.4 V and R=62 ohm.\nFinal: {\"answer\": 66.8929, \"unit\": \"W\"}", "dedupe_signature": "0a7ef64ceddb2a2424c4c718e5116359d6c1660a9a44e91df58e0e9fefa500a8", "difficulty": "easy", "final_answer": {"answer": 66.8929, "unit": "W"}, "id": "ohm_power_007673_64.4_62", "license": "Apache-2.0", "prompt": "A resistor has resistance 62 ohm and voltage 64.4 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=64.4 V and R=62 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 62.0, "voltage": 64.4}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 2.35 mol * 18.015 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 42.3353, \"unit\": \"g\"}", "dedupe_signature": "dbed4a988c2e003abde003452f811f9fe907dacc849de2e2caa9d861f14f17e2", "difficulty": "medium", "final_answer": {"answer": 42.3353, "unit": "g"}, "id": "stoich_mass_007675_water_2.35", "license": "Apache-2.0", "prompt": "A sample contains 2.35 mol of water. Using molar mass 18.015 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 2.35 mol * 18.015 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "water", "molar_mass": 18.015, "moles": 2.35}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 2425 mL to 2.425 L.\n3. Compute M = 2.005 / 2.425.\nFinal: {\"answer\": 0.8268, \"unit\": \"mol/L\"}", "dedupe_signature": "1f7e6533c92c2ac237d7045fee3c4922c5a654574cc72d51fe408b3069c97c40", "difficulty": "medium", "final_answer": {"answer": 0.8268, "unit": "mol/L"}, "id": "molarity_007676_2.005_2425", "license": "Apache-2.0", "prompt": "A solution contains 2.005 mol of solute in 2425 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 2425 mL to 2.425 L.\nCompute M = 2.005 / 2.425.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 2.005, "volume_ml": 2425}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.11 y, so each step multiplies y by 1 - h*0.11.\n3. Apply that update for 11 steps and round the final state.\nFinal: {\"answer\": 47.0739, \"unit\": \"state_units\"}", "dedupe_signature": "2deb22340c0ab25702bcee2acd342f555fb03038821c3f528b5f792ef7769368", "difficulty": "medium", "final_answer": {"answer": 47.0739, "unit": "state_units"}, "id": "euler_decay_007677_72.5_0.11_0.35_11", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.11 y with y(0)=72.5, step size h=0.35, for 11 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.11 y, so each step multiplies y by 1 - h*0.11.\nApply that update for 11 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 72.5, "rate": 0.11, "step": 0.35, "steps": 11}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.48 and add it to the current value.\nFinal: {\"answer\": [1.502, 1.742, -0.494], \"unit\": \"temperature_units\"}", "dedupe_signature": "2a700e533274841b2471d9ad2c8c1c9454175b1e3fc9d91b359d5289896ce2b2", "difficulty": "hard", "final_answer": {"answer": [1.502, 1.742, -0.494], "unit": "temperature_units"}, "id": "heat_step_007679_0.48_2.6_2.15_0.35_1.45_-1.5", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=2.6, right=-1.5; current interior values are [2.15, 0.35, 1.45]. Use r=0.48. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.48 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [2.15, 0.35, 1.45], "left": 2.6, "r": 0.48, "right": -1.5}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 32878.0 / 1000.\nFinal: {\"answer\": 32.878, \"unit\": \"kg\"}", "dedupe_signature": "a956f44ad17666e704cd2cc955d65d46acfe4629d389f2e4605793f72204e20e", "difficulty": "easy", "final_answer": {"answer": 32.878, "unit": "kg"}, "id": "unit_convert_007680_g_to_kg_32878", "license": "Apache-2.0", "prompt": "Convert 32878 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 32878.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 32878.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-5.0, 15.5], \"unit\": \"dimensionless\"}", "dedupe_signature": "24125abd577017d6d38616e9ecdb94f61ea67de15b0d2a24e50a10588f40f199", "difficulty": "medium", "final_answer": {"answer": [-5.0, 15.5], "unit": "dimensionless"}, "id": "line_two_point_007682_13.5_17.5_-5_15.5", "license": "Apache-2.0", "prompt": "A line passes through points (13.5, -52) and (17.5, -72). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 13.5, "x2": 17.5, "y1": -52.0, "y2": -72.0}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. velocity divided by time is acceleration\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "8533c54fc4100f1979a0d923008a514d9f170f44685f1f1decf2da4088f482df", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_007683_inconsistent_c1271127_897591", "license": "Apache-2.0", "prompt": "In student derivation case 897591, check dimensional consistency for x = v / t. The left side has dimensions m and the right side has dimensions m/s^2. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nvelocity divided by time is acceleration\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "x = v / t"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef center_values_007684(values):\n    if not values:\n        raise ValueError('center_values requires at least one value')\n    mean = sum(values) / len(values)\n    return [value - mean for value in values]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"center_values_007684\"}", "dedupe_signature": "d41b28afe53b85987a7f691d891e22dd13417ed2e3a21b1c408d47ad3ceb591d", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "center_values_007684"}, "id": "code_007684_center_values_007684", "license": "Apache-2.0", "prompt": "Write a Python function center_values_007684(values) that subtracts the arithmetic mean from each value and returns a new list. Raise ValueError for an empty input. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "center_values_007684"}, "verifier": {"function": "center_values_007684", "tests": ["out = center_values_007684([1, 2, 3]); assert out == [-1, 0, 1]", "assert center_values_007684([5]) == [0]", "try:\n    center_values_007684([])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: required_fields, allowed_transformations.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"required_fields\", \"allowed_transformations\"]}", "dedupe_signature": "3dd86f5607dd8b497479944148043e7138787e163f7f139dbee970e03eba7ae9", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["required_fields", "allowed_transformations"]}, "id": "abstain_007685_required_fields_allowed_transformations", "license": "Apache-2.0", "prompt": "Write a sanitizer for valid warehouse invoice records in release 416289, but the prompt does not state which fields are required or which transformations are allowed. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: required_fields, allowed_transformations.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["required_fields", "allowed_transformations"]}, "verifier": {"missing": ["required_fields", "allowed_transformations"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 16.5 kg and a = 12.65 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 208.725, \"unit\": \"N\"}", "dedupe_signature": "79d8b9b025ca01317b9d8057ecf2ef16a92b2cbeda73d80b80dd21cbc89fad3a", "difficulty": "easy", "final_answer": {"answer": 208.725, "unit": "N"}, "id": "force_007686_16.5_12.65", "license": "Apache-2.0", "prompt": "A cart has mass 16.5 kg and measured acceleration 12.65 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 16.5 kg and a = 12.65 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 12.65, "mass": 16.5}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 40.65^2 and multiply by 0.5 * 7.3.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 6031.3421, \"unit\": \"J\"}", "dedupe_signature": "281ef5b0faa6ad5a9ba6d23c58b219bef7f491bcf58fa7070648fc526e96a93b", "difficulty": "easy", "final_answer": {"answer": 6031.3421, "unit": "J"}, "id": "ke_007687_7.3_40.65", "license": "Apache-2.0", "prompt": "A body of mass 7.3 kg moves at 40.65 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 40.65^2 and multiply by 0.5 * 7.3.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 7.3, "velocity": 40.65}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=58 degrees through the sine of 2 theta.\n3. Substitute v=68.2 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 426.1475, \"unit\": \"m\"}", "dedupe_signature": "f244e58497331eb71f9cd039f495462f51b8de36b175b801948cb953ae14e6de", "difficulty": "medium", "final_answer": {"answer": 426.1475, "unit": "m"}, "id": "projectile_range_007688_68.2_58", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 68.2 m/s and angle 58 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=58 degrees through the sine of 2 theta.\nSubstitute v=68.2 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 58, "gravity": 9.81, "speed": 68.2}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 1.86 * 8.314 * 587 / 107.5.\nFinal: {\"answer\": 84.4409, \"unit\": \"kPa\"}", "dedupe_signature": "5792045ee9daa40847e95b5f222e6c890af989b418bd916a855fd2a97bf93495", "difficulty": "medium", "final_answer": {"answer": 84.4409, "unit": "kPa"}, "id": "ideal_gas_007689_1.86_587_107.5", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=1.86 mol, T=587 K, and V=107.5 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 1.86 * 8.314 * 587 / 107.5.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 1.86, "temp_k": 587, "volume_l": 107.5}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=733.5 mg, t=175 h, and T_half=98 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 212.7387, \"unit\": \"mg\"}", "dedupe_signature": "e8bb327ffbb2196e20066b99a8ae3c3d7de798ce98d152067f1484f88d83be13", "difficulty": "medium", "final_answer": {"answer": 212.7387, "unit": "mg"}, "id": "half_life_007692_733.5_98_175", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 733.5 mg. Its half-life is 98 hours. How many mg remain after 175 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=733.5 mg, t=175 h, and T_half=98 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 175.0, "half_life": 98.0, "initial_amount": 733.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 3980 mL to 3.98 L.\n3. Compute M = 4.585 / 3.98.\nFinal: {\"answer\": 1.152, \"unit\": \"mol/L\"}", "dedupe_signature": "0eaea8ae890f619a3e582a5f9e750b356cf96860aa130be67e3ef904cdbf6286", "difficulty": "medium", "final_answer": {"answer": 1.152, "unit": "mol/L"}, "id": "molarity_007694_4.585_3980", "license": "Apache-2.0", "prompt": "A solution contains 4.585 mol of solute in 3980 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 3980 mL to 3.98 L.\nCompute M = 4.585 / 3.98.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 4.585, "volume_ml": 3980}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.17 y, so each step multiplies y by 1 - h*0.17.\n3. Apply that update for 5 steps and round the final state.\nFinal: {\"answer\": 6.321, \"unit\": \"state_units\"}", "dedupe_signature": "56d7d3fa32ef799ee3f4cf580487f786b013fad83c16226627fab5c93ba3c562", "difficulty": "medium", "final_answer": {"answer": 6.321, "unit": "state_units"}, "id": "euler_decay_007695_14.5_0.17_0.9_5", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.17 y with y(0)=14.5, step size h=0.9, for 5 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.17 y, so each step multiplies y by 1 - h*0.17.\nApply that update for 5 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 14.5, "rate": 0.17, "step": 0.9, "steps": 5}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.16 and add it to the current value.\nFinal: {\"answer\": [-0.912, -0.702, 0.474], \"unit\": \"temperature_units\"}", "dedupe_signature": "d7260f7c80c4264c701070420d0983db990fc2e6c48adf3b042a9ef219418cd9", "difficulty": "hard", "final_answer": {"answer": [-0.912, -0.702, 0.474], "unit": "temperature_units"}, "id": "heat_step_007697_0.16_1.2_-1.4_-0.95_1.05_-0.55", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.2, right=-0.55; current interior values are [-1.4, -0.95, 1.05]. Use r=0.16. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.16 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-1.4, -0.95, 1.05], "left": 1.2, "r": 0.16, "right": -0.55}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 47969.0 / 1000.\nFinal: {\"answer\": 47.969, \"unit\": \"kg\"}", "dedupe_signature": "a205e078905270ea4bb3efd3b1ccff06fbf1b8648f7d49e1b306fdac2dd39144", "difficulty": "easy", "final_answer": {"answer": 47.969, "unit": "kg"}, "id": "unit_convert_007698_g_to_kg_47969", "license": "Apache-2.0", "prompt": "Convert 47969 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 47969.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 47969.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=263 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-34.6109, -281.8831], \"unit\": \"N\"}", "dedupe_signature": "d00d2e5230d571424d48f2dd4bea9482a98fd717af2b4e57df35b3b1438cd7a4", "difficulty": "medium", "final_answer": {"answer": [-34.6109, -281.8831], "unit": "N"}, "id": "vector_components_007699_284_263", "license": "Apache-2.0", "prompt": "A vector has magnitude 284 N at 263 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=263 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 263, "magnitude": 284.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. coulomb per second is ampere\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "deca17057c0a7fb741eb272901c66d8dd9a80e953f27e0675adfd09d23825624", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_007701_consistent_8b38953d_142122", "license": "Apache-2.0", "prompt": "In quality-control check case 142122, check dimensional consistency for I = Q / t. The left side has dimensions A and the right side has dimensions A. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\ncoulomb per second is ampere\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "I = Q / t"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef center_values_007702(values):\n    if not values:\n        raise ValueError('center_values requires at least one value')\n    mean = sum(values) / len(values)\n    return [value - mean for value in values]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"center_values_007702\"}", "dedupe_signature": "a017a7e4bcc41f53e93f99141452faae49e0da2cd61a922383c4c95d29ae91f8", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "center_values_007702"}, "id": "code_007702_center_values_007702", "license": "Apache-2.0", "prompt": "Write a Python function center_values_007702(values) that subtracts the arithmetic mean from each value and returns a new list. Raise ValueError for an empty input. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "center_values_007702"}, "verifier": {"function": "center_values_007702", "tests": ["out = center_values_007702([1, 2, 3]); assert out == [-1, 0, 1]", "assert center_values_007702([5]) == [0]", "try:\n    center_values_007702([])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: required_fields, allowed_transformations.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"required_fields\", \"allowed_transformations\"]}", "dedupe_signature": "0576fe9411a751d875e31b8d7cb96ddbfdc05dfaa4c1a81c573f1b095a1bc53c", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["required_fields", "allowed_transformations"]}, "id": "abstain_007703_required_fields_allowed_transformations", "license": "Apache-2.0", "prompt": "Write a sanitizer for valid laboratory clinical records in release 800003, but the prompt does not state which fields are required or which transformations are allowed. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: required_fields, allowed_transformations.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["required_fields", "allowed_transformations"]}, "verifier": {"missing": ["required_fields", "allowed_transformations"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=10 degrees through the sine of 2 theta.\n3. Substitute v=77.6 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 209.9453, \"unit\": \"m\"}", "dedupe_signature": "12586c6fbfdcea5041eb84cf4c0050044ba1f79bd0adb7f3be658dd71be4d172", "difficulty": "medium", "final_answer": {"answer": 209.9453, "unit": "m"}, "id": "projectile_range_007706_77.6_10", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 77.6 m/s and angle 10 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=10 degrees through the sine of 2 theta.\nSubstitute v=77.6 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 10, "gravity": 9.81, "speed": 77.6}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 4.84 * 8.314 * 481 / 50.9.\nFinal: {\"answer\": 380.2618, \"unit\": \"kPa\"}", "dedupe_signature": "600f5b3ce0bfcc9e4ee0d09865d4e38b54816e9d692e10fe038c02f2dceb8d3f", "difficulty": "medium", "final_answer": {"answer": 380.2618, "unit": "kPa"}, "id": "ideal_gas_007707_4.84_481_50.9", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=4.84 mol, T=481 K, and V=50.9 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 4.84 * 8.314 * 481 / 50.9.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 4.84, "temp_k": 481, "volume_l": 50.9}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1115 * 1.625 * 118.\nFinal: {\"answer\": 213801.25, \"unit\": \"J\"}", "dedupe_signature": "1ccff992de0faa06c071ab386ba6b8c0ebe64c27d438f1d670d6d278ffb3536e", "difficulty": "easy", "final_answer": {"answer": 213801.25, "unit": "J"}, "id": "heat_q_007708_1115_1.625_118", "license": "Apache-2.0", "prompt": "A 1115 g sample has specific heat 1.625 J/(g*K). How much heat is needed to raise its temperature by 118 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1115 * 1.625 * 118.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 118, "heat_capacity": 1.625, "mass_g": 1115}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=193.9 V and R=175.7 ohm.\nFinal: {\"answer\": 213.9853, \"unit\": \"W\"}", "dedupe_signature": "39a211be43f41bc78874577c97929b58b460ecad82e57cff8e117fab51ce115b", "difficulty": "easy", "final_answer": {"answer": 213.9853, "unit": "W"}, "id": "ohm_power_007709_193.9_175.7", "license": "Apache-2.0", "prompt": "A resistor has resistance 175.7 ohm and voltage 193.9 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=193.9 V and R=175.7 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 175.7, "voltage": 193.9}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 5.49 mol * 180.156 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 989.0564, \"unit\": \"g\"}", "dedupe_signature": "f9be8461620b17b8d917b309cb9a59cc770bf2eb83734ff1ba4af0e76876d3dd", "difficulty": "medium", "final_answer": {"answer": 989.0564, "unit": "g"}, "id": "stoich_mass_007711_glucose_5.49", "license": "Apache-2.0", "prompt": "A sample contains 5.49 mol of glucose. Using molar mass 180.156 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 5.49 mol * 180.156 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "glucose", "molar_mass": 180.156, "moles": 5.49}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 240 mL to 0.24 L.\n3. Compute M = 1.555 / 0.24.\nFinal: {\"answer\": 6.4792, \"unit\": \"mol/L\"}", "dedupe_signature": "011d109737f349c634947644d81f8433eaaf55d4aa99dd9d302c103b3cbaa05d", "difficulty": "medium", "final_answer": {"answer": 6.4792, "unit": "mol/L"}, "id": "molarity_007712_1.555_240", "license": "Apache-2.0", "prompt": "A solution contains 1.555 mol of solute in 240 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 240 mL to 0.24 L.\nCompute M = 1.555 / 0.24.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 1.555, "volume_ml": 240}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.4 y, so each step multiplies y by 1 - h*0.4.\n3. Apply that update for 6 steps and round the final state.\nFinal: {\"answer\": 8.9493, \"unit\": \"state_units\"}", "dedupe_signature": "e843367a0ef2858e45dd0d1fecaef4406609572cb73a3743642495f96952caf1", "difficulty": "medium", "final_answer": {"answer": 8.9493, "unit": "state_units"}, "id": "euler_decay_007713_54.5_0.4_0.65_6", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.4 y with y(0)=54.5, step size h=0.65, for 6 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.4 y, so each step multiplies y by 1 - h*0.4.\nApply that update for 6 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 54.5, "rate": 0.4, "step": 0.65, "steps": 6}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(9.7)=22.34 and f(16.5)=44.1.\n3. The interval width is 6.8.\nFinal: {\"answer\": 225.896, \"unit\": \"area_units\"}", "dedupe_signature": "65c64e713257b3019767dbbcdd37393c7522b3e82b525d8164f43fa638a6bd80", "difficulty": "medium", "final_answer": {"answer": 225.896, "unit": "area_units"}, "id": "trapz_linear_007714_3.2_-8.7_9.7_16.5", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=3.2x+-8.7 from x=9.7 to x=16.5. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(9.7)=22.34 and f(16.5)=44.1.\nThe interval width is 6.8.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -8.7, "slope": 3.2, "x0": 9.7, "x1": 16.5}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.08 and add it to the current value.\nFinal: {\"answer\": [1.268, 2.39, -0.626], \"unit\": \"temperature_units\"}", "dedupe_signature": "924b5f3fe83241dc319b8a1acd32e2a3d6a88e11ff11061c4f526f9c90710167", "difficulty": "hard", "final_answer": {"answer": [1.268, 2.39, -0.626], "unit": "temperature_units"}, "id": "heat_step_007715_0.08_2.5_1.0_2.85_-1.05_0.35", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=2.5, right=0.35; current interior values are [1.0, 2.85, -1.05]. Use r=0.08. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.08 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [1.0, 2.85, -1.05], "left": 2.5, "r": 0.08, "right": 0.35}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-3.65, 11.75], \"unit\": \"dimensionless\"}", "dedupe_signature": "a4fdf28776c644255381886ab268c30852d295922038af65545d3e164fb4d8f7", "difficulty": "medium", "final_answer": {"answer": [-3.65, 11.75], "unit": "dimensionless"}, "id": "line_two_point_007718_2_4.25_-3.65_11.75", "license": "Apache-2.0", "prompt": "A line passes through points (2, 4.45) and (4.25, -3.7625). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 2.0, "x2": 4.25, "y1": 4.45, "y2": -3.7624999999999993}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. energy divided by length is force, not spring constant\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "4b7efe36cd40a0136dab0afe0d3b8f8c832f757b7917ffcdd0d274cb4044379f", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_007719_inconsistent_56040f5d_573589", "license": "Apache-2.0", "prompt": "In lab notebook case 573589, check dimensional consistency for k = E / x. The left side has dimensions N/m and the right side has dimensions J/m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nenergy divided by length is force, not spring constant\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "k = E / x"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef finite_differences_007720(values):\n    return [values[i + 1] - values[i] for i in range(len(values) - 1)]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"finite_differences_007720\"}", "dedupe_signature": "fc57392fe409d30aa06f0abca8394e534b6ae3ca32c26637e131597742be2095", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "finite_differences_007720"}, "id": "code_007720_finite_differences_007720", "license": "Apache-2.0", "prompt": "Write a Python function finite_differences_007720(values) that returns the list of successive differences values[i+1] - values[i]. It must return [] for fewer than two values. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "finite_differences_007720"}, "verifier": {"function": "finite_differences_007720", "tests": ["assert finite_differences_007720([1, 4, 9, 16]) == [3, 5, 7]", "assert finite_differences_007720([5]) == []", "assert finite_differences_007720([]) == []"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: recurrence, objective, tie_breaking_rule.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"recurrence\", \"objective\", \"tie_breaking_rule\"]}", "dedupe_signature": "1af7afcc0de2de96db3f81fc95809ec54610bddc4bbc201ca48a592fcfa26ccd", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["recurrence", "objective", "tie_breaking_rule"]}, "id": "abstain_007721_recurrence_objective_tie_breaking_rule", "license": "Apache-2.0", "prompt": "Write a dynamic-programming solver for a scheduler scoring problem with 3843 items and budget 27545, but the recurrence, objective, and tie-breaking rule are all absent. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: recurrence, objective, tie_breaking_rule.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["recurrence", "objective", "tie_breaking_rule"]}, "verifier": {"missing": ["recurrence", "objective", "tie_breaking_rule"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 38.6^2 and multiply by 0.5 * 23.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 17134.54, \"unit\": \"J\"}", "dedupe_signature": "4f72150747129a09dea12b7ec1c5bcd12009fdfb8813b66fa0bc3308c25f9141", "difficulty": "easy", "final_answer": {"answer": 17134.54, "unit": "J"}, "id": "ke_007723_23_38.6", "license": "Apache-2.0", "prompt": "A body of mass 23 kg moves at 38.6 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 38.6^2 and multiply by 0.5 * 23.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 23.0, "velocity": 38.6}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=43 degrees through the sine of 2 theta.\n3. Substitute v=9.7 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 9.5679, \"unit\": \"m\"}", "dedupe_signature": "49298d6ce748741a8eaf69b6da9f72843ae6b2a1ab9918de0ed3cab54c769ee9", "difficulty": "medium", "final_answer": {"answer": 9.5679, "unit": "m"}, "id": "projectile_range_007724_9.7_43", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 9.7 m/s and angle 43 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=43 degrees through the sine of 2 theta.\nSubstitute v=9.7 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 43, "gravity": 9.81, "speed": 9.7}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 2.69 * 8.314 * 544 / 59.8.\nFinal: {\"answer\": 203.4511, \"unit\": \"kPa\"}", "dedupe_signature": "0b2657344e46660a9c368764ae7cb8d227a16836f763d682e0a439f254ae6310", "difficulty": "medium", "final_answer": {"answer": 203.4511, "unit": "kPa"}, "id": "ideal_gas_007725_2.69_544_59.8", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=2.69 mol, T=544 K, and V=59.8 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 2.69 * 8.314 * 544 / 59.8.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 2.69, "temp_k": 544, "volume_l": 59.8}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 465 * 1.355 * 119.\nFinal: {\"answer\": 74978.925, \"unit\": \"J\"}", "dedupe_signature": "0cdd863411d2784057ce894a09f4c171a38f6c8dd8ae5fd67247d17617f5f839", "difficulty": "easy", "final_answer": {"answer": 74978.925, "unit": "J"}, "id": "heat_q_007726_465_1.355_119", "license": "Apache-2.0", "prompt": "A 465 g sample has specific heat 1.355 J/(g*K). How much heat is needed to raise its temperature by 119 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 465 * 1.355 * 119.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 119, "heat_capacity": 1.355, "mass_g": 465}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=230.3 V and R=130.3 ohm.\nFinal: {\"answer\": 407.046, \"unit\": \"W\"}", "dedupe_signature": "9347e26929ed2fbf2a5149b52771f4bd6469fbe8bb3d30c92d227349c9bb9af6", "difficulty": "easy", "final_answer": {"answer": 407.046, "unit": "W"}, "id": "ohm_power_007727_230.3_130.3", "license": "Apache-2.0", "prompt": "A resistor has resistance 130.3 ohm and voltage 230.3 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=230.3 V and R=130.3 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 130.3, "voltage": 230.3}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=166.5 mg, t=62.5 h, and T_half=79.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 96.5507, \"unit\": \"mg\"}", "dedupe_signature": "b8e78ace5942f2e0f6d7b5d76b04e8687c04f42046aa8e6c50d6f8529aad6fdf", "difficulty": "medium", "final_answer": {"answer": 96.5507, "unit": "mg"}, "id": "half_life_007728_166.5_79.5_62.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 166.5 mg. Its half-life is 79.5 hours. How many mg remain after 62.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=166.5 mg, t=62.5 h, and T_half=79.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 62.5, "half_life": 79.5, "initial_amount": 166.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 0.41 mol * 44.01 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 18.0441, \"unit\": \"g\"}", "dedupe_signature": "f59f79a25169e02dba04276e97d2207176cd8f10536bfdf0e1ec5868ce3c417e", "difficulty": "medium", "final_answer": {"answer": 18.0441, "unit": "g"}, "id": "stoich_mass_007729_carbon_dioxide_0.41", "license": "Apache-2.0", "prompt": "A sample contains 0.41 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 0.41 mol * 44.01 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "carbon dioxide", "molar_mass": 44.01, "moles": 0.41}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.39 y, so each step multiplies y by 1 - h*0.39.\n3. Apply that update for 9 steps and round the final state.\nFinal: {\"answer\": 3.4877, \"unit\": \"state_units\"}", "dedupe_signature": "8bdffd3ee24e08db562b05ec75968c823f8c43ea1c86bf2579becad0c85bf356", "difficulty": "medium", "final_answer": {"answer": 3.4877, "unit": "state_units"}, "id": "euler_decay_007731_6_0.39_0.15_9", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.39 y with y(0)=6, step size h=0.15, for 9 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.39 y, so each step multiplies y by 1 - h*0.39.\nApply that update for 9 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 6.0, "rate": 0.39, "step": 0.15, "steps": 9}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(2.5)=26.25 and f(10)=51.\n3. The interval width is 7.5.\nFinal: {\"answer\": 289.6875, \"unit\": \"area_units\"}", "dedupe_signature": "88008b234abb5276cc5e9b670969c4b314fe2afb398ebe50fa10f19b80c83599", "difficulty": "medium", "final_answer": {"answer": 289.6875, "unit": "area_units"}, "id": "trapz_linear_007732_3.3_18_2.5_10", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=3.3x+18 from x=2.5 to x=10. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(2.5)=26.25 and f(10)=51.\nThe interval width is 7.5.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 18.0, "slope": 3.3, "x0": 2.5, "x1": 10.0}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 31235.0 / 1000.\nFinal: {\"answer\": 31.235, \"unit\": \"kg\"}", "dedupe_signature": "98dad2f5eec29164a71738ff68eb04f7be63f728516fd3dbd952073c3d6e52f7", "difficulty": "easy", "final_answer": {"answer": 31.235, "unit": "kg"}, "id": "unit_convert_007734_g_to_kg_31235", "license": "Apache-2.0", "prompt": "Convert 31235 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 31235.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 31235.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=114 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-21.3537, 47.9611], \"unit\": \"N\"}", "dedupe_signature": "96ad5eee253a485d82aaeb6fb1174822502d3514feae8401662798cfa329e620", "difficulty": "medium", "final_answer": {"answer": [-21.3537, 47.9611], "unit": "N"}, "id": "vector_components_007735_52.5_114", "license": "Apache-2.0", "prompt": "A vector has magnitude 52.5 N at 114 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=114 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 114, "magnitude": 52.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-5.3, 7.0], \"unit\": \"dimensionless\"}", "dedupe_signature": "fea14780304412e0c835527808d25bf7a41dd5275077d4bf473de93c186a2b02", "difficulty": "medium", "final_answer": {"answer": [-5.3, 7.0], "unit": "dimensionless"}, "id": "line_two_point_007736_-10.75_-1.25_-5.3_7", "license": "Apache-2.0", "prompt": "A line passes through points (-10.75, 63.975) and (-1.25, 13.625). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -10.75, "x2": -1.25, "y1": 63.975, "y2": 13.625}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. m*v is momentum, not energy\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "b334d182703724fbd375cd25de72469d47bb7b3121e227b95837171fb7ebbcea", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_007737_inconsistent_1e14b074_892293", "license": "Apache-2.0", "prompt": "In lab notebook case 892293, check dimensional consistency for E = m * v. The left side has dimensions kg*m^2/s^2 and the right side has dimensions kg*m/s. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nm*v is momentum, not energy\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "E = m * v"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef weighted_sum_007738(values, weights):\n    if len(values) != len(weights):\n        raise ValueError('length mismatch')\n    return sum(value * weight for value, weight in zip(values, weights))\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"weighted_sum_007738\"}", "dedupe_signature": "81b7f64c1ccd452b19db5c626c229828fb44b4f6a07964f497be634dd03b35af", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "weighted_sum_007738"}, "id": "code_007738_weighted_sum_007738", "license": "Apache-2.0", "prompt": "Write a Python function weighted_sum_007738(values, weights) that returns sum(value*weight). Raise ValueError when the two inputs have different lengths. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "weighted_sum_007738"}, "verifier": {"function": "weighted_sum_007738", "tests": ["assert weighted_sum_007738([2, 3], [4, 5]) == 23", "assert weighted_sum_007738([], []) == 0", "try:\n    weighted_sum_007738([1], [1, 2])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: recurrence, objective, tie_breaking_rule.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"recurrence\", \"objective\", \"tie_breaking_rule\"]}", "dedupe_signature": "0935cd282807ded4e647eac45724a93147c5e78b201ed6f3d8d13f3cdf9ecafd", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["recurrence", "objective", "tie_breaking_rule"]}, "id": "abstain_007739_recurrence_objective_tie_breaking_rule", "license": "Apache-2.0", "prompt": "Write a dynamic-programming solver for a routing scoring problem with 2751 items and budget 96720, but the recurrence, objective, and tie-breaking rule are all absent. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: recurrence, objective, tie_breaking_rule.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["recurrence", "objective", "tie_breaking_rule"]}, "verifier": {"missing": ["recurrence", "objective", "tie_breaking_rule"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 26.25^2 and multiply by 0.5 * 19.75.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 6804.4922, \"unit\": \"J\"}", "dedupe_signature": "28f473d6a63013a1cd454d0492a05aae256df17545dfd373acc9761cf66487f6", "difficulty": "easy", "final_answer": {"answer": 6804.4922, "unit": "J"}, "id": "ke_007741_19.75_26.25", "license": "Apache-2.0", "prompt": "A body of mass 19.75 kg moves at 26.25 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 26.25^2 and multiply by 0.5 * 19.75.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 19.75, "velocity": 26.25}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 1.37 * 8.314 * 505 / 107.6.\nFinal: {\"answer\": 53.4576, \"unit\": \"kPa\"}", "dedupe_signature": "4a91a1d94fd603d25a9bfa40c4a9e0ddf517b4699c1d6037eafcc9ff6ccf39cc", "difficulty": "medium", "final_answer": {"answer": 53.4576, "unit": "kPa"}, "id": "ideal_gas_007743_1.37_505_107.6", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=1.37 mol, T=505 K, and V=107.6 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 1.37 * 8.314 * 505 / 107.6.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 1.37, "temp_k": 505, "volume_l": 107.6}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 595 * 3.005 * 11.\nFinal: {\"answer\": 19667.725, \"unit\": \"J\"}", "dedupe_signature": "c221e0a9bfefbf314c7f757c9ed8a2f0bb68d289b6d5259491f656974f3bca26", "difficulty": "easy", "final_answer": {"answer": 19667.725, "unit": "J"}, "id": "heat_q_007744_595_3.005_11", "license": "Apache-2.0", "prompt": "A 595 g sample has specific heat 3.005 J/(g*K). How much heat is needed to raise its temperature by 11 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 595 * 3.005 * 11.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 11, "heat_capacity": 3.005, "mass_g": 595}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=133.8 V and R=119.5 ohm.\nFinal: {\"answer\": 149.8112, \"unit\": \"W\"}", "dedupe_signature": "d512035b891b6216f017f500ad0cc0addc5ae24f05847ce103c2d356bf1f4b26", "difficulty": "easy", "final_answer": {"answer": 149.8112, "unit": "W"}, "id": "ohm_power_007745_133.8_119.5", "license": "Apache-2.0", "prompt": "A resistor has resistance 119.5 ohm and voltage 133.8 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=133.8 V and R=119.5 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 119.5, "voltage": 133.8}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=915 mg, t=161.5 h, and T_half=66.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 169.9606, \"unit\": \"mg\"}", "dedupe_signature": "2fc34bc6a4e25f3768edb1dcc56fd5f86deca39d7cfb808afce331868e3d4058", "difficulty": "medium", "final_answer": {"answer": 169.9606, "unit": "mg"}, "id": "half_life_007746_915_66.5_161.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 915 mg. Its half-life is 66.5 hours. How many mg remain after 161.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=915 mg, t=161.5 h, and T_half=66.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 161.5, "half_life": 66.5, "initial_amount": 915.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 3.25 mol * 58.44 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 189.93, \"unit\": \"g\"}", "dedupe_signature": "ba09d2fc1f36447a1b7b38ae0b757f6965df08f5778ae0571dcdcd991576c1d0", "difficulty": "medium", "final_answer": {"answer": 189.93, "unit": "g"}, "id": "stoich_mass_007747_sodium_chloride_3.25", "license": "Apache-2.0", "prompt": "A sample contains 3.25 mol of sodium chloride. Using molar mass 58.44 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 3.25 mol * 58.44 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "sodium chloride", "molar_mass": 58.44, "moles": 3.25}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 1495 mL to 1.495 L.\n3. Compute M = 4.96 / 1.495.\nFinal: {\"answer\": 3.3177, \"unit\": \"mol/L\"}", "dedupe_signature": "f8057ed2528f05294f99a3eae76cf5d17a2ac653a9b42f8cd84d13989ae8488b", "difficulty": "medium", "final_answer": {"answer": 3.3177, "unit": "mol/L"}, "id": "molarity_007748_4.96_1495", "license": "Apache-2.0", "prompt": "A solution contains 4.96 mol of solute in 1495 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 1495 mL to 1.495 L.\nCompute M = 4.96 / 1.495.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 4.96, "volume_ml": 1495}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.08 and add it to the current value.\nFinal: {\"answer\": [0.968, 2.156, 1.054], \"unit\": \"temperature_units\"}", "dedupe_signature": "1ef4e16d015b1853468e6877489d9e012312ad7c3ac652b3c0456353d9e4b42f", "difficulty": "hard", "final_answer": {"answer": [0.968, 2.156, 1.054], "unit": "temperature_units"}, "id": "heat_step_007751_0.08_1.3_0.8_2.4_0.95_0.8", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1.3, right=0.8; current interior values are [0.8, 2.4, 0.95]. Use r=0.08. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.08 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [0.8, 2.4, 0.95], "left": 1.3, "r": 0.08, "right": 0.8}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kelvin equals Celsius plus 273.15.\n2. Apply the conversion factor directly to the given value.\n3. Compute 152.5 + 273.15.\nFinal: {\"answer\": 425.65, \"unit\": \"K\"}", "dedupe_signature": "b3a4c82a372417590423b91d2a7a91dbfb1288062c65dfd5ec4ebf59d3ff7f0a", "difficulty": "easy", "final_answer": {"answer": 425.65, "unit": "K"}, "id": "unit_convert_007752_c_to_k_152.5", "license": "Apache-2.0", "prompt": "Convert 152.5 degC to K. Return the converted value with unit.", "reasoning_trace": "Kelvin equals Celsius plus 273.15.\nApply the conversion factor directly to the given value.\nCompute 152.5 + 273.15.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 152.5}, "verifier": {"formula": "value + 273.15", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=235 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-29.2524, -41.7768], \"unit\": \"N\"}", "dedupe_signature": "36ed08163a5c2b1dc6ccee7bc6174217dd641e571c31f264a97ebd89fd5ac014", "difficulty": "medium", "final_answer": {"answer": [-29.2524, -41.7768], "unit": "N"}, "id": "vector_components_007753_51_235", "license": "Apache-2.0", "prompt": "A vector has magnitude 51 N at 235 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=235 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 235, "magnitude": 51.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. energy divided by length is force, not spring constant\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "4f537b6bffc506f503d292bbddcb23457a9171cbe24a515f8eff149eda84f13f", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_007755_inconsistent_56040f5d_691242", "license": "Apache-2.0", "prompt": "In sensor calibration case 691242, check dimensional consistency for k = E / x. The left side has dimensions N/m and the right side has dimensions J/m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nenergy divided by length is force, not spring constant\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "k = E / x"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef normalize_007756(values):\n    total = sum(values)\n    if total == 0:\n        raise ValueError('cannot normalize zero-sum values')\n    return [v / total for v in values]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"normalize_007756\"}", "dedupe_signature": "aaf6c7cce3182de008dfdaae84cf694dc54749c2a3239f40c1bc1c82694145eb", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "normalize_007756"}, "id": "code_007756_normalize_007756", "license": "Apache-2.0", "prompt": "Write a Python function normalize_007756(values) that returns a new list whose values sum to 1. Raise ValueError if the sum is zero. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "normalize_007756"}, "verifier": {"function": "normalize_007756", "tests": ["out = normalize_007756([2, 3, 5]); assert len(out) == 3", "assert abs(sum(normalize_007756([2, 3, 5])) - 1.0) < 1e-12", "assert normalize_007756([1, 1]) == [0.5, 0.5]", "try:\n    normalize_007756([1, -1])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: volume.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"volume\"]}", "dedupe_signature": "ef716370b1b0c6804606808d42500aa7eaccf4552a2aac81425cbf2e7f27eba4", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["volume"]}, "id": "abstain_007757_volume", "license": "Apache-2.0", "prompt": "Compute pressure from the ideal gas law. The prompt gives n=0.82 mol and T=378 K, but does not give volume. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: volume.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["volume"]}, "verifier": {"missing": ["volume"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 16.1 kg and a = 14.9 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 239.89, \"unit\": \"N\"}", "dedupe_signature": "17aa1167c4ca3886383cdfebdb83180fc31905c645a5eb708aef61b266418cdc", "difficulty": "easy", "final_answer": {"answer": 239.89, "unit": "N"}, "id": "force_007758_16.1_14.9", "license": "Apache-2.0", "prompt": "A cart has mass 16.1 kg and measured acceleration 14.9 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 16.1 kg and a = 14.9 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 14.9, "mass": 16.1}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 25.35^2 and multiply by 0.5 * 4.4.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 1413.7695, \"unit\": \"J\"}", "dedupe_signature": "c305d26749ba8b58448d4e54f2f236c0f96fc4f3f214721fc45c153a84c347b7", "difficulty": "easy", "final_answer": {"answer": 1413.7695, "unit": "J"}, "id": "ke_007759_4.4_25.35", "license": "Apache-2.0", "prompt": "A body of mass 4.4 kg moves at 25.35 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 25.35^2 and multiply by 0.5 * 4.4.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 4.4, "velocity": 25.35}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=12 degrees through the sine of 2 theta.\n3. Substitute v=51 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 107.8412, \"unit\": \"m\"}", "dedupe_signature": "0843c26d05d2c33110fd1434469f1e7eb884e594459087fab3bade3f94a47c89", "difficulty": "medium", "final_answer": {"answer": 107.8412, "unit": "m"}, "id": "projectile_range_007760_51_12", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 51 m/s and angle 12 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=12 degrees through the sine of 2 theta.\nSubstitute v=51 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 12, "gravity": 9.81, "speed": 51.0}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 3.71 * 8.314 * 434 / 48.0.\nFinal: {\"answer\": 278.8897, \"unit\": \"kPa\"}", "dedupe_signature": "8a7234f2c03f25b58a935fb4465e03b5205592bd5014f605264f39e00503b043", "difficulty": "medium", "final_answer": {"answer": 278.8897, "unit": "kPa"}, "id": "ideal_gas_007761_3.71_434_48.0", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=3.71 mol, T=434 K, and V=48.0 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 3.71 * 8.314 * 434 / 48.0.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 3.71, "temp_k": 434, "volume_l": 48.0}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 365 * 4.555 * 8.\nFinal: {\"answer\": 13300.6, \"unit\": \"J\"}", "dedupe_signature": "ce55f30f37dbfe14ca481de2fa11574be5a35a5172a7521edfd2df7888bbe7a5", "difficulty": "easy", "final_answer": {"answer": 13300.6, "unit": "J"}, "id": "heat_q_007762_365_4.555_8", "license": "Apache-2.0", "prompt": "A 365 g sample has specific heat 4.555 J/(g*K). How much heat is needed to raise its temperature by 8 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 365 * 4.555 * 8.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 8, "heat_capacity": 4.555, "mass_g": 365}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=188.1 V and R=143.1 ohm.\nFinal: {\"answer\": 247.2509, \"unit\": \"W\"}", "dedupe_signature": "31103e15d33ac2390ff42ffd2ccaebd4a9ce9f45fb6c256f04b12e3d9f332b9c", "difficulty": "easy", "final_answer": {"answer": 247.2509, "unit": "W"}, "id": "ohm_power_007763_188.1_143.1", "license": "Apache-2.0", "prompt": "A resistor has resistance 143.1 ohm and voltage 188.1 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=188.1 V and R=143.1 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 143.1, "voltage": 188.1}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=780.5 mg, t=266 h, and T_half=49.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 18.8242, \"unit\": \"mg\"}", "dedupe_signature": "52926051ce923a905200541cbc27c9de25366013d2286fcd1920a2b3276b8091", "difficulty": "medium", "final_answer": {"answer": 18.8242, "unit": "mg"}, "id": "half_life_007764_780.5_49.5_266", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 780.5 mg. Its half-life is 49.5 hours. How many mg remain after 266 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=780.5 mg, t=266 h, and T_half=49.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 266.0, "half_life": 49.5, "initial_amount": 780.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 3.97 mol * 44.01 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 174.7197, \"unit\": \"g\"}", "dedupe_signature": "d67a477e311956259147a154352e78217a892157ffa9c9b086ffa6c101b8f7bb", "difficulty": "medium", "final_answer": {"answer": 174.7197, "unit": "g"}, "id": "stoich_mass_007765_carbon_dioxide_3.97", "license": "Apache-2.0", "prompt": "A sample contains 3.97 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 3.97 mol * 44.01 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "carbon dioxide", "molar_mass": 44.01, "moles": 3.97}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 2645 mL to 2.645 L.\n3. Compute M = 2.07 / 2.645.\nFinal: {\"answer\": 0.7826, \"unit\": \"mol/L\"}", "dedupe_signature": "ac654dbe0e35ee0fd3c18354b713579225f1488e142bc1a838dcd4adffc10da7", "difficulty": "medium", "final_answer": {"answer": 0.7826, "unit": "mol/L"}, "id": "molarity_007766_2.07_2645", "license": "Apache-2.0", "prompt": "A solution contains 2.07 mol of solute in 2645 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 2645 mL to 2.645 L.\nCompute M = 2.07 / 2.645.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 2.07, "volume_ml": 2645}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.84 y, so each step multiplies y by 1 - h*0.84.\n3. Apply that update for 7 steps and round the final state.\nFinal: {\"answer\": 7.8736, \"unit\": \"state_units\"}", "dedupe_signature": "5c61f34a2563f9fdd4d78010a3905c433db9b16fcb807986c98acee9c8769c93", "difficulty": "medium", "final_answer": {"answer": 7.8736, "unit": "state_units"}, "id": "euler_decay_007767_41_0.84_0.25_7", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.84 y with y(0)=41, step size h=0.25, for 7 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.84 y, so each step multiplies y by 1 - h*0.84.\nApply that update for 7 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 41.0, "rate": 0.84, "step": 0.25, "steps": 7}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-9.9)=76.8 and f(-7.3)=61.2.\n3. The interval width is 2.6.\nFinal: {\"answer\": 179.4, \"unit\": \"area_units\"}", "dedupe_signature": "9c32beb315c3b17e7c8d14ad23397e0f7624c7fb8103026712b7bb080e59f094", "difficulty": "medium", "final_answer": {"answer": 179.4, "unit": "area_units"}, "id": "trapz_linear_007768_-6_17.4_-9.9_-7.3", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-6x+17.4 from x=-9.9 to x=-7.3. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-9.9)=76.8 and f(-7.3)=61.2.\nThe interval width is 2.6.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 17.4, "slope": -6.0, "x0": -9.9, "x1": -7.300000000000001}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.38 and add it to the current value.\nFinal: {\"answer\": [1.153, 1.935, 0.902], \"unit\": \"temperature_units\"}", "dedupe_signature": "64c346881aca6fbf3f0ef0c382200edacbb04cd46fb9f49768d7f22b144b621b", "difficulty": "hard", "final_answer": {"answer": [1.153, 1.935, 0.902], "unit": "temperature_units"}, "id": "heat_step_007769_0.38_0.5_1.4_1.65_2.65_-0.95", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=0.5, right=-0.95; current interior values are [1.4, 1.65, 2.65]. Use r=0.38. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.38 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [1.4, 1.65, 2.65], "left": 0.5, "r": 0.38, "right": -0.95}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kelvin equals Celsius plus 273.15.\n2. Apply the conversion factor directly to the given value.\n3. Compute 85.0 + 273.15.\nFinal: {\"answer\": 358.15, \"unit\": \"K\"}", "dedupe_signature": "f1ca43b25262e6015c9f108d5c8d70f8c02489dac16856cbc41966c1ea48e823", "difficulty": "easy", "final_answer": {"answer": 358.15, "unit": "K"}, "id": "unit_convert_007770_c_to_k_85", "license": "Apache-2.0", "prompt": "Convert 85 degC to K. Return the converted value with unit.", "reasoning_trace": "Kelvin equals Celsius plus 273.15.\nApply the conversion factor directly to the given value.\nCompute 85.0 + 273.15.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 85.0}, "verifier": {"formula": "value + 273.15", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=117 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-68.3256, 134.0965], \"unit\": \"N\"}", "dedupe_signature": "cb84118fb4b4efe508cfed4027bb2792dc99501df858a9acea7b953da806255c", "difficulty": "medium", "final_answer": {"answer": [-68.3256, 134.0965], "unit": "N"}, "id": "vector_components_007771_150.5_117", "license": "Apache-2.0", "prompt": "A vector has magnitude 150.5 N at 117 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=117 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 117, "magnitude": 150.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [0.55, -29.0], \"unit\": \"dimensionless\"}", "dedupe_signature": "2c3ca820a6020d547da14c9e418070d48b1dacccce5af8f449c044efb757bdd1", "difficulty": "medium", "final_answer": {"answer": [0.55, -29.0], "unit": "dimensionless"}, "id": "line_two_point_007772_8.25_20_0.55_-29", "license": "Apache-2.0", "prompt": "A line passes through points (8.25, -24.4625) and (20, -18). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": 8.25, "x2": 20.0, "y1": -24.4625, "y2": -18.0}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. velocity times time gives distance, not acceleration\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "b17d1252b301b9e48c5bb3bf04d6777db2023202801adbe3cb176b20c28d967f", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_007773_inconsistent_7481c798_610843", "license": "Apache-2.0", "prompt": "In student derivation case 610843, check dimensional consistency for a = v * t. The left side has dimensions m/s^2 and the right side has dimensions m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nvelocity times time gives distance, not acceleration\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "a = v * t"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef safe_mean_007774(values):\n    if not values:\n        raise ValueError('safe_mean requires at least one value')\n    return sum(values) / len(values)\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"safe_mean_007774\"}", "dedupe_signature": "68431934e4084bbea06c198903c50d91025a6743d6b14f949152df3616549de6", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "safe_mean_007774"}, "id": "code_007774_safe_mean_007774", "license": "Apache-2.0", "prompt": "Write a Python function safe_mean_007774(values) that returns the arithmetic mean. It must raise ValueError for an empty input and must not mutate the input list. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "safe_mean_007774"}, "verifier": {"function": "safe_mean_007774", "tests": ["assert safe_mean_007774([2, 4, 6]) == 4", "xs = [1, 2, 3]; assert safe_mean_007774(xs) == 2 and xs == [1, 2, 3]", "try:\n    safe_mean_007774([])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: left_boundary, right_boundary.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"left_boundary\", \"right_boundary\"]}", "dedupe_signature": "36aa97276ce7b35073988895fc337446ce6f81a0f9ff201f0d161667306c5b7b", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["left_boundary", "right_boundary"]}, "id": "abstain_007775_left_boundary_right_boundary", "license": "Apache-2.0", "prompt": "Solve the 1D heat equation after one finite-difference step. The prompt gives r=0.16 and interior values [-1.7, 0.2, 1.6], but gives no boundary values. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: left_boundary, right_boundary.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["left_boundary", "right_boundary"]}, "verifier": {"missing": ["left_boundary", "right_boundary"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 1.75 kg and a = 4.5 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 7.875, \"unit\": \"N\"}", "dedupe_signature": "17ea7ca43bb3ea9135bf82d379783f3cc764c30b3c01306cf9865a2623dd25cf", "difficulty": "easy", "final_answer": {"answer": 7.875, "unit": "N"}, "id": "force_007776_1.75_4.5", "license": "Apache-2.0", "prompt": "A cart has mass 1.75 kg and measured acceleration 4.5 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 1.75 kg and a = 4.5 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 4.5, "mass": 1.75}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 8^2 and multiply by 0.5 * 16.05.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 513.6, \"unit\": \"J\"}", "dedupe_signature": "8e9b2f2b563b7eae2384ee5ce5e22ff83d1b45d5f9d1fbc1208cbbeaf32eedde", "difficulty": "easy", "final_answer": {"answer": 513.6, "unit": "J"}, "id": "ke_007777_16.05_8", "license": "Apache-2.0", "prompt": "A body of mass 16.05 kg moves at 8 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 8^2 and multiply by 0.5 * 16.05.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 16.05, "velocity": 8.0}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=83 degrees through the sine of 2 theta.\n3. Substitute v=83.9 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 173.5922, \"unit\": \"m\"}", "dedupe_signature": "e8745d8adfe9fca931a898259ba16d04e9e1e7bd8b90dc81cf86670bbf36aa51", "difficulty": "medium", "final_answer": {"answer": 173.5922, "unit": "m"}, "id": "projectile_range_007778_83.9_83", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 83.9 m/s and angle 83 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=83 degrees through the sine of 2 theta.\nSubstitute v=83.9 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 83, "gravity": 9.81, "speed": 83.9}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 5.4 * 8.314 * 502 / 67.9.\nFinal: {\"answer\": 331.9233, \"unit\": \"kPa\"}", "dedupe_signature": "824c307639d3d4db49d647c5791f34e701e9df9f0e63674c5ae0f15d8f5dfe8f", "difficulty": "medium", "final_answer": {"answer": 331.9233, "unit": "kPa"}, "id": "ideal_gas_007779_5.4_502_67.9", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=5.4 mol, T=502 K, and V=67.9 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 5.4 * 8.314 * 502 / 67.9.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 5.4, "temp_k": 502, "volume_l": 67.9}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 530 * 1.38 * 2.\nFinal: {\"answer\": 1462.8, \"unit\": \"J\"}", "dedupe_signature": "d253c4e2d6af8918f9b9b107318cb1b54aebb67572f8829be4c6c4c9b1697c26", "difficulty": "easy", "final_answer": {"answer": 1462.8, "unit": "J"}, "id": "heat_q_007780_530_1.38_2", "license": "Apache-2.0", "prompt": "A 530 g sample has specific heat 1.38 J/(g*K). How much heat is needed to raise its temperature by 2 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 530 * 1.38 * 2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 2, "heat_capacity": 1.38, "mass_g": 530}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=156.8 V and R=26.4 ohm.\nFinal: {\"answer\": 931.297, \"unit\": \"W\"}", "dedupe_signature": "8c0464589acaa22ce337ca496ae24b884597f1a75183a398a56f7c6758057751", "difficulty": "easy", "final_answer": {"answer": 931.297, "unit": "W"}, "id": "ohm_power_007781_156.8_26.4", "license": "Apache-2.0", "prompt": "A resistor has resistance 26.4 ohm and voltage 156.8 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=156.8 V and R=26.4 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 26.4, "voltage": 156.8}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 1.88 mol * 100.087 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 188.1636, \"unit\": \"g\"}", "dedupe_signature": "557a37d8dd9933b8c548385605741eccee6ee89c906a468f9cb6f1d6a871c9d2", "difficulty": "medium", "final_answer": {"answer": 188.1636, "unit": "g"}, "id": "stoich_mass_007783_calcium_carbonate_1.88", "license": "Apache-2.0", "prompt": "A sample contains 1.88 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 1.88 mol * 100.087 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "calcium carbonate", "molar_mass": 100.087, "moles": 1.88}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 1900 mL to 1.9 L.\n3. Compute M = 1.005 / 1.9.\nFinal: {\"answer\": 0.5289, \"unit\": \"mol/L\"}", "dedupe_signature": "7c83189ff8c482df41c827f05d6be2294cd1e4d71a3b2f9277f27147c706ee2b", "difficulty": "medium", "final_answer": {"answer": 0.5289, "unit": "mol/L"}, "id": "molarity_007784_1.005_1900", "license": "Apache-2.0", "prompt": "A solution contains 1.005 mol of solute in 1900 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 1900 mL to 1.9 L.\nCompute M = 1.005 / 1.9.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 1.005, "volume_ml": 1900}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.31 y, so each step multiplies y by 1 - h*0.31.\n3. Apply that update for 11 steps and round the final state.\nFinal: {\"answer\": 5.0758, \"unit\": \"state_units\"}", "dedupe_signature": "9545425e1c1b6f46feaf110e20e8f10994bbba8ac3eafc3e1fe7e71556eac62c", "difficulty": "medium", "final_answer": {"answer": 5.0758, "unit": "state_units"}, "id": "euler_decay_007785_26.5_0.31_0.45_11", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.31 y with y(0)=26.5, step size h=0.45, for 11 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.31 y, so each step multiplies y by 1 - h*0.31.\nApply that update for 11 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 26.5, "rate": 0.31, "step": 0.45, "steps": 11}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(6.6)=-31.18 and f(12.5)=-65.4.\n3. The interval width is 5.9.\nFinal: {\"answer\": -284.911, \"unit\": \"area_units\"}", "dedupe_signature": "86fc92488b05b82da8c154aa4178c06769dc8630e91688324e67b8735f4297a4", "difficulty": "medium", "final_answer": {"answer": -284.911, "unit": "area_units"}, "id": "trapz_linear_007786_-5.8_7.1_6.6_12.5", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-5.8x+7.1 from x=6.6 to x=12.5. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(6.6)=-31.18 and f(12.5)=-65.4.\nThe interval width is 5.9.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 7.1, "slope": -5.8, "x0": 6.6, "x1": 12.5}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 100 centimeters in one meter.\n2. Apply the conversion factor directly to the given value.\n3. Compute 1826.5 / 100.\nFinal: {\"answer\": 18.265, \"unit\": \"m\"}", "dedupe_signature": "3fe63b2ce7583060959393c7b147cf7e66256487b177953a804f232657d23ad3", "difficulty": "easy", "final_answer": {"answer": 18.265, "unit": "m"}, "id": "unit_convert_007788_cm_to_m_1826.5", "license": "Apache-2.0", "prompt": "Convert 1826.5 cm to m. Return the converted value with unit.", "reasoning_trace": "There are 100 centimeters in one meter.\nApply the conversion factor directly to the given value.\nCompute 1826.5 / 100.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 1826.5}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=18 degrees and keep the unit as newtons.\nFinal: {\"answer\": [356.6462, 115.8814], \"unit\": \"N\"}", "dedupe_signature": "a6ef52e182d0c70137530f5e202cd6fec4911a709c75b94aa87fb4edf9d0269f", "difficulty": "medium", "final_answer": {"answer": [356.6462, 115.8814], "unit": "N"}, "id": "vector_components_007789_375_18", "license": "Apache-2.0", "prompt": "A vector has magnitude 375 N at 18 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=18 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 18, "magnitude": 375.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-4.35, -26.5], \"unit\": \"dimensionless\"}", "dedupe_signature": "baeb7ab7f44f840ce26ebefcd1f24c5150d109a5ab0558e66662badcd8d19277", "difficulty": "medium", "final_answer": {"answer": [-4.35, -26.5], "unit": "dimensionless"}, "id": "line_two_point_007790_-12.75_-8_-4.35_-26.5", "license": "Apache-2.0", "prompt": "A line passes through points (-12.75, 28.9625) and (-8, 8.3). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -12.75, "x2": -8.0, "y1": 28.9625, "y2": 8.299999999999997}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. volt squared divided by ohm is watt\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "cd6c0ccd97d93f22625ef9073e20531e21c998fe680580d1f59aba185c78ad58", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_007791_consistent_82e93f3d_307487", "license": "Apache-2.0", "prompt": "In lab notebook case 307487, check dimensional consistency for P = V^2 / R. The left side has dimensions W and the right side has dimensions W. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nvolt squared divided by ohm is watt\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "P = V^2 / R"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 4.5 kg and a = 4.85 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 21.825, \"unit\": \"N\"}", "dedupe_signature": "39d5afe9daa716b0baa38f64c90b0c923e38200db7c23316d9580a021b81c44f", "difficulty": "easy", "final_answer": {"answer": 21.825, "unit": "N"}, "id": "force_007794_4.5_4.85", "license": "Apache-2.0", "prompt": "A cart has mass 4.5 kg and measured acceleration 4.85 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 4.5 kg and a = 4.85 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 4.85, "mass": 4.5}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 22.6^2 and multiply by 0.5 * 13.05.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 3332.709, \"unit\": \"J\"}", "dedupe_signature": "4caa335f976c2ca39ee8768121ac1ba66d6a2079f33c46d6845eeecbb066bd3d", "difficulty": "easy", "final_answer": {"answer": 3332.709, "unit": "J"}, "id": "ke_007795_13.05_22.6", "license": "Apache-2.0", "prompt": "A body of mass 13.05 kg moves at 22.6 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 22.6^2 and multiply by 0.5 * 13.05.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 13.05, "velocity": 22.6}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 4.12 * 8.314 * 360 / 71.2.\nFinal: {\"answer\": 173.1928, \"unit\": \"kPa\"}", "dedupe_signature": "05ec20e28da49c5b73b77b0fec6aacf42c2a4b7f155138cd544e76d54c8450c5", "difficulty": "medium", "final_answer": {"answer": 173.1928, "unit": "kPa"}, "id": "ideal_gas_007797_4.12_360_71.2", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=4.12 mol, T=360 K, and V=71.2 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 4.12 * 8.314 * 360 / 71.2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 4.12, "temp_k": 360, "volume_l": 71.2}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 590 * 1.995 * 32.\nFinal: {\"answer\": 37665.6, \"unit\": \"J\"}", "dedupe_signature": "3fa19ad1855445e52388db66834c365a69c5689b45a7141ce93726e34f89f4c4", "difficulty": "easy", "final_answer": {"answer": 37665.6, "unit": "J"}, "id": "heat_q_007798_590_1.995_32", "license": "Apache-2.0", "prompt": "A 590 g sample has specific heat 1.995 J/(g*K). How much heat is needed to raise its temperature by 32 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 590 * 1.995 * 32.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 32, "heat_capacity": 1.995, "mass_g": 590}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=180.5 V and R=120.6 ohm.\nFinal: {\"answer\": 270.1513, \"unit\": \"W\"}", "dedupe_signature": "73dd11a3c8f52f4c3a0975cb446eeb7091e949f2ad3da7b746d62b4fae10c906", "difficulty": "easy", "final_answer": {"answer": 270.1513, "unit": "W"}, "id": "ohm_power_007799_180.5_120.6", "license": "Apache-2.0", "prompt": "A resistor has resistance 120.6 ohm and voltage 180.5 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=180.5 V and R=120.6 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 120.6, "voltage": 180.5}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 1.62 mol * 18.015 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 29.1843, \"unit\": \"g\"}", "dedupe_signature": "a20f4a20abbd2e5b623209445cb4c40436431e06ca99d78f63f93fa229341aaa", "difficulty": "medium", "final_answer": {"answer": 29.1843, "unit": "g"}, "id": "stoich_mass_007801_water_1.62", "license": "Apache-2.0", "prompt": "A sample contains 1.62 mol of water. Using molar mass 18.015 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 1.62 mol * 18.015 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "water", "molar_mass": 18.015, "moles": 1.62}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 640 mL to 0.64 L.\n3. Compute M = 4.2 / 0.64.\nFinal: {\"answer\": 6.5625, \"unit\": \"mol/L\"}", "dedupe_signature": "87ee5b62e7a33bd9d7cda3ac72bd1ca01e5c0d32cfe9d96a83d19bafe257ecf3", "difficulty": "medium", "final_answer": {"answer": 6.5625, "unit": "mol/L"}, "id": "molarity_007802_4.2_640", "license": "Apache-2.0", "prompt": "A solution contains 4.2 mol of solute in 640 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 640 mL to 0.64 L.\nCompute M = 4.2 / 0.64.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 4.2, "volume_ml": 640}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.17 y, so each step multiplies y by 1 - h*0.17.\n3. Apply that update for 5 steps and round the final state.\nFinal: {\"answer\": 6.3416, \"unit\": \"state_units\"}", "dedupe_signature": "014bf08be9b8ebc523539a7e183fd00c1a7de6ac77a00fafd82b8b3469aeda5e", "difficulty": "medium", "final_answer": {"answer": 6.3416, "unit": "state_units"}, "id": "euler_decay_007803_47.5_0.17_1.95_5", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.17 y with y(0)=47.5, step size h=1.95, for 5 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.17 y, so each step multiplies y by 1 - h*0.17.\nApply that update for 5 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 47.5, "rate": 0.17, "step": 1.95, "steps": 5}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-6.2)=26.08 and f(-3.4)=19.36.\n3. The interval width is 2.8.\nFinal: {\"answer\": 63.616, \"unit\": \"area_units\"}", "dedupe_signature": "cf1861e74708d4dd02fa973b57a542c054f52c85508c1f7f306d057432f7331b", "difficulty": "medium", "final_answer": {"answer": 63.616, "unit": "area_units"}, "id": "trapz_linear_007804_-2.4_11.2_-6.2_-3.4", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-2.4x+11.2 from x=-6.2 to x=-3.4. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-6.2)=26.08 and f(-3.4)=19.36.\nThe interval width is 2.8.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 11.2, "slope": -2.4, "x0": -6.2, "x1": -3.4000000000000004}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 22364.0 / 1000.\nFinal: {\"answer\": 22.364, \"unit\": \"kg\"}", "dedupe_signature": "180465e1cfb4e16a0f68a210d84a495cd9c918690fe85a4c44da6bb62979bdd7", "difficulty": "easy", "final_answer": {"answer": 22.364, "unit": "kg"}, "id": "unit_convert_007806_g_to_kg_22364", "license": "Apache-2.0", "prompt": "Convert 22364 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 22364.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 22364.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=94 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-5.5805, 79.8051], \"unit\": \"N\"}", "dedupe_signature": "cd85b8a8a2369ddb2f1d94c98c787801af9ec4f030fdcfc483f46ab719ae5d17", "difficulty": "medium", "final_answer": {"answer": [-5.5805, 79.8051], "unit": "N"}, "id": "vector_components_007807_80_94", "license": "Apache-2.0", "prompt": "A vector has magnitude 80 N at 94 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=94 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 94, "magnitude": 80.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-1.9, 27.75], \"unit\": \"dimensionless\"}", "dedupe_signature": "4d90eaa2509ca335b12fc4315fcd50edbcb5bb001e06f66222d2bc3f27928e00", "difficulty": "medium", "final_answer": {"answer": [-1.9, 27.75], "unit": "dimensionless"}, "id": "line_two_point_007808_-4.5_8.5_-1.9_27.75", "license": "Apache-2.0", "prompt": "A line passes through points (-4.5, 36.3) and (8.5, 11.6). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -4.5, "x2": 8.5, "y1": 36.3, "y2": 11.600000000000001}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef finite_differences_007810(values):\n    return [values[i + 1] - values[i] for i in range(len(values) - 1)]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"finite_differences_007810\"}", "dedupe_signature": "bf0887110c3ad0d0ef2acadf1374e0ea824f9d63f454c7f2a21f61093586df4d", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "finite_differences_007810"}, "id": "code_007810_finite_differences_007810", "license": "Apache-2.0", "prompt": "Write a Python function finite_differences_007810(values) that returns the list of successive differences values[i+1] - values[i]. It must return [] for fewer than two values. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "finite_differences_007810"}, "verifier": {"function": "finite_differences_007810", "tests": ["assert finite_differences_007810([1, 4, 9, 16]) == [3, 5, 7]", "assert finite_differences_007810([5]) == []", "assert finite_differences_007810([]) == []"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: volume.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"volume\"]}", "dedupe_signature": "801d340bc248074bad641e75a25bb8dfa6c38ebdc8a3ff7586c3cffac41d2f64", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["volume"]}, "id": "abstain_007811_volume", "license": "Apache-2.0", "prompt": "Compute pressure from the ideal gas law. The prompt gives n=0.38 mol and T=520 K, but does not give volume. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: volume.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["volume"]}, "verifier": {"missing": ["volume"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=69 degrees through the sine of 2 theta.\n3. Substitute v=69.5 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 329.4667, \"unit\": \"m\"}", "dedupe_signature": "58b69f78c4dc084e3f2de489c4ff0c6ff922b4920acf01690abbf302c0508284", "difficulty": "medium", "final_answer": {"answer": 329.4667, "unit": "m"}, "id": "projectile_range_007814_69.5_69", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 69.5 m/s and angle 69 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=69 degrees through the sine of 2 theta.\nSubstitute v=69.5 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 69, "gravity": 9.81, "speed": 69.5}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 0.25 * 8.314 * 473 / 54.9.\nFinal: {\"answer\": 17.9077, \"unit\": \"kPa\"}", "dedupe_signature": "317a3aa72e1c5f1201271a7f3bc706182e60fe9aab6480a68321ffe38a4e9a86", "difficulty": "medium", "final_answer": {"answer": 17.9077, "unit": "kPa"}, "id": "ideal_gas_007815_0.25_473_54.9", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=0.25 mol, T=473 K, and V=54.9 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 0.25 * 8.314 * 473 / 54.9.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 0.25, "temp_k": 473, "volume_l": 54.9}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1890 * 2.415 * 6.\nFinal: {\"answer\": 27386.1, \"unit\": \"J\"}", "dedupe_signature": "92e03c0fd6398932cc870af2ea50298be523d307d4b537b8efc903d49083cdb0", "difficulty": "easy", "final_answer": {"answer": 27386.1, "unit": "J"}, "id": "heat_q_007816_1890_2.415_6", "license": "Apache-2.0", "prompt": "A 1890 g sample has specific heat 2.415 J/(g*K). How much heat is needed to raise its temperature by 6 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1890 * 2.415 * 6.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 6, "heat_capacity": 2.415, "mass_g": 1890}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=190.4 V and R=112.9 ohm.\nFinal: {\"answer\": 321.0997, \"unit\": \"W\"}", "dedupe_signature": "a95b772bdc6ecda822a8670c2dbc4c5b1a5725e759e4f49e11fa29450fbc20bd", "difficulty": "easy", "final_answer": {"answer": 321.0997, "unit": "W"}, "id": "ohm_power_007817_190.4_112.9", "license": "Apache-2.0", "prompt": "A resistor has resistance 112.9 ohm and voltage 190.4 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=190.4 V and R=112.9 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 112.9, "voltage": 190.4}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=827.5 mg, t=19.5 h, and T_half=50.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 633.1822, \"unit\": \"mg\"}", "dedupe_signature": "6511cdcaef6958588f0025713213b44c4a3d1b8869cd881581d222a2976f9cda", "difficulty": "medium", "final_answer": {"answer": 633.1822, "unit": "mg"}, "id": "half_life_007818_827.5_50.5_19.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 827.5 mg. Its half-life is 50.5 hours. How many mg remain after 19.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=827.5 mg, t=19.5 h, and T_half=50.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 19.5, "half_life": 50.5, "initial_amount": 827.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 1.36 mol * 44.01 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 59.8536, \"unit\": \"g\"}", "dedupe_signature": "3e133eaed7cf4f7cede09815a101bbc3a3c1f70a5d98646a4923dc3c10e489a2", "difficulty": "medium", "final_answer": {"answer": 59.8536, "unit": "g"}, "id": "stoich_mass_007819_carbon_dioxide_1.36", "license": "Apache-2.0", "prompt": "A sample contains 1.36 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 1.36 mol * 44.01 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "carbon dioxide", "molar_mass": 44.01, "moles": 1.36}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.08 y, so each step multiplies y by 1 - h*0.08.\n3. Apply that update for 5 steps and round the final state.\nFinal: {\"answer\": 6.7712, \"unit\": \"state_units\"}", "dedupe_signature": "629ac206feade4cc0f9aa544122c055c611a29bdef820630cd5255f59c5a37d4", "difficulty": "medium", "final_answer": {"answer": 6.7712, "unit": "state_units"}, "id": "euler_decay_007821_10.5_0.08_1.05_5", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.08 y with y(0)=10.5, step size h=1.05, for 5 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.08 y, so each step multiplies y by 1 - h*0.08.\nApply that update for 5 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 10.5, "rate": 0.08, "step": 1.05, "steps": 5}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 100 centimeters in one meter.\n2. Apply the conversion factor directly to the given value.\n3. Compute 3819.5 / 100.\nFinal: {\"answer\": 38.195, \"unit\": \"m\"}", "dedupe_signature": "e65f60aa4ecff264c0a672ab271665d03820aa451ac52f6e2a60e34c48562413", "difficulty": "easy", "final_answer": {"answer": 38.195, "unit": "m"}, "id": "unit_convert_007824_cm_to_m_3819.5", "license": "Apache-2.0", "prompt": "Convert 3819.5 cm to m. Return the converted value with unit.", "reasoning_trace": "There are 100 centimeters in one meter.\nApply the conversion factor directly to the given value.\nCompute 3819.5 / 100.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 3819.5}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=312 degrees and keep the unit as newtons.\nFinal: {\"answer\": [53.5304, -59.4516], \"unit\": \"N\"}", "dedupe_signature": "105ba6b26c1feaeba682d71893c0a6d773aa92d86e867f76c02454782c642e56", "difficulty": "medium", "final_answer": {"answer": [53.5304, -59.4516], "unit": "N"}, "id": "vector_components_007825_80_312", "license": "Apache-2.0", "prompt": "A vector has magnitude 80 N at 312 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=312 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 312, "magnitude": 80.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [0.4, -5.25], \"unit\": \"dimensionless\"}", "dedupe_signature": "fe24b256d5278783747cfb56244f958f484e1fcffb95b63ec66d4ef956feea8b", "difficulty": "medium", "final_answer": {"answer": [0.4, -5.25], "unit": "dimensionless"}, "id": "line_two_point_007826_-8.25_0.25_0.4_-5.25", "license": "Apache-2.0", "prompt": "A line passes through points (-8.25, -8.55) and (0.25, -5.15). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -8.25, "x2": 0.25, "y1": -8.55, "y2": -5.15}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. m*v is momentum, not energy\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "b3aa4f2275a338aae1d70da43475af59fc815c1e375f64093747c4cdca0d5497", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_007827_inconsistent_1e14b074_665462", "license": "Apache-2.0", "prompt": "In quality-control check case 665462, check dimensional consistency for E = m * v. The left side has dimensions kg*m^2/s^2 and the right side has dimensions kg*m/s. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nm*v is momentum, not energy\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "E = m * v"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: required_fields, allowed_transformations.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"required_fields\", \"allowed_transformations\"]}", "dedupe_signature": "e83dfc83aae69c9055fcbf2218d804a01cba67e45fcf08a90244bf31b7ef70d5", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["required_fields", "allowed_transformations"]}, "id": "abstain_007829_required_fields_allowed_transformations", "license": "Apache-2.0", "prompt": "Write a sanitizer for valid mobile clinical records in release 776263, but the prompt does not state which fields are required or which transformations are allowed. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: required_fields, allowed_transformations.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["required_fields", "allowed_transformations"]}, "verifier": {"missing": ["required_fields", "allowed_transformations"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 11.45 kg and a = 0.25 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 2.8625, \"unit\": \"N\"}", "dedupe_signature": "2a7f5d269c9929007a1f0ea8145c70ddd5e2bb9833cc9d5c1fe7d903d05bdfde", "difficulty": "easy", "final_answer": {"answer": 2.8625, "unit": "N"}, "id": "force_007830_11.45_0.25", "license": "Apache-2.0", "prompt": "A cart has mass 11.45 kg and measured acceleration 0.25 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 11.45 kg and a = 0.25 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 0.25, "mass": 11.45}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 11.25^2 and multiply by 0.5 * 19.8.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 1252.9688, \"unit\": \"J\"}", "dedupe_signature": "ec454215af9fc952448fa13367e4c13a3e3af7a581a46b9e51da154963250628", "difficulty": "easy", "final_answer": {"answer": 1252.9688, "unit": "J"}, "id": "ke_007831_19.8_11.25", "license": "Apache-2.0", "prompt": "A body of mass 19.8 kg moves at 11.25 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 11.25^2 and multiply by 0.5 * 19.8.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 19.8, "velocity": 11.25}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 4.42 * 8.314 * 377 / 70.2.\nFinal: {\"answer\": 197.3497, \"unit\": \"kPa\"}", "dedupe_signature": "cc8765b14c78bf0fefe69e694c60b81fad4c1027f35be7877ca1063a80513771", "difficulty": "medium", "final_answer": {"answer": 197.3497, "unit": "kPa"}, "id": "ideal_gas_007833_4.42_377_70.2", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=4.42 mol, T=377 K, and V=70.2 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 4.42 * 8.314 * 377 / 70.2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 4.42, "temp_k": 377, "volume_l": 70.2}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 470 * 1.65 * 23.\nFinal: {\"answer\": 17836.5, \"unit\": \"J\"}", "dedupe_signature": "d99c624482d88a42e6c5adb013ba1cc9e8c1199e2fb97484e1def1b16c278d97", "difficulty": "easy", "final_answer": {"answer": 17836.5, "unit": "J"}, "id": "heat_q_007834_470_1.65_23", "license": "Apache-2.0", "prompt": "A 470 g sample has specific heat 1.65 J/(g*K). How much heat is needed to raise its temperature by 23 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 470 * 1.65 * 23.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 23, "heat_capacity": 1.65, "mass_g": 470}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=209 V and R=124 ohm.\nFinal: {\"answer\": 352.2661, \"unit\": \"W\"}", "dedupe_signature": "910b1c8a4f87de223c2481efa0620641f6d0868e94a8fbd6aae0c94e111d4084", "difficulty": "easy", "final_answer": {"answer": 352.2661, "unit": "W"}, "id": "ohm_power_007835_209_124", "license": "Apache-2.0", "prompt": "A resistor has resistance 124 ohm and voltage 209 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=209 V and R=124 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 124.0, "voltage": 209.0}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=778.5 mg, t=330 h, and T_half=37.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 1.7466, \"unit\": \"mg\"}", "dedupe_signature": "af1559e43e5e7fd657c7d259a0e52e21929cf259d92c20feb6106834e7d4fd99", "difficulty": "medium", "final_answer": {"answer": 1.7466, "unit": "mg"}, "id": "half_life_007836_778.5_37.5_330", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 778.5 mg. Its half-life is 37.5 hours. How many mg remain after 330 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=778.5 mg, t=330 h, and T_half=37.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 330.0, "half_life": 37.5, "initial_amount": 778.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 4.51 mol * 58.44 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 263.5644, \"unit\": \"g\"}", "dedupe_signature": "6a8d2c267fb94a4f3b79e5cffeeb9b47e6e3a578133f51138da6116881e1ff65", "difficulty": "medium", "final_answer": {"answer": 263.5644, "unit": "g"}, "id": "stoich_mass_007837_sodium_chloride_4.51", "license": "Apache-2.0", "prompt": "A sample contains 4.51 mol of sodium chloride. Using molar mass 58.44 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 4.51 mol * 58.44 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "sodium chloride", "molar_mass": 58.44, "moles": 4.51}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 4265 mL to 4.265 L.\n3. Compute M = 0.685 / 4.265.\nFinal: {\"answer\": 0.1606, \"unit\": \"mol/L\"}", "dedupe_signature": "4cca1b7ea9dd4b9d35164f14dc0fe848909f09f524eaf9f88db32c60de1a8b50", "difficulty": "medium", "final_answer": {"answer": 0.1606, "unit": "mol/L"}, "id": "molarity_007838_0.685_4265", "license": "Apache-2.0", "prompt": "A solution contains 0.685 mol of solute in 4265 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 4265 mL to 4.265 L.\nCompute M = 0.685 / 4.265.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 0.685, "volume_ml": 4265}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.28 y, so each step multiplies y by 1 - h*0.28.\n3. Apply that update for 6 steps and round the final state.\nFinal: {\"answer\": 0.1324, \"unit\": \"state_units\"}", "dedupe_signature": "cf8e96cf016a9e6f05d325628eb8ee0bf31ba769f298d724a99df3d10177338d", "difficulty": "medium", "final_answer": {"answer": 0.1324, "unit": "state_units"}, "id": "euler_decay_007839_2_0.28_1.3_6", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.28 y with y(0)=2, step size h=1.3, for 6 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.28 y, so each step multiplies y by 1 - h*0.28.\nApply that update for 6 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 2.0, "rate": 0.28, "step": 1.3, "steps": 6}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-5.3)=17.76 and f(-0.6)=2.72.\n3. The interval width is 4.7.\nFinal: {\"answer\": 48.128, \"unit\": \"area_units\"}", "dedupe_signature": "42dde0ab3aeff3921f70bdc9a158fc4da58eddf5d184f16080c147b7882c5366", "difficulty": "medium", "final_answer": {"answer": 48.128, "unit": "area_units"}, "id": "trapz_linear_007840_-3.2_0.8_-5.3_-0.6", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-3.2x+0.8 from x=-5.3 to x=-0.6. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-5.3)=17.76 and f(-0.6)=2.72.\nThe interval width is 4.7.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 0.8, "slope": -3.2, "x0": -5.3, "x1": -0.5999999999999996}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.16 and add it to the current value.\nFinal: {\"answer\": [0.926, -0.388, 1.472], \"unit\": \"temperature_units\"}", "dedupe_signature": "cb1f0fc76f1c8f8e9a2adcebc5d484b340ca86f475a3362f59380a22cb1a8537", "difficulty": "hard", "final_answer": {"answer": [0.926, -0.388, 1.472], "unit": "temperature_units"}, "id": "heat_step_007841_0.16_0.7_1.55_-1.5_2.4_0.5", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=0.7, right=0.5; current interior values are [1.55, -1.5, 2.4]. Use r=0.16. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.16 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [1.55, -1.5, 2.4], "left": 0.7, "r": 0.16, "right": 0.5}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=340 degrees and keep the unit as newtons.\nFinal: {\"answer\": [77.9945, -28.3877], \"unit\": \"N\"}", "dedupe_signature": "0153db064b5b032cfd734bf9983ab4dcddd3827b133327feadcbe7e6cbab219c", "difficulty": "medium", "final_answer": {"answer": [77.9945, -28.3877], "unit": "N"}, "id": "vector_components_007843_83_340", "license": "Apache-2.0", "prompt": "A vector has magnitude 83 N at 340 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=340 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 340, "magnitude": 83.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [7.15, 14.25], \"unit\": \"dimensionless\"}", "dedupe_signature": "ed1d14e0646286b1be285fcfe85bf16ef588e5144dd6e94b52cce03583a03968", "difficulty": "medium", "final_answer": {"answer": [7.15, 14.25], "unit": "dimensionless"}, "id": "line_two_point_007844_-5.5_4.25_7.15_14.25", "license": "Apache-2.0", "prompt": "A line passes through points (-5.5, -25.075) and (4.25, 44.6375). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -5.5, "x2": 4.25, "y1": -25.075000000000003, "y2": 44.6375}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. density times acceleration times height gives kg/(m*s^2), or pascal\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "5c63e9a5f7c134d08325beed0c5e0d5f3444d236b31299ac34870fd0485adbb5", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_007845_consistent_b7d3eed1_486336", "license": "Apache-2.0", "prompt": "In field worksheet case 486336, check dimensional consistency for p = rho * g * h. The left side has dimensions Pa and the right side has dimensions Pa. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\ndensity times acceleration times height gives kg/(m*s^2), or pascal\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "p = rho * g * h"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef running_total_007846(values):\n    total = 0\n    out = []\n    for value in values:\n        total += value\n        out.append(total)\n    return out\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"running_total_007846\"}", "dedupe_signature": "17955d6fb2a36e2c43e2c2b81471c51cbc5ea83efc6f1a13d2182fd114eec69a", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "running_total_007846"}, "id": "code_007846_running_total_007846", "license": "Apache-2.0", "prompt": "Write a Python function running_total_007846(values) that returns cumulative sums as a new list. It must not mutate the input list. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "running_total_007846"}, "verifier": {"function": "running_total_007846", "tests": ["assert running_total_007846([1, 2, 3]) == [1, 3, 6]", "xs = [4, -1, 2]; assert running_total_007846(xs) == [4, 3, 5] and xs == [4, -1, 2]", "assert running_total_007846([]) == []"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: volume.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"volume\"]}", "dedupe_signature": "4f1b60eb33a5216576a4f492d96af7d765e176c54de2b0476e5e9a658402a996", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["volume"]}, "id": "abstain_007847_volume", "license": "Apache-2.0", "prompt": "Compute pressure from the ideal gas law. The prompt gives n=1.29 mol and T=519 K, but does not give volume. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: volume.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["volume"]}, "verifier": {"missing": ["volume"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 8.2 kg and a = 13.25 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 108.65, \"unit\": \"N\"}", "dedupe_signature": "79d5b35d43ee5da74871ece1fff2339feb5b028cfdf6ed2232cf95d7a2d1e8e7", "difficulty": "easy", "final_answer": {"answer": 108.65, "unit": "N"}, "id": "force_007848_8.2_13.25", "license": "Apache-2.0", "prompt": "A cart has mass 8.2 kg and measured acceleration 13.25 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 8.2 kg and a = 13.25 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 13.25, "mass": 8.2}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 1.02 * 8.314 * 547 / 108.2.\nFinal: {\"answer\": 42.8717, \"unit\": \"kPa\"}", "dedupe_signature": "c4f4183c8d44754265f745067265111b54ff6c99d0f081dba3310d4692e002b0", "difficulty": "medium", "final_answer": {"answer": 42.8717, "unit": "kPa"}, "id": "ideal_gas_007851_1.02_547_108.2", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=1.02 mol, T=547 K, and V=108.2 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 1.02 * 8.314 * 547 / 108.2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 1.02, "temp_k": 547, "volume_l": 108.2}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 240 * 2.605 * 92.\nFinal: {\"answer\": 57518.4, \"unit\": \"J\"}", "dedupe_signature": "6245902dbe337d7c6d3871b2335930549f7c669b1c67ff33e227a0628c8a4bb0", "difficulty": "easy", "final_answer": {"answer": 57518.4, "unit": "J"}, "id": "heat_q_007852_240_2.605_92", "license": "Apache-2.0", "prompt": "A 240 g sample has specific heat 2.605 J/(g*K). How much heat is needed to raise its temperature by 92 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 240 * 2.605 * 92.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 92, "heat_capacity": 2.605, "mass_g": 240}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=964.5 mg, t=357.5 h, and T_half=6 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 0.0, \"unit\": \"mg\"}", "dedupe_signature": "596777fc9a164bd4e8a29d19b1ff4767ff1765a0fa0176f222fed77e23c5b5af", "difficulty": "medium", "final_answer": {"answer": 0.0, "unit": "mg"}, "id": "half_life_007854_964.5_6_357.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 964.5 mg. Its half-life is 6 hours. How many mg remain after 357.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=964.5 mg, t=357.5 h, and T_half=6 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 357.5, "half_life": 6.0, "initial_amount": 964.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 1700 mL to 1.7 L.\n3. Compute M = 3.39 / 1.7.\nFinal: {\"answer\": 1.9941, \"unit\": \"mol/L\"}", "dedupe_signature": "d125df7b08f7e3605c0bf588b245bea58879410a68e9aca8c8e7047c2638b344", "difficulty": "medium", "final_answer": {"answer": 1.9941, "unit": "mol/L"}, "id": "molarity_007856_3.39_1700", "license": "Apache-2.0", "prompt": "A solution contains 3.39 mol of solute in 1700 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 1700 mL to 1.7 L.\nCompute M = 3.39 / 1.7.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 3.39, "volume_ml": 1700}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.21 y, so each step multiplies y by 1 - h*0.21.\n3. Apply that update for 6 steps and round the final state.\nFinal: {\"answer\": 20.9128, \"unit\": \"state_units\"}", "dedupe_signature": "fd3a1d107ec20b78ff6078b95c2c0c989ca993c54b476cc3518306f01ba625cf", "difficulty": "medium", "final_answer": {"answer": 20.9128, "unit": "state_units"}, "id": "euler_decay_007857_73.5_0.21_0.9_6", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.21 y with y(0)=73.5, step size h=0.9, for 6 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.21 y, so each step multiplies y by 1 - h*0.21.\nApply that update for 6 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 73.5, "rate": 0.21, "step": 0.9, "steps": 6}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-4)=23.3 and f(-0.6)=18.2.\n3. The interval width is 3.4.\nFinal: {\"answer\": 70.55, \"unit\": \"area_units\"}", "dedupe_signature": "0ea098c7d4b8b0f1d19d0d30f9d922436e28a22b67a7a76cd2c621307127806f", "difficulty": "medium", "final_answer": {"answer": 70.55, "unit": "area_units"}, "id": "trapz_linear_007858_-1.5_17.3_-4_-0.6", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-1.5x+17.3 from x=-4 to x=-0.6. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-4)=23.3 and f(-0.6)=18.2.\nThe interval width is 3.4.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 17.3, "slope": -1.5, "x0": -4.0, "x1": -0.6000000000000001}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.4 and add it to the current value.\nFinal: {\"answer\": [-1.07, 0.67, 0.0], \"unit\": \"temperature_units\"}", "dedupe_signature": "11836e2f53291adafd73233238c9e5fb6281b1fec921161547c3182a2a214845", "difficulty": "hard", "final_answer": {"answer": [-1.07, 0.67, 0.0], "unit": "temperature_units"}, "id": "heat_step_007859_0.4_-1.35_1.25_-1.95_1.4_1.25", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-1.35, right=1.25; current interior values are [1.25, -1.95, 1.4]. Use r=0.4. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.4 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [1.25, -1.95, 1.4], "left": -1.35, "r": 0.4, "right": 1.25}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 100 centimeters in one meter.\n2. Apply the conversion factor directly to the given value.\n3. Compute 4918.5 / 100.\nFinal: {\"answer\": 49.185, \"unit\": \"m\"}", "dedupe_signature": "12637fd4641d07dcee310c9119f8e1538ca86d0256882bdcc4ae4a7b22bee511", "difficulty": "easy", "final_answer": {"answer": 49.185, "unit": "m"}, "id": "unit_convert_007860_cm_to_m_4918.5", "license": "Apache-2.0", "prompt": "Convert 4918.5 cm to m. Return the converted value with unit.", "reasoning_trace": "There are 100 centimeters in one meter.\nApply the conversion factor directly to the given value.\nCompute 4918.5 / 100.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 4918.5}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-4.1, 10.75], \"unit\": \"dimensionless\"}", "dedupe_signature": "5720018138a5d3cfe410a852e68d60333aa7969bcc3424f293b4ba8712a38344", "difficulty": "medium", "final_answer": {"answer": [-4.1, 10.75], "unit": "dimensionless"}, "id": "line_two_point_007862_-1_2_-4.1_10.75", "license": "Apache-2.0", "prompt": "A line passes through points (-1, 14.85) and (2, 2.55). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -1.0, "x2": 2.0, "y1": 14.85, "y2": 2.5500000000000007}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. mass times acceleration has newton dimensions\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "222ec0f7d5ba32461d7a1cbca748dc36e46873f6642edc1c9f540a4b56a288e9", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_007863_consistent_03f5e041_453055", "license": "Apache-2.0", "prompt": "In sensor calibration case 453055, check dimensional consistency for F = m * a. The left side has dimensions kg*m/s^2 and the right side has dimensions kg*m/s^2. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nmass times acceleration has newton dimensions\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "F = m * a"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef weighted_sum_007864(values, weights):\n    if len(values) != len(weights):\n        raise ValueError('length mismatch')\n    return sum(value * weight for value, weight in zip(values, weights))\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"weighted_sum_007864\"}", "dedupe_signature": "bcb4389959c946365a16dd418fb20fc3e3571b18c776fd0215a0d9c1a5a2255f", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "weighted_sum_007864"}, "id": "code_007864_weighted_sum_007864", "license": "Apache-2.0", "prompt": "Write a Python function weighted_sum_007864(values, weights) that returns sum(value*weight). Raise ValueError when the two inputs have different lengths. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "weighted_sum_007864"}, "verifier": {"function": "weighted_sum_007864", "tests": ["assert weighted_sum_007864([2, 3], [4, 5]) == 23", "assert weighted_sum_007864([], []) == 0", "try:\n    weighted_sum_007864([1], [1, 2])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: required_fields, allowed_transformations.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"required_fields\", \"allowed_transformations\"]}", "dedupe_signature": "5d960d31f5a290158611f7384c9326cce5776fdad794f83c504347a1268f6690", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["required_fields", "allowed_transformations"]}, "id": "abstain_007865_required_fields_allowed_transformations", "license": "Apache-2.0", "prompt": "Write a sanitizer for valid registry clinical records in release 169886, but the prompt does not state which fields are required or which transformations are allowed. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: required_fields, allowed_transformations.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["required_fields", "allowed_transformations"]}, "verifier": {"missing": ["required_fields", "allowed_transformations"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 1.6 kg and a = 15.85 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 25.36, \"unit\": \"N\"}", "dedupe_signature": "24cededa54e65897d4513ea79e33139a67588be33bcb30e25f67d06d36f733e9", "difficulty": "easy", "final_answer": {"answer": 25.36, "unit": "N"}, "id": "force_007866_1.6_15.85", "license": "Apache-2.0", "prompt": "A cart has mass 1.6 kg and measured acceleration 15.85 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 1.6 kg and a = 15.85 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 15.85, "mass": 1.6}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 12.9^2 and multiply by 0.5 * 26.6.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 2213.253, \"unit\": \"J\"}", "dedupe_signature": "aa05cf17e2c331733ed76c40d9abf9d1b0e9190207380d79a91483527b3164f3", "difficulty": "easy", "final_answer": {"answer": 2213.253, "unit": "J"}, "id": "ke_007867_26.6_12.9", "license": "Apache-2.0", "prompt": "A body of mass 26.6 kg moves at 12.9 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 12.9^2 and multiply by 0.5 * 26.6.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 26.6, "velocity": 12.9}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=18 degrees through the sine of 2 theta.\n3. Substitute v=41.3 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 102.1997, \"unit\": \"m\"}", "dedupe_signature": "3c6de7f71d036dd02ae5081cee972dd9323e22e9b158fa7e574b1b862cf45ece", "difficulty": "medium", "final_answer": {"answer": 102.1997, "unit": "m"}, "id": "projectile_range_007868_41.3_18", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 41.3 m/s and angle 18 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=18 degrees through the sine of 2 theta.\nSubstitute v=41.3 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 18, "gravity": 9.81, "speed": 41.3}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 1.73 * 8.314 * 615 / 94.9.\nFinal: {\"answer\": 93.2105, \"unit\": \"kPa\"}", "dedupe_signature": "5d3186032be80be01963f0f3bfadd0a9865de3acd6065421d8761f123b516cc7", "difficulty": "medium", "final_answer": {"answer": 93.2105, "unit": "kPa"}, "id": "ideal_gas_007869_1.73_615_94.9", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=1.73 mol, T=615 K, and V=94.9 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 1.73 * 8.314 * 615 / 94.9.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 1.73, "temp_k": 615, "volume_l": 94.9}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 385 * 4.72 * 41.\nFinal: {\"answer\": 74505.2, \"unit\": \"J\"}", "dedupe_signature": "055ad14d5dc476715402df13abd32e2c3f816437d08c6cfd4e9d39555befc485", "difficulty": "easy", "final_answer": {"answer": 74505.2, "unit": "J"}, "id": "heat_q_007870_385_4.72_41", "license": "Apache-2.0", "prompt": "A 385 g sample has specific heat 4.72 J/(g*K). How much heat is needed to raise its temperature by 41 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 385 * 4.72 * 41.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 41, "heat_capacity": 4.72, "mass_g": 385}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=12.5 V and R=124 ohm.\nFinal: {\"answer\": 1.2601, \"unit\": \"W\"}", "dedupe_signature": "eab834c1f88d90372555ac2b206399f126e938dd01079c9b44ef963f58e51391", "difficulty": "easy", "final_answer": {"answer": 1.2601, "unit": "W"}, "id": "ohm_power_007871_12.5_124", "license": "Apache-2.0", "prompt": "A resistor has resistance 124 ohm and voltage 12.5 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=12.5 V and R=124 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 124.0, "voltage": 12.5}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=398 mg, t=355.5 h, and T_half=23.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 0.0111, \"unit\": \"mg\"}", "dedupe_signature": "ccad3cfdd89b8bcfbe0fea911f163839fc1375ff54d543a025ac4bd8867decb2", "difficulty": "medium", "final_answer": {"answer": 0.0111, "unit": "mg"}, "id": "half_life_007872_398_23.5_355.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 398 mg. Its half-life is 23.5 hours. How many mg remain after 355.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=398 mg, t=355.5 h, and T_half=23.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 355.5, "half_life": 23.5, "initial_amount": 398.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 5.65 mol * 100.087 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 565.4916, \"unit\": \"g\"}", "dedupe_signature": "0c589a2e49cc90ea69e5c396569bcaffe554b70e26a42864f85bff52a0541257", "difficulty": "medium", "final_answer": {"answer": 565.4916, "unit": "g"}, "id": "stoich_mass_007873_calcium_carbonate_5.65", "license": "Apache-2.0", "prompt": "A sample contains 5.65 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 5.65 mol * 100.087 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "calcium carbonate", "molar_mass": 100.087, "moles": 5.65}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 690 mL to 0.69 L.\n3. Compute M = 3.085 / 0.69.\nFinal: {\"answer\": 4.471, \"unit\": \"mol/L\"}", "dedupe_signature": "5438285a7dcc68b4429b9b87d42ba0bd9c2c2ba3ed149c4308e1066b0e31ab2d", "difficulty": "medium", "final_answer": {"answer": 4.471, "unit": "mol/L"}, "id": "molarity_007874_3.085_690", "license": "Apache-2.0", "prompt": "A solution contains 3.085 mol of solute in 690 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 690 mL to 0.69 L.\nCompute M = 3.085 / 0.69.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 3.085, "volume_ml": 690}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(0.9)=2.15 and f(9.6)=41.3.\n3. The interval width is 8.7.\nFinal: {\"answer\": 189.0075, \"unit\": \"area_units\"}", "dedupe_signature": "a9710be023a1123545f99358a640ba0fe68a484ca9fb5a26e2c953bd133607d4", "difficulty": "medium", "final_answer": {"answer": 189.0075, "unit": "area_units"}, "id": "trapz_linear_007876_4.5_-1.9_0.9_9.6", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=4.5x+-1.9 from x=0.9 to x=9.6. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(0.9)=2.15 and f(9.6)=41.3.\nThe interval width is 8.7.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -1.9, "slope": 4.5, "x0": 0.9, "x1": 9.6}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=96 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-32.1948, 306.3127], \"unit\": \"N\"}", "dedupe_signature": "8ff0f809bd14d9e2e1ebc0a74299c5b06ea918e64d71e573d5f36f0c7cbf56ae", "difficulty": "medium", "final_answer": {"answer": [-32.1948, 306.3127], "unit": "N"}, "id": "vector_components_007879_308_96", "license": "Apache-2.0", "prompt": "A vector has magnitude 308 N at 96 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=96 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 96, "magnitude": 308.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [-9.8, -12.5], \"unit\": \"dimensionless\"}", "dedupe_signature": "70e5cdb794a7bceb39fae1be197a652c4151446a8f2fee5f9996379620bbb0f0", "difficulty": "medium", "final_answer": {"answer": [-9.8, -12.5], "unit": "dimensionless"}, "id": "line_two_point_007880_-14_-12_-9.8_-12.5", "license": "Apache-2.0", "prompt": "A line passes through points (-14, 124.7) and (-12, 105.1). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -14.0, "x2": -12.0, "y1": 124.70000000000002, "y2": 105.10000000000001}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\nimport math\n\ndef unit_vector_007882(x, y):\n    norm = math.hypot(x, y)\n    if norm == 0:\n        raise ValueError('zero vector has no direction')\n    return (x / norm, y / norm)\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"unit_vector_007882\"}", "dedupe_signature": "85f6e000cb4897314857c45e469b200f70dd6a7a5f960eca1e9a553eae98d68a", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "unit_vector_007882"}, "id": "code_007882_unit_vector_007882", "license": "Apache-2.0", "prompt": "Write a Python function unit_vector_007882(x, y) that returns the 2D unit vector as a tuple. Raise ValueError for the zero vector. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "unit_vector_007882"}, "verifier": {"function": "unit_vector_007882", "tests": ["ux, uy = unit_vector_007882(3, 4); assert abs(ux - 0.6) < 1e-12 and abs(uy - 0.8) < 1e-12", "assert unit_vector_007882(0, 5) == (0, 1)", "try:\n    unit_vector_007882(0, 0)\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: required_fields, allowed_transformations.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"required_fields\", \"allowed_transformations\"]}", "dedupe_signature": "bccf0d75e9c958bfa6a95ba4db62e909809fb6512bb7e1149341c8b9651e3d8b", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["required_fields", "allowed_transformations"]}, "id": "abstain_007883_required_fields_allowed_transformations", "license": "Apache-2.0", "prompt": "Write a sanitizer for valid laboratory crop records in release 226488, but the prompt does not state which fields are required or which transformations are allowed. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: required_fields, allowed_transformations.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["required_fields", "allowed_transformations"]}, "verifier": {"missing": ["required_fields", "allowed_transformations"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 22.75^2 and multiply by 0.5 * 1.35.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 349.3547, \"unit\": \"J\"}", "dedupe_signature": "25677f1fe142f35a07f57118e0b0684893968e2e9420ff47659dcbd3458cbed0", "difficulty": "easy", "final_answer": {"answer": 349.3547, "unit": "J"}, "id": "ke_007885_1.35_22.75", "license": "Apache-2.0", "prompt": "A body of mass 1.35 kg moves at 22.75 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 22.75^2 and multiply by 0.5 * 1.35.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 1.35, "velocity": 22.75}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=33 degrees through the sine of 2 theta.\n3. Substitute v=8.6 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 6.8874, \"unit\": \"m\"}", "dedupe_signature": "0a8620658a9d6a98df9f23859fc13bddf22c826ebb97751beddc2eb663d94bc9", "difficulty": "medium", "final_answer": {"answer": 6.8874, "unit": "m"}, "id": "projectile_range_007886_8.6_33", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 8.6 m/s and angle 33 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=33 degrees through the sine of 2 theta.\nSubstitute v=8.6 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 33, "gravity": 9.81, "speed": 8.6}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 5.11 * 8.314 * 256 / 101.9.\nFinal: {\"answer\": 106.7325, \"unit\": \"kPa\"}", "dedupe_signature": "1eef368dd866f7b661208e250759b08d9380af53426f25b6327cc57a481d32fa", "difficulty": "medium", "final_answer": {"answer": 106.7325, "unit": "kPa"}, "id": "ideal_gas_007887_5.11_256_101.9", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=5.11 mol, T=256 K, and V=101.9 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 5.11 * 8.314 * 256 / 101.9.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 5.11, "temp_k": 256, "volume_l": 101.9}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 370 * 2.04 * 29.\nFinal: {\"answer\": 21889.2, \"unit\": \"J\"}", "dedupe_signature": "3654686718ab190545db42fa7abcde138abb9cf074a4d08e36a863db2c40f6c6", "difficulty": "easy", "final_answer": {"answer": 21889.2, "unit": "J"}, "id": "heat_q_007888_370_2.04_29", "license": "Apache-2.0", "prompt": "A 370 g sample has specific heat 2.04 J/(g*K). How much heat is needed to raise its temperature by 29 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 370 * 2.04 * 29.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 29, "heat_capacity": 2.04, "mass_g": 370}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=239.8 V and R=67.9 ohm.\nFinal: {\"answer\": 846.8931, \"unit\": \"W\"}", "dedupe_signature": "750ed4bbae8a1a2f5be48055069cd76fca67bea00eecadf3c5e8498b510eea7a", "difficulty": "easy", "final_answer": {"answer": 846.8931, "unit": "W"}, "id": "ohm_power_007889_239.8_67.9", "license": "Apache-2.0", "prompt": "A resistor has resistance 67.9 ohm and voltage 239.8 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=239.8 V and R=67.9 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 67.9, "voltage": 239.8}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=336 mg, t=252.5 h, and T_half=88 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 45.9821, \"unit\": \"mg\"}", "dedupe_signature": "879ee03ca7ce1db5fa71d0e8c6d50729cfb38a42c48f1715f76f4451ce1bec99", "difficulty": "medium", "final_answer": {"answer": 45.9821, "unit": "mg"}, "id": "half_life_007890_336_88_252.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 336 mg. Its half-life is 88 hours. How many mg remain after 252.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=336 mg, t=252.5 h, and T_half=88 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 252.5, "half_life": 88.0, "initial_amount": 336.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 5.6 mol * 44.01 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 246.456, \"unit\": \"g\"}", "dedupe_signature": "b2dc2bee33b61cf6fc476e1e65385b92195bc1483224bf02a6afaf90c5ad1de4", "difficulty": "medium", "final_answer": {"answer": 246.456, "unit": "g"}, "id": "stoich_mass_007891_carbon_dioxide_5.6", "license": "Apache-2.0", "prompt": "A sample contains 5.6 mol of carbon dioxide. Using molar mass 44.01 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 5.6 mol * 44.01 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "carbon dioxide", "molar_mass": 44.01, "moles": 5.6}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 2075 mL to 2.075 L.\n3. Compute M = 0.455 / 2.075.\nFinal: {\"answer\": 0.2193, \"unit\": \"mol/L\"}", "dedupe_signature": "0c4bff6ab985445e6df83b1c2365e145a97f0cf054e8017ff2e4c536d22f3034", "difficulty": "medium", "final_answer": {"answer": 0.2193, "unit": "mol/L"}, "id": "molarity_007892_0.455_2075", "license": "Apache-2.0", "prompt": "A solution contains 0.455 mol of solute in 2075 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 2075 mL to 2.075 L.\nCompute M = 0.455 / 2.075.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 0.455, "volume_ml": 2075}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.73 y, so each step multiplies y by 1 - h*0.73.\n3. Apply that update for 12 steps and round the final state.\nFinal: {\"answer\": 0.0, \"unit\": \"state_units\"}", "dedupe_signature": "3bc76405cce014c5d36dafef2703b14b5b8ab42915d72142b31c734a8df7a03e", "difficulty": "medium", "final_answer": {"answer": 0.0, "unit": "state_units"}, "id": "euler_decay_007893_66.5_0.73_1.35_12", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.73 y with y(0)=66.5, step size h=1.35, for 12 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.73 y, so each step multiplies y by 1 - h*0.73.\nApply that update for 12 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 66.5, "rate": 0.73, "step": 1.35, "steps": 12}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-8.1)=25.22 and f(-4.3)=16.86.\n3. The interval width is 3.8.\nFinal: {\"answer\": 79.952, \"unit\": \"area_units\"}", "dedupe_signature": "5712ed60accd6f8b8306c2cfa6c4ef9271f369c5c42de3475c2ff3f4771d5db3", "difficulty": "medium", "final_answer": {"answer": 79.952, "unit": "area_units"}, "id": "trapz_linear_007894_-2.2_7.4_-8.1_-4.3", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-2.2x+7.4 from x=-8.1 to x=-4.3. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-8.1)=25.22 and f(-4.3)=16.86.\nThe interval width is 3.8.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 7.4, "slope": -2.2, "x0": -8.1, "x1": -4.3}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 4485.0 / 1000.\nFinal: {\"answer\": 4.485, \"unit\": \"kg\"}", "dedupe_signature": "e422c1ee956c04c982366da98a101e37ae32ae78cd8d1bf849eaee6165d10a12", "difficulty": "easy", "final_answer": {"answer": 4.485, "unit": "kg"}, "id": "unit_convert_007896_g_to_kg_4485", "license": "Apache-2.0", "prompt": "Convert 4485 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 4485.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 4485.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=10 degrees and keep the unit as newtons.\nFinal: {\"answer\": [399.8319, 70.5012], \"unit\": \"N\"}", "dedupe_signature": "17600541bbbd8ff1a917a73e4d03664758038621753cf54cf2cae8bb755af87d", "difficulty": "medium", "final_answer": {"answer": [399.8319, 70.5012], "unit": "N"}, "id": "vector_components_007897_406_10", "license": "Apache-2.0", "prompt": "A vector has magnitude 406 N at 10 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=10 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 10, "magnitude": 406.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. velocity times time gives distance, not acceleration\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "28fde3fd6ae9f267f6f3cba92063499750d7838d4a4168c7a17405b2d69c31a4", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_007899_inconsistent_7481c798_69127", "license": "Apache-2.0", "prompt": "In quality-control check case 69127, check dimensional consistency for a = v * t. The left side has dimensions m/s^2 and the right side has dimensions m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nvelocity times time gives distance, not acceleration\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "a = v * t"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: recurrence, objective, tie_breaking_rule.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"recurrence\", \"objective\", \"tie_breaking_rule\"]}", "dedupe_signature": "66e20bc19ed59d24f42533ae00746ab6ea68ee263240ded22ae711bb2d7f3791", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["recurrence", "objective", "tie_breaking_rule"]}, "id": "abstain_007901_recurrence_objective_tie_breaking_rule", "license": "Apache-2.0", "prompt": "Write a dynamic-programming solver for a allocation scoring problem with 253 items and budget 85325, but the recurrence, objective, and tie-breaking rule are all absent. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: recurrence, objective, tie_breaking_rule.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["recurrence", "objective", "tie_breaking_rule"]}, "verifier": {"missing": ["recurrence", "objective", "tie_breaking_rule"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 12.3 kg and a = 14.65 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 180.195, \"unit\": \"N\"}", "dedupe_signature": "cbeef0091046e17c25bc6e40181f0e1493da6f3ee797f9484948a2729e0351d8", "difficulty": "easy", "final_answer": {"answer": 180.195, "unit": "N"}, "id": "force_007902_12.3_14.65", "license": "Apache-2.0", "prompt": "A cart has mass 12.3 kg and measured acceleration 14.65 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 12.3 kg and a = 14.65 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 14.65, "mass": 12.3}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 7.85^2 and multiply by 0.5 * 24.6.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 757.9567, \"unit\": \"J\"}", "dedupe_signature": "1c2c8e831f248772668e80e74dcfdedccc10ecc8e76c0d4bebf6ddf2465af9dd", "difficulty": "easy", "final_answer": {"answer": 757.9567, "unit": "J"}, "id": "ke_007903_24.6_7.85", "license": "Apache-2.0", "prompt": "A body of mass 24.6 kg moves at 7.85 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 7.85^2 and multiply by 0.5 * 24.6.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 24.6, "velocity": 7.85}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 825 * 1.015 * 89.\nFinal: {\"answer\": 74526.375, \"unit\": \"J\"}", "dedupe_signature": "ff836845fa8773ac413dca1514e3f48ac6b2e139bf8870e603c09aaff3e3deca", "difficulty": "easy", "final_answer": {"answer": 74526.375, "unit": "J"}, "id": "heat_q_007906_825_1.015_89", "license": "Apache-2.0", "prompt": "A 825 g sample has specific heat 1.015 J/(g*K). How much heat is needed to raise its temperature by 89 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 825 * 1.015 * 89.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 89, "heat_capacity": 1.015, "mass_g": 825}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=189 V and R=48.9 ohm.\nFinal: {\"answer\": 730.4908, \"unit\": \"W\"}", "dedupe_signature": "31914a0cdade295f9f0b50359f7a5f5f6fdfa1dcd3b6baf3e0633a4c7c95ebc2", "difficulty": "easy", "final_answer": {"answer": 730.4908, "unit": "W"}, "id": "ohm_power_007907_189_48.9", "license": "Apache-2.0", "prompt": "A resistor has resistance 48.9 ohm and voltage 189 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=189 V and R=48.9 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 48.9, "voltage": 189.0}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 4550 mL to 4.55 L.\n3. Compute M = 1.145 / 4.55.\nFinal: {\"answer\": 0.2516, \"unit\": \"mol/L\"}", "dedupe_signature": "435d645aec6c05e1a1465941917732b03ea32951bc047d06ffca6bd675911368", "difficulty": "medium", "final_answer": {"answer": 0.2516, "unit": "mol/L"}, "id": "molarity_007910_1.145_4550", "license": "Apache-2.0", "prompt": "A solution contains 1.145 mol of solute in 4550 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 4550 mL to 4.55 L.\nCompute M = 1.145 / 4.55.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 1.145, "volume_ml": 4550}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.56 y, so each step multiplies y by 1 - h*0.56.\n3. Apply that update for 8 steps and round the final state.\nFinal: {\"answer\": 0.0, \"unit\": \"state_units\"}", "dedupe_signature": "375cac16d5dfc801fd5d7813b5f75bbf8c8b3a694724713c2eefd32a319e2e7b", "difficulty": "medium", "final_answer": {"answer": 0.0, "unit": "state_units"}, "id": "euler_decay_007911_12.5_0.56_1.65_8", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.56 y with y(0)=12.5, step size h=1.65, for 8 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.56 y, so each step multiplies y by 1 - h*0.56.\nApply that update for 8 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 12.5, "rate": 0.56, "step": 1.65, "steps": 8}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(0.4)=21.62 and f(5.6)=59.58.\n3. The interval width is 5.2.\nFinal: {\"answer\": 211.12, \"unit\": \"area_units\"}", "dedupe_signature": "d38d83eeb9419607f2d1934b5eb8b5e7758a5927d9fd12b549bbc2cc80a7a87c", "difficulty": "medium", "final_answer": {"answer": 211.12, "unit": "area_units"}, "id": "trapz_linear_007912_7.3_18.7_0.4_5.6", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=7.3x+18.7 from x=0.4 to x=5.6. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(0.4)=21.62 and f(5.6)=59.58.\nThe interval width is 5.2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 18.7, "slope": 7.3, "x0": 0.4, "x1": 5.6000000000000005}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=118 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-53.0503, 99.7731], \"unit\": \"N\"}", "dedupe_signature": "af853472861f41a3223ea8398219c8d32a2f803f763385a6b17655ebd63da4a2", "difficulty": "medium", "final_answer": {"answer": [-53.0503, 99.7731], "unit": "N"}, "id": "vector_components_007915_113_118", "license": "Apache-2.0", "prompt": "A vector has magnitude 113 N at 118 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=118 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 118, "magnitude": 113.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [8.95, -17.25], \"unit\": \"dimensionless\"}", "dedupe_signature": "baf2a196e09c8f99dc83dfe3287e7a0119e07fbb678ff9ceb3657140d877b8da", "difficulty": "medium", "final_answer": {"answer": [8.95, -17.25], "unit": "dimensionless"}, "id": "line_two_point_007916_-2.5_7.75_8.95_-17.25", "license": "Apache-2.0", "prompt": "A line passes through points (-2.5, -39.625) and (7.75, 52.1125). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -2.5, "x2": 7.75, "y1": -39.625, "y2": 52.1125}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. m*v is momentum, not energy\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "16c206d8e4e3aaf30fcad6f412ec78b6bbc556cb950197fd5d71205262b15c97", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_007917_inconsistent_1e14b074_777754", "license": "Apache-2.0", "prompt": "In instrument manual case 777754, check dimensional consistency for E = m * v. The left side has dimensions kg*m^2/s^2 and the right side has dimensions kg*m/s. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nm*v is momentum, not energy\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "E = m * v"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef running_total_007918(values):\n    total = 0\n    out = []\n    for value in values:\n        total += value\n        out.append(total)\n    return out\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"running_total_007918\"}", "dedupe_signature": "735639a85149995c63dedccecc3b2ea5173b3043100226654c69db0143977d96", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "running_total_007918"}, "id": "code_007918_running_total_007918", "license": "Apache-2.0", "prompt": "Write a Python function running_total_007918(values) that returns cumulative sums as a new list. It must not mutate the input list. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "running_total_007918"}, "verifier": {"function": "running_total_007918", "tests": ["assert running_total_007918([1, 2, 3]) == [1, 3, 6]", "xs = [4, -1, 2]; assert running_total_007918(xs) == [4, 3, 5] and xs == [4, -1, 2]", "assert running_total_007918([]) == []"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: required_fields, allowed_transformations.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"required_fields\", \"allowed_transformations\"]}", "dedupe_signature": "80f64fb1a89a720eebe24981fa0a5e283aae82178f02640e23efdd81e3dc8b13", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["required_fields", "allowed_transformations"]}, "id": "abstain_007919_required_fields_allowed_transformations", "license": "Apache-2.0", "prompt": "Write a sanitizer for valid field crop records in release 575884, but the prompt does not state which fields are required or which transformations are allowed. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: required_fields, allowed_transformations.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["required_fields", "allowed_transformations"]}, "verifier": {"missing": ["required_fields", "allowed_transformations"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 24.8 kg and a = 5.1 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 126.48, \"unit\": \"N\"}", "dedupe_signature": "97b4ba46fc3ce94af8497441ab30697f8d012ab47ce5fd86b051bf6a9bf72974", "difficulty": "easy", "final_answer": {"answer": 126.48, "unit": "N"}, "id": "force_007920_24.8_5.1", "license": "Apache-2.0", "prompt": "A cart has mass 24.8 kg and measured acceleration 5.1 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 24.8 kg and a = 5.1 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 5.1, "mass": 24.8}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 32.95^2 and multiply by 0.5 * 18.6.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 10097.0333, \"unit\": \"J\"}", "dedupe_signature": "ffb46c99c42ff7d030260b782c9e491e03b779e85c8647d6ba2c60b9d3afcc10", "difficulty": "easy", "final_answer": {"answer": 10097.0333, "unit": "J"}, "id": "ke_007921_18.6_32.95", "license": "Apache-2.0", "prompt": "A body of mass 18.6 kg moves at 32.95 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 32.95^2 and multiply by 0.5 * 18.6.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 18.6, "velocity": 32.95}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=20 degrees through the sine of 2 theta.\n3. Substitute v=25.9 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 43.954, \"unit\": \"m\"}", "dedupe_signature": "dd6ffe2d32a309cff157da5b31f815258eb19845208655417ee71b7d1b907101", "difficulty": "medium", "final_answer": {"answer": 43.954, "unit": "m"}, "id": "projectile_range_007922_25.9_20", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 25.9 m/s and angle 20 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=20 degrees through the sine of 2 theta.\nSubstitute v=25.9 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 20, "gravity": 9.81, "speed": 25.9}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 4.9 * 8.314 * 458 / 97.8.\nFinal: {\"answer\": 190.7799, \"unit\": \"kPa\"}", "dedupe_signature": "a8cf5e858dd98c929f9996b1c66d6da728064c143aa1073d99a06f397abe4bef", "difficulty": "medium", "final_answer": {"answer": 190.7799, "unit": "kPa"}, "id": "ideal_gas_007923_4.9_458_97.8", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=4.9 mol, T=458 K, and V=97.8 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 4.9 * 8.314 * 458 / 97.8.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 4.9, "temp_k": 458, "volume_l": 97.8}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1880 * 2.255 * 71.\nFinal: {\"answer\": 300997.4, \"unit\": \"J\"}", "dedupe_signature": "691471facd5bc2251993bbdd8b9072c50f1ca1a5d07992e85bc8070bb9d4f0b5", "difficulty": "easy", "final_answer": {"answer": 300997.4, "unit": "J"}, "id": "heat_q_007924_1880_2.255_71", "license": "Apache-2.0", "prompt": "A 1880 g sample has specific heat 2.255 J/(g*K). How much heat is needed to raise its temperature by 71 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1880 * 2.255 * 71.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 71, "heat_capacity": 2.255, "mass_g": 1880}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=130.2 V and R=43.9 ohm.\nFinal: {\"answer\": 386.1513, \"unit\": \"W\"}", "dedupe_signature": "f7a43e4f5ab218006668b76f2eb72fd5ba62e7931d79e66f0ba50215bba6e7ee", "difficulty": "easy", "final_answer": {"answer": 386.1513, "unit": "W"}, "id": "ohm_power_007925_130.2_43.9", "license": "Apache-2.0", "prompt": "A resistor has resistance 43.9 ohm and voltage 130.2 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=130.2 V and R=43.9 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 43.9, "voltage": 130.2}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=100.5 mg, t=9.5 h, and T_half=4 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 19.374, \"unit\": \"mg\"}", "dedupe_signature": "fa51115691110b42a61398eb4aa39f518854df90ded045f4bf327c617fb96e72", "difficulty": "medium", "final_answer": {"answer": 19.374, "unit": "mg"}, "id": "half_life_007926_100.5_4_9.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 100.5 mg. Its half-life is 4 hours. How many mg remain after 9.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=100.5 mg, t=9.5 h, and T_half=4 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 9.5, "half_life": 4.0, "initial_amount": 100.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 5.03 mol * 100.087 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 503.4376, \"unit\": \"g\"}", "dedupe_signature": "3734307101fbff0f8610f65ae03eadfde0a86e569b5ba8c98402740cb20d4b25", "difficulty": "medium", "final_answer": {"answer": 503.4376, "unit": "g"}, "id": "stoich_mass_007927_calcium_carbonate_5.03", "license": "Apache-2.0", "prompt": "A sample contains 5.03 mol of calcium carbonate. Using molar mass 100.087 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 5.03 mol * 100.087 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "calcium carbonate", "molar_mass": 100.087, "moles": 5.03}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 280 mL to 0.28 L.\n3. Compute M = 3.095 / 0.28.\nFinal: {\"answer\": 11.0536, \"unit\": \"mol/L\"}", "dedupe_signature": "ccef3f4093d3b296368c625faddf4817d18cdfc91b46c31f4690b92372b2ffc1", "difficulty": "medium", "final_answer": {"answer": 11.0536, "unit": "mol/L"}, "id": "molarity_007928_3.095_280", "license": "Apache-2.0", "prompt": "A solution contains 3.095 mol of solute in 280 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 280 mL to 0.28 L.\nCompute M = 3.095 / 0.28.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 3.095, "volume_ml": 280}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.56 y, so each step multiplies y by 1 - h*0.56.\n3. Apply that update for 2 steps and round the final state.\nFinal: {\"answer\": 33.5622, \"unit\": \"state_units\"}", "dedupe_signature": "cb0f80648d2d9994b16d53a5b1e21a6db78328b1b12959b0822c9295e601ae7e", "difficulty": "medium", "final_answer": {"answer": 33.5622, "unit": "state_units"}, "id": "euler_decay_007929_40_0.56_0.15_2", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.56 y with y(0)=40, step size h=0.15, for 2 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.56 y, so each step multiplies y by 1 - h*0.56.\nApply that update for 2 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 40.0, "rate": 0.56, "step": 0.15, "steps": 2}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(2.5)=7.25 and f(7.4)=-0.1.\n3. The interval width is 4.9.\nFinal: {\"answer\": 17.5175, \"unit\": \"area_units\"}", "dedupe_signature": "d12aff523c9ddc4c55f8d7c637abf4d1c60f8f87aa9fca0b71f7527189054737", "difficulty": "medium", "final_answer": {"answer": 17.5175, "unit": "area_units"}, "id": "trapz_linear_007930_-1.5_11_2.5_7.4", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-1.5x+11 from x=2.5 to x=7.4. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(2.5)=7.25 and f(7.4)=-0.1.\nThe interval width is 4.9.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 11.0, "slope": -1.5, "x0": 2.5, "x1": 7.4}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kelvin equals Celsius plus 273.15.\n2. Apply the conversion factor directly to the given value.\n3. Compute 192.5 + 273.15.\nFinal: {\"answer\": 465.65, \"unit\": \"K\"}", "dedupe_signature": "b13085f1905a6e14ea668f965015777e87af799d6506c3be0093646f826093d1", "difficulty": "easy", "final_answer": {"answer": 465.65, "unit": "K"}, "id": "unit_convert_007932_c_to_k_192.5", "license": "Apache-2.0", "prompt": "Convert 192.5 degC to K. Return the converted value with unit.", "reasoning_trace": "Kelvin equals Celsius plus 273.15.\nApply the conversion factor directly to the given value.\nCompute 192.5 + 273.15.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 192.5}, "verifier": {"formula": "value + 273.15", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=338 degrees and keep the unit as newtons.\nFinal: {\"answer\": [4.6359, -1.873], \"unit\": \"N\"}", "dedupe_signature": "567af6c6f3d053f1f61e851ee7b55c99c24cf2dc568924d346615792f961d543", "difficulty": "medium", "final_answer": {"answer": [4.6359, -1.873], "unit": "N"}, "id": "vector_components_007933_5_338", "license": "Apache-2.0", "prompt": "A vector has magnitude 5 N at 338 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=338 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 338, "magnitude": 5.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [7.7, 16.0], \"unit\": \"dimensionless\"}", "dedupe_signature": "09afc4f32f66c9c45b169c511861cd531ef5dfb052b129439383c0cc6d707098", "difficulty": "medium", "final_answer": {"answer": [7.7, 16.0], "unit": "dimensionless"}, "id": "line_two_point_007934_-18.75_-14.5_7.7_16", "license": "Apache-2.0", "prompt": "A line passes through points (-18.75, -128.375) and (-14.5, -95.65). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -18.75, "x2": -14.5, "y1": -128.375, "y2": -95.65}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. lever arm times force has torque dimensions\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "ce8ef34beb35832ba06edb1a1d2c9860973b85956fc7ff42aaafa18033211d0f", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_007935_consistent_5ca82cb9_324738", "license": "Apache-2.0", "prompt": "In field worksheet case 324738, check dimensional consistency for tau = r * F. The left side has dimensions N*m and the right side has dimensions N*m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nlever arm times force has torque dimensions\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "tau = r * F"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef normalize_007936(values):\n    total = sum(values)\n    if total == 0:\n        raise ValueError('cannot normalize zero-sum values')\n    return [v / total for v in values]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"normalize_007936\"}", "dedupe_signature": "2c43ecd3465221b4e77f7844cd8072019b8277ffdc2797befa5354a02a1b9e8d", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "normalize_007936"}, "id": "code_007936_normalize_007936", "license": "Apache-2.0", "prompt": "Write a Python function normalize_007936(values) that returns a new list whose values sum to 1. Raise ValueError if the sum is zero. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "normalize_007936"}, "verifier": {"function": "normalize_007936", "tests": ["out = normalize_007936([2, 3, 5]); assert len(out) == 3", "assert abs(sum(normalize_007936([2, 3, 5])) - 1.0) < 1e-12", "assert normalize_007936([1, 1]) == [0.5, 0.5]", "try:\n    normalize_007936([1, -1])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: required_fields, allowed_transformations.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"required_fields\", \"allowed_transformations\"]}", "dedupe_signature": "78f98212b2d5839872d295a4493cd660f9a452d2b8937845a25b4a6fe42fcef0", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["required_fields", "allowed_transformations"]}, "id": "abstain_007937_required_fields_allowed_transformations", "license": "Apache-2.0", "prompt": "Write a sanitizer for valid field survey records in release 518908, but the prompt does not state which fields are required or which transformations are allowed. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: required_fields, allowed_transformations.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["required_fields", "allowed_transformations"]}, "verifier": {"missing": ["required_fields", "allowed_transformations"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 16.95 kg and a = 11.75 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 199.1625, \"unit\": \"N\"}", "dedupe_signature": "8fd9843af41952a86661d6746921e9e7c626ce448497d00b57adb3b871c059ec", "difficulty": "easy", "final_answer": {"answer": 199.1625, "unit": "N"}, "id": "force_007938_16.95_11.75", "license": "Apache-2.0", "prompt": "A cart has mass 16.95 kg and measured acceleration 11.75 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 16.95 kg and a = 11.75 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 11.75, "mass": 16.95}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=79 degrees through the sine of 2 theta.\n3. Substitute v=42.9 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 70.2783, \"unit\": \"m\"}", "dedupe_signature": "467345110e4f43e5b80db1e35dfaa5b09399d522e565e686c2b44f3d0b9d9cc0", "difficulty": "medium", "final_answer": {"answer": 70.2783, "unit": "m"}, "id": "projectile_range_007940_42.9_79", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 42.9 m/s and angle 79 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=79 degrees through the sine of 2 theta.\nSubstitute v=42.9 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 79, "gravity": 9.81, "speed": 42.9}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 3.68 * 8.314 * 244 / 37.2.\nFinal: {\"answer\": 200.6803, \"unit\": \"kPa\"}", "dedupe_signature": "d619ea96443c5d418c926c3ebd1c6f09039ea8186d669ad0c4d3f351c1c78569", "difficulty": "medium", "final_answer": {"answer": 200.6803, "unit": "kPa"}, "id": "ideal_gas_007941_3.68_244_37.2", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=3.68 mol, T=244 K, and V=37.2 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 3.68 * 8.314 * 244 / 37.2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 3.68, "temp_k": 244, "volume_l": 37.2}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 430 * 4.865 * 58.\nFinal: {\"answer\": 121333.1, \"unit\": \"J\"}", "dedupe_signature": "1b0096001d3cd50223ffd331d82b5dacfa80e225fbd72299a9eb128e70f8a045", "difficulty": "easy", "final_answer": {"answer": 121333.1, "unit": "J"}, "id": "heat_q_007942_430_4.865_58", "license": "Apache-2.0", "prompt": "A 430 g sample has specific heat 4.865 J/(g*K). How much heat is needed to raise its temperature by 58 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 430 * 4.865 * 58.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 58, "heat_capacity": 4.865, "mass_g": 430}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=203.4 V and R=23.3 ohm.\nFinal: {\"answer\": 1775.6034, \"unit\": \"W\"}", "dedupe_signature": "6ff6e79e9fa44b644efbc58491ae949067cc3edef2d1fbf36d6bb98c44489187", "difficulty": "easy", "final_answer": {"answer": 1775.6034, "unit": "W"}, "id": "ohm_power_007943_203.4_23.3", "license": "Apache-2.0", "prompt": "A resistor has resistance 23.3 ohm and voltage 203.4 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=203.4 V and R=23.3 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 23.3, "voltage": 203.4}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=504.5 mg, t=143.5 h, and T_half=17.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 1.7156, \"unit\": \"mg\"}", "dedupe_signature": "56584829dd37754bab585e0a857feb79e7c93d45dc124625af7e38ee7471c44e", "difficulty": "medium", "final_answer": {"answer": 1.7156, "unit": "mg"}, "id": "half_life_007944_504.5_17.5_143.5", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 504.5 mg. Its half-life is 17.5 hours. How many mg remain after 143.5 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=504.5 mg, t=143.5 h, and T_half=17.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 143.5, "half_life": 17.5, "initial_amount": 504.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 7.66 mol * 18.015 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 137.9949, \"unit\": \"g\"}", "dedupe_signature": "2293a9c5cc1422dbd11b1045ebc15b923cc63f503453d7320041ebfa30a025d3", "difficulty": "medium", "final_answer": {"answer": 137.9949, "unit": "g"}, "id": "stoich_mass_007945_water_7.66", "license": "Apache-2.0", "prompt": "A sample contains 7.66 mol of water. Using molar mass 18.015 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 7.66 mol * 18.015 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "water", "molar_mass": 18.015, "moles": 7.66}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 2870 mL to 2.87 L.\n3. Compute M = 0.89 / 2.87.\nFinal: {\"answer\": 0.3101, \"unit\": \"mol/L\"}", "dedupe_signature": "861dab031797d41782aa3d0cd50e5d4f98314402da32811abb58f0c39a7cbdd9", "difficulty": "medium", "final_answer": {"answer": 0.3101, "unit": "mol/L"}, "id": "molarity_007946_0.89_2870", "license": "Apache-2.0", "prompt": "A solution contains 0.89 mol of solute in 2870 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 2870 mL to 2.87 L.\nCompute M = 0.89 / 2.87.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 0.89, "volume_ml": 2870}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-7)=31.9 and f(-2.7)=1.37.\n3. The interval width is 4.3.\nFinal: {\"answer\": 71.5305, \"unit\": \"area_units\"}", "dedupe_signature": "4fe8ac7efd8f25f4d0a0cdf40629915328aef5651e2f8d736e829637a06a6814", "difficulty": "medium", "final_answer": {"answer": 71.5305, "unit": "area_units"}, "id": "trapz_linear_007948_-7.1_-17.8_-7_-2.7", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-7.1x+-17.8 from x=-7 to x=-2.7. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-7)=31.9 and f(-2.7)=1.37.\nThe interval width is 4.3.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -17.8, "slope": -7.1, "x0": -7.0, "x1": -2.7}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.42 and add it to the current value.\nFinal: {\"answer\": [0.516, 0.451, 1.157], \"unit\": \"temperature_units\"}", "dedupe_signature": "7577cd2e94f762a176496ee38e90febb8c472e4af57082aad04d8aae19cca11b", "difficulty": "hard", "final_answer": {"answer": [0.516, 0.451, 1.157], "unit": "temperature_units"}, "id": "heat_step_007949_0.42_-0.5_-0.45_1.9_0.8_0.55", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-0.5, right=0.55; current interior values are [-0.45, 1.9, 0.8]. Use r=0.42. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.42 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-0.45, 1.9, 0.8], "left": -0.5, "r": 0.42, "right": 0.55}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 37632.0 / 1000.\nFinal: {\"answer\": 37.632, \"unit\": \"kg\"}", "dedupe_signature": "5c20a78259fe23aa9eb4b4dd1582abb2499dd7a44497b496c4b2389a1c748602", "difficulty": "easy", "final_answer": {"answer": 37.632, "unit": "kg"}, "id": "unit_convert_007950_g_to_kg_37632", "license": "Apache-2.0", "prompt": "Convert 37632 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 37632.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 37632.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=167 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-77.4624, 17.8836], \"unit\": \"N\"}", "dedupe_signature": "8060afbf1d06c0c03afe7ef1b9bac3f3877c98e72912b6feeb939bc55424aeac", "difficulty": "medium", "final_answer": {"answer": [-77.4624, 17.8836], "unit": "N"}, "id": "vector_components_007951_79.5_167", "license": "Apache-2.0", "prompt": "A vector has magnitude 79.5 N at 167 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=167 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 167, "magnitude": 79.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. speed squared over acceleration has units of meters\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "418678a72aea6c91747e6111d538fa5f8046db228f87956f209df53f65e755de", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_007953_consistent_741d4e34_791958", "license": "Apache-2.0", "prompt": "In sensor calibration case 791958, check dimensional consistency for R = v^2 * sin(theta) / g. The left side has dimensions m and the right side has dimensions m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nspeed squared over acceleration has units of meters\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "R = v^2 * sin(theta) / g"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef safe_mean_007954(values):\n    if not values:\n        raise ValueError('safe_mean requires at least one value')\n    return sum(values) / len(values)\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"safe_mean_007954\"}", "dedupe_signature": "2881856b6d6db756fc823af671925696f79a862277c2a6a8333cddfb0aab5a84", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "safe_mean_007954"}, "id": "code_007954_safe_mean_007954", "license": "Apache-2.0", "prompt": "Write a Python function safe_mean_007954(values) that returns the arithmetic mean. It must raise ValueError for an empty input and must not mutate the input list. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "safe_mean_007954"}, "verifier": {"function": "safe_mean_007954", "tests": ["assert safe_mean_007954([2, 4, 6]) == 4", "xs = [1, 2, 3]; assert safe_mean_007954(xs) == 2 and xs == [1, 2, 3]", "try:\n    safe_mean_007954([])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: recurrence, objective, tie_breaking_rule.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"recurrence\", \"objective\", \"tie_breaking_rule\"]}", "dedupe_signature": "ee4d103ebb2f26a41795ff5d2054203a2c6da97661b6c68bb28c8f5591838367", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["recurrence", "objective", "tie_breaking_rule"]}, "id": "abstain_007955_recurrence_objective_tie_breaking_rule", "license": "Apache-2.0", "prompt": "Write a dynamic-programming solver for a alignment scoring problem with 3709 items and budget 2270, but the recurrence, objective, and tie-breaking rule are all absent. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: recurrence, objective, tie_breaking_rule.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["recurrence", "objective", "tie_breaking_rule"]}, "verifier": {"missing": ["recurrence", "objective", "tie_breaking_rule"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 17 kg and a = 8.8 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 149.6, \"unit\": \"N\"}", "dedupe_signature": "ac783a286a915cf9ee939270e05b89bb91d7273eb4772d646c1ced39b854f6eb", "difficulty": "easy", "final_answer": {"answer": 149.6, "unit": "N"}, "id": "force_007956_17_8.8", "license": "Apache-2.0", "prompt": "A cart has mass 17 kg and measured acceleration 8.8 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 17 kg and a = 8.8 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 8.8, "mass": 17.0}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 37.5^2 and multiply by 0.5 * 21.55.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 15152.3438, \"unit\": \"J\"}", "dedupe_signature": "be96456305dc81d11e69d392e5bd2b89061092b8aeaf2cad96491840ab0f842a", "difficulty": "easy", "final_answer": {"answer": 15152.3438, "unit": "J"}, "id": "ke_007957_21.55_37.5", "license": "Apache-2.0", "prompt": "A body of mass 21.55 kg moves at 37.5 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 37.5^2 and multiply by 0.5 * 21.55.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 21.55, "velocity": 37.5}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 4.69 * 8.314 * 430 / 47.6.\nFinal: {\"answer\": 352.2446, \"unit\": \"kPa\"}", "dedupe_signature": "7c377208a4b69daeb436890ec89bba119bf1484cbf58fbafe959b621eb1f1c21", "difficulty": "medium", "final_answer": {"answer": 352.2446, "unit": "kPa"}, "id": "ideal_gas_007959_4.69_430_47.6", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=4.69 mol, T=430 K, and V=47.6 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 4.69 * 8.314 * 430 / 47.6.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 4.69, "temp_k": 430, "volume_l": 47.6}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 385 * 4.7 * 87.\nFinal: {\"answer\": 157426.5, \"unit\": \"J\"}", "dedupe_signature": "38021fbb33fca47e70cf696966988c4a98e4de681e3aa3baba50a2f4e2730a84", "difficulty": "easy", "final_answer": {"answer": 157426.5, "unit": "J"}, "id": "heat_q_007960_385_4.7_87", "license": "Apache-2.0", "prompt": "A 385 g sample has specific heat 4.7 J/(g*K). How much heat is needed to raise its temperature by 87 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 385 * 4.7 * 87.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 87, "heat_capacity": 4.7, "mass_g": 385}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=202.7 V and R=99.3 ohm.\nFinal: {\"answer\": 413.7693, \"unit\": \"W\"}", "dedupe_signature": "517a72557d39fc5682eac92a0b8a3c3c7c18786c10eb384b1c1442b11ecfe88e", "difficulty": "easy", "final_answer": {"answer": 413.7693, "unit": "W"}, "id": "ohm_power_007961_202.7_99.3", "license": "Apache-2.0", "prompt": "A resistor has resistance 99.3 ohm and voltage 202.7 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=202.7 V and R=99.3 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 99.3, "voltage": 202.7}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 5.17 mol * 18.015 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 93.1376, \"unit\": \"g\"}", "dedupe_signature": "a0e7e2e42fc425030ad32c864d86d8063864fd2798c2c544285595976c05f198", "difficulty": "medium", "final_answer": {"answer": 93.1376, "unit": "g"}, "id": "stoich_mass_007963_water_5.17", "license": "Apache-2.0", "prompt": "A sample contains 5.17 mol of water. Using molar mass 18.015 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 5.17 mol * 18.015 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "water", "molar_mass": 18.015, "moles": 5.17}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 4435 mL to 4.435 L.\n3. Compute M = 0.695 / 4.435.\nFinal: {\"answer\": 0.1567, \"unit\": \"mol/L\"}", "dedupe_signature": "2afff8058b4e2ec00f6e48ee0f17de3ebb947430ea0e582c3962c41c9f095861", "difficulty": "medium", "final_answer": {"answer": 0.1567, "unit": "mol/L"}, "id": "molarity_007964_0.695_4435", "license": "Apache-2.0", "prompt": "A solution contains 0.695 mol of solute in 4435 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 4435 mL to 4.435 L.\nCompute M = 0.695 / 4.435.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 0.695, "volume_ml": 4435}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.66 y, so each step multiplies y by 1 - h*0.66.\n3. Apply that update for 12 steps and round the final state.\nFinal: {\"answer\": 0.001, \"unit\": \"state_units\"}", "dedupe_signature": "7b71c77ee9b122c90509a02caa70235d2e57f1a295c64c02cd29db14ac230f14", "difficulty": "medium", "final_answer": {"answer": 0.001, "unit": "state_units"}, "id": "euler_decay_007965_49.5_0.66_0.9_12", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.66 y with y(0)=49.5, step size h=0.9, for 12 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.66 y, so each step multiplies y by 1 - h*0.66.\nApply that update for 12 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 49.5, "rate": 0.66, "step": 0.9, "steps": 12}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-0.5)=15.4 and f(3.4)=39.58.\n3. The interval width is 3.9.\nFinal: {\"answer\": 107.211, \"unit\": \"area_units\"}", "dedupe_signature": "e72859bf76f005698cdc3bd65bcdd439e1f66e6712ccb40c9d15bf5b9e458805", "difficulty": "medium", "final_answer": {"answer": 107.211, "unit": "area_units"}, "id": "trapz_linear_007966_6.2_18.5_-0.5_3.4", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=6.2x+18.5 from x=-0.5 to x=3.4. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-0.5)=15.4 and f(3.4)=39.58.\nThe interval width is 3.9.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 18.5, "slope": 6.2, "x0": -0.5, "x1": 3.4}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.12 and add it to the current value.\nFinal: {\"answer\": [1.876, 1.632, -0.326], \"unit\": \"temperature_units\"}", "dedupe_signature": "8f7c47c644621fdbfb4a590d47c08e5105271f6ef457f8c34f6c66601dcfee70", "difficulty": "hard", "final_answer": {"answer": [1.876, 1.632, -0.326], "unit": "temperature_units"}, "id": "heat_step_007967_0.12_-1.2_2.35_1.95_-1.1_2.3", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-1.2, right=2.3; current interior values are [2.35, 1.95, -1.1]. Use r=0.12. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.12 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [2.35, 1.95, -1.1], "left": -1.2, "r": 0.12, "right": 2.3}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 100 centimeters in one meter.\n2. Apply the conversion factor directly to the given value.\n3. Compute 2135.5 / 100.\nFinal: {\"answer\": 21.355, \"unit\": \"m\"}", "dedupe_signature": "8f64de5262ac5ca35ffadd98a8fe3fb15c9cdfcd73789fefcee6c2c7c82dc3be", "difficulty": "easy", "final_answer": {"answer": 21.355, "unit": "m"}, "id": "unit_convert_007968_cm_to_m_2135.5", "license": "Apache-2.0", "prompt": "Convert 2135.5 cm to m. Return the converted value with unit.", "reasoning_trace": "There are 100 centimeters in one meter.\nApply the conversion factor directly to the given value.\nCompute 2135.5 / 100.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 2135.5}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=274 degrees and keep the unit as newtons.\nFinal: {\"answer\": [16.602, -237.4202], \"unit\": \"N\"}", "dedupe_signature": "f74e956e6ab55b6aee6da30d69c337ff5fd1c5a8ea844e79c3f4d00cb82308a3", "difficulty": "medium", "final_answer": {"answer": [16.602, -237.4202], "unit": "N"}, "id": "vector_components_007969_238_274", "license": "Apache-2.0", "prompt": "A vector has magnitude 238 N at 274 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=274 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 274, "magnitude": 238.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. mass times acceleration has newton dimensions\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "886dcfdab66db7fbb9c441e69ee21c753754b497cdd9cd48b02f943eb3b39145", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_007971_consistent_03f5e041_730427", "license": "Apache-2.0", "prompt": "In lab notebook case 730427, check dimensional consistency for F = m * a. The left side has dimensions kg*m/s^2 and the right side has dimensions kg*m/s^2. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nmass times acceleration has newton dimensions\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "F = m * a"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef normalize_007972(values):\n    total = sum(values)\n    if total == 0:\n        raise ValueError('cannot normalize zero-sum values')\n    return [v / total for v in values]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"normalize_007972\"}", "dedupe_signature": "ff3314bd120a8e07c5601c51fbefaaab5975019193e73718bfc9ce720d9509c6", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "normalize_007972"}, "id": "code_007972_normalize_007972", "license": "Apache-2.0", "prompt": "Write a Python function normalize_007972(values) that returns a new list whose values sum to 1. Raise ValueError if the sum is zero. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "normalize_007972"}, "verifier": {"function": "normalize_007972", "tests": ["out = normalize_007972([2, 3, 5]); assert len(out) == 3", "assert abs(sum(normalize_007972([2, 3, 5])) - 1.0) < 1e-12", "assert normalize_007972([1, 1]) == [0.5, 0.5]", "try:\n    normalize_007972([1, -1])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: required_fields, allowed_transformations.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"required_fields\", \"allowed_transformations\"]}", "dedupe_signature": "1aeece2df1a649fb22651439bda838966cf7906ad5eb196cc2ea1a9f253824df", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["required_fields", "allowed_transformations"]}, "id": "abstain_007973_required_fields_allowed_transformations", "license": "Apache-2.0", "prompt": "Write a sanitizer for valid warehouse experiment records in release 16210, but the prompt does not state which fields are required or which transformations are allowed. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: required_fields, allowed_transformations.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["required_fields", "allowed_transformations"]}, "verifier": {"missing": ["required_fields", "allowed_transformations"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 20.65 kg and a = 0.5 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 10.325, \"unit\": \"N\"}", "dedupe_signature": "aa7d173bd0f90ab97428bef6c70c332dd5e7631330b5e6c518806ddd8a76d346", "difficulty": "easy", "final_answer": {"answer": 10.325, "unit": "N"}, "id": "force_007974_20.65_0.5", "license": "Apache-2.0", "prompt": "A cart has mass 20.65 kg and measured acceleration 0.5 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 20.65 kg and a = 0.5 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 0.5, "mass": 20.65}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 31.4^2 and multiply by 0.5 * 12.8.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 6310.144, \"unit\": \"J\"}", "dedupe_signature": "750cf77097f85d4cd8715c9a189d911003d2e33be5ea5dd27e4050bd15dbc183", "difficulty": "easy", "final_answer": {"answer": 6310.144, "unit": "J"}, "id": "ke_007975_12.8_31.4", "license": "Apache-2.0", "prompt": "A body of mass 12.8 kg moves at 31.4 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 31.4^2 and multiply by 0.5 * 12.8.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 12.8, "velocity": 31.4}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=56 degrees through the sine of 2 theta.\n3. Substitute v=40.9 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 158.1042, \"unit\": \"m\"}", "dedupe_signature": "34a24be0604038d363ad9d472baf7b2ea2ad8f2737e108a6915d88cbf40f2396", "difficulty": "medium", "final_answer": {"answer": 158.1042, "unit": "m"}, "id": "projectile_range_007976_40.9_56", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 40.9 m/s and angle 56 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=56 degrees through the sine of 2 theta.\nSubstitute v=40.9 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 56, "gravity": 9.81, "speed": 40.9}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 3.48 * 8.314 * 332 / 89.2.\nFinal: {\"answer\": 107.6868, \"unit\": \"kPa\"}", "dedupe_signature": "bcc161249d37cb59c313446d173a7d403b935a317b59fa7eb64bbdc82e29f373", "difficulty": "medium", "final_answer": {"answer": 107.6868, "unit": "kPa"}, "id": "ideal_gas_007977_3.48_332_89.2", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=3.48 mol, T=332 K, and V=89.2 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 3.48 * 8.314 * 332 / 89.2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 3.48, "temp_k": 332, "volume_l": 89.2}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 650 * 4.49 * 59.\nFinal: {\"answer\": 172191.5, \"unit\": \"J\"}", "dedupe_signature": "1ed3489d9eb50a5030f165e464a73bbd890b428e6deaeabe64193cc8b42ce6f7", "difficulty": "easy", "final_answer": {"answer": 172191.5, "unit": "J"}, "id": "heat_q_007978_650_4.49_59", "license": "Apache-2.0", "prompt": "A 650 g sample has specific heat 4.49 J/(g*K). How much heat is needed to raise its temperature by 59 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 650 * 4.49 * 59.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 59, "heat_capacity": 4.49, "mass_g": 650}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=750 mg, t=292 h, and T_half=96 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 91.0811, \"unit\": \"mg\"}", "dedupe_signature": "19d4aff1126f66bf7655dbce1c22974dbd6b9663997707d2999c253f35d12480", "difficulty": "medium", "final_answer": {"answer": 91.0811, "unit": "mg"}, "id": "half_life_007980_750_96_292", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 750 mg. Its half-life is 96 hours. How many mg remain after 292 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=750 mg, t=292 h, and T_half=96 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 292.0, "half_life": 96.0, "initial_amount": 750.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 0.59 mol * 58.44 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 34.4796, \"unit\": \"g\"}", "dedupe_signature": "c0368f93cf465ca6e35bccd899e0c25fe2927be1021e17dfe4a7913f58a9490c", "difficulty": "medium", "final_answer": {"answer": 34.4796, "unit": "g"}, "id": "stoich_mass_007981_sodium_chloride_0.59", "license": "Apache-2.0", "prompt": "A sample contains 0.59 mol of sodium chloride. Using molar mass 58.44 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 0.59 mol * 58.44 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "sodium chloride", "molar_mass": 58.44, "moles": 0.59}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 1285 mL to 1.285 L.\n3. Compute M = 0.395 / 1.285.\nFinal: {\"answer\": 0.3074, \"unit\": \"mol/L\"}", "dedupe_signature": "b3a70283a693fa6214b2a24f7ac99685871b521dad649a041ca322ec59f359ca", "difficulty": "medium", "final_answer": {"answer": 0.3074, "unit": "mol/L"}, "id": "molarity_007982_0.395_1285", "license": "Apache-2.0", "prompt": "A solution contains 0.395 mol of solute in 1285 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 1285 mL to 1.285 L.\nCompute M = 0.395 / 1.285.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 0.395, "volume_ml": 1285}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.17 y, so each step multiplies y by 1 - h*0.17.\n3. Apply that update for 3 steps and round the final state.\nFinal: {\"answer\": 18.2, \"unit\": \"state_units\"}", "dedupe_signature": "c806173bef432678e95ae6e42c614b4b5482fd279be446a4a25d927df5315016", "difficulty": "medium", "final_answer": {"answer": 18.2, "unit": "state_units"}, "id": "euler_decay_007983_56.5_0.17_1.85_3", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.17 y with y(0)=56.5, step size h=1.85, for 3 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.17 y, so each step multiplies y by 1 - h*0.17.\nApply that update for 3 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 56.5, "rate": 0.17, "step": 1.85, "steps": 3}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(0.9)=-8.03 and f(3.6)=-12.62.\n3. The interval width is 2.7.\nFinal: {\"answer\": -27.8775, \"unit\": \"area_units\"}", "dedupe_signature": "0de95624c3a83e492a86f180029d26110c1fd62c768b7ae402e7e06c347393df", "difficulty": "medium", "final_answer": {"answer": -27.8775, "unit": "area_units"}, "id": "trapz_linear_007984_-1.7_-6.5_0.9_3.6", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-1.7x+-6.5 from x=0.9 to x=3.6. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(0.9)=-8.03 and f(3.6)=-12.62.\nThe interval width is 2.7.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -6.5, "slope": -1.7, "x0": 0.9, "x1": 3.6}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 100 centimeters in one meter.\n2. Apply the conversion factor directly to the given value.\n3. Compute 1591.0 / 100.\nFinal: {\"answer\": 15.91, \"unit\": \"m\"}", "dedupe_signature": "be022344b312ab044f2d5f7528138b712317e021863764d1207d88f1ee0a4415", "difficulty": "easy", "final_answer": {"answer": 15.91, "unit": "m"}, "id": "unit_convert_007986_cm_to_m_1591", "license": "Apache-2.0", "prompt": "Convert 1591 cm to m. Return the converted value with unit.", "reasoning_trace": "There are 100 centimeters in one meter.\nApply the conversion factor directly to the given value.\nCompute 1591.0 / 100.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 1591.0}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=130 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-129.8431, 154.741], \"unit\": \"N\"}", "dedupe_signature": "338c890752311927f6d0e042de88b61252a3ff5b8c778c07a3a4e660317a0694", "difficulty": "medium", "final_answer": {"answer": [-129.8431, 154.741], "unit": "N"}, "id": "vector_components_007987_202_130", "license": "Apache-2.0", "prompt": "A vector has magnitude 202 N at 130 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=130 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 130, "magnitude": 202.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. coulomb per second is ampere\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "7d13f0350c750e6a8ae31ba264f1ca9816048ffa1be2ef8683caef266fce17cc", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_007989_consistent_8b38953d_665977", "license": "Apache-2.0", "prompt": "In lab notebook case 665977, check dimensional consistency for I = Q / t. The left side has dimensions A and the right side has dimensions A. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\ncoulomb per second is ampere\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "I = Q / t"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef normalize_007990(values):\n    total = sum(values)\n    if total == 0:\n        raise ValueError('cannot normalize zero-sum values')\n    return [v / total for v in values]\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"normalize_007990\"}", "dedupe_signature": "4e15ae32cd3de47035461bf6d7fb0a3b5dfb26adcce7526d36669de64755d3a1", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "normalize_007990"}, "id": "code_007990_normalize_007990", "license": "Apache-2.0", "prompt": "Write a Python function normalize_007990(values) that returns a new list whose values sum to 1. Raise ValueError if the sum is zero. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "normalize_007990"}, "verifier": {"function": "normalize_007990", "tests": ["out = normalize_007990([2, 3, 5]); assert len(out) == 3", "assert abs(sum(normalize_007990([2, 3, 5])) - 1.0) < 1e-12", "assert normalize_007990([1, 1]) == [0.5, 0.5]", "try:\n    normalize_007990([1, -1])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 12.2^2 and multiply by 0.5 * 3.7.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 275.354, \"unit\": \"J\"}", "dedupe_signature": "b83423d1837d93dc8fa1dad5ddc222279710d2f8a881ab5c65944f18a5db4563", "difficulty": "easy", "final_answer": {"answer": 275.354, "unit": "J"}, "id": "ke_007993_3.7_12.2", "license": "Apache-2.0", "prompt": "A body of mass 3.7 kg moves at 12.2 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 12.2^2 and multiply by 0.5 * 3.7.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 3.7, "velocity": 12.2}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=20 degrees through the sine of 2 theta.\n3. Substitute v=18.4 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 22.1837, \"unit\": \"m\"}", "dedupe_signature": "885ac4046fb38a0de450bc52a6e9754527b13013699d263329b098e75c819ef4", "difficulty": "medium", "final_answer": {"answer": 22.1837, "unit": "m"}, "id": "projectile_range_007994_18.4_20", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 18.4 m/s and angle 20 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=20 degrees through the sine of 2 theta.\nSubstitute v=18.4 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 20, "gravity": 9.81, "speed": 18.4}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 3.11 * 8.314 * 301 / 32.0.\nFinal: {\"answer\": 243.2131, \"unit\": \"kPa\"}", "dedupe_signature": "1934ad33e820e5c2dd35170d7437f88a1cbe6bf7a4eef2c1057012d9c0abbea5", "difficulty": "medium", "final_answer": {"answer": 243.2131, "unit": "kPa"}, "id": "ideal_gas_007995_3.11_301_32.0", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=3.11 mol, T=301 K, and V=32.0 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 3.11 * 8.314 * 301 / 32.0.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 3.11, "temp_k": 301, "volume_l": 32.0}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=127.6 V and R=83.7 ohm.\nFinal: {\"answer\": 194.5252, \"unit\": \"W\"}", "dedupe_signature": "9519710782b67488e84dbf22dfcb23bec89884aa9b9c1178b2abab754e984e16", "difficulty": "easy", "final_answer": {"answer": 194.5252, "unit": "W"}, "id": "ohm_power_007997_127.6_83.7", "license": "Apache-2.0", "prompt": "A resistor has resistance 83.7 ohm and voltage 127.6 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=127.6 V and R=83.7 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 83.7, "voltage": 127.6}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 655 mL to 0.655 L.\n3. Compute M = 3.54 / 0.655.\nFinal: {\"answer\": 5.4046, \"unit\": \"mol/L\"}", "dedupe_signature": "d416820a6414c9da616e37e5d4e44366e3dbe498d6d3880d2c435ed459ed5e8f", "difficulty": "medium", "final_answer": {"answer": 5.4046, "unit": "mol/L"}, "id": "molarity_008000_3.54_655", "license": "Apache-2.0", "prompt": "A solution contains 3.54 mol of solute in 655 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 655 mL to 0.655 L.\nCompute M = 3.54 / 0.655.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 3.54, "volume_ml": 655}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.17 y, so each step multiplies y by 1 - h*0.17.\n3. Apply that update for 12 steps and round the final state.\nFinal: {\"answer\": 18.0123, \"unit\": \"state_units\"}", "dedupe_signature": "81a4d8a5880b8ccc9a7da7687e7d5d9e43ef75ab6aaa0596b3aa7a1c438abef2", "difficulty": "medium", "final_answer": {"answer": 18.0123, "unit": "state_units"}, "id": "euler_decay_008001_58.5_0.17_0.55_12", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.17 y with y(0)=58.5, step size h=0.55, for 12 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.17 y, so each step multiplies y by 1 - h*0.17.\nApply that update for 12 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 58.5, "rate": 0.17, "step": 0.55, "steps": 12}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(1.3)=9.43 and f(10.1)=63.11.\n3. The interval width is 8.8.\nFinal: {\"answer\": 319.176, \"unit\": \"area_units\"}", "dedupe_signature": "4ef02b22a5d9eba1c33ac8606f9932d7f934e75449bcc83b1565106616a645cd", "difficulty": "medium", "final_answer": {"answer": 319.176, "unit": "area_units"}, "id": "trapz_linear_008002_6.1_1.5_1.3_10.1", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=6.1x+1.5 from x=1.3 to x=10.1. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(1.3)=9.43 and f(10.1)=63.11.\nThe interval width is 8.8.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": 1.5, "slope": 6.1, "x0": 1.3, "x1": 10.100000000000001}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.04 and add it to the current value.\nFinal: {\"answer\": [-0.16, -1.382, 1.126], \"unit\": \"temperature_units\"}", "dedupe_signature": "0bf4aaf214dcf9830724721b0ca2e8e2b17916d08c97c436418792721dd0f5e5", "difficulty": "hard", "final_answer": {"answer": [-0.16, -1.382, 1.126], "unit": "temperature_units"}, "id": "heat_step_008003_0.04_2.15_-0.2_-1.55_1.3_-0.2", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=2.15, right=-0.2; current interior values are [-0.2, -1.55, 1.3]. Use r=0.04. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.04 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [-0.2, -1.55, 1.3], "left": 2.15, "r": 0.04, "right": -0.2}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 22137.0 / 1000.\nFinal: {\"answer\": 22.137, \"unit\": \"kg\"}", "dedupe_signature": "c679f9ed8df2b57bdc9c8b4fd2fa91bf6bf4b8499dcd726879d7411bdb678a01", "difficulty": "easy", "final_answer": {"answer": 22.137, "unit": "kg"}, "id": "unit_convert_008004_g_to_kg_22137", "license": "Apache-2.0", "prompt": "Convert 22137 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 22137.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 22137.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=164 degrees and keep the unit as newtons.\nFinal: {\"answer\": [-411.42, 117.9728], \"unit\": \"N\"}", "dedupe_signature": "0e3c088892bd136eb24e3cd18d7c565dce0b82d73595df56d53ce6931ca9adc1", "difficulty": "medium", "final_answer": {"answer": [-411.42, 117.9728], "unit": "N"}, "id": "vector_components_008005_428_164", "license": "Apache-2.0", "prompt": "A vector has magnitude 428 N at 164 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=164 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 164, "magnitude": 428.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [4.1, -6.25], \"unit\": \"dimensionless\"}", "dedupe_signature": "998fdbcce9b8c9f8964764db776566d436c9e1fb611cf36c90dac38ab69133d3", "difficulty": "medium", "final_answer": {"answer": [4.1, -6.25], "unit": "dimensionless"}, "id": "line_two_point_008006_-19.25_-16.75_4.1_-6.25", "license": "Apache-2.0", "prompt": "A line passes through points (-19.25, -85.175) and (-16.75, -74.925). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -19.25, "x2": -16.75, "y1": -85.175, "y2": -74.925}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. volt squared divided by ohm is watt\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "36d8efb85f070a2aa04e13ca98c65532e65b0a74dee43c3e6088699b4240bc42", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_008007_consistent_82e93f3d_174150", "license": "Apache-2.0", "prompt": "In student derivation case 174150, check dimensional consistency for P = V^2 / R. The left side has dimensions W and the right side has dimensions W. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nvolt squared divided by ohm is watt\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "P = V^2 / R"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef safe_mean_008008(values):\n    if not values:\n        raise ValueError('safe_mean requires at least one value')\n    return sum(values) / len(values)\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"safe_mean_008008\"}", "dedupe_signature": "16cc31de66c579d5d417dd4793369f54d9a66f26d8d7c29376250e2a18752009", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "safe_mean_008008"}, "id": "code_008008_safe_mean_008008", "license": "Apache-2.0", "prompt": "Write a Python function safe_mean_008008(values) that returns the arithmetic mean. It must raise ValueError for an empty input and must not mutate the input list. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "safe_mean_008008"}, "verifier": {"function": "safe_mean_008008", "tests": ["assert safe_mean_008008([2, 4, 6]) == 4", "xs = [1, 2, 3]; assert safe_mean_008008(xs) == 2 and xs == [1, 2, 3]", "try:\n    safe_mean_008008([])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 3.25^2 and multiply by 0.5 * 10.15.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 53.6047, \"unit\": \"J\"}", "dedupe_signature": "c3bb395bc59c8a3ded42f625c2d8d902c0fb283ce879735b109ec59e7fba8649", "difficulty": "easy", "final_answer": {"answer": 53.6047, "unit": "J"}, "id": "ke_008011_10.15_3.25", "license": "Apache-2.0", "prompt": "A body of mass 10.15 kg moves at 3.25 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 3.25^2 and multiply by 0.5 * 10.15.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 10.15, "velocity": 3.25}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=68 degrees through the sine of 2 theta.\n3. Substitute v=81.1 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 465.7405, \"unit\": \"m\"}", "dedupe_signature": "0dd69f512ef2da5bd369c79a6f4cf7b91f075efd39e20c104b8a09f7653f7e2b", "difficulty": "medium", "final_answer": {"answer": 465.7405, "unit": "m"}, "id": "projectile_range_008012_81.1_68", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 81.1 m/s and angle 68 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=68 degrees through the sine of 2 theta.\nSubstitute v=81.1 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 68, "gravity": 9.81, "speed": 81.1}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 0.39 * 8.314 * 442 / 72.6.\nFinal: {\"answer\": 19.7406, \"unit\": \"kPa\"}", "dedupe_signature": "6a28c89dff953c2bc1c06c7e0582d9ff6311ebc05686f2b85db834b96a4f9791", "difficulty": "medium", "final_answer": {"answer": 19.7406, "unit": "kPa"}, "id": "ideal_gas_008013_0.39_442_72.6", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=0.39 mol, T=442 K, and V=72.6 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 0.39 * 8.314 * 442 / 72.6.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 0.39, "temp_k": 442, "volume_l": 72.6}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1195 * 1.42 * 16.\nFinal: {\"answer\": 27150.4, \"unit\": \"J\"}", "dedupe_signature": "3d4d5d2416ac7d01b2f0213c29dd2eff4bda6a05d602c6e9f5cbd8afce927411", "difficulty": "easy", "final_answer": {"answer": 27150.4, "unit": "J"}, "id": "heat_q_008014_1195_1.42_16", "license": "Apache-2.0", "prompt": "A 1195 g sample has specific heat 1.42 J/(g*K). How much heat is needed to raise its temperature by 16 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1195 * 1.42 * 16.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 16, "heat_capacity": 1.42, "mass_g": 1195}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=62.5 V and R=129 ohm.\nFinal: {\"answer\": 30.281, \"unit\": \"W\"}", "dedupe_signature": "3bc7364a9971adb77b0a2ab1c4b9020e1af5e2368f21101550de4b78c1663eb4", "difficulty": "easy", "final_answer": {"answer": 30.281, "unit": "W"}, "id": "ohm_power_008015_62.5_129", "license": "Apache-2.0", "prompt": "A resistor has resistance 129 ohm and voltage 62.5 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=62.5 V and R=129 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 129.0, "voltage": 62.5}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=858.5 mg, t=334 h, and T_half=42.5 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 3.6983, \"unit\": \"mg\"}", "dedupe_signature": "035b013bf2b0fe7fbc3e90feeda9c13ecafde7ec6c936eb057637be883d8cc9e", "difficulty": "medium", "final_answer": {"answer": 3.6983, "unit": "mg"}, "id": "half_life_008016_858.5_42.5_334", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 858.5 mg. Its half-life is 42.5 hours. How many mg remain after 334 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=858.5 mg, t=334 h, and T_half=42.5 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 334.0, "half_life": 42.5, "initial_amount": 858.5}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(0.8)=-1.72 and f(2.8)=3.48.\n3. The interval width is 2.\nFinal: {\"answer\": 1.76, \"unit\": \"area_units\"}", "dedupe_signature": "9b4309356f3591a041219f8e055950ab2b3e077c22a6533f5a74df2f11d8d807", "difficulty": "medium", "final_answer": {"answer": 1.76, "unit": "area_units"}, "id": "trapz_linear_008020_2.6_-3.8_0.8_2.8", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=2.6x+-3.8 from x=0.8 to x=2.8. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(0.8)=-1.72 and f(2.8)=3.48.\nThe interval width is 2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -3.8, "slope": 2.6, "x0": 0.8, "x1": 2.8}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.02 and add it to the current value.\nFinal: {\"answer\": [2.325, 2.054, 1.86], \"unit\": \"temperature_units\"}", "dedupe_signature": "9df337574d9df9521e76ce1f5b4d2768ab2e30621620fff965dfde1b5ce80579", "difficulty": "hard", "final_answer": {"answer": [2.325, 2.054, 1.86], "unit": "temperature_units"}, "id": "heat_step_008021_0.02_-1.0_2.4_2.05_1.9_-0.25", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=-1, right=-0.25; current interior values are [2.4, 2.05, 1.9]. Use r=0.02. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.02 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [2.4, 2.05, 1.9], "left": -1.0, "r": 0.02, "right": -0.25}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 1000 grams in one kilogram.\n2. Apply the conversion factor directly to the given value.\n3. Compute 12111.0 / 1000.\nFinal: {\"answer\": 12.111, \"unit\": \"kg\"}", "dedupe_signature": "5e4502f7e563dfb92102e3bbdd7d6e7995e9cda94049d2f4438417f018d3001d", "difficulty": "easy", "final_answer": {"answer": 12.111, "unit": "kg"}, "id": "unit_convert_008022_g_to_kg_12111", "license": "Apache-2.0", "prompt": "Convert 12111 g to kg. Return the converted value with unit.", "reasoning_trace": "There are 1000 grams in one kilogram.\nApply the conversion factor directly to the given value.\nCompute 12111.0 / 1000.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 12111.0}, "verifier": {"formula": "value / 1000", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=7 degrees and keep the unit as newtons.\nFinal: {\"answer\": [446.1495, 54.7803], \"unit\": \"N\"}", "dedupe_signature": "903876fa0f4abb8f144d273d65b12f429580662b56f69ed22738760c3a91d617", "difficulty": "medium", "final_answer": {"answer": [446.1495, 54.7803], "unit": "N"}, "id": "vector_components_008023_449.5_7", "license": "Apache-2.0", "prompt": "A vector has magnitude 449.5 N at 7 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=7 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 7, "magnitude": 449.5}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [9.4, 15.25], \"unit\": \"dimensionless\"}", "dedupe_signature": "f5060242dd119e67f2ddf2fcfbe13e70028bfa928f5bcba66eee019d8c5855eb", "difficulty": "medium", "final_answer": {"answer": [9.4, 15.25], "unit": "dimensionless"}, "id": "line_two_point_008024_-17_-9_9.4_15.25", "license": "Apache-2.0", "prompt": "A line passes through points (-17, -144.55) and (-9, -69.35). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -17.0, "x2": -9.0, "y1": -144.55, "y2": -69.35000000000001}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. grams cancel with J/(g*K), and kelvin cancels, leaving joules\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"consistent\"}", "dedupe_signature": "63ba01ba79e59960379e67bd685f4f9affcd608ec0b1681327e7e613c4ff31c0", "difficulty": "medium", "final_answer": {"answer": "consistent"}, "id": "dimensional_008025_consistent_4153435f_25112", "license": "Apache-2.0", "prompt": "In simulation spec case 25112, check dimensional consistency for Q = m * c * DeltaT. The left side has dimensions J and the right side has dimensions J. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\ngrams cancel with J/(g*K), and kelvin cancels, leaving joules\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "consistent", "equation": "Q = m * c * DeltaT"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef safe_mean_008026(values):\n    if not values:\n        raise ValueError('safe_mean requires at least one value')\n    return sum(values) / len(values)\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"safe_mean_008026\"}", "dedupe_signature": "e48ce85d8b360a76c57e4bf4ee1da9a3354d2387384b5aaba74b8d29e7c428fb", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "safe_mean_008026"}, "id": "code_008026_safe_mean_008026", "license": "Apache-2.0", "prompt": "Write a Python function safe_mean_008026(values) that returns the arithmetic mean. It must raise ValueError for an empty input and must not mutate the input list. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "safe_mean_008026"}, "verifier": {"function": "safe_mean_008026", "tests": ["assert safe_mean_008026([2, 4, 6]) == 4", "xs = [1, 2, 3]; assert safe_mean_008026(xs) == 2 and xs == [1, 2, 3]", "try:\n    safe_mean_008026([])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: target_schema, valid_examples.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"target_schema\", \"valid_examples\"]}", "dedupe_signature": "c7bd1c7c4a9be2c2cc7530ed41b9811450052049f03cf4d7e7a65b84d0ab9536", "difficulty": "medium", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["target_schema", "valid_examples"]}, "id": "abstain_008027_target_schema_valid_examples", "license": "Apache-2.0", "prompt": "Write a parser that converts each laboratory sensor record from batch 943161 into the correct schema, but the prompt does not include the target schema or examples. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: target_schema, valid_examples.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "code_abstention", "variables": {"missing": ["target_schema", "valid_examples"]}, "verifier": {"missing": ["target_schema", "valid_examples"], "type": "abstention"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Newton's second law F = m a.\n2. Substitute m = 10.65 kg and a = 14.4 m/s^2.\n3. The unit kg*m/s^2 is one newton.\nFinal: {\"answer\": 153.36, \"unit\": \"N\"}", "dedupe_signature": "770d6aad06588e4d75cff420dc497ab94c920b1444b618fa8bd623493b3dbcc2", "difficulty": "easy", "final_answer": {"answer": 153.36, "unit": "N"}, "id": "force_008028_10.65_14.4", "license": "Apache-2.0", "prompt": "A cart has mass 10.65 kg and measured acceleration 14.4 m/s^2. Compute the net force. Check the SI units and give only the final JSON after reasoning.", "reasoning_trace": "Use Newton's second law F = m a.\nSubstitute m = 10.65 kg and a = 14.4 m/s^2.\nThe unit kg*m/s^2 is one newton.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"acceleration": 14.4, "mass": 10.65}, "verifier": {"formula": "mass * acceleration", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Kinetic energy is KE = 1/2 m v^2.\n2. Compute v^2 = 27.2^2 and multiply by 0.5 * 22.45.\n3. The unit kg*m^2/s^2 is one joule.\nFinal: {\"answer\": 8304.704, \"unit\": \"J\"}", "dedupe_signature": "e91218d08f3ea231771a640acba87c60854c74623804fbaca8785ca8df3c9270", "difficulty": "easy", "final_answer": {"answer": 8304.704, "unit": "J"}, "id": "ke_008029_22.45_27.2", "license": "Apache-2.0", "prompt": "A body of mass 22.45 kg moves at 27.2 m/s. Find its kinetic energy in joules with unit reasoning.", "reasoning_trace": "Kinetic energy is KE = 1/2 m v^2.\nCompute v^2 = 27.2^2 and multiply by 0.5 * 22.45.\nThe unit kg*m^2/s^2 is one joule.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"mass": 22.45, "velocity": 27.2}, "verifier": {"formula": "0.5 * mass * velocity ** 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. For level-ground projectile motion, R = v^2 sin(2 theta) / g.\n2. Convert theta=57 degrees through the sine of 2 theta.\n3. Substitute v=20.4 m/s and g=9.81 m/s^2.\nFinal: {\"answer\": 38.7544, \"unit\": \"m\"}", "dedupe_signature": "e1a0a27445f2c56001a2c9ca5651ab01187c89db477bafb247754c9cb2b90fee", "difficulty": "medium", "final_answer": {"answer": 38.7544, "unit": "m"}, "id": "projectile_range_008030_20.4_57", "license": "Apache-2.0", "prompt": "A projectile is launched on level ground with no air resistance at speed 20.4 m/s and angle 57 degrees. Compute the horizontal range in meters using g=9.81 m/s^2.", "reasoning_trace": "For level-ground projectile motion, R = v^2 sin(2 theta) / g.\nConvert theta=57 degrees through the sine of 2 theta.\nSubstitute v=20.4 m/s and g=9.81 m/s^2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_checked_mechanics", "variables": {"angle_deg": 57, "gravity": 9.81, "speed": 20.4}, "verifier": {"formula": "speed ** 2 * math.sin(math.radians(2 * angle_deg)) / gravity", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use the ideal gas law P V = n R T.\n2. Because R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\n3. Compute P = 4.08 * 8.314 * 332 / 15.8.\nFinal: {\"answer\": 712.7729, \"unit\": \"kPa\"}", "dedupe_signature": "466b0080e53b3022cb591d5ed87a8b845455a9f9bceb96cd89f398f0802770da", "difficulty": "medium", "final_answer": {"answer": 712.7729, "unit": "kPa"}, "id": "ideal_gas_008031_4.08_332_15.8", "license": "Apache-2.0", "prompt": "An ideal gas sample has n=4.08 mol, T=332 K, and V=15.8 L. Using R=8.314 kPa*L/(mol*K), compute the pressure in kPa.", "reasoning_trace": "Use the ideal gas law P V = n R T.\nBecause R is in kPa*L/(mol*K) and V is in L, the pressure comes out in kPa.\nCompute P = 4.08 * 8.314 * 332 / 15.8.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"n_mol": 4.08, "temp_k": 332, "volume_l": 15.8}, "verifier": {"formula": "n_mol * 8.314 * temp_k / volume_l", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Use Q = m c DeltaT.\n2. The mass is already in grams, matching the specific heat denominator.\n3. Compute Q = 1555 * 1.755 * 64.\nFinal: {\"answer\": 174657.6, \"unit\": \"J\"}", "dedupe_signature": "1960f7b72568bf82c2b1d3e0b40369acaff506e03ecef122df68e2cc91fb122a", "difficulty": "easy", "final_answer": {"answer": 174657.6, "unit": "J"}, "id": "heat_q_008032_1555_1.755_64", "license": "Apache-2.0", "prompt": "A 1555 g sample has specific heat 1.755 J/(g*K). How much heat is needed to raise its temperature by 64 K?", "reasoning_trace": "Use Q = m c DeltaT.\nThe mass is already in grams, matching the specific heat denominator.\nCompute Q = 1555 * 1.755 * 64.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "thermodynamics", "variables": {"delta_t": 64, "heat_capacity": 1.755, "mass_g": 1555}, "verifier": {"formula": "mass_g * heat_capacity * delta_t", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Ohm's law gives I = V / R.\n2. Power can be written as P = V I = V^2 / R.\n3. Substitute V=142.1 V and R=40.1 ohm.\nFinal: {\"answer\": 503.5514, \"unit\": \"W\"}", "dedupe_signature": "f2d72d9179022ada2bde75c2d5774db6c41025fa54ecafd492f4d7173ced2df3", "difficulty": "easy", "final_answer": {"answer": 503.5514, "unit": "W"}, "id": "ohm_power_008033_142.1_40.1", "license": "Apache-2.0", "prompt": "A resistor has resistance 40.1 ohm and voltage 142.1 V across it. Compute the dissipated power in watts.", "reasoning_trace": "Ohm's law gives I = V / R.\nPower can be written as P = V I = V^2 / R.\nSubstitute V=142.1 V and R=40.1 ohm.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "electric_circuits", "variables": {"resistance": 40.1, "voltage": 142.1}, "verifier": {"formula": "voltage ** 2 / resistance", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\n2. Use N0=45 mg, t=16 h, and T_half=92 h.\n3. The remaining amount has the same mass unit as the initial amount.\nFinal: {\"answer\": 39.8896, \"unit\": \"mg\"}", "dedupe_signature": "d2132d5c44b8a3f4e0d444770317fe82e56c63813c90467d300f0fdb95ef2769", "difficulty": "medium", "final_answer": {"answer": 39.8896, "unit": "mg"}, "id": "half_life_008034_45_92_16", "license": "Apache-2.0", "prompt": "A radioactive sample starts with 45 mg. Its half-life is 92 hours. How many mg remain after 16 hours?", "reasoning_trace": "Radioactive decay by half-life follows N(t)=N0*(1/2)^(t/T_half).\nUse N0=45 mg, t=16 h, and T_half=92 h.\nThe remaining amount has the same mass unit as the initial amount.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "exponential_decay", "variables": {"elapsed_time": 16.0, "half_life": 92.0, "initial_amount": 45.0}, "verifier": {"formula": "initial_amount * 0.5 ** (elapsed_time / half_life)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Mass equals amount in moles times molar mass.\n2. Use m = 3.61 mol * 180.156 g/mol.\n3. The mole unit cancels, leaving grams.\nFinal: {\"answer\": 650.3632, \"unit\": \"g\"}", "dedupe_signature": "4921c6602d51385a11fb5807ad1fad12331c0e442fd770760806975f56963d2d", "difficulty": "medium", "final_answer": {"answer": 650.3632, "unit": "g"}, "id": "stoich_mass_008035_glucose_3.61", "license": "Apache-2.0", "prompt": "A sample contains 3.61 mol of glucose. Using molar mass 180.156 g/mol, compute the sample mass in grams.", "reasoning_trace": "Mass equals amount in moles times molar mass.\nUse m = 3.61 mol * 180.156 g/mol.\nThe mole unit cancels, leaving grams.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_stoichiometry", "variables": {"compound": "glucose", "molar_mass": 180.156, "moles": 3.61}, "verifier": {"formula": "moles * molar_mass", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Molarity is moles of solute divided by solution volume in liters.\n2. Convert 2155 mL to 2.155 L.\n3. Compute M = 3.995 / 2.155.\nFinal: {\"answer\": 1.8538, \"unit\": \"mol/L\"}", "dedupe_signature": "9f4dcc3365f7ed602c650c7cc1d4982befd895742d3dcf79c8d00404eaf8396b", "difficulty": "medium", "final_answer": {"answer": 1.8538, "unit": "mol/L"}, "id": "molarity_008036_3.995_2155", "license": "Apache-2.0", "prompt": "A solution contains 3.995 mol of solute in 2155 mL of solution. Compute the molarity in mol/L.", "reasoning_trace": "Molarity is moles of solute divided by solution volume in liters.\nConvert 2155 mL to 2.155 L.\nCompute M = 3.995 / 2.155.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "chemistry_solutions", "variables": {"moles": 3.995, "volume_ml": 2155}, "verifier": {"formula": "moles / (volume_ml / 1000)", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Explicit Euler updates y_{n+1} = y_n + h f(y_n).\n2. Here f(y) = -0.76 y, so each step multiplies y by 1 - h*0.76.\n3. Apply that update for 3 steps and round the final state.\nFinal: {\"answer\": -1.0706, \"unit\": \"state_units\"}", "dedupe_signature": "a3989ff51b2e37a01e6ac37eaa2f62a6c8b07eadf9958023bf9818c5044498aa", "difficulty": "medium", "final_answer": {"answer": -1.0706, "unit": "state_units"}, "id": "euler_decay_008037_43_0.76_1.7_3", "license": "Apache-2.0", "prompt": "Use explicit Euler on dy/dt = -0.76 y with y(0)=43, step size h=1.7, for 3 steps. What is y after the final step?", "reasoning_trace": "Explicit Euler updates y_{n+1} = y_n + h f(y_n).\nHere f(y) = -0.76 y, so each step multiplies y by 1 - h*0.76.\nApply that update for 3 steps and round the final state.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_ode", "variables": {"initial_y": 43.0, "rate": 0.76, "step": 1.7, "steps": 3}, "verifier": {"tolerance": 0.0001, "type": "euler_decay"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\n2. Evaluate f(-4.3)=8.81 and f(0.9)=-20.83.\n3. The interval width is 5.2.\nFinal: {\"answer\": -31.252, \"unit\": \"area_units\"}", "dedupe_signature": "8fad0536cdb807d6d5a3d5d8a4449160cc9479f1523ea757407c0dd885e44aac", "difficulty": "medium", "final_answer": {"answer": -31.252, "unit": "area_units"}, "id": "trapz_linear_008038_-5.7_-15.7_-4.3_0.9", "license": "Apache-2.0", "prompt": "Use the trapezoid rule with one interval to approximate the integral of f(x)=-5.7x+-15.7 from x=-4.3 to x=0.9. Return the numeric integral estimate.", "reasoning_trace": "The one-interval trapezoid rule is (b-a)*(f(a)+f(b))/2.\nEvaluate f(-4.3)=8.81 and f(0.9)=-20.83.\nThe interval width is 5.2.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "numerical_integration", "variables": {"intercept": -15.7, "slope": -5.7, "x0": -4.3, "x1": 0.9000000000000004}, "verifier": {"formula": "(x1 - x0) * ((slope * x0 + intercept) + (slope * x1 + intercept)) / 2", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Keep the boundary values fixed and update only the three interior grid points.\n2. For each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\n3. Multiply each Laplacian by r=0.18 and add it to the current value.\nFinal: {\"answer\": [1.497, 0.111, -0.401], \"unit\": \"temperature_units\"}", "dedupe_signature": "e4c29624959ac41a78691374989912d5dbdcd33607924ddd8fc3bff94f10f393", "difficulty": "hard", "final_answer": {"answer": [1.497, 0.111, -0.401], "unit": "temperature_units"}, "id": "heat_step_008039_0.18_1.0_2.1_-0.15_-0.95_1.3", "license": "Apache-2.0", "prompt": "For the 1D heat equation explicit finite-difference step, use u_i(next)=u_i+r*(u_{i-1}-2*u_i+u_{i+1}). Boundary values are left=1, right=1.3; current interior values are [2.1, -0.15, -0.95]. Use r=0.18. Return the next interior vector.", "reasoning_trace": "Keep the boundary values fixed and update only the three interior grid points.\nFor each interior point, compute the discrete Laplacian u_{i-1}-2*u_i+u_{i+1}.\nMultiply each Laplacian by r=0.18 and add it to the current value.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "finite_difference_pde", "variables": {"interior": [2.1, -0.15, -0.95], "left": 1.0, "r": 0.18, "right": 1.3}, "verifier": {"tolerance": 0.0001, "type": "heat_step"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. There are 100 centimeters in one meter.\n2. Apply the conversion factor directly to the given value.\n3. Compute 3349.0 / 100.\nFinal: {\"answer\": 33.49, \"unit\": \"m\"}", "dedupe_signature": "abd0a3918735605108a1f1174f3e011caa0c83cb5b6268dbfebdb55991ea89db", "difficulty": "easy", "final_answer": {"answer": 33.49, "unit": "m"}, "id": "unit_convert_008040_cm_to_m_3349", "license": "Apache-2.0", "prompt": "Convert 3349 cm to m. Return the converted value with unit.", "reasoning_trace": "There are 100 centimeters in one meter.\nApply the conversion factor directly to the given value.\nCompute 3349.0 / 100.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "unit_conversion", "variables": {"value": 3349.0}, "verifier": {"formula": "value / 100", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The x component is magnitude times cos(theta).\n2. The y component is magnitude times sin(theta).\n3. Use theta=86 degrees and keep the unit as newtons.\nFinal: {\"answer\": [8.8591, 126.6906], \"unit\": \"N\"}", "dedupe_signature": "92ed1807b0b038b0ffa8a194abc94507a2f5723710141c27079214057fbf569d", "difficulty": "medium", "final_answer": {"answer": [8.8591, 126.6906], "unit": "N"}, "id": "vector_components_008041_127_86", "license": "Apache-2.0", "prompt": "A vector has magnitude 127 N at 86 degrees counterclockwise from the +x axis. Return its [x, y] components in newtons.", "reasoning_trace": "The x component is magnitude times cos(theta).\nThe y component is magnitude times sin(theta).\nUse theta=86 degrees and keep the unit as newtons.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "vector_reasoning", "variables": {"angle_deg": 86, "magnitude": 127.0}, "verifier": {"formula": "[magnitude * math.cos(math.radians(angle_deg)), magnitude * math.sin(math.radians(angle_deg))]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The slope is (y2-y1)/(x2-x1).\n2. The intercept is y1 - slope*x1.\n3. Return the pair in [slope, intercept] order.\nFinal: {\"answer\": [1.75, -3.0], \"unit\": \"dimensionless\"}", "dedupe_signature": "a9b667fd000ceecb98f48013a23ea42fd55c8710cb18d3707cfb4e9b0886b3c5", "difficulty": "medium", "final_answer": {"answer": [1.75, -3.0], "unit": "dimensionless"}, "id": "line_two_point_008042_-2.5_11.75_1.75_-3", "license": "Apache-2.0", "prompt": "A line passes through points (-2.5, -7.375) and (11.75, 17.5625). Return [slope, intercept] for y = slope*x + intercept.", "reasoning_trace": "The slope is (y2-y1)/(x2-x1).\nThe intercept is y1 - slope*x1.\nReturn the pair in [slope, intercept] order.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "linear_modeling", "variables": {"x1": -2.5, "x2": 11.75, "y1": -7.375, "y2": 17.5625}, "verifier": {"formula": "[(y2 - y1) / (x2 - x1), y1 - ((y2 - y1) / (x2 - x1)) * x1]", "tolerance": 0.0001, "type": "formula"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Compare the dimensions on both sides of the equation.\n2. velocity times time gives distance, not acceleration\n3. The equation is valid only if both sides have identical dimensions.\nFinal: {\"answer\": \"inconsistent\"}", "dedupe_signature": "595b1cbdd4c84d1e9c79122aac379125d9f446aa59fe85239e69b4b2cffbb87c", "difficulty": "medium", "final_answer": {"answer": "inconsistent"}, "id": "dimensional_008043_inconsistent_7481c798_781658", "license": "Apache-2.0", "prompt": "In simulation spec case 781658, check dimensional consistency for a = v * t. The left side has dimensions m/s^2 and the right side has dimensions m. Return consistent or inconsistent with a brief reason.", "reasoning_trace": "Compare the dimensions on both sides of the equation.\nvelocity times time gives distance, not acceleration\nThe equation is valid only if both sides have identical dimensions.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "dimensional_analysis", "variables": {"answer": "inconsistent", "equation": "a = v * t"}, "verifier": {"type": "exact"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. The function contract has a normal path and at least one edge case.\n2. The implementation checks the edge case before returning the normal result.\n\n```python\ndef safe_mean_008044(values):\n    if not values:\n        raise ValueError('safe_mean requires at least one value')\n    return sum(values) / len(values)\n```\nFinal: {\"answer\": \"python_code\", \"function\": \"safe_mean_008044\"}", "dedupe_signature": "fb6f2b2577e1ff8cbd2ee227fd068caa4723b1450e6f1f2e875124fba16486a7", "difficulty": "medium", "final_answer": {"answer": "python_code", "function": "safe_mean_008044"}, "id": "code_008044_safe_mean_008044", "license": "Apache-2.0", "prompt": "Write a Python function safe_mean_008044(values) that returns the arithmetic mean. It must raise ValueError for an empty input and must not mutate the input list. Return a single fenced Python code block.", "reasoning_trace": "Identify required edge cases before writing the function.\nImplement the shortest total function that satisfies the stated contract.\nAvoid global state and return deterministic outputs.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "python_code_generation", "variables": {"function": "safe_mean_008044"}, "verifier": {"function": "safe_mean_008044", "tests": ["assert safe_mean_008044([2, 4, 6]) == 4", "xs = [1, 2, 3]; assert safe_mean_008044(xs) == 2 and xs == [1, 2, 3]", "try:\n    safe_mean_008044([])\n    raise AssertionError('expected ValueError')\nexcept ValueError:\n    pass"], "type": "python_tests"}}
{"category": "science_math_code", "completion": "Reasoning:\n1. Check whether all variables required by the governing equation or specification are present.\n2. The missing required information is: rate_constant, number_of_steps.\n3. A numeric or code answer would require inventing unstated assumptions, so abstain.\nFinal: {\"answer\": \"INSUFFICIENT_INFO\", \"missing\": [\"rate_constant\", \"number_of_steps\"]}", "dedupe_signature": "ef72d0d1e7d5be5ec9fd863c3cb8a2eaf04586a8006af3b5421018667a3a1700", "difficulty": "hard", "final_answer": {"answer": "INSUFFICIENT_INFO", "missing": ["rate_constant", "number_of_steps"]}, "id": "abstain_008045_rate_constant_number_of_steps", "license": "Apache-2.0", "prompt": "Use explicit Euler for dy/dt = -k y. The prompt gives y(0)=9 and h=1.35, but omits both k and the number of steps. If there is insufficient information, say so explicitly.", "reasoning_trace": "Check whether all variables required by the governing equation or specification are present.\nThe missing required information is: rate_constant, number_of_steps.\nA numeric or code answer would require inventing unstated assumptions, so abstain.", "source": "programmatic_synthetic_verified", "split": "train", "task_family": "scientific_abstention", "variables": {"missing": ["rate_constant", "number_of_steps"]}, "verifier": {"missing": ["rate_constant", "number_of_steps"], "type": "abstention"}}